ACCUPLACER Exam — Questions and Answers

Question 1: Read: 'The novel received glowing reviews from critics worldwide.' What does 'glowing' mean here?

Shining with light
Negative
Very positive (Correct answer)
Confusing

Correct answer: Very positive

In this context 'glowing' means highly favorable or very positive.

Question 2: Gary never takes advice; he always insists on doing things his own way. Which word would best describe Gary?

intelligent
wary
flippant
stubborn (Correct answer)

Correct answer: stubborn

The description 'never takes advice' and 'always insists on doing things his own way' directly defines the trait of stubbornness. A stubborn person is unwilling to change their mind or actions, even when presented with good reasons or alternative suggestions. Therefore, 'stubborn' is the best word to describe Gary.

Question 3: What is the best version of the underlined part of this sentence? One of the choices involves leaving the sentence as it is written. Daniel found that when it came to the need for 8 hours of sleep every night, he was an exception to the rule<\/u>.

he was an exception to the rule (Correct answer)
he excepted the rule because he was
he was excepting the rule
the exception to the rule was him

Correct answer: he was an exception to the rule

The original phrase 'he was an exception to the rule' is grammatically correct and uses the standard idiom. It clearly conveys that Daniel did not conform to the general rule of needing 8 hours of sleep. Options A, B, and C introduce grammatical errors, change the meaning, or use incorrect verb forms ('excepted' or 'excepting').

Question 4: What is 1/4 written as a percent?

4%
40%
14%
25% (Correct answer)

Correct answer: 25%

1/4 equals 0.25, which is 25%.

Question 5: A car travels 180 miles in 3 hours. At the same rate, how far will it travel in 5 hours?

300 miles (Correct answer)
270 miles
320 miles
360 miles

Correct answer: 300 miles

The speed is 60 mph; in 5 hours the car travels 60 × 5 = 300 miles.

Question 6: It began to rain, and everyone at the picnic ran to the trees to take shelter. Rewrite, beginning - with Everyone at the picnic ran to the trees to take shelter The next words will be

and it began to rain
although it began to rain
beginning to rain
when it began to rain (Correct answer)

Correct answer: when it began to rain

The original sentence describes a sequence of events: first it rained, then people ran for shelter. When rewriting to begin with 'Everyone at the picnic ran to the trees to take shelter,' a temporal clause is needed to indicate *when* this action occurred. 'When it began to rain' correctly establishes this chronological relationship, making the sentence grammatically sound and logically consistent.

Question 7: Which of the following is the inverse function of f(x) = 3x − 6?

f⁻¹(x) = (x − 6)/3
f⁻¹(x) = x/3 − 6
f⁻¹(x) = 3x + 6
f⁻¹(x) = (x + 6)/3 (Correct answer)

Correct answer: f⁻¹(x) = (x + 6)/3

Swap x and y in y = 3x − 6, then solve for y: x = 3y − 6 → y = (x + 6)/3.

Question 8: Which of the following is a factor of x2−x−12 ?

(x+4)
(x+2)
(x−3)
(x+3) (Correct answer)

Correct answer: (x+3)

To find the factors of the quadratic expression x² - x - 12, we look for two numbers that multiply to -12 and add up to -1 (the coefficient of x). These numbers are 3 and -4. Therefore, the quadratic factors into (x + 3)(x - 4). Among the given options, (x+3) is a factor.

Question 9: 36÷1.5=

2.4
2.8
28
24 (Correct answer)

Correct answer: 24

To divide 36 by 1.5, it's helpful to eliminate the decimal in the divisor. Multiply both the dividend (36) and the divisor (1.5) by 10 to get 360 ÷ 15. Performing this division, 360 divided by 15 equals 24.

Question 10: A function is defined as f(x) = −2x + 7. Over which interval is f(x) > 0?

x > 7/2
x > 7
x < 7/2 (Correct answer)
x < −7/2

Correct answer: x < 7/2

Set −2x + 7 > 0 → −2x > −7 → x < 7/2 (inequality flips when dividing by a negative).

Question 11: Which word is a synonym for 'rapid'?

Slow
Quick (Correct answer)
Steady
Quiet

Correct answer: Quick

'Rapid' means fast, so 'quick' is its synonym.

Question 12: If 3 pounds of apples cost $6, what is the cost per pound?

$18
$3
$2 (Correct answer)
$1.50

Correct answer: $2

$6 ÷ 3 pounds = $2 per pound.

Question 13: Which scatterplot description indicates a strong negative correlation?

Points cluster tightly along a line sloping downward (Correct answer)
Points form a U shape
Points are randomly scattered
Points cluster along a line sloping upward

Correct answer: Points cluster tightly along a line sloping downward

A strong negative correlation means data points fall close to a downward-sloping line.

Question 14: Choose the correctly punctuated sentence.

After the movie we ate, dinner.
After, the movie we ate dinner.
After the movie, we ate dinner. (Correct answer)
After the movie we, ate dinner.

