20 free ACCUPLACER practice questions

Correct answer: B · Community gardens can strengthen ties among neighbors.

Determining central ideas is one of the Information and Ideas skills that College Board's Program Manual lists for the Reading test. The first sentence sets up a contrast with "but ... another reason," and everything after it develops that reason: shared work builds lasting connections, and those connections lead to joint projects such as block cleanups. So the central idea is that community gardens can strengthen ties among neighbors. The passage never compares community gardens with home gardens, so the harvest choice adds a claim. The block cleanups are an example of the main idea, not something planners prefer to gardens. Sharing tools is one detail of how neighbors connect, and the passage says nothing about the tools' cost.

Look for this next time: A main idea covers the whole passage; watch for a contrast word such as "but" that signals where the author's focus lies.

Correct answer: D · To set up an assumption that the rest of the passage overturns

Analyzing purpose and text structure are Rhetoric skills on the Reading test. The first sentence tells us what Maria assumed: that the bakery had closed for good. The rest of the passage shows that assumption was wrong, because the paper comes down and the shop is reopening. So the sentence's job is to set up an expectation that the later sentences overturn. The new counters appear only in the third sentence, not the first. The passage never says why the daughter reopened the shop; it says only that she is reopening it with her grandmother's recipes. Nothing suggests Maria preferred another bakery; she simply believed this one had closed.

Look for this next time: To find a sentence's purpose, ask what it does for the passage as a whole, such as setting up a claim the rest overturns.

Correct answer: A · Free fares are likely to bring in more bus riders.

Analyzing multiple texts is the Synthesis category of the Reading test, which uses paired passages. Passage 1 says free fares will draw new riders; Passage 2 says the planner agrees that ridership may rise. That shared point is the answer. The authors part ways on traffic: Passage 1 expects relief, while Passage 2 warns that crowding could send riders back to their cars, so traffic relief is not agreed. Buying more buses first is the planner's concern only, and even the planner does not say fares should wait. Passage 1 says cost keeps residents from trying the bus, which is narrower than saying cost is the main reason people drive, and Passage 2 does not address it.

Look for this next time: For paired passages, find a claim both authors make, then check that neither one qualifies or rejects it.

Correct answer: C · frank

Vocabulary in context is one of the four Reading categories in College Board's Program Manual. The colon tells you that the second half of the sentence explains the first: the report "listed every missed deadline" and "named the budget decisions" behind them. A report that lays out every problem and its causes is open and direct, so "frank" fits. "Brief" contradicts the detail of a report that lists every missed deadline. "Hopeful" describes a mood the sentence never shows; it is about problems, not optimism. "Confusing" clashes with a report that names exact causes. When a word is unfamiliar, the explanation after a colon or dash is often the strongest clue.

Look for this next time: Use nearby explanation, especially after a colon or dash, to pin down a word's meaning in context.

Correct answer: D · hours, so more students now

Sentence structure is part of the Standard English Conventions category of the Writing test. "The library extended its weekend hours" and "more students now study there on Sundays" are both independent clauses, and joining them with only a comma creates a comma splice, so the sentence cannot stay as it is. Adding a coordinating conjunction after the comma, as in "hours, so more students," joins the clauses correctly, and "so" also shows the cause-and-effect link. Removing the comma creates a run-on sentence. Putting a comma after "and" separates the conjunction from the clause it introduces. A period or a semicolon would also fix the sentence, but neither is offered here.

Look for this next time: Join two independent clauses with a comma plus a coordinating conjunction, a semicolon, or a period, never a comma alone.

Correct answer: A · has

Subject-verb agreement is a conventions-of-usage skill on the Writing test. The subject of the sentence is "collection," which is singular; "of old maps" and "in the museum's basement" are prepositional phrases that describe it but do not change its number. A singular subject takes "has," giving "The collection ... has been moved." "Have" agrees with "maps," the nearest noun, which is the trap the sentence sets. "Are having been moved" is not a correct verb form, and it is plural as well. "Were been moved" is not a correct verb form either. To check agreement, read the sentence without the phrases between the subject and the verb: "The collection has been moved."

Look for this next time: Find the true subject, skipping phrases such as "of old maps," and make the verb agree with it.

Correct answer: B · As a result,

Choosing logical transitions is part of the Expression of Ideas category of the Writing test. The first sentence gives a result of the solar panels, lower bills, and the second gives the district's response: adding panels to more schools. Because the second sentence follows from the first, "As a result" shows the cause-and-effect link. "However" and "In contrast" signal opposition, but expanding a program that saved money is not a contrast with that savings. "For example" would introduce an instance of the first sentence's point, and the district's plan is a consequence of the savings, not an example of them. Read both sentences and name their relationship before you choose.

Look for this next time: Name the relationship between two sentences, such as cause and effect, contrast, or example, before choosing a transition.

