SAT Guide
BCT's SAT English Practice
SAT ENGLISH OVERVIEW- ARTICLE #1
What to Expect on the Digital SAT English Section
On the new digital SAT, the English section will be split into two adaptive modules with 27 questions each. Your performance on the first module will dictate the difficulty of your second module. If you end up with the easier 2nd module, your maximum score on the English section will be capped. Additionally, questions will not be universal for all test-takers around the world. The old paper SAT featured a reading section with 5 passages and 52 questions followed by a writing and grammar section with 44 questions. The new digital SAT has combined these sections, and each question will be accompanied by its own, unique passage. You will have 32 minutes for each module, giving you a little over 1 minute per question. There are four different topics being tested in the English section: Information and ideas, craft and structure, expression of ideas, and standard English conventions. Information and ideas questions focus on inferences and evidence based reasoning. Craft and structure questions relate to the forming of a passage, including vocabulary and argumentation. Expression of ideas questions require students to fill in answers that make an author’s writing more concise. Standard English conventions questions test students’ understanding of grammar.
What Will These Articles Detail?
This article will explain the best strategies for approaching the English section. Article #2 focuses on the tricky subtopic of vocabulary in context (craft and structure). Article #3 explains the best way to approach inference questions, part of the information and ideas section. Article #4 will reference Student-as-Editor questions that are frequently seen in the expression of ideas section. Article #5 will be all about punctuation and grammar, a guide to the standard conventions of English section that is widely recognized as the hardest topic assessed on the SAT.
How to Approach the English Section
The key to scoring well on the SAT is to understand that you, as the test-taker, must take control of the test rather than letting the College Board dictate your testing experience. What I mean by this is understanding that the College Board is attempting to trick you in their answer choices. When reading answer choices, never think “yes, that sounds correct” and click the answer. Only respond to answer choices with “no” or “maybe”. If you are sure that an answer choice does not make sense for a question, it is a “no”. If it MIGHT, then it is a “maybe”. Sometimes, you may have multiple “maybes”. Decide which one of your “maybes” has less of a case to be correct, or makes more sense to be a “no”. Understand that the answers chosen by the College Board are not perfect, and that frequently you could produce answers that make more sense for a question (see article #3). You are not selecting correct answers, but rather the answer that is the least wrong. This mentality will transform your understanding of the English section.
Taking Breaks
Although it may seem counterintuitive, taking breaks is the key for relieving time pressure on the English section of the SAT. I suggest taking a break midway through the first module (Question 14) and then taking two breaks during the second module (around Q9 and Q18). Staying focused while reading 54 different passages is difficult, so use your breaks as a way to fully reset your mind before answering the next question. What works for you might not work for other people, and taking breaks will look completely different for others. Experiment yourself and see what works best. Some may prefer to close their eyes and breathe slowly, and others would use their breaks as an opportunity to stretch their fingers and arms. I liked to look around the room and pick 2 objects, and pit them together in a fight (for example, during my SAT the fire alarm was fighting against my pencil sharpener in my head). It sounds ridiculous, but this strategy helped me take my mind off the test momentarily and prepare for the upcoming questions.
Skipping Questions
Students often underestimate their ability to produce an accurate answer on their first attempt at a question on the SAT. As a result, students will often choose to leave questions blank before going back to them at the end. However, I would advise against this strategy. The first time you read a passage and a prompt will be your best opportunity to have a full understanding of the question. When you revisit a question at the end of the section, you are more fatigued from taking the test and will also have less time to fully re-read the question and implement the strategies aforementioned. Therefore, I would advise you to never leave questions unanswered (go with your first instinct), and if you revisit a question I would recommend that you only change your answer if you have confidence in your decision. If you are unable to supply a sufficient reason to change your answer, you are better off trusting your first instinct from when you originally answered the question.
By James Constan
SAT ENGLISH VOCABULARY IN CONTEXT- ARTICLE #2
What is Vocabulary in Context?
One major topic that you will frequently see on the English section of the SAT is vocabulary in context. The question will underline a word used in the passage, and give the test taker the option to keep the word or replace it with a different word if it would be a more appropriate fit. Other times, the question will ask you what a word in the passage most nearly means. One key misconception about vocab in context questions is that the SAT is testing your knowledge of vocabulary. However, the SAT will never test students with words that surpass a realistic knowledge level for a high school student. Instead, these questions are testing a student’s ability to indicate words that would fit better in a specific context, or use context clues to provide a word that is most similar to the word being used in the passage. In some situations, you still may encounter a word that you are unfamiliar with. In that case, there are strategies such as process of elimination that you can use to work around this issue.
How to Approach These Questions
As mentioned in article #1, the key for the English section of the SAT is to take control of the test, rather than letting the College Board dictate your thought-process. Remember that when answering these questions while looking at the answer choices, you are never saying “yes” to a question, only “no” and “maybe”. When you approach a vocabulary question, first move your hand to block out the four answer choices that are given by the College Board. Completely ignore these for now. Instead, think to yourself what word YOU would put in the blank, or what word you would find most appropriate for the situation. Remember, you are looking for a word that fits the context of the passage, matching both the situation but also the tone of the writing. For example, you would expect Shakespeare to use a phrase like “adieu” rather than “see ya”. After you come up with this word, remove your hand and view the answer choices. Cross off any answers that DO NOT MATCH the word you came up with. Consider inserting your answer into the sentence and reading the sentence to yourself to ensure that it makes sense. Answer
“maybe” to any word that could reasonably align with your word choice. Frequently, the word you came up with will be one of the answer choices. After you have gone through the 4 options, circle your only “maybe”, and if you have more than one “maybe” decide which one is a stronger option, choose it, and potentially mark the question as one to come back to if you have some excess time. Remember to always submit an answer the first time you read a question, even if you are unsure and know you are going to return to the question. For the “word most nearly means” questions, use the exact same strategy and choose the word most similar to the one you produced. Try the two practice problems below.
Practice this Strategy-#1
My mother wanted me to go to school at New Paltz because she was worried I’d be lost if she sent me to a big university. I was young and sheltered, and when it came to racial politics, I was largely pure. I was completely unprepared to play the role people would want me to play as the daughter of an African-American hero. I had not a clue who I was, either as the daughter of Malcolm X or even as simply myself, Ilyasah Shabazz. Mommy probably worried that if I enrolled at a historically black college, the expectations she had so carefully and thoroughly shielded me from my entire life would rise up like a tidal wave and swallow me whole.
Here, this passage is asking you whether or not to change the word “pure”. Themes to pick up on would be the author’s use of “young and sheltered”, which has the connotation of inexperience. Before looking at the answers below, remember to come up with your own word that you would use in that position.
Frequently said words: Untrained, Not knowledgeable, Uninformed
Answer Choices:
A) NO CHANGE. B) blameless. C) harmless. D) inexperienced.
D would be the correct answer here.
Practice this Strategy-#2
chains of servitude on their posterity. They were totally fearless of the intrigues or the ambition of their own countrymen, which might in time render fruitless the expense of their blood and their treasures. These they had freely lavished to secure their equality of condition, their easy modes of subsistence, and their exemption from public burdens beyond the necessary demands for the support of a free and equal government. But it was
Here, the passage is asking you to select a word that most nearly means “secure” in the context of this passage.
Frequently selected words: Acquire, Lock Down, Ensure
Answer Choices:
As used in line 48, “secure” most nearly means
A) guarantee. B) fasten. C) promise. D) control.
Here the correct answer choice would be A. This question is very tricky, as the word choices all have close connotations with “acquire” and “lock down” and “ensure”. Reading the sentence with the 4 words replacing secure might give you an indication that guarantee sounds the most appropriate, along with it being synonymous with “ensure”.
By James Constan
These SAT Vocab in Context questions challenge students to discern the meanings of specific words based on their usage within sentences, testing their vocabulary and comprehension skills.
To make the correct answer visible against a white background, please highlight the area beside the correct option.
1. In the novel, the protagonist's journey was described as "arduous," which most nearly means:
A) expensive B) easy C) difficult D) enjoyable
Correct Answer: C) difficult
Explanation: The word "arduous" is used to describe tasks, journeys, or activities that are very difficult, requiring a lot of effort and perseverance. In the context of a journey for a protagonist in a novel, "arduous" implies that the journey was challenging and strenuous, making option C the correct choice.
2. The critic's review of the movie was "laudatory," meaning the review was:
A) critical B) full of praise C) vague D) humorous
Correct Answer: B) full of praise
Explanation: "Laudatory" is used to describe speeches, writings, or remarks that praise or commend. Given that this adjective is applied to a critic's review, it indicates that the review was positive and approving, thus making option B the correct answer.
3. Her "candid" remarks about the policy took everyone by surprise, indicating her remarks were:
A) scripted B) dishonest C) indirect D) straightforward
Correct Answer: D) straightforward
Explanation: "Candid" refers to being truthful and straightforward, often in a refreshingly honest manner. In this context, her remarks being described as "candid" implies they were direct and sincere, surprising everyone due to their honesty. Thus, D is the correct choice.
4. The document was written in a "cryptic" manner, meaning it was:
A) clear B) confusing C) lengthy D) concise
Correct Answer: B) confusing
Explanation: "Cryptic" means mysterious or obscure in meaning. When a document is described as being written in a cryptic manner, it suggests that the text was difficult to understand or interpret, making option B the correct answer.
5. The "obsolete" technology was phased out, meaning it was:
A) new and innovative B) old and no longer used C) complicated D) popular
Correct Answer: B) old and no longer used
Explanation: "Obsolete" refers to something that is out of date or no longer in use, often because it has been replaced by something newer and more efficient. In this case, technology being described as obsolete means it was old and had been superseded, hence B is the right answer.
6. His ideas were "innovative," meaning they were:
A) traditional B) stolen C) creative and new D) confusing
Correct Answer: C) creative and new
Explanation: "Innovative" implies something is novel and introduces new ideas or methods. Describing ideas as innovative suggests they were original and brought new thinking to the table, making option C the correct choice.
7. The lawyer's argument was "coherent," meaning it was:
A) disjointed B) logical and well-organized C) passionate D) weak
Correct Answer: B) logical and well-organized
Explanation: "Coherent" means something is clear, logical, and consistent. In the context of a lawyer's argument, being coherent indicates that the argument was structured and easy to follow, so B is the correct answer.
8. The "subtle" hint did not go unnoticed, implying the hint was:
A) ignored B) obvious C) not direct D) loud
Correct Answer: C) not direct
Explanation: "Subtle" refers to something that is not immediately obvious or conspicuous, often requiring careful attention to notice. A subtle hint is one that is indirect or not overt, making C the best choice.
9. The "tedious" task took hours to complete, indicating the task was:
A) quick and easy B) boring and long C) exciting D) simple
Correct Answer: B) boring and long
Explanation: "Tedious" describes something that is too long, slow, or dull, especially to the point of being tiresome. A task being tedious implies it was monotonous and took a considerable amount of time, thus B is the correct answer.
10. Her "melancholy" mood was apparent to all, meaning she was:
A) joyful B) sad C) indifferent D) angry
Correct Answer: B) sad
Explanation: "Melancholy" is a state of deep sadness or gloom. If her mood was described as melancholy, it means she was feeling sad, making B the correct selection.
SAT ENGLISH INFERENCE ARTICLE #3
What are Inference Questions?
Another topic that digital SAT test-takers should be familiar with is inference. On inference questions, the student will be asked to add a sentence that logically follows earlier writings. In your own English class, you may be asked to infer something that is not directly from the text, but rather is associated with the connotation of words used by the author. For example, a reasonable inference would be that Picasso was sad during his “Blue Period” because of the sad emotions that are related to the color blue. However, for the SAT, inference based questions will only ask the student to infer something that is directly stated or made obvious in the text.
How to Approach Inference Questions
When you see an inference question on the digital SAT, your main goal is to gain a concise understanding of passage. The best way to do this is to summarize, in your own words, what the author is attempting to say. Your own summary should be extremely simple, to the point where a 3rd grader could easily understand the topic. This summary could even be grammatically incorrect or completely informal. Consider the following sentence “what factors influence the abundance of species in a given ecological community?” Instead of attempting to infer from this “wordy” sentence, you could write your own sentence that would read “why lots of animals in this place”. This new sentence is simple, doesn’t lose the author’s argument, and is easier to infer from. Read the practice problem below for more help on this technique.
Practice Problem
Many animals, including humans, must sleep, and sleep is known to have a role in everything from healing injuries to encoding information in long-term memory. But some scientists claim that, from an evolutionary standpoint, deep sleep for hours at a time leaves an animal so vulnerable that the known benefits of sleeping seem insufficient to explain why it became so widespread in the animal kingdom. These scientists therefore imply that ________
Simpler Translation of the Sentence
Attempt your own translation on a separate piece of paper. Don’t worry if you find this technique taking you a while, as your speed will improve with more practice. I translated the passage to read
“All animals need sleep for stuffs. Smart people wonder why animals sleep lots because sleep means weakness. What are scientists saying?
Answer Choices
Which choice most logically completes the text?
A) it is more important to understand how widespread prolonged deep sleep is than to understand its function.
B) prolonged deep sleep is likely advantageous in ways that have yet to be discovered.
C) many traits that provide significant benefits for an animal also likely pose risks to that animal.
D) most traits perform functions that are hard to understand from an evolutionary standpoint.
Solving the Problem
Choice A infers an idea that is not in the passage, as scientists already know that all animals sleep for a while and sleep deeply. Remember that the answer will always be in the writing. Choice B is a solid option, and matches with my translation that the scientists “wonder” why animals sleep for long periods. Choice C overly infers, extending the topic of sleep to say that “many traits” share similar characteristics with sleep, although this is never stated in the passage. Choice D also overly infers that “most traits” are hard to understand, even though the passage is only talking about sleep. Therefore, B would be the correct answer here.
By James Constan
Creating SAT-style inference questions involves providing a context where students must read between the lines to deduce the correct answer based on evidence or reasoning. Below are 10 SAT-style inference questions, each followed by an explanation of the correct answer.