Correct answer: After the movie, we ate dinner.

A comma follows the introductory phrase "After the movie."

Question 15: A survey of 200 students found that 60 prefer math. What percentage prefer math?

40%
25%
30% (Correct answer)
20%

Correct answer: 30%

(60 ÷ 200) × 100 = 30%.

Question 16: Which word correctly completes the sentence? He has lived here ___ 2010.

from
since (Correct answer)
for
during

Correct answer: since

"Since" is used with a specific starting point in time.

Question 17: Choose the best word: "He spoke in a _____ voice so the baby would not wake up."

soft (Correct answer)
shrill
booming
harsh

Correct answer: soft

A "soft" voice is quiet and gentle, appropriate to avoid waking a baby.

Question 18: Read: 'Despite the heavy rain, the players continued the match.' What does the passage imply about the players?

They disliked the sport
They never started the match
They stopped because of the rain
They were determined to keep playing (Correct answer)

Correct answer: They were determined to keep playing

The word 'despite' signals they kept playing in spite of the rain, showing determination.

Question 19: Evaluate: log₂(32)

6
8
4
5 (Correct answer)

Correct answer: 5

2⁵ = 32, so log₂(32) = 5.

Question 20: In a passage, a scientist is repeatedly called 'a tireless seeker of truth.' This characterization is meant to make the reader view her as:

Lazy and careless
Admirable and dedicated (Correct answer)
Indifferent
Dishonest

Correct answer: Admirable and dedicated

Calling her tireless and truth-seeking presents her positively.

Question 21: Choose the correct word(s) for the blank in this sentence: Nancy’s new pug is the ____-looking dog I have ever seen, with its beady eyes and wrinkly face.

funnier
more funny
funniest (Correct answer)
most funnily

Correct answer: funniest

The phrase 'the ____-looking dog I have ever seen' indicates a comparison among all dogs the speaker has encountered, requiring the superlative form of the adjective. For the adjective 'funny,' the superlative form is 'funniest,' describing the dog as having the most amusing appearance.

Question 22: 7 2<\/sup>&frasl;3<\/sub> + 4 1<\/sup>&frasl;4<\/sub>

11 3<\/sup>&frasl;7<\/sub>
12 1<\/sup>&frasl;8<\/sub>
1111<\/sup>&frasl;12<\/sub> (Correct answer)
11 5<\/sup>&frasl;12<\/sub>

Correct answer: 1111<\/sup>&frasl;12<\/sub>

To add mixed numbers, first add the whole number parts: 7 + 4 = 11. Next, add the fractional parts: 2/3 + 1/4. Find a common denominator for the fractions, which is 12. Convert 2/3 to 8/12 and 1/4 to 3/12. Adding these gives 8/12 + 3/12 = 11/12. Combine the whole number and fraction to get the final answer: 11 11/12.

Question 23: Which of the following is considered a MECHANICAL error in essay writing?

Starting a new paragraph for each main idea
Writing a three-sentence introduction
Spelling the same word incorrectly throughout the essay (Correct answer)
Using a counterargument in the body paragraphs

Correct answer: Spelling the same word incorrectly throughout the essay

Spelling errors are mechanical errors that affect the polish and credibility of the essay; WritePlacer scoring considers mechanics including spelling, punctuation, and capitalization.

Question 24: –3(5 – 6) – 4(2 – 3) =

–1
1
7 (Correct answer)
–7

Correct answer: 7

Follow the order of operations (PEMDAS/BODMAS). First, evaluate the expressions inside the parentheses: (5 – 6) = –1 and (2 – 3) = –1. The expression becomes –3(–1) – 4(–1). Next, perform the multiplications: –3(–1) = 3 and –4(–1) = 4. Finally, perform the subtraction: 3 – (–4) which simplifies to 3 + 4 = 7.

Question 25: What is 144 ÷ 12?

14
16
10
12 (Correct answer)

Correct answer: 12

12 × 12 = 144, so 144 ÷ 12 = 12.

Question 26: A large fish tank is 6 feet wide, 2 feet long, and 5 feet tall. If the tank is currently filled with 20 cubic feet of water, then what fraction of the tank is empty?

1<\/sup>&frasl;6<\/sub>
1<\/sup>&frasl;2<\/sub>
1<\/sup>&frasl;3<\/sub>
2<\/sup>&frasl;3<\/sub> (Correct answer)

Correct answer: 2<\/sup>&frasl;3<\/sub>

First, calculate the total volume of the fish tank: length * width * height = 2 feet * 6 feet * 5 feet = 60 cubic feet. The tank is filled with 20 cubic feet of water, so the empty volume is 60 - 20 = 40 cubic feet. To find the fraction of the tank that is empty, divide the empty volume by the total volume: 40/60, which simplifies to 2/3.

