Question 1

A chemist mixes two solutions. The first contains $\dfrac{3}{4}$ liters of acid, and the second contains $\dfrac{2}{3}$ liters of acid. What is the total amount of acid in both solutions, expressed as a simplified fraction?

Accepted Answer

$\dfrac{17}{12}$

Question 2

A company’s profit $P$ (in thousands of dollars) after $x$ years is modeled by $P(x) = 2x^2 - 5x + 3$. What is the degree of this polynomial, and is it a monomial, binomial, trinomial, or none of these?

Accepted Answer

Degree 2, trinomial

Question 3

Simplify the expression using the laws of exponents: $\left( x^3 y^2 \right)^2$

Accepted Answer

$x^6 y^4$

Question 4

A hiker descends from a mountain peak at 1,200 feet above sea level to a valley at -350 feet. What is the total change in elevation?

Accepted Answer

$1,550$ feet

Question 5

Which of the following numbers is both a rational and an integer?

Accepted Answer

$-7$

Question 6

A rectangular garden has a length of $2x + 5$ meters and a width of $x - 3$ meters. What is the area of the garden, expressed as a simplified polynomial?

Accepted Answer

$2x^2 - x - 15$

Question 7

Solve for $x$: $5(x - 2) = 3x + 8$

Accepted Answer

$x = 6$

Question 8

Which of the following expressions is equivalent to $\dfrac{2}{3} \div \dfrac{4}{9}$?

Question 9

A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. Write an algebraic expression for the total cost $C$ of renting a car and driving $m$ miles.

Accepted Answer

$C = 0.2m + 25$

Question 10

Simplify the expression: $-3[2x - (4 - x)]$

Question 11

Which of the following is the additive inverse of $-15$?

Accepted Answer

$15$

Question 12

A biologist observes that a bacteria population triples every hour. If the initial population is $P_0$, which expression models the population after $t$ hours?

Accepted Answer

$P_0 \cdot 3^t$

Question 13

Which of the following is a solution to the equation $2x^2 - 8 = 0$?

Accepted Answer

$x = 2$

Question 14

Simplify the expression: $\dfrac{5}{8} - \dfrac{1}{4}$

Accepted Answer

$\dfrac{3}{8}$

Question 15

Which of the following is the reciprocal of $-\dfrac{7}{3}$?

Accepted Answer

$-\dfrac{3}{7}$

Question 16

A rectangular field has an area of $60$ square meters and a width of $5$ meters. What is the length of the field?

Accepted Answer

$12$ meters

Question 17

Simplify the expression: $2x^2 + 3x - 4x^2 + x$

Question 18

Which of the following is a solution to the equation $x + 5 = 2x - 3$?

Accepted Answer

$x = 8$

Question 19

Evaluate $(-2)^3$.

Accepted Answer

$-8$

College Algebra Fundamentals: Equations, Expressions, and Polynomials

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