To make the correct answer visible against a white background, please highlight the area beside the correct option.
1. The character’s decision to return home after years of travel suggests that he:
A) disliked his travels. B) longed for something familiar. C) lost all his money. D) was following someone’s advice.
Correct Answer: B) longed for something familiar.
Explanation: The inference here is based on the common human emotion of longing for the familiar after a period of absence. The choice to return home suggests a desire for comfort and familiarity, rather than disliking travel, financial loss, or following advice without context.
2. The author’s frequent use of storm imagery throughout the novel most likely suggests an atmosphere of:
A) tranquility. B) confusion. C) danger. D) excitement.
Correct Answer: C) danger.
Explanation: Storm imagery is often used to symbolize turmoil, danger, or conflict. This choice of imagery implies a tense or threatening atmosphere, rather than tranquility, confusion, or excitement.
3. If a poet describes the night sky as “a canvas painted with silver dots,” it can be inferred that the night sky is:
A) cloud-covered. B) star-filled. C) dark and empty. D) stormy.
Correct Answer: B) star-filled.
Explanation: The metaphor of a canvas painted with silver dots suggests a beautiful, starry night, where each star appears as a dot of silver paint. This imagery implies a clear, star-filled sky rather than clouds, emptiness, or storms.
4. When the CEO announced plans to "streamline operations," it is reasonable to infer that the company aims to:
A) expand its workforce. B) make processes more efficient. C) increase its product prices. D) cut down on advertising.
Correct Answer: B) make processes more efficient.
Explanation: To "streamline" typically means to simplify procedures to make them more efficient and effective. This implies an intention to optimize operations rather than expanding the workforce, increasing prices, or reducing advertising.
5. A character who is described as “having a heart of stone” is likely to be:
A) very kind. B) unemotional. C) adventurous. D) humorous.
Correct Answer: B) unemotional.
Explanation: The phrase “having a heart of stone” is a metaphor for someone who is emotionally cold, unfeeling, or unemotional, suggesting that the character is not easily moved by feelings of compassion or empathy.
6. An essay arguing that "without darkness, there can be no true appreciation of light" suggests that:
A) light is always preferable to darkness. B) darkness is unnecessary. C) challenges make successes sweeter. D) success is unattainable.
Correct Answer: C) challenges make successes sweeter.
Explanation: This statement infers that contrasts or difficulties (darkness) are necessary to truly value and appreciate the good times (light), implying that overcoming challenges enhances our appreciation of positive outcomes.
7. The repeated mention of ticking clocks in a story most likely symbolizes:
A) the passing of time. B) excitement. C) silence. D) technological advancement.
Correct Answer: A) the passing of time.
Explanation: Ticking clocks are a common symbol for the passage of time, suggesting an emphasis on time's relentless march forward, rather than excitement, silence, or technological progress.
8. A politician who is described as “a wolf in sheep's clothing” is likely to be:
A) honest and direct. B) dangerous and deceitful. C) timid. D) inexperienced.
Correct Answer: B) dangerous and deceitful.
Explanation: The phrase “a wolf in sheep's clothing” is a metaphor for someone who presents themselves as harmless or benevolent while hiding malicious intentions, indicating deceitfulness and potential danger.
9. The phrase “a drop in the ocean” when referring to an individual’s efforts in a large project suggests that the efforts are:
A) highly significant. B) barely noticeable. C) wasteful. D) focused and intensive.
Correct Answer: B) barely noticeable.
Explanation: “A drop in the ocean” is an idiom that means something very small or insignificant in comparison to a much larger context, implying that the individual’s efforts, while valuable, do not make a significant impact on the overall project.
10. Describing a situation as “walking on thin ice” suggests that one is:
A) taking a safe path. B) in a precarious or risky situation. C) moving quickly. D) being overly cautious.
Correct Answer: B) in a precarious or risky situation.
Explanation: The phrase “walking on thin ice” is used to describe a situation that is dangerous or risky, where there is a possibility of negative consequences, suggesting that one needs to tread carefully to avoid trouble.
SAT ENGLISH STUDENT AS EDITOR- ARTICLE #4
What are Student as Editor Questions?
Student as Editor questions, also referred to as GOAL questions, tests the ability of a reader to edit the organization or concision of a passage. Test-takers will have to add, replace, and delete information from passages that match the tone and sequence of the writing. A Student as Editor question may ask you if adding a sentence to the end of a passage makes sense, or if a certain choice best sets up information that will be revealed later in the passage. For Student as Editor questions, figuring out exactly what the question is asking you to do is the key for success.
How to Approach These Questions
Your main focus on Student as Editor questions is understanding what the College Board is asking you. Although this may seem obvious, Student as Editor questions are tricky because usually all 4 choices are grammatically correct and also fit the passage. However, only one of these choices will actually fit the prompt given by the question. A more grammar based question would ask something such as “which transition word is the most logical” (see below) whereas an evidence based question could ask something such as “which choice provides the best supporting evidence for this argument.”
Practice this Strategy-Problem 1
Iraqi artist Nazik Al-Malaika, celebrated as the first Arabic poet to write in free verse, didn’t reject traditional forms entirely; her poem “Elegy for a Woman of No Importance” consists of two ten-line stanzas and a standard number of syllables. Even in this superficially traditional work, ________ Al-Malaika was breaking new ground by memorializing an anonymous woman rather than a famous man.
Approaching this Question
As stated above, figuring out exactly what the question is asking you is the key for success. Here, the prompt is asking you to put a transition into a passage that connects two different ideas. The first idea states that Al-Malaika didn’t always write poems in her classic free verse style. The second idea states that Al-Malaika was still successful in creating groundbreaking work. A key word to highlight here would be “even”.
Answer Choices
Which choice completes the text with the most logical transition?
A) in fact, B) though, C) therefore, D) moreover,
Correct Answer: Choice A is wrong because “in fact” would only work if the second sentence was attempting to strengthen an idea earlier in the passage. Choice B is a “maybe” because “though” corresponds well with “even” to explain a connection between Al-Malaika’s success in multiple forms. Choice C is wrong because “therefore” would only be correct if it followed a sentence that made a claim with another similar claim or supporting evidence. Choice D cannot be right because like “therefore”, “moreover” would only join two sentences that state the same ideas. As it is our only “maybe”, choice B must be correct.
Practice this Strategy-Problem 2
In a series from 2009, entitled Goddess or Monster, Alonso Guevara depicts prominent women of mythology. One painting from the series, “The Three Graces,” modernizes the Three Graces of mythology: goddesses of beauty, creativity, fertility, and charm. Guevara’s depiction of the graces shows three women clad in chic black dresses and heels, laughing glamorously and sitting on a deep red couch. (6) With this painting, Guevara seems to be considering what modern society would deem as the most desirable qualities for women. She establishes herself not only as an artist with an interesting perspective on femininity, but as one who is ready to be understood in the global and historical context of the art world.
Approaching this Question
Here, the question is asking you to replace the underlined sentence with a more appropriate sentence that leads into the discussion of Guevara that follows (no change is also an answer). The first sentence describes Guevara’s work, focusing specifically on her work depicting women. The last sentence describes Guevara as an artist who is attempting to give viewpoints on feminism and gain global recognition. We should be looking to replace the underlined sentence with a sentence that links Guevara’s paintings of women and her depiction of feminism.
Answer Choices
Which choice best leads into the discussion of Guevara in the following sentence?
A) NO CHANGE B) A motif famously depicted by Antonio Canova, the Three Graces prove excellent subject matter for Guevara. C) This painting allows Guevara to express what she sees in the myth of the Three Graces. D) Choosing the familiar motif of the three graces as subject matter allows Guevara to explore the implications of feminine desirability.
Correct Answer: Choice A is tricky, as it states how Guevara uses her paintings to evaluate societies view on desirable qualities of women, which can somewhat relate to the second sentence. We’ll keep it as a “maybe” for now. Choice B talks about her “The Three Graces” painting, but that is not the focus of the second sentence and must be wrong. Again, choice C overly focuses on this specific painting which is irrelevant to the overall theme of the question. Choice D is solid, and introduces motifs from the painting to show Guevara as a painter who explored feminism and the result of desirability. Choice D is better than choice A, and is the correct answer here because A is less specific than choice D in leading the passage forward about her exploration of feminism.
By James Constan
Student as Editor questions for the SAT focus on editing for organization, concision, and overall effectiveness within a passage. These questions challenge students to apply their understanding of grammar, style, and argument structure to improve a piece of writing. Below are 10 practice questions designed to simulate the "Student as Editor" experience, complete with explanations for the correct answers.
To make the correct answer visible against a white background, please highlight the area beside the correct option.
1. Which transition word best connects two ideas about the benefits and drawbacks of social media?
A) Furthermore, B) However, C) Additionally, D) For instance,
Correct Answer: B) However,
Explanation: The question suggests a contrast between the benefits and drawbacks of social media, making "However," the most logical choice as it introduces a contrast or opposition between two ideas.
2. To add a concluding sentence to a passage discussing the history of the telescope, which choice best reflects the passage's tone and content?
A) In conclusion, telescopes are expensive to make. B) Ultimately, the telescope has vastly expanded our understanding of the universe. C) Telescopes are often found in observatories. D) Many famous astronomers have used telescopes.
Correct Answer: B) Ultimately, the telescope has vastly expanded our understanding of the universe.
Explanation: This option provides a broad and impactful conclusion that matches the historical and scientific significance of the telescope discussed in the passage.
3. Which sentence should be deleted to improve concision in a passage about renewable energy?
A) Renewable energy sources like solar and wind are becoming more popular. B) Many countries are investing in renewable energy. C) However, the transition to renewable energy is not without challenges. D) Interestingly, solar panels can be used to power homes.
Correct Answer: D) Interestingly, solar panels can be used to power homes.
Explanation: This sentence, while informative, diverges from the main focus on the popularity and challenges of renewable energy, making it the best choice for deletion to improve concision.
4. In a passage arguing for more public parks, which choice provides the best supporting evidence?
A) Parks provide a place for children to play. B) Many cities are known for their beautiful parks. C) Studies show that access to green space can improve mental health and community well-being. D) Parks often have walking paths and benches.
Correct Answer: C) Studies show that access to green space can improve mental health and community well-being.
Explanation: This option directly supports the argument by providing evidence of the benefits of public parks, making it the strongest choice for backing up the passage's main point.
5. Which sentence best sets up information that will be revealed later in a passage about the impact of bees on agriculture?
A) Bees come in various species, each with its own unique behaviors. B) Without bees, many of the foods we take for granted would not exist. C) Beekeeping is a popular hobby among nature enthusiasts. D) Flowers have evolved to attract bees for pollination.
Correct Answer: B) Without bees, many of the foods we take for granted would not exist.
Explanation: This sentence introduces a critical idea that can be expanded upon with details about the specific roles bees play in agriculture, setting up the reader for information on their impact.
6. To improve the flow of a passage on the evolution of computers, which sentence should be moved to the beginning?
A) Early computers were large machines used primarily by the military. B) Today, computers can fit in the palm of your hand. C) The first computers were invented in the 1940s. D) Computing technology has advanced rapidly over the decades.
Correct Answer: C) The first computers were invented in the 1940s.
Explanation: Starting with the historical origin of computers sets a chronological framework for the passage, improving its overall organization and flow.
7. In a passage discussing climate change, which sentence unnecessarily repeats information and should be removed?
A) Climate change is leading to higher global temperatures. B) The Earth is experiencing an increase in average temperatures. C) Rising temperatures can have severe environmental impacts. D) Efforts to mitigate climate change include reducing carbon emissions.
Correct Answer: B) The Earth is experiencing an increase in average temperatures.
Explanation: This sentence repeats the idea presented in option A, making it redundant and a good candidate for removal to avoid unnecessary repetition.
8. For a paragraph explaining the process of photosynthesis, which sentence adds unnecessary detail and distracts from the main topic?
A) Photosynthesis is how plants convert sunlight into energy. B) Chlorophyll gives plants their green color and plays a key role in photosynthesis. C) Some plants also use photosynthesis to produce flowers and fruits. D) The oxygen produced by photosynthesis is essential for human survival.
Correct Answer: C) Some plants also use photosynthesis to produce flowers and fruits.
Explanation: While related to plant biology, this sentence distracts from the core explanation of photosynthesis as a process of converting sunlight into energy, making it the best choice for deletion.
9. In a passage about the benefits of reading, which choice best strengthens the argument by providing a specific example?
A) Reading can be a relaxing hobby. B) Many people enjoy reading in their free time. C) A study found that reading for 20 minutes a day can improve memory and cognitive function. D) There are thousands of books available on a variety of topics.
Correct Answer: C) A study found that reading for 20 minutes a day can improve memory and cognitive function.
Explanation: Providing a specific study as evidence offers concrete support for the benefits of reading, making this the strongest option to strengthen the argument.
10. To ensure a passage on the history of cinema begins with an engaging hook, which sentence should be added at the start?
A) The first film was created over a century ago. B) There are many genres of film. C) Movies are a popular form of entertainment. D) Famous directors include Alfred Hitchcock and Steven Spielberg.
Correct Answer: A) The first film was created over a century ago.
Explanation: Starting with a historical fact about the origin of cinema provides an intriguing and relevant hook that engages readers and sets the stage for a discussion on the history of film.
SAT ENGLISH PUNCTUATION REVIEW SHEET- ARTICLE #5
Punctuation Questions
On the digital SAT, there will be 11-15 “Standard English Conventions” questions. Widely recognized to be one of the hardest topics quizzed on the SAT, standard English conventions questions are all about grammar. Unlike other topics previously covered, there are no great strategies for tackling these questions, although there are some helpful tips and tricks. Your best bet to maximize points on these questions is to study your punctuation rules. Make sure to read period to period, rather than stopping at the underlined part to answer the grammar question. Below, punctuation rules for commas, dashes, semicolons, colons, and apostrophes will be outlined.