Question 27: What is the slope of the line passing through (2, 3) and (6, 11)?

2 (Correct answer)
4
1
3

Correct answer: 2

Slope = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.

Question 28: What is the sum of 1/2 and 1/3?

1/6
5/6 (Correct answer)
2/6
2/5

Correct answer: 5/6

Using a common denominator of 6: 3/6 + 2/6 = 5/6.

Question 29: The wheel is considered one of the most important mechanical inventions of all time. Many technologies since the invention of the wheel have been based on its principles, and since the industrial revolution, the wheel has been a basic element of nearly every machine constructed by humankind. No one knows the exact time and place of the invention of the wheel, but its beginnings can be seen across many ancient civilizations. The passage suggests that the wheel is an important invention because it

is one of the world’s oldest inventions
can be traced to many ancient cultures
is one the world’s most famous inventions
forms the basis of so many later inventions (Correct answer)

Correct answer: forms the basis of so many later inventions

The passage emphasizes the wheel's importance by stating that 'Many technologies since the invention of the wheel have been based on its principles' and that it is a 'basic element of nearly every machine constructed by humankind.' This highlights its foundational role in subsequent mechanical innovations. Its significance stems from its influence on countless later inventions.

Question 30: Select the most concise version: "Due to the fact that it was raining, the game was canceled."

On account of the rain that fell, the game was canceled.
Due to the fact that it rained, the game was canceled.
The game was canceled, this was because it was raining.
Because it was raining, the game was canceled. (Correct answer)

Correct answer: Because it was raining, the game was canceled.

"Because" replaces the wordy phrase "due to the fact that" without losing meaning.

Question 31: What is the value of 4³ ÷ 2²?

8
32
16 (Correct answer)
4

Correct answer: 16

4³ = 64 and 2² = 4, so 64 ÷ 4 = 16.

Question 32: Which value of x satisfies 2^(x+1) = 16?

x = 4
x = 3 (Correct answer)
x = 2
x = 5

Correct answer: x = 3

16 = 2⁴, so 2^(x+1) = 2⁴ means x + 1 = 4, giving x = 3.

Question 33: Which sentence is the best topic sentence for a paragraph about reducing plastic waste?

Plastic was invented in the early 1900s.
Glass is heavier than plastic.
Cutting plastic use starts with simple daily habits. (Correct answer)
My neighbor recycles every week.

Correct answer: Cutting plastic use starts with simple daily habits.

A topic sentence states the paragraph's main idea broadly.

Question 34: What is the domain of f(x) = 1/(x − 4)?

All real numbers
x > 4
x ≠ 4 (Correct answer)
x ≠ −4

Correct answer: x ≠ 4

The function is undefined when the denominator equals zero, i.e., when x = 4, so the domain is all real numbers except 4.

Question 35: \t Dr. Ellen Ochoa is an inventor and is also the first female Hispanic astronaut. Her inventions include technology to help robots inspect equipment in space to maintain safety and quality control on spacecraft. Before retiring, she logged more than 1,000 hours in space across several space missions. According to the passage, Dr. Ochoa is the first

Hispanic woman to travel into space (Correct answer)
inventor to travel into space
woman to travel into space
Hispanic person to travel into space

Correct answer: Hispanic woman to travel into space

The passage clearly states, "Dr. Ellen Ochoa is an inventor and is also the first female Hispanic astronaut." This sentence directly identifies her as the first woman of Hispanic descent to achieve the status of an astronaut and travel into space.

Question 36: What is 0.6 written as a fraction in lowest terms?

6/100
1/6
2/3
3/5 (Correct answer)

Correct answer: 3/5

0.6 = 6/10, which reduces to 3/5.

Question 37: If f(x) = x² + 1 and g(x) = 2x, what is f(g(3))?

19
49
37 (Correct answer)
13

Correct answer: 37

g(3) = 6, then f(6) = 6² + 1 = 37.

Question 38: Which inequality is represented by the statement 'twice a number is at most 14'?

2n ≤ 14 (Correct answer)
2n < 14
2n ≥ 14
2n > 14

Correct answer: 2n ≤ 14

'At most 14' means less than or equal to 14, so the inequality is 2n ≤ 14.

Question 39: A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?

2/5
3/10
1/5
1/2 (Correct answer)

Correct answer: 1/2

There are 5 blue marbles out of 10 total, giving a probability of 5/10 = 1/2.

Question 40: To walk, biking, and driving are Pat’s favorite ways of getting around.

To walk, biking, and driving
To walk, to bike, and also driving
To walk, biking, and to drive
Walking, biking, and driving (Correct answer)

Correct answer: Walking, biking, and driving

The original sentence lacks parallel structure, mixing an infinitive ('To walk') with two gerunds ('biking,' 'driving'). To achieve parallelism, all items in a list should be in the same grammatical form. Changing 'To walk' to 'Walking' creates a consistent list of gerunds, making the sentence grammatically correct and balanced.

