ACCUPLACER Elementary Algebra Test — Questions and Answers

Question 1: If A represents the number of apples purchased at 15 cents each, and B represents the number of bananas purchased at 10 cents each, which of the following represents the total value of the purchases in cents?

A + B
25(A + B)
10A + 15B
15A + 10B (Correct answer)

Correct answer: 15A + 10B

To find the total value, you multiply the number of each item by its respective cost and then add those products together. If 'A' represents the number of apples at 15 cents each, their total cost is 15A. If 'B' represents the number of bananas at 10 cents each, their total cost is 10B. Therefore, the total value of the purchases is 15A + 10B.

Question 2: √2 × √15 = ?

√17
√30 (Correct answer)
17
30

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 3: What is the value of the expression 2x2 + 3xy – 4y2 when x = 2 and y = –4?

–80 (Correct answer)
–32
32
80

Correct answer: –80

To evaluate the expression, substitute x = 2 and y = –4 into 2x² + 3xy – 4y². This yields 2(2)² + 3(2)(-4) – 4(-4)². First, calculate the powers: 2(4) + 3(2)(-4) – 4(16). Then, perform multiplications: 8 + (-24) – 64. Finally, perform additions and subtractions: 8 – 24 – 64 = -16 – 64 = -80.

Question 4: (3x – 2y) 2 =

9x2 – 4y2
9x2 + 4y2
9x2 – 6xy + 4y2
9x2 – 12xy + 4y2 (Correct answer)

Correct answer: 9x2 – 12xy + 4y2

To expand (3x – 2y)², you multiply the expression by itself: (3x – 2y)(3x – 2y). Using the FOIL method (First, Outer, Inner, Last), you get: (3x * 3x) + (3x * -2y) + (-2y * 3x) + (-2y * -2y). This simplifies to 9x² – 6xy – 6xy + 4y², which further combines to 9x² – 12xy + 4y².

Question 5: If 2x – 3(x + 4) = –5, then x =

–17
–7 (Correct answer)
7
17

Correct answer: –7

To solve 2x – 3(x + 4) = –5, first distribute the –3: 2x – 3x – 12 = –5. Combine like terms to get –x – 12 = –5. Add 12 to both sides, resulting in –x = 7. Finally, multiply by –1 to find x = –7.

Question 6: –3(5 – 6) – 4(2 – 3) =

–7
–1
1
7 (Correct answer)

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 7: If 5t + 2 = 6, then t =

8
5.4
4.5 (Correct answer)
-8

Correct answer: 4.5

To solve the equation 5t + 2 = 6, one first subtracts 2 from both sides, resulting in 5t = 4. Dividing by 5 then yields t = 0.8. The provided correct answer of 4.5 is inconsistent with the given equation, as 5(4.5) + 2 equals 24.5, not 6.

Question 8: For which of the following equations are x = 5 and x = –5 both solutions?

x2 + 25 = 0
x2 – 25 = 0 (Correct answer)
x2 + 10x – 25 = 0
x2 – 5x – 25 = 0

Correct answer: x2 – 25 = 0

An equation has x = 5 and x = –5 as solutions if substituting these values makes the equation true. The equation x² – 25 = 0 is a difference of squares, which factors into (x – 5)(x + 5) = 0. Setting each factor to zero yields x = 5 and x = –5. Other options do not satisfy both solutions.

Question 9: Which of the following is a factor of both x2 – x – 6 and x2 – 5x + 6?

x – 3 (Correct answer)
x – 2
x + 2
x + 3

Correct answer: x – 3

To find a common factor, factor both quadratic expressions. x² – x – 6 factors into (x – 3)(x + 2). x² – 5x + 6 factors into (x – 3)(x – 2). The common factor present in both factorizations is (x – 3).

Question 10: A rectangular yard has area 96 square feet. If the width of the yard is 4 feet less than the length, what is the perimeter, in feet, of the yard?

40 (Correct answer)
44
48
52

Correct answer: 40

Let the length be L and the width be W. We are given Area = L * W = 96 and W = L – 4. Substitute W into the area equation: L(L – 4) = 96, which simplifies to L² – 4L – 96 = 0. Factoring gives (L – 12)(L + 8) = 0, so L = 12 (since length must be positive). Then W = 12 – 4 = 8. The perimeter is 2L + 2W = 2(12) + 2(8) = 24 + 16 = 40 feet.

Question 11: . On Monday, it took Helen 3 hours to do a page of science homework exercises. The next day she did the same number of exercises in 2 hours. If her average rate on Monday was p exercises per hour, what was her average rate the next day, in terms of p?

2(p + 1) exercises per hour
3(p – 1) exercises per hour
3 p exercises per hour
3. 2 p exercises per hour (Correct answer)

Correct answer: 3. 2 p exercises per hour

Helen's total work on Monday was her rate (p exercises/hour) multiplied by her time (3 hours), which equals 3p exercises. Since she did the same number of exercises on Tuesday in 2 hours, her average rate on Tuesday is the total exercises divided by the time: (3p exercises) / (2 hours) = 3/2 p exercises per hour. This corresponds to option D, assuming '3. 2 p' is a typo for 3/2 p or 1.5p. Other options do not correctly represent this inverse relationship between rate and time for a fixed amount of work.

ACCUPLACER Elementary Algebra Test

If A represents the number of apples purchased at 15 cents each, and B represents the number of bananas purchased at 10 cents each, which of the following represents the total value of the purchases in cents?