Commas
Commas are used after any introductory words/phrases, such as in the sentence “to get good sleep, James listened to calming music before bed.”The SAT also expects you to know the Oxford comma, which separates items in a list, such as in the sentence “James slept for a while. He missed his alarms at eight, nine, and ten.” Commas also work to divide non-essential clauses, like in the sentence “James, who was very well rested, had a great day at school.” The punctuation on the sides of a non-essential clause must match, and if you can read the sentence without a clause and it still makes grammatical sense, the clause is non-essential. The comma, along with a conjunction, can work to join two independent clauses, such as in the sentence “James had a great day at school,but he had a lot of homework”.
Dashes
Dashes, like commas, can also divide non-essential clauses, like in the following “James-who had a lot of homework-was very tired.” Dashes can be used just like the word “because”, being placed before explanations, like in the sentence “James was very tired - he had a long day.”
Colons
Colons can be used after complete sentences to set up items in a list, such as in the sentence “James wanted to sleep, but he had tests in lots of subjects on Tuesday: Math, Science, and English.” Colons can never be used alongside transitional words or conjunctions. Colons can also be used after complete sentences to set up additional details, like in the sentence “James was worried about his tests on Tuesday, and he summed up his confidence in one phrase: ‘I am nervous.’”
Semicolons
Semicolons can be used to join two complete sentences without the use of a conjunction, like in the sentence “James was lucky in his math test and got an 100; he was less lucky in English, and got a 32.” Semicolons can also be used in the very rare case of separating items in a list that has internal punctuation, like in the sentence “James wanted to go to college in any city, except for a few: Tampa, Florida; Jacksonville, Florida; and Springfield, Oregon.”
Apostrophes
Apostrophes indicate contractions, with the apostrophe replacing the letter that would usually exist. For example, “it is” is shortened to “it’s”, and “you are” is shortened to “you’re”. Apostrophes are also used for possession, and if the word “doing the possessing” is singular, the apostrophe comes before the s, and if the word “doing the possessing” is plural, the apostrophe comes after the s (Jayan’s car vs students’ cars). However, if a word is already plural without an s being added, the apostrophe still goes before the s (women’s, children’s).
By James Constan
These are SAT punctuation review questions, here are 10 punctuation-related questions focusing on commas, dashes, semicolons, colons, and apostrophes.
To make the correct answer visible against a white background, please highlight the area beside the correct option.
1. Choose the sentence that correctly uses commas.
A) To prepare for the exam, Sarah reviewed her notes, and ate a healthy breakfast. B) To prepare for the exam Sarah reviewed her notes and ate a healthy breakfast. C) To prepare for the exam, Sarah reviewed her notes and ate a healthy breakfast. D) To prepare for the exam Sarah, reviewed her notes, and ate a healthy breakfast.
Correct Answer: C) To prepare for the exam, Sarah reviewed her notes and ate a healthy breakfast.
Explanation: This sentence correctly uses a comma after the introductory phrase and does not unnecessarily separate the verb from its subject, following standard comma usage rules.
2. Which sentence correctly uses dashes to add emphasis?
A) My brother—who loves cooking—made dinner tonight. B) My brother - who loves cooking - made dinner tonight. C) My brother -who loves cooking-made dinner tonight. D) My brother - who loves cooking, made dinner tonight.
Correct Answer: A) My brother—who loves cooking—made dinner tonight.
Explanation: The dashes correctly set off a non-essential clause without spaces, adding emphasis to the information that the brother enjoys cooking.
3. Select the sentence that correctly uses a semicolon.
A) Lisa practiced piano for hours; her performance was flawless. B) Lisa practiced piano for hours, her performance was flawless. C) Lisa practiced piano for hours: her performance was flawless. D) Lisa practiced piano for hours her performance was flawless.
Correct Answer: A) Lisa practiced piano for hours; her performance was flawless.
Explanation: This sentence correctly uses a semicolon to connect two independent clauses without a conjunction, demonstrating the proper use of semicolons to join closely related ideas.
4. Which sentence correctly employs a colon?
A) Before the game, the coach told us: "Give it your all, leave nothing on the field." B) Before the game the coach told us, "Give it your all, leave nothing on the field." C) Before the game, the coach told us, "Give it your all: leave nothing on the field." D) Before the game: the coach told us, "Give it your all, leave nothing on the field."
Correct Answer: A) Before the game, the coach told us: "Give it your all, leave nothing on the field."
Explanation: This sentence correctly uses a colon to introduce a quote following a complete sentence, aligning with the rule that colons can introduce additional details or quotes after complete sentences.
5. Choose the sentence that correctly uses an apostrophe for possession.
A) The students' books were left in the classroom. B) The student's books were left in the classroom. C) The students books were left in the classroom. D) The students' books was left in the classroom.
Correct Answer: A) The students' books were left in the classroom.
Explanation: This sentence correctly places the apostrophe after "students" to show possession by more than one student, adhering to the rule for plural possession.
6. Which sentence demonstrates the correct use of commas in a list?
A) We need to buy eggs, milk, bread and cheese. B) We need to buy eggs milk, bread, and cheese. C) We need to buy eggs, milk, bread, and cheese. D) We need to buy eggs milk bread and cheese.
Correct Answer: C) We need to buy eggs, milk, bread, and cheese.
Explanation: This sentence correctly uses commas to separate items in a list, including the Oxford comma before "and," which is expected on the SAT.
7. Identify the sentence that correctly uses commas for a non-essential clause.
A) My sister, a nurse, is moving to Canada. B) My sister a nurse is moving to Canada. C) My sister, a nurse is moving to Canada. D) My sister a nurse, is moving to Canada.
Correct Answer: A) My sister, a nurse, is moving to Canada.
Explanation: This sentence correctly uses commas to set off the non-essential clause "a nurse," which provides additional information about the sister but is not necessary for the sentence's main meaning.
8. Select the sentence that correctly employs dashes for additional information.
A) The award-winning poet -driven by her passion for nature- spoke at the university. B) The award-winning poet driven by her passion for nature - spoke at the university. C) The award-winning poet driven by her passion for nature spoke at the university. D) The award-winning poet - driven by her passion for nature - spoke at the university.
Correct Answer: D) The award-winning poet - driven by her passion for nature - spoke at the university.
Explanation: This sentence correctly uses dashes to add extra information about the poet's motivation, clearly separating the additional information from the rest of the sentence.
9. Which sentence correctly uses a colon to introduce a list?
A) For dinner we're having: chicken, vegetables, and rice. B) For dinner, we're having: chicken, vegetables, and rice. C) For dinner, we're having chicken, vegetables, and rice. D) We're having for dinner: chicken, vegetables, and rice.
Correct Answer: B) For dinner, we're having: chicken, vegetables, and rice.
Explanation: This sentence correctly uses a colon after a complete sentence to introduce a list, following the rule that colons can introduce lists after complete statements.
10. Choose the sentence that correctly uses apostrophes for contractions.
A) It's going to rain today, so you'll need an umbrella. B) Its going to rain today, so you'll need an umbrella. C) It's going to rain today, so youll need an umbrella. D) Its going to rain today, so youll need an umbrella.
Correct Answer: A) It's going to rain today, so you'll need an umbrella.
Explanation: This sentence correctly uses apostrophes to form contractions for "it is" and "you will," adhering to the rule that apostrophes replace omitted letters in contractions.
Mastering the English language is key to SAT success, combining vocabulary, grammar, and comprehension challenges. These exercises are crafted to boost your language skills, mixing vocab in context, inference, editing, and punctuation for a well-rounded prep. Dive into these questions to sharpen your text analysis, editing precision, and punctuation use, crucial for a top SAT score.
To make the correct answer visible against a white background, please highlight the area beside the correct option.
1. Vocab in Context + Punctuation:
Choose the sentence that correctly uses the word "indigenous" and applies commas appropriately. A) The indigenous species of the island, are remarkably adapted to their environment. B) Indigenous species, of the island are remarkably adapted to their environment. C) The indigenous, species of the island are remarkably adapted to their environment. D) The indigenous species of the island are remarkably adapted to their environment.
Correct Answer: D) The indigenous species of the island are remarkably adapted to their environment.
Explanation: This sentence correctly uses "indigenous" to refer to species native to the island and applies commas appropriately, showing no need for a comma after "indigenous."
2. Inference + Student as Editor:
Given a passage about the impact of digital technology on reading habits, which concluding sentence best supports and enhances the passage's argument? A) Many people enjoy using digital devices for various activities. B) Thus, while digital technology presents challenges, it also offers opportunities to foster a new generation of readers. C) Digital technology has changed how we communicate daily. D) Reading physical books has its unique charm that technology cannot replace.
Correct Answer: B) Thus, while digital technology presents challenges, it also offers opportunities to foster a new generation of readers.
Explanation: This option directly addresses the passage's focus on the impact of digital technology on reading, making an inference that balances both the challenges and opportunities presented.
3. Punctuation + Vocab in Context:
Select the sentence that correctly uses a semicolon and the word "ephemeral." A) The beauty of the sunset is ephemeral; it lasts only a moment before fading. B) The beauty of the sunset; is ephemeral it lasts only a moment before fading. C) The beauty of the sunset is ephemeral, it lasts only a moment; before fading. D) The beauty of the sunset is; ephemeral, it lasts only a moment before fading.
Correct Answer: A) The beauty of the sunset is ephemeral; it lasts only a moment before fading.
Explanation: This sentence correctly uses "ephemeral" to describe the fleeting nature of the sunset's beauty and employs a semicolon to join two closely related independent clauses.
4. Student as Editor + Inference:
In a passage discussing the benefits of exercise, which sentence should be added to effectively set up the subsequent discussion on mental health improvements? A) Exercise is also known to improve cardiovascular health. B) Moreover, the mental health benefits of regular physical activity cannot be overstated. C) Many people use exercise as a way to meet new friends. D) Exercising outdoors can provide additional benefits due to exposure to sunlight.
Correct Answer: B) Moreover, the mental health benefits of regular physical activity cannot be overstated.
Explanation: This sentence introduces the topic of mental health benefits directly and effectively, setting the stage for a detailed discussion on this aspect of exercise.
5. Punctuation + Inference:
Which sentence correctly uses commas and makes an appropriate inference about the character's feelings? A) Faced with the decision, Maria, feeling overwhelmed, chose to ask for advice. B) Faced with the decision Maria feeling overwhelmed, chose to ask for advice. C) Faced with the decision, Maria feeling overwhelmed chose, to ask for advice. D) Faced, with the decision, Maria, feeling overwhelmed chose to ask for advice.
Correct Answer: A) Faced with the decision, Maria, feeling overwhelmed, chose to ask for advice.
Explanation: This sentence correctly places commas around the non-essential clause "feeling overwhelmed," which makes an inference about Maria's emotional state, leading her to seek advice.
6. Vocab in Context + Student as Editor:
In a passage about sustainable farming, which sentence correctly uses the word "mitigate" and improves the passage's flow? A) To mitigate the effects of climate change, farmers use cover crops to improve soil health. B) Farmers mitigate, by using cover crops to improve soil health. C) Mitigate, farmers use cover crops to improve soil health to lessen climate change effects. D) Farmers, to mitigate use cover crops to improve soil health.
Correct Answer: A) To mitigate the effects of climate change, farmers use cover crops to improve soil health.
Explanation: This sentence correctly uses "mitigate" in the context of reducing the effects of climate change and maintains smooth and logical flow within the passage.
7. Inference + Punctuation:
Choose the sentence that makes a clear inference about the future and correctly uses a colon. A) If current trends continue: we can expect major technological advances within the next decade. B) If current trends continue, we can expect: major technological advances within the next decade. C) If current trends continue we can expect major technological advances: within the next decade. D) If current trends continue, we can expect major technological advances within the next decade.
Correct Answer: D) If current trends continue, we can expect major technological advances within the next decade.
Explanation: This sentence infers future technological progress based on current trends and uses punctuation correctly, with no need for a colon in this context.
8. Student as Editor + Vocab in Context:
In a paragraph detailing a scientific experiment, which choice best introduces a result using the word "consequently" and maintains paragraph cohesion? A) Consequently, the results were surprising. B) The results were, consequently, surprising. C) Surprisingly, the results showed what we expected. D) The results were surprising; consequently, they challenged our hypotheses.
Correct Answer: D) The results were surprising; consequently, they challenged our hypotheses.
Explanation: This option correctly uses "consequently" to link the surprising results to the impact on the scientists' hypotheses, enhancing the paragraph's logical flow.
9. Punctuation + Inference:
Which sentence correctly uses dashes to add non-essential information that provides an inference about the subject's expertise? A) The professor—an expert in medieval history—will be leading the seminar. B) The professor, an expert in medieval history, will be leading the seminar. C) The professor - an expert in medieval history will be leading the seminar. D) The professor an expert in medieval history - will be leading the seminar.
Correct Answer: A) The professor—an expert in medieval history—will be leading the seminar.
Explanation: This sentence uses dashes correctly to insert non-essential information that infers the professor's area of expertise, adding context to the seminar topic.
10. Vocab in Context + Punctuation:
Select the sentence that correctly uses the word "transient" and appropriately employs commas. A) The beauty of cherry blossoms is transient, lasting only a few days. B) The beauty of cherry blossoms is, transient lasting only a few days. C) The beauty, of cherry blossoms is transient lasting only a few days. D) The beauty of cherry blossoms, is transient, lasting only a few days.
Correct Answer: A) The beauty of cherry blossoms is transient, lasting only a few days.
11. Vocab in Context + Inference:
A sentence in a biography states, "Despite his myriad achievements, the scientist remained humble, attributing his success to his team." What can we infer about the scientist's character? A) He was arrogant. B) He was ambitious. C) He valued teamwork. D) He worked alone.
Correct Answer: C) He valued teamwork.
Explanation: The use of "attributing his success to his team" suggests that the scientist recognized and appreciated the efforts of his colleagues, indicating he valued teamwork.
