Question 1

Which of the following is a linear equation in one variable?

Accepted Answer

$x + 5 = 0$

Question 2

A chemist needs to prepare 100 mL of a solution that is 30% acid by mixing a 20% acid solution and a 50% acid solution. Let $x$ be the amount (in mL) of the 20% solution used. Which equation models this situation?

Accepted Answer

$0.2x + 0.5(100-x) = 30$

Question 3

Solve the equation $2x - 5 = 9$.

Accepted Answer

$x = 7$

Question 4

Which of the following steps is NOT a valid operation for producing an equivalent equation?

Accepted Answer

Multiplying both sides by zero

Question 5

A box is to be made by cutting equal squares from each corner of a square piece of metal with side $x$ meters and folding up the sides. If the box must have a volume of $500$ m$^3$ and the height is $5$ m, what equation must $x$ satisfy?

Accepted Answer

$5(x-5)^2 = 500$

Question 6

Which of the following quadratic equations has no real solutions?

Accepted Answer

$x^2 + x + 1 = 0$

Question 7

If $x^2 - 6x + 9 = 0$, what is the solution set?

Accepted Answer

$\{3\}$

Question 8

A worker is paid $1.5$ times the regular hourly wage for overtime and double time for Sundays. If she worked $40$ regular hours, $6$ overtime hours, and $4$ Sunday hours for a total of $\$1083$, what is her regular hourly wage?

Accepted Answer

$\$19.00$

Question 9

Solve the quadratic equation $x^2 - 5x = 0$ by factoring.

Accepted Answer

$x = 0$ or $x = 5$

Question 10

Which of the following is the correct quadratic formula for solving $ax^2 + bx + c = 0$?

Accepted Answer

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Question 11

What is the solution set for $x^2 = -25$ in the complex number system?

Accepted Answer

$\{-5i, 5i\}$

Question 12

Which of the following statements about complex numbers is TRUE?

Accepted Answer

The product of a complex number and its conjugate is always a real number.

Question 13

What is the standard form of $\frac{2 + 3i}{1 - i}$?

Accepted Answer

$\frac{5}{2} + \frac{7}{2}i$

Question 14

If $i$ is the imaginary unit, what is $i^{23}$?

Accepted Answer

$-i$

Question 15

Which of the following best describes the solutions to the equation $x^2 + 2x + 6 = 0$?

Accepted Answer

Two complex conjugate solutions

Question 16

Convert $68^{\circ}F$ to Celsius using the formula $C = \frac{5}{9}(F - 32)$. What is the result?

Accepted Answer

$20^{\circ}C$

Question 17

Which of the following is the principal square root of $-36$?

Accepted Answer

$6i$

Question 18

If $z = 3 + 4i$, what is $z \cdot \overline{z}$?

Accepted Answer

$25$

Question 19

Which of the following best describes the discriminant $b^2 - 4ac$ of a quadratic equation $ax^2 + bx + c = 0$?

Accepted Answer

All of the above are correct.

College Algebra: Equations and Inequalities – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards