ACCUPLACER Elementary Algebra Test

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?

Accepted Answer

15A + 10B

Answer

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 = ?

Accepted Answer

√30

Answer

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?

Accepted Answer

–80

Answer

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  =

Accepted Answer

9x2  – 12xy + 4y2

Answer

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 =

Accepted Answer

–7

Answer

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.

Accuplacer Practice Test

Accuplacer Practice Test

ACCUPLACER Elementary Algebra Test