12. Student as Editor + Punctuation:
Which addition best enhances the clarity of a passage about the Renaissance, while correctly using a semicolon? A) The Renaissance was a period of great artistic achievement; which led to innovations in various fields. B) The Renaissance; a period of great artistic achievement, led to innovations in various fields. C) The Renaissance was a period of great artistic achievement; it led to innovations in various fields. D) The Renaissance, was a period of great artistic achievement; led to innovations in various fields.
Correct Answer: C) The Renaissance was a period of great artistic achievement; it led to innovations in various fields.
Explanation: This sentence correctly uses a semicolon to connect two independent but related clauses, enhancing clarity and flow.
13. Inference + Vocab in Context:
The novel describes a character "wandering through the labyrinthine streets of the old city." What can be inferred about the city's layout? A) It is modern and well-organized. B) It is confusing and maze-like. C) It is small and insignificant. D) It is newly built.
Correct Answer: B) It is confusing and maze-like.
Explanation: "Labyrinthine" suggests complexity and a maze-like structure, implying the city's streets are confusing and intricate.
14. Punctuation + Student as Editor:
In a detailed discussion on climate change, which sentence is extraneous and disrupts the passage's focus, necessitating its removal? A) Increasing global temperatures have led to more extreme weather patterns. B) Many scientists agree on the urgent need for reduced carbon emissions. C) Interestingly, the history of climate science dates back over a century. D) Actions to combat climate change include renewable energy investments.
Correct Answer: C) Interestingly, the history of climate science dates back over a century.
Explanation: While interesting, this sentence diverts attention from the passage's focus on current issues and actions related to climate change.
15. Vocab in Context + Punctuation:
Choose the sentence that correctly uses "pernicious" and applies commas properly. A) Misinformation can be pernicious, it spreads quickly and deceives many. B) Misinformation, can be pernicious; it spreads quickly and deceives many. C) Misinformation can be pernicious; it spreads quickly and deceives many. D) Misinformation can be, pernicious it spreads quickly and deceives many.
Correct Answer: C) Misinformation can be pernicious; it spreads quickly and deceives many.
Explanation: "Pernicious" means harmful, especially in a gradual or subtle way. The semicolon correctly links two closely related independent clauses.
16. Inference + Student as Editor:
A passage on the exploration of Mars ends with, "The quest for knowledge pushes humanity to its limits and beyond." What concluding statement best reinforces the passage's theme? A) Space exploration is expensive and risky. B) Thus, exploring Mars represents the pinnacle of human curiosity and determination. C) Many countries have space programs. D) Robots and satellites have been used in space exploration.
Correct Answer: B) Thus, exploring Mars represents the pinnacle of human curiosity and determination.
Explanation: This option directly ties back to the theme of pursuing knowledge and the human spirit of exploration, effectively concluding the passage.
17. Punctuation + Vocab in Context:
Which sentence correctly uses "ephemeral" and a colon? A) The fame of internet celebrities is often ephemeral: their popularity fades quickly. B) The fame of internet celebrities: is often ephemeral their popularity fades quickly. C) The fame, of internet celebrities is often ephemeral: their popularity fades quickly. D) The fame of internet celebrities is often ephemeral, their popularity: fades quickly.
Correct Answer: A) The fame of internet celebrities is often ephemeral: their popularity fades quickly.
Explanation: This sentence correctly uses "ephemeral" to describe the short-lived nature of internet fame and employs a colon to introduce an explanation.
18. Student as Editor + Inference:
In a passage about the impact of technology on society, which sentence unnecessarily repeats information and should be removed for conciseness? A) Technology has transformed how we communicate, work, and learn. B) Digital tools have revolutionized communication, education, and employment. C) Smartphones and social media have changed our daily lives. D) The invention of the internet has had a profound effect on modern life.
Correct Answer: B) Digital tools have revolutionized communication, education, and employment.
Explanation: This sentence repeats the idea presented in A, making it redundant and a candidate for removal to enhance conciseness.
19. Vocab in Context + Punctuation:
Select the sentence that accurately uses "inundate" and correctly employs commas. A) After the storm, the coastal village was inundate, with water covering the streets. B) After the storm, the coastal village was, inundate with water covering the streets. C) After the storm; the coastal village was inundated, with water covering the streets. D) After the storm, the coastal village was inundated, with water covering the streets.
Correct Answer: D) After the storm, the coastal village was inundated, with water covering the streets.
Explanation: "Inundated" means overwhelmed or flooded, and this sentence correctly uses the term and commas to describe the aftermath of the storm.
20. Inference + Student as Editor:
A paragraph in an article about renewable energy concludes with, "The shift towards renewable sources is not just beneficial but necessary for our planet's future." What sentence should precede this conclusion for the best logical flow? A) Renewable energy technologies are still in development. B) Critics argue that renewable energy cannot replace fossil fuels entirely. C) However, the environmental and economic benefits of renewable energy cannot be ignored. D) Fossil fuels have been used for centuries.
Correct Answer: C) However, the environmental and economic benefits of renewable energy cannot be ignored.
Explanation: This sentence provides a counterpoint to potential criticisms and sets up the concluding statement by highlighting the importance of renewable energy, ensuring a smooth and logical transition.
21. Punctuation + Vocab in Context:
Choose the sentence that correctly applies dashes and uses "austere." A) The room's décor was austere - simple and unadorned - which matched her minimalist taste. B) The room's décor was austere, simple and unadorned, which matched her minimalist taste. C) The room's décor was - austere simple and unadorned - which matched her minimalist taste. D) The room's décor was austere - simple and unadorned which matched her minimalist taste.
Correct Answer: A) The room's décor was austere - simple and unadorned - which matched her minimalist taste.
Explanation: "Austere" means severe or strict in manner, attitude, or appearance. This sentence correctly uses dashes to add non-essential information that clarifies the meaning of "austere" and matches the syntax and style requirements.
22. Student as Editor + Inference:
In an essay on the role of education in societal change, which sentence best introduces a paragraph on education's impact on economic development? A) Education has been shown to improve individual livelihoods and enhance societal prosperity. B) Many countries invest heavily in their education systems. C) Schools are an important part of community life. D) The history of education is long and varied.
Correct Answer: A) Education has been shown to improve individual livelihoods and enhance societal prosperity.
Explanation: This option directly sets up the discussion on how education influences economic development, providing a logical and thematic bridge to the forthcoming paragraph.
23. Punctuation + Vocab in Context:
Which sentence correctly uses "mitigate" and properly employs a colon? A) Companies are taking steps to mitigate: their environmental impact by reducing emissions. B) Companies are taking steps to mitigate their environmental impact: by reducing emissions. C) To mitigate: their environmental impact, companies are reducing emissions. D) To mitigate their environmental impact, companies are reducing emissions: adopting sustainable practices.
Correct Answer: D) To mitigate their environmental impact, companies are reducing emissions: adopting sustainable practices.
Explanation: This sentence uses "mitigate" correctly to indicate the reduction of harm or severity, and a colon is properly used to introduce a list of specific actions taken by companies.
24. Inference + Student as Editor:
A narrative about a young athlete's journey mentions, "Despite the setbacks, her determination never waned." What conclusion can be drawn about her character? A) She easily gives up. B) She lacks motivation. C) She is resilient and determined. D) She does not face challenges.
Correct Answer: C) She is resilient and determined.
Explanation: The phrase "her determination never waned" implies that she remained steadfast and committed in the face of difficulties, indicating resilience and determination.
25. Vocab in Context + Punctuation:
Identify the sentence that correctly uses "transient" and accurately applies commas. A) The joy of catching the first fish of the day is, transient, lasting only a moment. B) The joy of catching the first fish of the day is transient, lasting only a moment. C) The joy of catching the first fish of the day, is transient lasting only a moment. D) The joy of catching the first fish of the day is transient; lasting only a moment.
Correct Answer: B) The joy of catching the first fish of the day is transient, lasting only a moment.
Explanation: "Transient" correctly describes the brief nature of the joy, and the comma is appropriately used to separate the main clause from the modifying phrase that follows, enhancing clarity and flow.
26. Inference + Punctuation:
Which sentence correctly infers a reason for an action while accurately using commas? A) Having missed the deadline, Sarah, decided to request an extension. B) Having missed the deadline Sarah, decided, to request an extension. C) Having missed the deadline, Sarah decided to request an extension. D) Having missed, the deadline, Sarah decided to request an extension.
Correct Answer: C) Having missed the deadline, Sarah decided to request an extension.
Explanation: This sentence correctly uses a comma after the introductory phrase and before the main clause, clearly inferring that missing the deadline was the reason Sarah decided to request an extension.
27. Vocab in Context + Student as Editor:
In a passage about digital privacy, which sentence best uses "ubiquitous" to enhance the argument? A) The ubiquitous nature of smartphones has made privacy more complex. B) Smartphones are popular. C) Many people use smartphones for various tasks. D) Ubiquitous, smartphones have changed how we manage privacy.
Correct Answer: A) The ubiquitous nature of smartphones has made privacy more complex.
Explanation: This sentence correctly uses "ubiquitous" to describe the widespread presence of smartphones, linking it directly to the complexity of privacy in the digital age, thereby enhancing the passage's argument.
28. Punctuation + Inference:
Select the sentence that makes an appropriate inference about a past event and correctly uses dashes. A) The vase was shattered on the floor—evidence of the cat's nighttime adventures. B) The vase was shattered on the floor, evidence—of the cat's nighttime adventures. C) The vase was shattered on the floor—evidence, of the cat's nighttime adventures. D) The vase—was shattered on the floor evidence of the cat's nighttime adventures.
Correct Answer: A) The vase was shattered on the floor—evidence of the cat's nighttime adventures.
Explanation: This sentence correctly uses dashes to add a non-essential clause that provides an inference about how the vase came to be shattered, linking it to the cat's actions.
29. Student as Editor + Vocab in Context:
For a paragraph detailing advancements in renewable energy, which sentence best incorporates "innovative" and maintains paragraph coherence? A) Solar panels are popular. B) The innovative design of wind turbines has increased efficiency. C) There are many types of renewable energy. D) Renewable energy is important for the environment.
Correct Answer: B) The innovative design of wind turbines has increased efficiency.
Explanation: This option specifically highlights the role of innovation in improving wind turbine efficiency, directly supporting the paragraph's focus on advancements in renewable energy.
30. Inference + Punctuation:
Which sentence correctly uses a colon to introduce a conclusion drawn from evidence? A) The experiment's results were clear: the new treatment was effective. B) The experiment's results were clear, the new treatment: was effective. C) The experiment's results: were clear the new treatment was effective. D) The experiment's results were clear the new treatment: was effective.
Correct Answer: A) The experiment's results were clear: the new treatment was effective.
Explanation: This sentence appropriately uses a colon to introduce a conclusion that directly follows from the preceding evidence, effectively summarizing the experiment's outcome.
31. Vocab in Context + Student as Editor:
In a discussion on classical music's impact, which sentence effectively uses "transcendent" while enhancing the passage's message? A) Classical music is nice. B) The transcendent quality of classical music can elevate the human spirit. C) People have listened to classical music for centuries. D) Many composers have written classical music.
Correct Answer: B) The transcendent quality of classical music can elevate the human spirit.
Explanation: This sentence meaningfully incorporates "transcendent" to describe classical music's ability to go beyond the ordinary and positively affect the human spirit, aligning well with the passage's focus.
32. Punctuation + Inference:
Choose the sentence that infers a character's future actions and correctly uses commas for a list. A) Armed with determination, resilience, and courage, she was ready to face her challenges. B) Armed with determination resilience and courage she was ready, to face her challenges. C) Armed with determination, resilience and courage, she was ready to face her challenges. D) Armed, with determination, resilience, and courage she was ready to face her challenges.
Correct Answer: A) Armed with determination, resilience, and courage, she was ready to face her challenges.
Explanation: This sentence correctly uses commas to separate items in a list and infers that these qualities equip her to tackle future challenges.
33. Inference + Vocab in Context:
The article states, "The CEO's approach was often seen as draconian, but it led to unprecedented growth." What can be inferred about the CEO's management style? A) It was lenient and forgiving. B) It was strict and possibly harsh. C) It was ineffective. D) It was universally admired.
Correct Answer: B) It was strict and possibly harsh.
Explanation: "Draconian" suggests a very strict, possibly harsh approach, implying that while the CEO's methods were severe, they were effective in achieving significant growth.
34. Student as Editor + Punctuation:
Which sentence should be added to effectively transition between paragraphs about the history and the future of space exploration, while correctly using semicolons? A) The history of space exploration is fascinating; but the future holds even greater promise. B) The history of space exploration is fascinating; the future holds even greater promise. C) The history of space exploration; is fascinating, the future holds even greater promise. D) The history of space exploration is fascinating, the future; holds even greater promise.
Correct Answer: B) The history of space exploration is fascinating; the future holds even greater promise.
Explanation: This sentence uses a semicolon correctly to link two closely related but independent clauses, serving as an effective transition that compares the past and future of space exploration.
35. Vocab in Context + Inference:
In a narrative about an ancient city, the author describes it as "a place where myths and reality converge." What can be inferred about the city? A) It is purely fictional. B) It is known for its boring history. C) It has a rich and mystical history. D) It was recently discovered.
Correct Answer: C) It has a rich and mystical history.
Explanation: The description suggests the city has a deep, possibly mystical history where legends and actual events are intertwined, hinting at its cultural and historical significance.
36. Inference + Vocab in Context:
In a story about a pioneer woman, the line reads, "Amid the harsh wilderness, she found solace in the boundless skies." What does this suggest about her feelings towards her environment? A) She was intimidated by the wilderness. B) She felt at peace with nature. C) She wanted to return to civilization. D) She was indifferent to her surroundings.
Correct Answer: B) She felt at peace with nature.
Explanation: The word "solace" implies comfort or consolation in times of distress. This suggests that despite the "harsh wilderness," she draws peace and comfort from the natural beauty of the skies, indicating a positive connection with her environment.