Question 41: Which detail would best support a main idea that 'exercise improves memory'?

A history of the Olympic Games
A study showing runners scored higher on recall tests (Correct answer)
A recipe for a sports drink
A list of popular running shoes

Correct answer: A study showing runners scored higher on recall tests

A study linking running to better recall directly supports the claim.

Question 42: What does the prefix 'un-' usually mean in words like 'unhappy' and 'unfair'?

Too much
Before
Not (Correct answer)
Again

Correct answer: Not

The prefix 'un-' means 'not,' reversing the meaning of the root word.

Question 43: What is the y-intercept of the function f(x) = 3x² − 4x + 2?

−4
2 (Correct answer)
3
0

Correct answer: 2

The y-intercept occurs at x = 0: f(0) = 3(0) − 4(0) + 2 = 2.

Question 44: The mean of five numbers is 10. Four of the numbers are 8, 11, 9, and 12. What is the fifth number?

8
12
10 (Correct answer)
11

Correct answer: 10

The sum must be 5 × 10 = 50; subtracting the four known values: 50 − 40 = 10.

Question 45: What is 7/8 − 1/2?

3/8 (Correct answer)
1/2
1/4
6/6

Correct answer: 3/8

1/2 = 4/8, so 7/8 - 4/8 = 3/8.

Question 46: What is the best version of the underlined part of this sentence? One of the choices involves leaving the sentence as it is written. Because of his fame in the music industry, Tupac was able to become starring in various films<\/u>, before his death in 1996.

starring variously in films
become starring in various films
various films becomes the star
become the star of various films (Correct answer)

Correct answer: become the star of various films

The phrase 'become starring in various films' is grammatically awkward and incorrect. To express that Tupac took on leading roles in films, a more appropriate and grammatically correct phrasing is needed. Option A, 'become the star of various films,' clearly and correctly conveys that he achieved a starring role or status in films.

Question 47: Erica bought 3 1 2 yards of fabric. If she uses 2 3 of the fabric to make a curtain, how much will she have left?

two and one third yards
one third yard
one and one sixth yards
one sixth yard (Correct answer)

Correct answer: one sixth yard

Erica bought 3 1/2 yards of fabric, which is equivalent to 7/2 yards. If she uses 2/3 of the fabric, the fraction of fabric she has left is 1 - 2/3 = 1/3. To find the actual amount left, multiply this remaining fraction by the total fabric: (1/3) × (7/2) = 7/6 yards. This is equivalent to 1 and 1/6 yards, not one sixth yard.

Question 48: Pick the best transition: It was late; ___, we kept working.

however (Correct answer)
moreover
because
therefore

Correct answer: however

"However" signals the contrast between lateness and continuing to work.

Question 49: Read: 'The detective examined every clue meticulously.' What does 'meticulously' mean?

Quickly
Carelessly
Very carefully (Correct answer)
Rarely

Correct answer: Very carefully

'Meticulously' means with great attention to detail and care.

Question 50: Which expression is equivalent to (2x³y²)²?

4x⁶y⁴ (Correct answer)
4x⁵y⁴
4x⁶y²
2x⁶y⁴

Correct answer: 4x⁶y⁴

Square each factor: 2² = 4, (x³)² = x⁶, (y²)² = y⁴, giving 4x⁶y⁴.

Question 51: Solve for x: |2x − 3| = 7

x = 5 or x = −2 (Correct answer)
x = 5 only
x = −2 only
x = 2 or x = −5

Correct answer: x = 5 or x = −2

Set 2x − 3 = 7 giving x = 5, and 2x − 3 = −7 giving x = −2.

Question 52: A data set has values 4, 7, 7, 9, 13. What is the median?

7.5
7 (Correct answer)
8
9

Correct answer: 7

When values are arranged in order, the middle value of five numbers is the third one, which is 7.

Question 53: √2 × √15 = ?

17
30
√17
√30 (Correct answer)

Correct answer: √30

When multiplying two square roots, you can multiply the numbers inside the square roots together and keep them under a single square root sign. So, √2 × √15 becomes √(2 × 15), which simplifies to √30.

Question 54: Simplify: √(75)

3√5
5√15
15√3
5√3 (Correct answer)

Correct answer: 5√3

75 = 25 × 3, so √75 = √25 · √3 = 5√3.

Question 55: George furnished his house with items he found at second-hand stores and yard sales. What word best describes George?

thrifty (Correct answer)
extravagant
imaginative
arrogant

Correct answer: thrifty

George furnished his house with items from 'second-hand stores and yard sales.' This practice indicates a deliberate effort to save money by buying used items rather than new, expensive ones. This behavior is characteristic of someone who is thrifty or economical.