Correct answer: C · Sentence 3

Keeping a text focused is a development skill in the Expression of Ideas category of the Writing test. The paragraph is about the tutoring program: who it pairs (sentence 1), how and where tutoring happens (sentence 2), and what it achieved (sentence 4). Sentence 3 shifts to the library building's architect and date, which says nothing about the program, so deleting it keeps the paragraph on topic. Sentence 1 introduces the program and is needed. Sentence 2 mentions the library, but it gives a program detail, the meeting schedule and place, so it belongs. Sentence 4 states the program's results, the strongest support the paragraph offers.

Look for this next time: Delete a sentence when it shifts away from the paragraph's focus, even if it mentions a word the paragraph uses.

Correct answer: A · 3 1/3

Fraction operations are a knowledge and skill category of the Arithmetic test. The question asks how many 3/4-cup portions fit in 2 1/2 cups, which is a division: 2 1/2 ÷ 3/4. Step by step: write the mixed number as an improper fraction, 2 1/2 = 5/2. Dividing by 3/4 means multiplying by its reciprocal, 4/3: 5/2 × 4/3 = 20/6 = 10/3. As a mixed number, 10/3 = 3 1/3 batches. The answer 1 7/8 comes from multiplying 5/2 × 3/4 = 15/8 instead of dividing. The answer 2 2/3 divides only the whole 2 cups by 3/4 and drops the extra 1/2 cup. And 3/10 divides the wrong way, 3/4 ÷ 5/2.

Look for this next time: To find how many portions fit, divide; dividing by a fraction means multiplying by its reciprocal.

Correct answer: C · $71.40

Percentage is one of the Arithmetic test's knowledge and skill categories. Work in order. The discount is 15% of $80: 0.15 × 80 = $12, so the sale price is 80 − 12 = $68. The tax is 5% of the sale price: 0.05 × 68 = $3.40, so the final cost is 68 + 3.40 = $71.40. In one step, 80 × 0.85 × 1.05 = 71.40. The $72.00 answer nets the two percents into a single 10% discount, but the 5% applies to a smaller amount than the 15% does, so they do not simply cancel. The $68.00 answer forgets the tax. The $64.60 answer subtracts the tax instead of adding it: 68 × 0.95.

Look for this next time: Apply successive percents one at a time, each to the current amount; 15% off then 5% tax is not 10% off.

Correct answer: D · $43.28

Decimal operations are an Arithmetic test category. Multiply 3.49 × 12.4 by splitting 12.4 into 12 + 0.4. First, 3.49 × 12 = 41.88. Next, 3.49 × 0.4 = 1.396. Adding gives 41.88 + 1.396 = 43.276. Rounded to the nearest cent, 43.276 becomes $43.28, because the thousandths digit is 6. A quick estimate confirms it: about $3.50 × 12 = $42, plus a little more. The answer $41.88 pays for only 12 gallons. The answer $432.76 misplaces the decimal point: the factors have two and one decimal places, so the product needs three. The answer $42.28 adds 0.4 to 41.88 instead of multiplying 0.4 by 3.49.

Look for this next time: Count the decimal places in both factors to place the point, and check the product with a quick estimate.

Correct answer: B · 3/5, 61%, 0.62, 5/8

Number comparisons and equivalents are an Arithmetic test category. Convert every value to a decimal first. 3/5 = 3 ÷ 5 = 0.60. 61% = 61 ÷ 100 = 0.61. 0.62 stays 0.62. 5/8 = 5 ÷ 8 = 0.625. From least to greatest, that is 0.60, 0.61, 0.62, 0.625, or 3/5, 61%, 0.62, 5/8. The first option lists the values from greatest to least. The third puts 61% ahead of 3/5 and 5/8 ahead of 0.62, so it gets both pairs backward. The last places 5/8 too early, probably by judging it from its small numerator and denominator rather than converting it.

Look for this next time: Convert fractions and percents to decimals before comparing; 5/8 = 0.625 and 3/5 = 0.6.

Correct answer: C · 85 miles

Ratio and proportional relationships are a category of the Quantitative Reasoning, Algebra, and Statistics test. The scale says every inch stands for 25 miles, so set up the proportion 1 inch / 25 miles = 3.4 inches / x miles. Solving, x = 3.4 × 25. Step by step: 3 × 25 = 75 and 0.4 × 25 = 10, so 75 + 10 = 85 miles. The answer 28.4 adds 25 and 3.4 instead of multiplying. About 7.4 miles divides 25 by 3.4, which inverts the scale. The answer 850 multiplies by 250, misplacing the decimal point. A check: 3.4 inches is a bit more than 3 inches, or a bit more than 75 miles.

Look for this next time: For a scale, multiply the map distance by the distance one unit represents, and check the size of the answer.