37. Student as Editor + Punctuation:
In a paragraph discussing the effects of global warming, which sentence adds unnecessary detail and should be eliminated to improve concision? A) Rising sea levels threaten coastal communities worldwide. B) Many species face the risk of extinction due to habitat loss. C) Interestingly, some scientists began studying global warming in the 19th century. D) Carbon emissions from human activities are a major contributor to climate change.
Correct Answer: C) Interestingly, some scientists began studying global warming in the 19th century.
Explanation: While historical context about the study of global warming is interesting, it diverts from the paragraph's focus on current effects and actions, making it the best choice for removal.
38. Punctuation + Vocab in Context:
Select the sentence that correctly uses "catalyst" and accurately employs semicolons. A) A significant conversation was the catalyst for change; it spurred the community to action. B) A significant conversation; was the catalyst for change it spurred the community to action. C) A significant conversation was the catalyst; for change, it spurred the community to action. D) A significant conversation was the catalyst for change, it spurred; the community to action.
Correct Answer: A) A significant conversation was the catalyst for change; it spurred the community to action.
Explanation: "Catalyst" refers to something that causes an important event to happen. The semicolon correctly links two independent clauses related by cause and effect without the need for a conjunction.
39. Inference + Student as Editor:
Given an article on technological advancements, which sentence best introduces a discussion on artificial intelligence (AI)? A) Many technologies have changed our lives in the past decade. B) The advent of AI represents a significant leap forward in our ability to process information. C) Computers are now more affordable than ever. D) The internet has revolutionized how we communicate.
Correct Answer: B) The advent of AI represents a significant leap forward in our ability to process information.
Explanation: This sentence directly sets up the topic of AI by highlighting its impact on information processing, making a smooth transition to the specific discussion on AI advancements.
40. Punctuation + Vocab in Context:
Which sentence correctly uses "conundrum" and properly employs commas? A) Facing a moral conundrum, Jane deliberated for hours, trying to make the right decision. B) Facing a moral, conundrum Jane deliberated for hours trying to make the right decision. C) Facing a moral conundrum Jane, deliberated for hours trying, to make the right decision. D) Facing, a moral conundrum Jane deliberated for hours trying to make the right decision.
Correct Answer: A) Facing a moral conundrum, Jane deliberated for hours, trying to make the right decision.
Explanation: "Conundrum" means a confusing and difficult problem or question. This sentence correctly places commas to set off the introductory phrase and an appositive, clarifying Jane's action in response to the conundrum.
41. Student as Editor + Inference:
In a narrative about a marathon runner's preparation, which concluding sentence best emphasizes the theme of perseverance? A) Running a marathon requires good shoes. B) Despite the challenges, his unyielding spirit saw him through to the finish line. C) Nutrition is important for endurance sports. D) He woke up early every day to train.
Correct Answer: B) Despite the challenges, his unyielding spirit saw him through to the finish line.
Explanation: This sentence directly infers the runner's perseverance and resilience, effectively encapsulating the theme of overcoming challenges through a steadfast spirit.
42. Punctuation + Vocab in Context:
Choose the sentence that accurately uses "intrinsic" and correctly applies colons. A) The intrinsic value of honesty: is recognized in many cultures. B) The intrinsic value of honesty is recognized: in many cultures. C) The intrinsic value of honesty; is recognized in many cultures. D) The intrinsic value of honesty is recognized in many cultures.
Correct Answer: D) The intrinsic value of honesty is recognized in many cultures.
Explanation: "Intrinsic" refers to something that is inherent or essential. This sentence correctly uses the word without the need for colons or semicolons, as it does not introduce a list or explanation requiring these punctuation marks.
43. Inference + Student as Editor:
In a discussion about renewable energy sources, which sentence effectively foreshadows the focus on solar power? A) Wind turbines are a common sight in many countries. B) The sun's energy offers an inexhaustible resource that could power our future. C) Renewable energy is gaining popularity around the world. D) Hydropower has been used for centuries.
Correct Answer: B) The sun's energy offers an inexhaustible resource that could power our future.
Explanation: This sentence makes a clear reference to the sun as a renewable energy source, setting up a logical transition to a more detailed discussion on solar power.
44. Punctuation + Vocab in Context:
Which sentence correctly uses "ambivalent" and accurately employs dashes? A) She felt ambivalent about the move - excited yet nervous - about starting over. B) She felt ambivalent about the move, excited yet nervous - about starting over. C) She felt - ambivalent about the move excited yet nervous about starting over. D) She felt ambivalent - about the move, excited yet nervous about starting over.
Correct Answer: A) She felt ambivalent about the move - excited yet nervous - about starting over.
Explanation: "Ambivalent" means having mixed feelings or contradictory ideas about something or someone. The sentence correctly uses dashes to set off additional information that explains the nature of her ambivalence.
45. Student as Editor + Inference:
A passage on the history of the printing press concludes with, "This invention democratized knowledge, making information accessible to many." What statement best supports this conclusion? A) The printing press was invented in the 15th century. B) Books were once handwritten and rare. C) Many famous books were published using the printing press. D) The printing press allowed for faster production of texts.
Correct Answer: D) The printing press allowed for faster production of texts.
Explanation: This option directly supports the conclusion by explaining how the printing press made information more accessible—through faster production, leading to increased availability of texts.
46. Punctuation + Vocab in Context:
Choose the sentence that correctly uses "ephemeral" and accurately employs commas. A) The beauty of fireworks, ephemeral yet unforgettable, lights up the night sky. B) The beauty of fireworks ephemeral, yet unforgettable lights up the night sky. C) The beauty of fireworks ephemeral yet, unforgettable, lights up the night sky. D) The beauty of fireworks, ephemeral, yet unforgettable, lights up the night sky.
Correct Answer: A) The beauty of fireworks, ephemeral yet unforgettable, lights up the night sky.
Explanation: "Ephemeral" means lasting for a very short time. This sentence correctly places commas to set off the phrase "ephemeral yet unforgettable," which describes the transient yet impactful nature of fireworks.
47. Student as Editor + Inference:
In an article about the decline of bee populations, which sentence best introduces the topic of the ecological impact? A) Bees are known for their role in pollination. B) Many people find bees to be a nuisance. C) The decline in bee populations poses a significant threat to global biodiversity. D) There are many types of bees around the world.
Correct Answer: C) The decline in bee populations poses a significant threat to global biodiversity.
Explanation: This sentence directly addresses the core issue of the article by linking the decline in bee populations to a broader ecological concern, setting up a focused discussion on the ecological impact.
48. Punctuation + Vocab in Context:
Which sentence correctly uses "divergent" and properly employs dashes? A) The committee's opinions were divergent—they ranged from strongly supportive to highly critical. B) The committee's opinions were—divergent they ranged from strongly supportive to highly critical. C) The committee's opinions, were divergent—they ranged from strongly supportive, to highly critical. D) The committee's, opinions were divergent—they ranged from strongly supportive to highly critical.
Correct Answer: A) The committee's opinions were divergent—they ranged from strongly supportive to highly critical.
Explanation: "Divergent" means tending to be different or develop in different directions. The sentence correctly uses dashes to add an independent clause that explains the range of opinions within the committee, providing clarity and emphasis.
49. Inference + Student as Editor:
A passage detailing an experiment concludes with, "The results challenged existing theories, suggesting new directions for research." Which sentence best precedes this conclusion? A) The methodology of the experiment was carefully designed. B) Previous theories had not accounted for these findings. C) The experiment was conducted over several months. D) Funding for further research is currently being sought.
Correct Answer: B) Previous theories had not accounted for these findings.
Explanation: This sentence directly sets the stage for the conclusion by indicating that the experiment's results were unexpected in the context of existing theories, naturally leading into the idea that new research directions are warranted.
50. Punctuation + Vocab in Context:
Select the sentence that accurately uses "anomaly" and correctly applies commas. A) The snowstorm in April was an anomaly, it defied the usual weather patterns of the region. B) The snowstorm in April, was an anomaly it defied the usual weather patterns of the region. C) The snowstorm in April was an anomaly; it defied the usual weather patterns of the region. D) The snowstorm in April was, an anomaly, it defied the usual weather patterns of the region.
Correct Answer: C) The snowstorm in April was an anomaly; it defied the usual weather patterns of the region.
Explanation: "Anomaly" refers to something that deviates from what is standard, normal, or expected. This sentence correctly uses a semicolon to link two closely related independent clauses, clarifying that the April snowstorm was unusual for the region.
Well done on completing these SAT practice problems. Your effort is crucial for improving your language skills for the SAT. Consistent practice is essential for progress. For additional exercises, consider using Khan Academy, which provides resources specifically for SAT preparation. Their platform can help you continue to refine your skills and identify areas needing improvement. Keep practicing, and good luck with your SAT preparation.
BCT's SAT Math Practice
Congratulations on starting the SAT math process! Although this test may appear nerve wracking and stressful, we’re here to give you the best tips and advice to perform your best.
The digital SAT is a computer-based test meaning that it is taken entirely on a computer. You will be allowed ‘scrap’ paper for any extra thinking, but this will not be graded. The test allows you to skip questions, flag questions to come back to for later, and provides a digital calculator for the math section. However, we strongly recommend bringing your own TI-84 calculator because they are easier to operate and you’re more likely to feel comfortable with a calculator you constantly use. There will also be a timer at the top of the screen to show students exactly how much time they have remaining in each section.
Dissimilarly to past standardized tests, the digital SAT is adaptive, meaning that questions increase in difficulty when more correct answers are produced.
There are four ‘modules’ in this test. The first two test your reading, language, and writing skills. The second two will test your math skills. The math section focuses on four key topics, including heart of algebra, problem solving and data analysis, passport to advanced math, and additional topics of math.
This guide will provide you with written tips and suggestions for attacking problems in each of the four main categories. Below will also be practice problems to help yourself best prepare. Remember, there are thousands of similar problems out there as well that you can easily use to practice. College Board, the creator of the SAT, has lots of practice math problems for students to use. Additionally, websites such as PrepSharp have PDFs of old SATs and answer keys that are available for free.
In regards to the math section, repetition is key. The more you practice, you will come to realize that the same types of problems will constantly come up, just with different numbers or slightly different wording. With lots of practice, you reach a point in which you’ve seen every type of problem. Once you reach this point, it’s important to continue to drill yourself to ensure that you feel comfortable in each area.
Believe it or not, the majority of the SAT math section involved problems that you’ve already seen before. The test includes huge amounts of algebra, geometry, and simple trigonometry, which are topics that most students have learned by the time they reach the SAT.
Happy studying! You’ve got this!
By Whitney Baron
Algebra is one of the biggest components of the SAT math section. This category hones in on fundamental algebraic concepts as well as other skills that serve as the ‘building blocks’ for college-level mathematics.
This Heart of Algebra section will definitely have linear equations and inequalities. This includes single-variable problems as well as two-variable systems of equations and inequalities. For single-variable problems, it’s best to solve them the standard algebraic way, by isolating ‘x’ or the variable that is given. For double-variable problems, however, it’s often a good idea to instead plug in the answer choices to help save time and avoid algebraic mistakes. This will allow you to spend more time on the harder questions. For inequalities, it’s very easy to get tricked by the direction of the inequalities. In order to avoid making these mistakes, it’s best to plug in numbers to prove to yourself that your answer is correct. Pick one number that is less than the number in the inequality and one that is greater. Plug both numbers in and make sure that only one of the sides is mathematically true. This is your correct answer.
You may be asked to solve equations and inequalities in context as well. This can exist in word problems or by being provided a graph to accompany the equations. For these, it’s best to imagine yourself in these problems and use logic to help yourself arrive at the best answer. This means remembering that you cannot have a negative amount of apples or a fraction of a shoe. This can help you reject wrong answers.
This section will also test your ability to create your own equations or inequalities when provided with a description or a graph. If it’s a singular variable equation, identify each part of the equation before looking at the choices. Identify the independent and dependent variables to help create a slope (think, by how much am I increasing or decreasing each time?). Also, identify the y-intercept (think, what am I starting with? What is my constant?) After this is found, then create your own equation and compare it to the other answers. This will prevent you from falling into traps with answer choices that look correct but aren’t.
This section also includes the interpretation of linear functions. This means not only understanding how to calculate slopes and intercepts, but it also includes understanding what each part means. These questions can often be wordy, so it’s a good idea to read the question and quickly reword the question in your own words to ensure that you understand exactly what is being asked. These questions may push you to gather several algebraic concepts together, such as remembering that slope is the change in y over the change in x or that functions do not exist if x values lead to more than one y value. It may be a good idea to refer back to algebra 1 notes or watch videos online to remind yourself of these simple, yet imperative concepts for the SAT.
By Whitney Baron
Question 1: Single Variable Linear Equation
Solve the equation: 2x + 3 = 15
- A) 6
- B) 5
- C) 7
- D) 4
Answer: B) 5
Explanation: Subtract 3 from both sides to get 2x = 12. Then, divide both sides by 2 to find x = 6.
Question 2: System of Linear Equations
Solve the system of equations:
x + 2y = 6
x - y = 2
- A) x = 2, y = 2
- B) x = 4, y = 1
- C) x = 3, y = 2
- D) x = 2, y = 1
Answer: B) x = 4, y = 1
Explanation: Subtract the second equation from the first to eliminate x and find 3y = 4, so y = 4/3. Substituting y into the second equation, solve for x = 2 + 4/3 = 10/3.
Question 3: Linear Inequality
Solve the inequality: -3x + 6 ≥ 9
- A) x ≤ -1
- B) x ≥ 1
- C) x ≤ 1
- D) x ≥ -1
Answer: A) x ≤ -1
Explanation: Subtract 6 from both sides to get -3x ≥ 3. Divide both sides by -3 and reverse the inequality, resulting in x ≤ -1.
Question 4: Linear Equation from a Word Problem
A car rental company charges a $50 fee plus $20 per day to rent a car. Which equation represents the total cost c for d days?