Question 56: 22.46 + 2.005 + 0.7 =

25.165 (Correct answer)
22.025
26.145
261.65

Correct answer: 25.165

To add decimals, align the numbers vertically by their decimal points. It's helpful to add trailing zeros so all numbers have the same number of decimal places: 22.460 + 2.005 + 0.700. Then, add each column from right to left, carrying over when necessary. The sum of these numbers is 25.165.

Question 57: Which of the following correctly lists the numbers in order from greatest to least?

0.605 > 7\/8 > 0.5 > 65%
7\/8 > 0.605 > 65% > 0.5
7\/8 > 0.605 > 0.5 > 65%
7\/8 > 65% > 0.605 > 0.5 (Correct answer)

Correct answer: 7\/8 > 65% > 0.605 > 0.5

To compare numbers in different formats, convert them all to decimals. 7/8 is 0.875, 65% is 0.65, 0.605 is already a decimal, and 0.5 is 0.500. Arranging these from greatest to least gives 0.875 (7/8), 0.65 (65%), 0.605, and 0.5 (0.5). Therefore, the correct order is 7/8 > 65% > 0.605 > 0.5.

Question 58: Read: 'The crowd was ecstatic when the home team scored the winning goal.' What does 'ecstatic' mean?

Overjoyed (Correct answer)
Bored
Sleepy
Angry

Correct answer: Overjoyed

'Ecstatic' means extremely happy or overjoyed.

Question 59: Which of the following is equivalent to the expression 3x² − 12x?

Both A and B (Correct answer)
3(x² − 4x)
3x(x + 4)
3x(x − 4)

Correct answer: Both A and B

Factor out 3x to get 3x(x − 4), which equals 3(x² − 4x), so both A and B are correct.

Question 60: The phrase 'a Herculean effort' is an example of what kind of language?

Hyperbole only
Alliteration
Onomatopoeia
Allusion (Correct answer)

Correct answer: Allusion

Referencing Hercules to imply great strength is an allusion.

Question 61: What are the solutions to x² − 5x + 6 = 0?

x = 2 and x = 3 (Correct answer)
x = 1 and x = 6
x = −2 and x = −3
x = −1 and x = −6

Correct answer: x = 2 and x = 3

Factor as (x − 2)(x − 3) = 0, giving x = 2 and x = 3.

Question 62: John is shopping for supplies for his office. Let x equal the number of pens he buys and y equal the number of pencils. If pens cost $0.45 and pencils cost $0.15, which of the following represents the total cost of his purchase?

3($0.15x+$0.05y) (Correct answer)
3($0.15x+$0.1y)
15($0.1x+$0.3y)
15($0.4x+$0.1y)

Correct answer: 3($0.15x+$0.05y)

The total cost is calculated by (cost per pen * number of pens) + (cost per pencil * number of pencils), which is $0.45x + $0.15y. Now, let's check the options. Option C is 3($0.15x + $0.05y). Distributing the 3 gives 3 * $0.15x + 3 * $0.05y = $0.45x + $0.15y. This matches the correct total cost expression.

Question 63: Which of the following best states the author's tone in 'Sadly, the old theater was demolished last week'?

Regretful (Correct answer)
Joyful
Excited
Angry

Correct answer: Regretful

The word 'sadly' shows a regretful or sorrowful tone.

Question 64: Identify the sentence type: "Although she was tired, she finished the race."

Compound
Simple
Run-on
Complex (Correct answer)

Correct answer: Complex

It joins a dependent clause and an independent clause, making it complex.

Question 65: 4(−7+5) − (−2)(6−11) = ____

14
-18 (Correct answer)
-12
2

Correct answer: -18

Following the order of operations, first solve the expressions within the parentheses. (-7 + 5) equals -2, and (6 - 11) equals -5. Now substitute these values back into the equation: 4(-2) - (-2)(-5). Perform the multiplications: 4(-2) = -8, and (-2)(-5) = 10. Finally, subtract the results: -8 - 10 = -18.

Question 66: What is the vertex of the parabola y = (x − 3)² + 5?

(3, −5)
(−3, 5)
(−3, −5)
(3, 5) (Correct answer)

Correct answer: (3, 5)

In vertex form y = (x − h)² + k, the vertex is (h, k) = (3, 5).

Question 67: Because light ______________ than sound, you may see lightning before hearing thunder.

will travel faster
having travelled faster
travelling faster
travels faster (Correct answer)

Correct answer: travels faster

This sentence describes a general scientific truth or a habitual action, which requires the simple present tense. 'Travels faster' correctly uses the simple present tense for the singular subject 'light.' The other options use incorrect verb forms or tenses for this context.

Question 68: What is the remainder when x³ − 2x + 4 is divided by (x − 1)?

3 (Correct answer)
1
2
0

Correct answer: 3

By the Remainder Theorem, substitute x = 1: 1 − 2 + 4 = 3.

Question 69: What is the mode of the data set: 5, 8, 3, 8, 7, 5, 8?

8 (Correct answer)
5
3
7

Correct answer: 8

The number 8 appears three times, more than any other value, making it the mode.

