Question 1

Which of the following is the correct simplification of the expression $2(3x - 4) - 5(x + 2)$?

Accepted Answer

$x - 14$

Question 2

A chemist mixes a solution that is $30\%$ acid with a solution that is $10\%$ acid to make $20$ liters of a $20\%$ acid solution. How many liters of the $30\%$ solution should be used?

Accepted Answer

$10$

Question 3

Which of the following is the correct solution to the equation $\dfrac{2x}{3} - 4 = 6$?

Accepted Answer

$x = 12$

Question 4

A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. If a customer paid $\$61$ for a rental, how many miles did they drive?

Accepted Answer

$150$

Question 5

Which of the following is the correct factorization of $x^2 - 9x + 20$?

Accepted Answer

$(x - 4)(x - 5)$

Question 6

If the line $y = -2x + 5$ represents the cost (in dollars) to produce $x$ units of a product, what does the slope of the line represent in this context?

Accepted Answer

The decrease in cost per additional unit produced

Question 7

Which of the following is the solution to the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$(3, 1)$

Question 8

Simplify the expression $\dfrac{3^4 \cdot 3^2}{3^3}$ using exponent rules.

Accepted Answer

$3^5$

Question 9

A rectangle has a length that is $4$ meters more than twice its width. If the perimeter is $28$ meters, what is the width?

Accepted Answer

$3$

Question 10

Which of the following is the correct graph of the equation $y = 2x - 3$?

Accepted Answer

A line with slope $2$ and $y$-intercept $-3$

Question 11

Which of the following is the correct solution to the inequality $5x - 7 < 3x + 1$?

Accepted Answer

$x < 4$

Question 12

A store is having a $25\%$ off sale. If an item’s sale price is $\$60$, what was its original price?

Accepted Answer

$\$75$

Question 13

Which of the following is the correct simplification of $-2[3 - 2(x - 4)]$?

Accepted Answer

$4x - 14$

Question 14

If $f(x) = 2x^2 - 3x + 1$, what is $f(-2)$?

Accepted Answer

$15$

Question 15

Which of the following is the correct factorization of $4x^2 - 25$?

Accepted Answer

$(2x + 5)(2x - 5)$

Question 16

A medical researcher is mixing two solutions: one is $40\%$ saline and the other is $10\%$ saline. How many liters of the $40\%$ solution should be mixed with $6$ liters of the $10\%$ solution to obtain a $25\%$ saline solution?

Accepted Answer

$6$

Question 17

Which of the following is the correct solution to the equation $\dfrac{5}{x} = 2$?

Accepted Answer

$x = 2.5$

Question 18

Simplify the expression $(2x^3y^2)(-3x^2y^4)$.

Accepted Answer

$-6x^5y^6$

Question 19

Which of the following is the correct solution to the system of equations: $\begin{cases} x + 2y = 8 \ 3x - y = 7 \end{cases}$?

Accepted Answer

$(2, 3)$

Question 20

Which of the following is the correct simplification of $\dfrac{2x^5}{4x^2}$?

Accepted Answer

$\dfrac{1}{2}x^3$

Elementary Algebra (MATH 090) Syllabus and Course Structure – University of Indianapolis

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