- A) c = 20 + 50d
- B) c = 50 + 20d
- C) c = 50d + 20
- D) c = 20d + 50
Answer: B) c = 50 + 20d
Explanation: The initial fee is $50 and the cost per day is $20. The equation c = 50 + 20d correctly represents the total cost as a function of days d.
Question 5: Graph Interpretation
A line in a graph has a slope of 5 and passes through the point (2, 3). Which of the following could be the equation of the line?
- A) y = 5x - 7
- B) y = 5x + 7
- C) y = 5x - 13
- D) y = 5x + 13
Answer: A) y = 5x - 7
Explanation: Substitute the point (2, 3) into the slope-intercept form to get 3 = 5*2 + b. Solving for b, b = -7. Therefore, the equation of the line is y = 5x - 7.
Question 6: Creating Equations from Descriptions
John has twice as many books as Peter. If Peter has p books, which equation describes the number of books John has?
- A) j = p + 2
- B) j = 2p
- C) j = 2 + p
- D) j = p/2
Answer: B) j = 2p
Explanation: Since John has twice as many books as Peter, the correct relationship between the number of books John has j and Peter has p is j = 2p.
Question 7: Two-Variable Linear Inequality
Which ordered pair (x, y) is a solution to the inequality 2x + 3y < 6?
- A) (0, 2)
- B) (1, 1)
- C) (0, 1)
- D) (2, 0)
Answer: C) (0, 1)
Explanation: Substituting the pairs into the inequality, only (0, 1) satisfies 20 + 31 < 6, which simplifies to 3 < 6.
Question 8: Single Variable Linear Equation
Solve for x: 5x - 10 = 0
- A) x = 2
- B) x = -2
- C) x = 10
- D) x = 0
Answer: A) x = 2
Explanation: Add 10 to both sides to get 5x = 10, then divide both sides by 5 to find x = 2.
Question 9: Linear Equation in Context
The total cost for t shirts at $15 each includes a $10 shipping fee. Which equation models the total cost c for t shirts?
- A) c = 15t + 10
- B) c = 10t + 15
- C) c = 15 + 10t
- D) c = 10 + 15t
Answer: D) c = 10 + 15t
Explanation: The cost of each shirt is $15 and the shipping fee is a flat $10. Thus, the total cost is represented by the equation c = 10 + 15t.
Question 10: Solving a Linear System by Substitution
Solve the system by substitution:
x + y = 7
y = 3x - 5
- A) x = 3, y = 4
- B) x = 4, y = 3
- C) x = 2, y = 5
- D) x = 5, y = 2
Answer: A) x = 3, y = 4
Explanation: Substitute y from the second equation into the first: x + 3x - 5 = 7. This simplifies to 4x - 5 = 7. Solving for x, we get x = 3. Substituting x = 3 into y = 3*3 - 5 gives y = 4.
The Problem Solving and Data Analysis will test your capabilities of analyzing and interpreting data presented in different formats. This section will also test your ability to use mathematical reasoning to support your answers.
In this section, you can definitely expect to encounter a set of data and be asked to draw conclusions from it. This data can be presented in graphs, tables, charts, etc. These questions may ask you to identify trends. When asked to do so, it’s crucial to combine both algebraic skills and logic. Although an answer may make perfect sense mathematically, it may not always make perfect sense logically, and vice versa. It’s important to remember that x represents the independent variable and that y represents the dependent variable. Also, remember that a slope represents the relationship between x and y, but is represented by ∆y / ∆x. For example, if looking at the relationship between time and distance, an appropriate unit would be feet per second, not seconds per feet. Additionally, if a graph represents the amount of people in a restaurant each hour, a final answer could not be expressed as a decimal (you cannot have a fraction of a person). For these, always round down. If you have 33.4 people / 1 hour, your answer should round down to 33.
These questions may also ask you to draw comparisons between data presented in different formats. For example, a question may ask about two runners as a function of distance / time. If given an equation, the slope would represent the speed (distance/time). The equation may also have a ‘b’ value or y-intercept. This may mean that the runner started ahead or behind (a positive number would mean they were ahead and a negative number would mean they were behind). If presented with information in a different format (a graph or a table). It’s best to create an equation in the y=mx+b format to help yourself more easily compare it to the other data. Be sure to plug in any final answers to make sure they make sense.
This section may also have questions about statistical concepts including mean, median, mode, range, standard deviation, and probability. While mean, median, mode, range, and probability may be familiar concepts, it may be smart to watch a video on them to refresh your mind. Standard deviation may seem new as well. This represents the spread of the data. While you will never be asked to calculate it, it’s possible you will be given two graphs and need to compare their standard deviations. Look at how spread out the data is and check for outliers or wide ranges. The greater the variation of points, the greater the standard deviation. For other statistical questions, make sure you’re careful when calculating values in your calculator. It’s easy to miss a button when typing so fast, and these can sometimes severely affect your answer.
You may also be asked about rates, ratios, and proportions as well. It’s important to memorize the percent change formula as well as how to identify slopes for these questions. If asked for a simplified answer, make sure to compare your initial answer (unsimplified) and final answer (simplified) in your calculator to make sure they’re equal and that you didn’t make an algebraic mistake. This goes for all questions. If possible, use your calculator to prove to yourself that you’re correct.
By Whitney Baron
Question 11: Analysis of Graphical Data
A line on a graph represents the growth of a plant over time. If the line has a slope of 0.5 and it passes through the point (4, 3), which equation best represents the plant's growth?
- A) y = 0.5x + 1
- B) y = 0.5x + 5
- C) y = 0.5x + 3
- D) y = 0.5x + 2
Answer: B) y = 0.5x + 5
Explanation: The equation of a line is y = mx + b. Substituting m = 0.5 and the point (4, 3) into the equation, solve for b: 3 = 0.5*4 + b, so b = 1. The equation becomes y = 0.5x + 1.
Question 12: Interpreting Data from Tables
A table displays the number of students in four classes: 25, 20, 30, and 35. What is the median number of students per class?
- A) 25
- B) 27.5
- C) 30
- D) 32.5
Answer: B) 27.5
Explanation: Arrange the numbers in order: 20, 25, 30, 35. The median is the average of the two middle numbers (25 and 30), which is (25+30)/2 = 27.5.
Question 13: Calculating Probability
A box contains 8 red, 3 blue, and 9 green marbles. What is the probability of drawing a green marble?
- A) 1/4
- B) 9/20
- C) 1/2
- D) 3/5
Answer: B) 9/20
Explanation: The total number of marbles is 8 + 3 + 9 = 20. The number of green marbles is 9, so the probability is 9/20.
Question 14: Comparing Graphs for Standard Deviation
Which set likely has a higher standard deviation if Set A's scores range from 65 to 85 and Set B's scores range from 55 to 95?
- A) Set A
- B) Set B
- C) Both have the same
- D) Cannot be determined
Answer: B) Set B
Explanation: Set B has a wider range of scores (40 points) compared to Set A (20 points), indicating a higher standard deviation.
Question 15: Understanding Rates and Slopes
If a car travels 300 miles in 5 hours, what is the slope of the distance vs. time graph for this journey?
- A) 60 miles per hour
- B) 5 miles per hour
- C) 300 miles per hour
- D) 1/60 miles per hour
Answer: A) 60 miles per hour
Explanation: The slope of the distance vs. time graph represents the speed, calculated as total distance divided by total time, which is 300/5 = 60 miles per hour.
Question 16: Identifying Misleading Graphical Data
A bar graph shows different brands of juice consumption in liters but uses non-uniform widths for each bar. What issue could this present?
- A) It may exaggerate differences in consumption.
- B) It correctly represents the data.
- C) It simplifies data interpretation.
- D) It underrepresents some brands.
Answer: A) It may exaggerate differences in consumption.
Explanation: Non-uniform bar widths can mislead by visually exaggerating the differences between the quantities represented, making some bars appear more significant due to their width.
Question 17: Calculating Percent Change
If a stock price increases from $120 to $150, what is the percent increase?
- A) 20%
- B) 25%
- C) 30%
- D) 50%
Answer: B) 25%
Explanation: Percent change is calculated as (change/original amount) x 100. The change is $150 - $120 = $30. So, (30/120) x 100 = 25%.
Question 18: Interpreting a Function in Context
A function describes the total cost (y) in dollars of producing x items, where y = 2x + 100. What does the 100 represent?
- A) Cost per item
- B) Total items produced
- C) Fixed cost
- D) Variable cost
Answer: C) Fixed cost
Explanation: In the equation y = 2x + 100, the term 100 represents the fixed cost, which does not change with the number of items produced.
Question 19: Mean, Median, Mode, and Range
Given the data set 4, 6, 9, 4, 6, 9, 10, what is the mode?
- A) 4
- B) 6
- C) 9
- D) 10
Answer: B) 6
Explanation: The mode is the number that appears most frequently in a data set. Both 6 and 9 appear three times, so the mode could be both 6 and 9.
Question 20: Solving for Variables in Proportions
If 5x = 3y and y = 15, what is x?
- A) 9
- B) 3
- C) 5
- D) 7
Answer: A) 9
Explanation: Substitute y = 15 into the equation: 5x = 3*15. Simplify to find 5x = 45, then divide by 5 to get x = 9.
The Passport to Advanced Math section will be one of the harder of the five sections. This section will test your ability to work with more complex mathematical concepts and push you to prove that you have the foundations needed for college-level math.
Quadratic equations and functions may be included in this section. Quick factoring will be very important for quadratics, so it is a good idea to refresh your abilities to factor trinomials. However, for non factorable functions, the key is to solve ‘backwards,’ which means plugging in the answer choices to see which one works. The SAT will often try to make you waste time using methods such as the quadratic formula or completing the square when the trick is usually to just plug in the multiple choice options and see which one works.
Exponential functions are also part of this section. For these questions, context and logic is key. The understanding of exponential growth and decay is crucial for this section (know that any rate of change greater than 1 is growth and that a rate of change less than 1 is decay). It’s also likely you will be asked to identify the meaning of certain numbers in a function, such as a principle/initial amounts, rates of change, how often the change occurs, etc. These questions will likely come up in the calculator section so it is best to utilize your calculator to make sure your answers make sense both mathematically and in the context of the problem. This will help you avoid traps. Logarithms may also be tested, but this is more unlikely and will always be solvable by using your calculator.
Basic trigonometry may also be tested. This includes knowing sine, cosine, and tangent well (think SOH CAH TOA). Be sure that your calculator is always in degree mode for this test especially regarding the trigonometric functions. You should also be sure to memorize the ‘special right triangles’ (30,60,90 and 45,45,90) and know the lengths of their corresponding sides. Remembering simple properties can be huge time savers, such as understanding that sin(30)=cos(60).
Complex numbers may also be tested. You will not be asked to graph them, but you may be asked to simplify complex expressions into the form of (a + bi). For these, it’s imperative to remember that i2 = -1 and other similar properties. Remember that a complex number will only ever have two parts, a real part (a) and an imaginary part (bi). If you have more than two parts, you can combine like terms.
This section may also address your understanding of function properties. This means knowing that functions must pass the ‘horizontal line test.’ This means that one x value cannot lead to two different y-values. Additionally, domains and ranges of functions may be tested. If you have your calculator for the question, put the function in and find the minimum or maximum if applicable. This will help you find the range. Most functions being tested on the SAT will have domains of all real numbers, but the calculator can also be used to find the domain. It’s important to understand how to apply domains and ranges to the context of problems as well. For example, if you get two answers for a problem but one of them is not in the domain, it’s obvious that the answer should be rejected and that the only correct answers fall in the domain and range.
Coordinate geometry may also be tested. This means understanding graphs of functions and inequalities and being able to identify whether or not a coordinate is a solution (use your calculator if applicable to verify). You may also need to find the distance between two coordinates by either using the distance formula or pythagorean theorem, or find the midpoint of two points by using the midpoint formula. It’s also important to remember that parallel lines have equal slopes and that perpendicular lines have negative reciprocal slopes.
Similarly to other sections, the calculator is key for these questions. You should always use your calculator if possible to verify that your answer is correct and avoid the traps that the SAT will try to make you fall into.
By Whitney Baron
Question 21: Quadratic Equations
Solve the quadratic equation: x squared minus 6x plus 8 equals 0
- A) x = 2, 4
- B) x = 1, 8
- C) x = -2, -4
- D) x = 3, 3
Answer: A) x = 2, 4
Explanation: Factor the quadratic equation to (x - 2)(x - 4) equals 0. Setting each factor equal to zero gives solutions x = 2 and x = 4.
Question 22: Exponential Functions
If the exponential function f(x) = 3 times 2 to the power of x represents the number of bacteria growing in a lab, what does the number 3 represent in this context?
- A) The rate of growth per hour
- B) The number of bacteria initially present
- C) The number of hours passed
- D) The total number of bacteria after one hour
Answer: B) The number of bacteria initially present
Explanation: The coefficient 3 in the exponential function f(x) represents the initial amount of bacteria present before any growth occurs.
Question 23: Simplifying Complex Numbers
Simplify the expression: (3 + 2i) + (4 - 5i)
- A) 7 - 3i
- B) 1 + 3i
- C) 7 + 3i
- D) 1 - 3i
Answer: A) 7 - 3i
Explanation: Combine like terms: 3 + 4 for the real parts and 2i - 5i for the imaginary parts, resulting in 7 - 3i.
Question 24: Basic Trigonometry
Calculate cos(30 degrees).
- A) square root of 3 divided by 2
- B) 1/2
- C) square root of 2 divided by 2
- D) 0.5
Answer: A) square root of 3 divided by 2
Explanation: From the special right triangles, specifically the 30-60-90 triangle, we know that cos(30 degrees) = square root of 3 divided by 2.
Question 25: Function Properties
If f(x) = x squared and it is known that f passes the horizontal line test, which of the following could be true about the domain of f?
- A) All real numbers
- B) x is greater than or equal to 0
- C) x is less than or equal to 0
- D) None of the above
Answer: D) None of the above
Explanation: The function f(x) = x squared does not pass the horizontal line test for any domain involving more than one x-value because it is not one-to-one; it has the same y-values for different x-values (e.g., f(1) = f(-1)).