Question 70: Identify the sentence error: "Walking to school, the rain began to fall."

Comma splice
Run-on sentence
Dangling modifier (Correct answer)
Subject-verb disagreement

Correct answer: Dangling modifier

The phrase "Walking to school" dangles because rain cannot walk.

Question 71: What is the period of the function y = cos(πx)?

1
2 (Correct answer)
π
2π

Correct answer: 2

Period = 2π ÷ B = 2π ÷ π = 2.

Question 72: If y = 2x + 5 and x = −3, what is y?

−11
1
−1 (Correct answer)
11

Correct answer: −1

Substitute x = −3: y = 2(−3) + 5 = −6 + 5 = −1.

Question 73: An author writes, 'Some claim the policy works, but the data tells a different story.' The author most likely believes the policy:

Is universally praised
Has no measurable effect to study
Should be expanded
Does not work as claimed (Correct answer)

Correct answer: Does not work as claimed

Contrasting claims with contradicting data signals the author's doubt.

Question 74: Solve the following system of equations for (x,y), 3x+4y = 25, x−2y = 5

(7, 1) (Correct answer)
(3, 1)
(2, 5)
(4, 3)

Correct answer: (7, 1)

Using the elimination method, multiply the second equation (x - 2y = 5) by 2 to get 2x - 4y = 10. Now add this new equation to the first equation (3x + 4y = 25): (3x + 4y) + (2x - 4y) = 25 + 10, which simplifies to 5x = 35. Dividing by 5 gives x = 7. Substitute x = 7 into the second original equation: 7 - 2y = 5. Subtract 7 from both sides: -2y = -2. Dividing by -2 gives y = 1. Thus, the solution is (7, 1).

Question 75: Larry was a loner in elementary school, but he grew up to have many friends in high school. Was Larry popular in elementary school?

Yes, Larry befriended more people in elementary school than in high school.
No, he was not. (Correct answer)
Yes, he was.
The sentence doesn’t say.

Correct answer: No, he was not.

The sentence explicitly states that 'Larry was a loner in elementary school.' A 'loner' is someone who prefers to be alone and typically does not have many friends, which directly implies he was not popular. The contrast with 'many friends in high school' further emphasizes his earlier solitude.

Question 76: When I was young, my mother told me that four-leafed clovers were rare, but that I could almost certainly find one if I looked hard enough. How likely was I to find a four-leafed clover?

there is no way to know
a little likely
fairly likely (Correct answer)
not very likely

Correct answer: fairly likely

While the mother mentioned clovers were 'rare,' she also added the crucial phrase 'almost certainly find one if I looked hard enough.' 'Almost certainly' indicates a very high probability, suggesting that finding one was indeed fairly likely with sufficient effort, despite their general rarity.

Question 77: Identify the sentence fragment.

The park was quiet today.
We enjoyed the run.
She ran quickly through the park.
Running quickly through the park. (Correct answer)

Correct answer: Running quickly through the park.

"Running quickly through the park" lacks a subject and main verb.

Question 78: Solve for x: 5x − 3 = 2x + 9

x = 6
x = 2
x = 4 (Correct answer)
x = 3

Correct answer: x = 4

Subtract 2x from both sides to get 3x − 3 = 9, then add 3 and divide by 3 to find x = 4.

Question 79: What is the amplitude of y = 4sin(2x)?

8
2
4 (Correct answer)
π

Correct answer: 4

The amplitude of y = A·sin(Bx) is |A|, which is 4.

Question 80: \t Leonardo da Vinci is not only one of the most famous artists in history, but he was also a botanist, a writer, and an inventor. Even though most of his inventions were not actually built in his lifetime, many of today’s modern machines can be traced back to some of his original designs. The parachute, the military tank, the bicycle, and even the airplane were foretold in the imaginative drawings that can still be seen in the fragments of da Vinci’s notebooks. Over 500 years ago, this man conceived ideas that were far ahead of his time. The author of this passage is praising da Vinci primarily for his

artistic talent
intelligence
fame
foresight (Correct answer)

Correct answer: foresight

The author praises da Vinci for conceiving ideas 'far ahead of his time,' noting that many modern machines can be traced back to his original designs. This highlights his ability to envision future technologies and concepts centuries before they became reality. This forward-thinking quality is best described as foresight.

Question 81: A store sells a jacket for $120 after applying a 20% discount. What was the original price?

$140
$160
$150 (Correct answer)
$144

Correct answer: $150

If $120 is 80% of the original price, divide $120 by 0.80 to get $150.

