Elementary Algebra Practice Test for the ACCUPLACER® test

Question 1

√ 4 × √ 5 =

Accepted Answer

2<span style="white-space: nowrap; font-size:larger"> √<span style="text-decoration:overline;"> 5 </span>

Answer

To solve this, first evaluate the square root of 4, which is 2. Then, multiply this result by the square root of 5. Since the square root of 5 cannot be simplified further into an integer, the expression becomes 2 times the square root of 5.

Question 2

4(| − 3 − 2|) − 5 =

Accepted Answer

15

Answer

First, calculate the value inside the absolute value bars: -3 - 2 equals -5. The absolute value of -5 is 5. Next, multiply this result by 4, which gives 20. Finally, subtract 5 from 20 to get the final answer of 15.

Question 3

−²⁄₃ + ¹⁄₆ ⋅ (−2) = ____

Accepted Answer

-1

Answer

Following the order of operations (PEMDAS/BODMAS), first perform the multiplication: (1/6) * (-2) = -2/6, which simplifies to -1/3. Now the expression is -2/3 + (-1/3). Adding these fractions with a common denominator gives -3/3, which simplifies to -1.

Question 4

Which of the following sequence of numbers lists the numbers from the least to the greatest?

Accepted Answer

−⁵⁄₆ < −∣−²⁄₃∣ < ¹⁄₂ = ⁴⁄₈ < ⁷⁄₂

Answer

To order these numbers, first convert them to decimals or fractions with a common denominator. -|-2/3| simplifies to -2/3 (approximately -0.667). -5/6 is approximately -0.833. 1/2 is 0.5, and 4/8 is also 0.5. 7/2 is 3.5. Arranging these values from least to greatest gives -0.833 < -0.667 < 0.5 = 0.5 < 3.5, which corresponds to -5/6 < -|-2/3| < 1/2 = 4/8 < 7/2.

Question 5

4(−7+5) − (−2)(6−11) = ____

Accepted Answer

-18

Answer

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.

Accuplacer Practice Test

Accuplacer Practice Test

Elementary Algebra Practice Test for the ACCUPLACER® test