Correct answer: A · x = 17

Solving linear equations in one variable is in the Linear Equations category of the QAS test. First distribute the 3: 3(x − 4) = 3x − 12, so 3x − 12 = 2x + 5. Subtract 2x from both sides: x − 12 = 5. Add 12 to both sides: x = 17. Check it in the original equation: 3(17 − 4) = 3 × 13 = 39, and 2(17) + 5 = 34 + 5 = 39. The answer 9 comes from distributing only to x and writing 3x − 4. The answer −7 comes from a sign error, 3x + 12 = 2x + 5. The answer 3.4 moves 2x to the left side without changing its sign, giving 5x − 12 = 5, so 5x = 17.

Look for this next time: Distribute to every term in the parentheses, collect the variable on one side, and check the solution in the original equation.

Correct answer: B · 2/9

Compound and conditional probability are in the Probability and Sets category of the QAS test. There are 5 + 3 + 2 = 10 marbles. The probability that the first is red is 5/10. Without replacement, 9 marbles remain and 4 of them are red, so the probability that the second is red is 4/9. Multiply: 5/10 × 4/9 = 20/90 = 2/9. The answer 1/4 assumes replacement, 5/10 × 5/10. The answer 1/2 is the probability for the first draw only. The answer 4/9 is the probability for the second draw alone, once a red has been removed. Both events must happen, so the two probabilities are multiplied.

Look for this next time: Without replacement, the second probability changes; multiply the probabilities of both draws.

Correct answer: D · The mean is 86, and the median is 85.

Calculating measures of center is part of the Descriptive Statistics category of the QAS test. The mean is the sum divided by the count: 72 + 85 + 85 + 90 + 98 = 430, and 430 ÷ 5 = 86. The median is the middle value of the ordered list; with five scores it is the third, 85. So the mean is 86 and the median is 85. The first option treats the median as the mean. The second option swaps the two values. The third option misnames the mode: the mode is the most frequent value, 85, which appears twice, while 90 appears once. A quick check of the mean: the scores' distances from 85 are −13, 0, 0, +5, and +13, which sum to 5, and 85 + 5 ÷ 5 = 86.

Look for this next time: Mean is the sum divided by the count; median is the middle of the ordered data; mode is the most frequent value.

Correct answer: D · x = 7 and x = −2

Factoring and quadratics are categories of the Advanced Algebra and Functions test. Look for two numbers whose product is −14 and whose sum is −5: −7 and 2, since −7 × 2 = −14 and −7 + 2 = −5. So x² − 5x − 14 = (x − 7)(x + 2). Setting each factor to zero gives x − 7 = 0, so x = 7, and x + 2 = 0, so x = −2. Check: 7² − 5(7) − 14 = 49 − 35 − 14 = 0, and (−2)² − 5(−2) − 14 = 4 + 10 − 14 = 0. The other choices get at least one sign wrong: each root has the opposite sign of the number in its factor.

Look for this next time: After factoring, set each factor to zero; the root has the opposite sign of the number in the factor.

Correct answer: B · 15

Evaluating functions is in the Functions category of the Advanced Algebra and Functions test. Substitute −2 for every x, using parentheses: f(−2) = 2(−2)² − 3(−2) + 1. Square first: (−2)² = 4, so 2 × 4 = 8. Next, −3 × (−2) = +6. Then 8 + 6 + 1 = 15. The answer 3 treats −3(−2) as −6. The answer −1 squares only the 2 and keeps the sign, writing −4 for (−2)². The answer 23 multiplies before squaring, (2 × −2)² = 16, which breaks the order of operations because the exponent applies only to x.

Look for this next time: Substitute negative values in parentheses, and square before multiplying by the coefficient.

Correct answer: A · 12,000(1.03)^t

Creating and interpreting exponential functions is part of the Exponential and Logarithmic Equations category of the AAF test. Growing by 3% a year means each year's population is 100% + 3% = 103% of the year before, so the yearly growth factor is 1.03. After t years, the population is 12,000 multiplied by 1.03 t times: 12,000(1.03)^t. After one year that gives 12,000 × 1.03 = 12,360, which is 360 more, 3% of 12,000. Using 0.03 as the base would shrink the population to 3% of itself each year. Adding 0.03t is a linear model that adds almost nothing. A base of 1.3 means 30% growth a year.

Look for this next time: For growth of r percent per period, multiply by (1 + r) each period: the model is initial × (1 + r)^t.

Correct answer: C · 5 units

Right-triangle trigonometry, including special triangles, is in the Trigonometry category of the Advanced Algebra and Functions test. Sine relates the opposite side to the hypotenuse: sin 30° = opposite / hypotenuse. Since sin 30° = 1/2, the opposite side is 10 × 1/2 = 5 units. The same result comes from the 30-60-90 triangle, whose sides are in the ratio 1 : √3 : 2; with a hypotenuse of 10, the short side, opposite 30°, is 5. The answer 5√3 is the side adjacent to the 30° angle, 10 × cos 30°. The answer 20 divides by sin 30° instead of multiplying. And 10√3 is longer than the hypotenuse, which no leg can be.

Look for this next time: In a 30-60-90 triangle, the side opposite 30° is half the hypotenuse.