Question 82: Which of the following correctly lists the numbers in order from greatest to least?ub>2

5⁄2 >3⁄4 > − 1⁄2 > − 1⁄4
3⁄4 > 5⁄2 > − 1⁄2 > −1⁄4
5⁄2 > 3⁄4 > − 1⁄4 > −1⁄2 (Correct answer)
-1⁄4> − 1⁄2 > 3⁄4 > 5⁄2

Correct answer: 5⁄2 > 3⁄4 > − 1⁄4 > −1⁄2

To order the numbers, it's helpful to convert them to decimals: 5/2 = 2.5, 3/4 = 0.75, -1/4 = -0.25, and -1/2 = -0.5. Arranging these from greatest to least gives 2.5 > 0.75 > -0.25 > -0.5. This corresponds to 5/2 > 3/4 > -1/4 > -1/2.

Question 83: Television has been introduced to almost every country in the world, reaching a large number of viewers on every continent. About 600 million people saw the first person walk on the moon, and a billion people watched the twentieth Olympic Games. Television has in many ways promoted understanding and cooperation among people. It does this by showing educational and cultural programs. From this passage, a reader can most reasonably conclude that the author believes that

not every country needs to have television
television can unify people from around the world
people spend too much time watching television
television is as important as schools (Correct answer)

Correct answer: television is as important as schools

The passage highlights television's global reach and its capacity to show "educational and cultural programs" that "promoted understanding and cooperation among people." By emphasizing its role in widespread education and fostering global understanding, the author implicitly places television in a foundational role for societal development and knowledge dissemination, much like schools. The sheer number of people who witnessed significant global events via television also underscores its power as a universal educator and unifier.

Question 84: What is 7 × 8?

56 (Correct answer)
48
54
63

Correct answer: 56

7 multiplied by 8 equals 56.

Question 85: With varying success, many women around the world today struggle for equal rights. Historically, women have achieved greater equality with men during periods of social adversity. The following factors initiated the greatest number of improvements for women: violent revolution, world war, and the rigors of pioneering in an undeveloped land. In all three cases, the essential element that improved the status of women was a shortage of men, which required women to perform many of society’s vital tasks. We can conclude from the information in this passage that

historically, women have only achieved equality through force
historically, the principle of equality alone has not been enough to secure women equal rights (Correct answer)
only pioneer women have been considered equal to men
women today are highly successful in winning equal rights

Correct answer: historically, the principle of equality alone has not been enough to secure women equal rights

The passage explicitly states that women achieved greater equality during periods of social adversity, and the 'essential element' was a shortage of men, requiring women to perform vital tasks. This indicates that practical necessity, rather than the inherent principle of equality, was the driving force behind historical gains for women. Thus, the principle of equality alone was insufficient to secure these rights.

Question 86: What is 1/5 written as a decimal?

0.5
0.05
0.15
0.2 (Correct answer)

Correct answer: 0.2

1 ÷ 5 = 0.2.

Question 87: Which word is an antonym for 'generous'?

Wealthy
Stingy (Correct answer)
Kind
Helpful

Correct answer: Stingy

'Stingy' means unwilling to give, the opposite of 'generous.'

Question 88: Which of the following is a zero of f(x) = x³ − x² − 6x?

x = 3 (Correct answer)
x = 1
x = 4
x = −2

Correct answer: x = 3

Factor: x(x² − x − 6) = x(x − 3)(x + 2), so zeros are x = 0, x = 3, and x = −2.

Question 89: In the words of Thomas De Quincey, “It is notorious that the memory strengthens as you lay burdens upon it.” If, like most people, you have trouble recalling the names of those you have just met, try this: The next time you are introduced, plan to remember the names. Say to yourself, “I’ll listen carefully; I’ll repeat each person’s name to be sure I’ve got it, and I will remember.” You’ll discover how effective this technique is and probably recall those names for the rest of your life. The quotation from De Quincey indicates that the memory

breaks down under great strain
improves if it is used often (Correct answer)
always operates at peak efficiency
becomes unreliable if it tires

Correct answer: improves if it is used often

The quotation states, 'It is notorious that the memory strengthens as you lay burdens upon it.' This directly implies that the more you use your memory (lay burdens upon it), the stronger (improves) it becomes. The passage then offers techniques to actively use memory, reinforcing the idea that consistent use enhances its capability.

Question 90: Identify the error: "Each of the students have submitted their essay."

Verb tense
Pronoun case
Verb agreement (Correct answer)
No error

Correct answer: Verb agreement

"Each" is singular, so it requires "has" rather than "have."

Question 91: Kazuko took her dog for a walk. They went to the park.

Kazuko and her dog went to the park, where she and the dog walked.
Kazuko took her dog for a walk to the park. (Correct answer)
Kazuko, going to the park, took her dog for a walk.
Kazuko took her dog for a walk because they went to the park

Correct answer: Kazuko took her dog for a walk to the park.

This question tests sentence combining for conciseness and clarity. Option B effectively combines the two original sentences by using a prepositional phrase ("to the park") to indicate the destination of the walk. This creates a single, grammatically correct, and more efficient sentence without losing any information or changing the meaning.

Question 92: What is the value of 2.5 × 0.4?