Question 26: Coordinate Geometry - Midpoint
Find the midpoint between the points (1, 2) and (3, 8).
- A) (2, 5)
- B) (2, 10)
- C) (4, 10)
- D) (1.5, 5)
Answer: A) (2, 5)
Explanation: Use the midpoint formula (x1 + x2 divided by 2, y1 + y2 divided by 2). Substituting in the given points yields (1 + 3 divided by 2, 2 + 8 divided by 2) = (2, 5).
Question 27: Solving Inequalities with Quadratics
Which x-values satisfy the inequality x squared minus x minus 6 is greater than 0?
- A) x is less than -2 or x is greater than 3
- B) x is greater than -2 and x is less than 3
- C) x is less than -3 or x is greater than 2
- D) x is greater than -3 and x is less than 2
Answer: A) x is less than -2 or x is greater than 3
Explanation: Factor the inequality to (x + 2)(x - 3) is greater than 0. The solution is x-values outside the roots, i.e., x is less than -2 or x is greater than 3.
Question 28: Properties of Exponents
Simplify (x cubed times x squared) squared.
- A) x to the power of 10
- B) x to the power of 6
- C) x to the power of 5
- D) x to the power of 12
Answer: A) x to the power of 10
Explanation: First multiply the exponents inside the parenthesis: x to the power of 3+2 = x to the power of 5. Then apply the exponent outside: (x to the power of 5) squared = x to the power of 10.
Question 29: Interpretation of Logarithmic Functions
If log base b of 64 equals 3, what is b?
- A) 4
- B) 6
- C) 8
- D) 2
Answer: A) 4
Explanation: The equation log base b of 64 equals 3 means that b cubed equals 64. Solving for b, we find b = 4 (since 4 cubed equals 64).
Question 30: Analyzing Functions and Their Graphs
What is the range of the function f(x) = square root of x?
- A) All real numbers
- B) x is greater than or equal to 0
- C) All positive real numbers including zero
- D) All positive real numbers
Answer: C) All positive real numbers including zero
Explanation: The function f(x) = square root of x is defined for x greater than or equal to 0 and results in non-negative real numbers (including zero), hence the range is all positive real numbers including zero.
While the previous articles covered most of what will be tested, there are a few miscellaneous topics.
Advanced topics in geometry may come up. This includes ratios in triangles (similar and congruent triangles). For similar triangles, remember that corresponding sides are proportional and that corresponding angles are equal. For congruent triangles, remember that corresponding sides are equal and corresponding angles are equal. You may also be asked about circles and have to use the completing the square method to find centers and/or radii of circles. Remember that the center of the circle will always be negation of what’s in the equation. For example, if the circle’s equation is (x-4)2 + (y+2)2 = 16, then the center is (4,-2) and not (-4,2). Also remember that radius is the square root of the right side of the equation. For the example above, the radius is NOT 16. It is √16, or 4.
You may also be asked to calculate areas, perimeters, volumes, surface areas, or circumferences of shapes. Remember to always refer to the reference sheet which will provide almost every formula needed, but remember how to logically find the perimeter of a square, rectangle, or triangle (2l+2w or s+s+s).
You should also understand geometric transformations. This includes translations (moving the shape up, down, left, or right), reflections (flipping the shape across the x-axis, y-axis, or a defined line such as x=3 or y=2), rotations (these will be simple, such as rotating 90, 180, or 270 degrees), and dilations (shrinking the shape by a factor (could be anything less than 1, such as ½) or stretching the shape by a factor (could be anything more than 1, such as 2)).
Absolute value functions may be tested as well. Remember that absolute values always make values positive, meaning that absolute values will always be above the x-axis unless translated downward. These questions will most likely be in the calculator section and it’s best to plug the function into the calculator (remember that you need to click the ‘math’ key and then move the arrow over once to the ‘num’ and then click the first option which says ‘abs’)
You may also be asked to state how many solutions there are to a system of equations. If the calculator is usable, put the functions into y1 and y2 and count the intersections. If not, take 10 seconds to make noticings about the equations you’re looking at. If they’re exactly the same, then there are infinitely many solutions. If they have the same slope but different y-intercepts, then they are parallel and have no solutions. If their slopes are negative reciprocals, then they are perpendicular and have one solution. If none of these tactics work, use either substitution (only if x or y doesn’t have a coefficient) or elimination (multiply by the smallest possible number). This will usually result in one solution.
The rest of the questions in this section are either too simple to fall under a category or are completely findable by using the calculator or a given formula. Remember, the key is to practice, practice, practice until you’ve seen every type of question! Repetition is everything! Good luck!
By Whitney Baron
Question 31: Circle Equations
Given the equation of a circle as (x - 3) squared + (y + 5) squared = 25, what is the center and radius of the circle?
- A) Center (3, -5), Radius 5
- B) Center (-3, 5), Radius 5
- C) Center (3, -5), Radius 25
- D) Center (-3, 5), Radius 25
Answer: A) Center (3, -5), Radius 5
Explanation: The center of a circle is the negation of the values inside the parentheses, so (3, -5). The radius is the square root of the value on the right side of the equation, which is sqrt(25) or 5.
Question 32: Area of a Triangle
A triangle has a base of 8 cm and a height of 5 cm. What is its area?
- A) 20 cm squared
- B) 40 cm squared
- C) 60 cm squared
- D) 80 cm squared
Answer: A) 20 cm squared
Explanation: The area of a triangle is calculated as 0.5 times base times height. Thus, 0.5 times 8 times 5 equals 20 cm squared.
Question 33: Geometric Transformations - Reflection
A point at (2, -3) is reflected over the y-axis. What are the coordinates of the reflected point?
- A) (2, 3)
- B) (-2, -3)
- C) (-2, 3)
- D) (2, -3)
Answer: B) (-2, -3)
Explanation: Reflecting a point over the y-axis changes the sign of the x-coordinate. The y-coordinate remains the same.
Question 34: Calculating Volumes
Find the volume of a cube whose side length is 4 cm.
- A) 16 cm cubed
- B) 32 cm cubed
- C) 64 cm cubed
- D) 128 cm cubed
Answer: C) 64 cm cubed
Explanation: The volume of a cube is side length cubed. Thus, 4 times 4 times 4 equals 64 cm cubed.
Question 35: Absolute Value Functions
Which graph represents the function f(x) = |x - 3|?
- A) A V-shape opening upwards, shifted 3 units right
- B) A V-shape opening upwards, shifted 3 units left
- C) A V-shape opening downwards, shifted 3 units right
- D) A V-shape opening downwards, shifted 3 units left
Answer: A) A V-shape opening upwards, shifted 3 units right
Explanation: The absolute value function |x - 3| shifts the basic V-shaped graph of |x| three units to the right.
Question 36: Similar Triangles
If two triangles are similar and the ratio of their corresponding sides is 3:4, what is the ratio of their areas?
- A) 3:4
- B) 9:16
- C) 12:16
- D) 6:8
Answer: B) 9:16
Explanation: The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Thus, (3/4) squared equals 9/16.
Question 37: Perimeter of a Rectangle
A rectangle has a length of 10 units and a width of 7 units. What is its perimeter?
- A) 17 units
- B) 34 units
- C) 70 units
- D) 140 units
Answer: B) 34 units
Explanation: The perimeter of a rectangle is calculated as 2 times (length plus width). Thus, 2 times (10 plus 7) equals 34 units.
Question 38: Solutions to a System of Equations
Given two lines described by the equations y = 2x + 3 and y = 2x - 4, how many solutions does the system have?
- A) None
- B) One
- C) Infinitely many
- D) Cannot be determined
Answer: A) None
Explanation: Since both lines have the same slope but different y-intercepts, they are parallel and do not intersect. Thus, there are no solutions.
Question 39: Circumference of a Circle
What is the circumference of a circle with a radius of 6 units? (Use π = 3.14)
- A) 12.56 units
- B) 18.84 units
- C) 37.68 units
- D) 75.36 units
Answer: C) 37.68 units
Explanation: The circumference of a circle is calculated as 2 times π times radius. Thus, 2 times 3.14 times 6 equals 37.68 units.
Question 40: Rotations in Geometry
A square is rotated 90 degrees clockwise about its center. Which statement is true about the square after the rotation?
- A) The square looks identical to its original position.
- B) The square's area has doubled.
- C) The square is flipped over one of its diagonals.
- D) None of the above.
Answer: A) The square looks identical to its original position.
Explanation: Rotating a square 90 degrees about its center does not change its appearance because of its symmetrical properties.
Question 41: Completing the Square
Given the equation of a circle: (x - 5) squared + (y + 3) squared = 49, what is the center and radius of the circle?
- A) Center (5, -3), Radius 7
- B) Center (-5, 3), Radius 7
- C) Center (5, -3), Radius 49
- D) Center (-5, 3), Radius 49
Answer: A) Center (5, -3), Radius 7
Explanation: The equation gives the center directly as the opposite signs of what's inside the parentheses, and the radius as the square root of the number on the right side.
Question 42: Interpreting Graphs
Which statement is true if the graph of a line in the coordinate plane has a negative slope?
- A) The line represents a proportional relationship.
- B) As x increases, y also increases.
- C) As x increases, y decreases.
- D) The line is horizontal.
Answer: C) As x increases, y decreases.
Explanation: A negative slope means that the line goes down as it moves from left to right, which indicates that y decreases as x increases.
Question 43: Simplifying Exponential Expressions
Simplify the expression 2 to the power of 3 times 2 to the power of 4.
- A) 2 to the power of 7
- B) 2 to the power of 12
- C) 8 to the power of 4
- D) 6 to the power of 7
Answer: A) 2 to the power of 7
Explanation: When multiplying like bases, you add the exponents, so 3 + 4 equals 7.
Question 44: Ratios in Geometry
Two rectangles are similar. The ratio of their lengths is 3 to 4, and the length of the smaller rectangle is 9 cm. What is the length of the larger rectangle?
- A) 12 cm
- B) 13 cm
- C) 14 cm
- D) 16 cm
Answer: A) 12 cm
Explanation: If the ratio is 3 to 4, and the smaller length is 9 (3 times 3), then the larger length is 4 times 3, which is 12 cm.
Question 45: Absolute Value Functions
What is the vertex of the graph of the function f(x) = |x + 2| - 5?
- A) (-2, 5)
- B) (-2, -5)
- C) (2, 5)
- D) (2, -5)
Answer: B) (-2, -5)
Explanation: The vertex of an absolute value function of the form |x - h| + k is (h, k). Here, h = -2 and k = -5.
Question 46: Triangle Perimeter
A triangle has sides of 6 cm, 8 cm, and 10 cm. What is its perimeter?
- A) 20 cm
- B) 24 cm
- C) 28 cm
- D) 30 cm
Answer: B) 24 cm
Explanation: Add the lengths of the sides: 6 + 8 + 10 equals 24 cm.
Question 47: Solving Systems by Elimination
Solve the system of equations: 3x + 2y = 6 and 5x - 2y = 10.
- A) x = 2, y = 0
- B) x = 3, y = 1
- C) x = 4, y = -1
- D) x = 5, y = -2
Answer: A) x = 2, y = 0
Explanation: Add the two equations to eliminate y, getting 8x = 16, so x = 2. Substitute back to find y = 0.
Question 48: Function Domain
What is the domain of the function f(x) = sqrt(x - 4)?
- A) x ≥ 4
- B) x ≤ 4
- C) x > 4
- D) x < 4
Answer: A) x ≥ 4
Explanation: The square root function requires the radicand to be non-negative. x - 4 must be ≥ 0, so x ≥ 4.
Question 49: Volume of a Cylinder
Find the volume of a cylinder with radius 3 cm and height 4 cm. Use π = 3.14.
- A) 113.04 cm cubed
- B) 150.72 cm cubed
- C) 226.08 cm cubed
- D) 339.12 cm cubed
Answer: A) 113.04 cm cubed
Explanation: The volume of a cylinder is πr squared h. Substituting r = 3 and h = 4, the volume is 3.14 times 9 times 4 equals 113.04 cm cubed.
Question 50: Trigonometry
Find the sine of 90 degrees.
- A) 0
- B) 0.5
- C) sqrt(2)/2
- D) 1
Answer: D) 1
Explanation: The sine of 90 degrees is 1, as it represents the maximum value of the sine function.
Question 51: Solving Quadratics by Factoring
Solve the equation: x squared minus 9x plus 18 equals 0.
- A) x = 3, 6
- B) x = 1, 18
- C) x = -3, -6
- D) x = 3, 3
Answer: A) x = 3, 6
Explanation: Factor the quadratic to (x - 3)(x - 6) = 0. Setting each factor to zero gives x = 3 or x = 6.
Question 52: Linear Inequalities
Which x-values satisfy the inequality 2x - 4 > 8?
- A) x > 6
- B) x > 4
- C) x < 6
- D) x < 4
Answer: A) x > 6
Explanation: Add 4 to both sides to get 2x > 12, then divide by 2, resulting in x > 6.
Question 53: Properties of Parallelograms
A parallelogram has base 8 cm and height 3 cm. What is its area?
- A) 11 cm squared
- B) 24 cm squared
- C) 48 cm squared
- D) 32 cm squared
Answer: B) 24 cm squared
Explanation: The area of a parallelogram is base times height, so 8 times 3 equals 24 cm squared.
Question 54: Probability
A bag contains 5 red balls and 3 green balls. What is the probability of drawing a green ball?
- A) 3/8
- B) 3/5
- C) 5/8
- D) 5/3
Answer: A) 3/8
Explanation: There are 3 green balls out of a total of 8 balls, so the probability is 3/8.
Question 55: Reflection over the Y-Axis
Point (3, 4) is reflected over the y-axis. What are the coordinates of the reflected point?
- A) (3, -4)
- B) (-3, 4)
- C) (-3, -4)
- D) (3, 4)
Answer: B) (-3, 4)
Explanation: Reflecting over the y-axis changes the sign of the x-coordinate but leaves the y-coordinate unchanged.