1.0 (Correct answer)
10
0.1
0.10

Correct answer: 1.0

25 × 4 = 100, with two decimal places gives 1.00.

Question 93: A car travels 150 miles in 3 hours. What is its average speed?

60 mph
50 mph (Correct answer)
45 mph
55 mph

Correct answer: 50 mph

Speed equals distance divided by time: 150 / 3 = 50 mph.

Question 94: The word 'ambiguous' most nearly means:

Clearly defined
Open to multiple interpretations (Correct answer)
Extremely long
Brightly colored

Correct answer: Open to multiple interpretations

'Ambiguous' describes something unclear or having more than one meaning.

Question 95: John is repainting the outside of his shed. The front and back of the shed are rectangles, 10 feet long and 8 feet high. The sides of the shed are also rectangular, but they are 12 feet long and 8 feet high. If one bucket of paint can cover exactly 50 square feet of the shed, how many buckets of paint should he have to buy to ensure the entire shed is painted and to have the smallest amount left over?

6 buckets
7 buckets
8 buckets (Correct answer)
9 buckets

Correct answer: 8 buckets

First, calculate the total surface area to be painted. The front and back are 10x8 feet, so 2 * (10*8) = 160 sq ft. The two sides are 12x8 feet, so 2 * (12*8) = 192 sq ft. The total area is 160 + 192 = 352 square feet. Since one bucket covers 50 square feet, divide the total area by the coverage per bucket: 352 / 50 = 7.04 buckets. To ensure the entire shed is painted, John must buy 8 buckets, as he cannot buy a fraction of a bucket.

Question 96: Graph of f(x) crosses the x-axis at x = −2 and x = 4. Which is a possible equation?

f(x) = (x + 2)(x − 4) (Correct answer)
f(x) = (x − 2)(x − 4)
f(x) = (x + 2)(x + 4)
f(x) = (x − 2)(x + 4)

Correct answer: f(x) = (x + 2)(x − 4)

Setting x + 2 = 0 gives x = −2 and x − 4 = 0 gives x = 4, matching both x-intercepts.

Question 97: What is 2/3 × 9?

3
18/3
4
6 (Correct answer)

Correct answer: 6

2/3 × 9 = 18/3 = 6.

Question 98: What is the average of 12, 18, and 30?

22
18
60
20 (Correct answer)

Correct answer: 20

(12 + 18 + 30) ÷ 3 = 60 ÷ 3 = 20.

Question 99: Simplify: (x³ · x²) ÷ x⁴

x²
x³
x (Correct answer)
x⁴

Correct answer: x

Multiply exponents in the numerator: x³ · x² = x⁵, then x⁵ ÷ x⁴ = x¹ = x.

Question 100: Which equation represents exponential decay?

y = 3(0.8)ˣ (Correct answer)
y = 5 + 2x
y = x²
y = 2(1.5)ˣ

Correct answer: y = 3(0.8)ˣ

A base between 0 and 1 (like 0.8) causes the function to decrease, representing exponential decay.

Question 101: Solve the system: 2x + y = 7 and x − y = 2.

x = 3, y = 1 (Correct answer)
x = 4, y = −1
x = 1, y = 5
x = 2, y = 3

Correct answer: x = 3, y = 1

Add the two equations to eliminate y: 3x = 9, so x = 3; then y = 7 − 2(3) = 1.

Question 102: Read: 'Unlike his brother, Tom enjoys quiet evenings at home.' What does 'unlike' signal?

Contrast (Correct answer)
Similarity
Sequence
Cause

Correct answer: Contrast

'Unlike' shows a contrast between Tom and his brother.

Question 103: 7.9 x 0.35 =

3.45
0.2765
0.345
2.765 (Correct answer)

Correct answer: 2.765

To multiply decimals, first multiply the numbers as if they were whole numbers: 79 multiplied by 35 equals 2765. Next, count the total number of decimal places in the original numbers (7.9 has one, 0.35 has two, for a total of three). Finally, place the decimal point in the product so there are three decimal places, resulting in 2.765.

Question 104: Which of the following is a rational number?

√9 (Correct answer)
π
√2
√5

Correct answer: √9

√9 = 3, which is an integer and therefore a rational number.

Question 105: A recipe uses 2.5 cups of flour for 12 cookies. How many cups are needed for 36 cookies?

6 cups
8 cups
7 cups
7.5 cups (Correct answer)

Correct answer: 7.5 cups

36 ÷ 12 = 3, so multiply 2.5 × 3 = 7.5 cups.

ACCUPLACER Exam

The ACCUPLACER is a computer-adaptive college placement test administered by College Board, used by colleges and universities to assess reading, writing, and math skills for course placement decisions.

105

Questions

120 min

Time Limit

To Pass

Checking for saved progress...

Exam Rules

You can skip questions and return to them later
Flag questions for review before submitting
No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
Your progress is auto-saved every 30 seconds