Question 56: Circle Radius from Equation
Given the circle's equation (x + 2) squared + (y - 2) squared = 16, what is the radius?
- A) 4
- B) 8
- C) 16
- D) 32
Answer: A) 4
Explanation: The radius of the circle is the square root of the right side of the equation, which is sqrt(16) or 4.
Question 57: Combining Like Terms
Simplify the expression: 5x + 3x - 2x.
- A) 6x
- B) 5x
- C) 4x
- D) x
Answer: A) 6x
Explanation: Combine like terms by adding the coefficients of x: 5 + 3 - 2 equals 6x.
Question 58: Exponential Decay
If a quantity decreases by 20% each hour, what is the decay factor in the function describing this situation?
- A) 0.2
- B) 0.8
- C) 1.2
- D) 1.8
Answer: B) 0.8
Explanation: A 20% decrease means the quantity retains 80% of its previous amount, represented by a decay factor of 0.8.
Question 59: System of Equations
Solve the system: y = 3x and y = x + 10.
- A) (5, 15)
- B) (5, 10)
- C) (10, 30)
- D) (10, 20)
Answer: A) (5, 15)
Explanation: Set the equations equal to find x: 3x = x + 10, solve to get x = 5. Substituting into y = 3x, y = 15.
Question 60: Midpoint Formula
Find the midpoint between points (-1, 2) and (3, -4).
- A) (1, -1)
- B) (2, -1)
- C) (1, 1)
- D) (0, 0)
Answer: A) (1, -1)
Explanation: Use the midpoint formula: (x1 + x2)/2, (y1 + y2)/2. Substituting in the given points yields ((-1 + 3)/2, (2 - 4)/2) = (1, -1).
Question 61: Complex Numbers
Simplify the expression: (3 + 4i) + (5 - 6i).
- A) 8 - 2i
- B) 2 + 8i
- C) 8 + 2i
- D) 2 - 8i
Answer: A) 8 - 2i
Explanation: Combine the real parts (3 + 5) and the imaginary parts (4i - 6i) to get 8 - 2i.
Question 62: Logarithmic Functions
If log base 3 of (x) equals 4, what is x?
- A) 12
- B) 81
- C) 64
- D) 9
Answer: B) 81
Explanation: Solving the equation log base 3 of x = 4 gives x = 3 to the power of 4, which is 81.
Question 63: Geometry - Circle Theorems
A chord is 8 cm from the center of a circle with a radius of 10 cm. What is the length of the chord?
- A) 12 cm
- B) 16 cm
- C) 18 cm
- D) 20 cm
Answer: B) 16 cm
Explanation: Using the Pythagorean theorem in the triangle formed by the radius, distance from the center to the chord, and half the chord length gives the half chord length as 6 cm. Thus, the chord is 2 times 6 cm = 12 cm.
Question 64: Function Transformations
Which graph represents the function f(x) = -|x| + 3?
- A) A V-shape opening upwards, shifted up 3 units
- B) A V-shape opening downwards, shifted up 3 units
- C) A V-shape opening upwards, shifted down 3 units
- D) A V-shape opening downwards, shifted down 3 units
Answer: B) A V-shape opening downwards, shifted up 3 units
Explanation: The negative sign in front of the absolute value indicates the V opens downward, and the +3 shifts the graph upward by 3 units.
Question 65: Trigonometry - Sine and Cosine Values
What is cos(45 degrees)?
- A) 0
- B) 0.5
- C) sqrt(2)/2
- D) sqrt(3)/2
Answer: C) sqrt(2)/2
Explanation: From the unit circle, cos(45 degrees) = sqrt(2)/2.
Question 66: Probability
A bag contains 4 red, 5 blue, and 6 green balls. What is the probability of drawing a red or a green ball?
- A) 5/15
- B) 10/15
- C) 6/15
- D) 9/15
Answer: B) 10/15
Explanation: There are 4 red and 6 green balls, making 10 favorable outcomes out of 15 total balls. Simplifying 10/15 gives 2/3.
Question 67: Quadratic Equations by Completing the Square
Solve by completing the square: x squared - 6x + 5 = 0.
- A) x = 1, 5
- B) x = 3 ± 2sqrt(2)
- C) x = -3 ± sqrt(2)
- D) x = 3 ± 2
Answer: B) x = 3 ± 2sqrt(2)
Explanation: Rearrange to x squared - 6x = -5, then add (6/2) squared = 9 to both sides to get (x - 3) squared = 4, and solve for x.
Question 68: Area of a Sector
Calculate the area of a sector with a central angle of 60 degrees and a radius of 4 cm.
- A) 2π cm squared
- B) 4π cm squared
- C) 6π cm squared
- D) 8π cm squared
Answer: B) 4π cm squared
Explanation: The area of a sector is (angle/360) times π times radius squared. (60/360) times π times 16 = 4π cm squared.
Question 69: Systems of Equations
Solve the system of equations: 2x - 3y = 6 and 4x + y = 1.
- A) x = 1, y = -3
- B) x = -1, y = 3
- C) x = 0, y = -1
- D) x = 1, y = -1
Answer: D) x = 1, y = -1
Explanation: Use elimination or substitution to solve the system and find x = 1, y = -1.
Question 70: Volume of a Cone
Find the volume of a cone with a radius of 3 cm and a height of 4 cm. Use π = 3.14.
- A) 12.56 cm cubed
- B) 25.12 cm cubed
- C) 37.68 cm cubed
- D) 50.24 cm cubed
Answer: C) 37.68 cm cubed
Explanation: The volume of a cone is (1/3)πr squared h. Substituting r = 3 and h = 4, the volume is (1/3) times 3.14 times 9 times 4 equals 37.68 cm cubed.
Question 71: Inequalities
Solve the inequality: 3(2x - 4) ≤ 6(x - 1)
- A) x ≤ 2
- B) x ≥ 2
- C) x ≤ 1
- D) x ≥ 1
Answer: B) x ≥ 2
Explanation: Simplify and solve the inequality: 6x - 12 ≤ 6x - 6. Subtract 6x from both sides, resulting in -12 ≤ -6, then add 12 to both sides to isolate x.
Question 72: Sine Rule in Triangles
Given triangle ABC where angle A is 45 degrees, angle B is 55 degrees, and side a (opposite angle A) is 7 cm, find side b (opposite angle B).
- A) 7.6 cm
- B) 7.8 cm
- C) 8.0 cm
- D) 8.2 cm
Answer: B) 7.8 cm
Explanation: Use the sine rule: a/sin(A) = b/sin(B). Substitute and solve for b using the known angles and side a.
Question 73: Coordinate Geometry - Distance Formula
Calculate the distance between points (3, 4) and (-1, 1).
- A) 2 sqrt(5)
- B) 5
- C) sqrt(29)
- D) sqrt(34)
Answer: C) sqrt(29)
Explanation: Use the distance formula: sqrt((x2 - x1) squared + (y2 - y1) squared). Substituting the given points results in sqrt((3 + 1) squared + (4 - 1) squared) = sqrt(29).
Question 74: Exponential Growth
A population doubles every 5 years. If the initial population is 1000, what will be the population after 20 years?
- A) 2000
- B) 4000
- C) 8000
- D) 16000
Answer: D) 16000
Explanation: The population doubles 4 times in 20 years (20/5). Starting from 1000, it becomes 2000, then 4000, 8000, and finally 16000.
Question 75: Tangent to a Circle
A line with slope -3 is tangent to a circle at point (4, 2). What is the equation of the line?
- A) y = -3x + 14
- B) y = -3x + 12
- C) y = -3x + 10
- D) y = -3x + 8
Answer: A) y = -3x + 14
Explanation: Use the point-slope form of the equation of a line: y - y1 = m(x - x1). Substitute m = -3, x1 = 4, and y1 = 2 to find y = -3x + 14.
Question 76: Perpendicular Lines
If line l has equation y = (2/3)x + 5, what is the slope of a line perpendicular to l?
- A) -3/2
- B) -2/3
- C) 3/2
- D) 2/3
Answer: A) -3/2
Explanation: Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 2/3 is -3/2.
Question 77: Identifying Function Types
Which type of function does the graph y = 1/(x - 2) represent?
- A) Linear
- B) Quadratic
- C) Exponential
- D) Rational
Answer: D) Rational
Explanation: The function y = 1/(x - 2) is a rational function because it involves a polynomial (in this case, a monomial) in the denominator.
Question 78: Mean and Standard Deviation
Given the set of numbers 5, 10, 15, 20, and 25, what is the mean and standard deviation?
- A) Mean = 15, Standard Deviation = 5
- B) Mean = 15, Standard Deviation = 7.5
- C) Mean = 20, Standard Deviation = 10
- D) Mean = 10, Standard Deviation = 2.5
Answer: A) Mean = 15, Standard Deviation = 7.5
Explanation: Calculate the mean as (5 + 10 + 15 + 20 + 25)/5 = 15. Calculate the standard deviation using the formula for population standard deviation.
Question 79: Areas of Composite Figures
Find the area of a shape consisting of a rectangle and a semicircle protruding from one side, where the rectangle's length is 10 units and width is 5 units, and the semicircle's diameter is 5 units.
- A) 50 + (5/8)π
- B) 75 + (5/4)π
- C) 50 + (25/8)π
- D) 75 + (25/4)π
Answer: C) 50 + (25/8)π
Explanation: The area of the rectangle is length times width = 50. The area of the semicircle is (1/2)π(radius squared) = (1/2)π(2.5 squared) = (25/8)π. Add these to get the total area.
Question 80: Solving Equations with Fractions
Solve the equation: 1/2x + 1/3 = 1/6x + 5/2.
- A) x = -3
- B) x = 3
- C) x = 1/3
- D) x = -1/3
Answer: A) x = -3
Explanation: Clear the fractions by multiplying through by a common denominator, then simplify and solve for x.
Question 81: Quadratic Equations
Solve the equation: x squared minus 4x minus 12 equals 0.
- A) x = 6, -2
- B) x = 4, 3
- C) x = -6, 2
- D) x = -4, 3
Answer: A) x = 6, -2
Explanation: Factor the quadratic to (x - 6)(x + 2) equals 0. The solutions are x = 6 and x = -2.
Question 82: Exponential Growth
A population of bacteria doubles every 3 hours. If initially there are 100 bacteria, how many bacteria will there be after 9 hours?
- A) 200
- B) 400
- C) 800
- D) 1600
Answer: D) 1600
Explanation: The population doubles 3 times in 9 hours (9 divided by 3). Start with 100 bacteria and double three times: 100 -> 200 -> 400 -> 800 -> 1600.
Question 83: Geometry - Circles
A circle has an equation (x-1) squared plus (y+2) squared equals 16. What are the coordinates of the center?
- A) (1, -2)
- B) (-1, 2)
- C) (1, 2)
- D) (-1, -2)
Answer: A) (1, -2)
Explanation: The center of the circle in the equation (x - h) squared plus (y - k) squared equals r squared is (h, k), giving (1, -2) here.
Question 84: Polynomial Functions
If f(x) = x cubed minus 4x squared plus x plus 6, what is f(-1)?
- A) 2
- B) 4
- C) -2
- D) 12
Answer: C) -2
Explanation: Substitute -1 for x in the polynomial and calculate f(-1) = (-1) cubed minus 4(-1) squared plus (-1) plus 6 = -1 minus 4 minus 1 plus 6 = -2.
Question 85: Systems of Equations
Solve the system: y equals 2x plus 3 and y equals -x plus 9.
- A) (2, 7)
- B) (3, 8)
- C) (2, 8)
- D) (3, 9)
Answer: A) (2, 7)
Explanation: Set the equations equal to each other to find x: 2x plus 3 equals -x plus 9. Solving for x gives x = 2. Substitute x = 2 back into any equation to find y = 7.
Question 86: Trigonometry - Sine and Cosine
If cos(theta) equals 0.6 and theta is in the first quadrant, what is sin(theta)?
- A) 0.8
- B) 0.6
- C) 0.4
- D) 0.2
Answer: A) 0.8
Explanation: Use the identity sin squared(theta) plus cos squared(theta) equals 1. Solving for sin(theta), sin(theta) equals the square root of 1 minus 0.36 equals 0.8.
Question 87: Functions - Domain and Range
Which of the following is the range of the function f(x) equals 1 divided by x?
- A) All real numbers except x equals 0
- B) All real numbers except y equals 0
- C) y greater than 0 only
- D) x greater than 0 only
Answer: B) All real numbers except y equals 0
Explanation: The function f(x) equals 1 divided by x is undefined at x equals 0 and never equals zero; thus, its range includes all real numbers except y equals 0.
Question 88: Geometry - Circle Theorems
Find the area of a sector with a central angle of 90 degrees and a radius of 10 cm.
- A) 25 pi cm squared
- B) 50 pi cm squared
- C) 75 pi cm squared
- D) 100 pi cm squared
Answer: B) 50 pi cm squared
Explanation: The area of a sector is (angle divided by 360) times pi times radius squared. Substitute the given values: (90 divided by 360) times pi times 100 equals 25 pi cm squared, which is a quarter of the circle's area.
Question 89: Polynomial Division
Divide x cubed plus 6x squared minus x minus 6 by x plus 3.
- A) x squared plus 3x minus 2
- B) x squared plus 3x minus 3
- C) x squared plus 3x minus 1
- D) x squared plus 3x plus 2
Answer: A) x squared plus 3x minus 2
Explanation: Use polynomial long division. The quotient of dividing x cubed plus 6x squared minus x minus 6 by x plus 3 is x squared plus 3x minus 2.
Question 90: Probability - Independent Events
If the probability of event A is 0.3 and the probability of event B is 0.4, what is the probability of both A and B occurring if they are independent?
- A) 0.12
- B) 0.7
- C) 0.5
- D) 0.1
Answer: A) 0.12
Explanation: For independent events, the probability of both occurring is the product of their probabilities. Multiply 0.3 times 0.4 equals 0.12.