Question 1

Which of the following is the correct factorization of $a^2 - b^2$?

Accepted Answer

$a^2 - b^2 = (a + b)(a - b)$

Question 2

Given the quadratic equation $4x^2 - 3x - 5 = 0$, what are the solutions using the quadratic formula?

Accepted Answer

$x = \dfrac{3 \pm \sqrt{71}}{8}$

Question 3

If $a < b$ and $c > 0$, which of the following is true according to the properties of inequalities?

Accepted Answer

$ac < bc$

Question 4

What is the result of $\sqrt{-a}$ for $a > 0$?

Accepted Answer

$\sqrt{-a} = i\sqrt{a}$

Question 5

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

Accepted Answer

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

Question 6

If $a < b$ and $c < 0$, what happens to the inequality when both sides are multiplied by $c$?

Accepted Answer

$ac > bc$

Question 7

A chemical reaction is modeled by the equation $x^2 - 6x + 9 = 0$. What is the concentration of $x$ at equilibrium?

Accepted Answer

$x = 3$

Question 8

Which of the following is the correct solution set for $x^2 + 4 = 0$?

Accepted Answer

$x = \pm 2i$

Question 9

A medical dosage calculation requires solving $2x^2 - 8x = 0$. What is the correct dosage value(s) for $x$?

Accepted Answer

$x = 0$ or $x = 4$

Question 10

If $a < b$, which of the following is always true after adding $c$ to both sides?

Accepted Answer

$a + c < b + c$

Question 11

A quadratic equation models the height $h$ (in meters) of a ball thrown upward: $h = -4.9t^2 + 20t + 1.5$. At what time $t$ does the ball reach its maximum height?

Accepted Answer

$t = 2.04$ seconds

Question 12

Which of the following is the correct solution for $x$ in $x^2 = 25$?

Accepted Answer

$x = 5$ or $x = -5$

Question 13

If $a < b$ and $c = 0$, what is the result of multiplying both sides by $c$?

Accepted Answer

$ac = bc = 0$

Question 14

A historical event is modeled by the equation $t^2 - 10t + 21 = 0$. What are the possible years $t$ when the event occurred?

Accepted Answer

$t = 3$ or $t = 7$

Question 15

Which of the following is the correct solution for $x$ in $x^2 + 2x + 1 = 0$?

Accepted Answer

$x = -1$

Question 16

If you divide both sides of an inequality by a negative number, what must you do to the inequality sign?

Accepted Answer

Reverse the inequality sign

Question 17

Which of the following is the correct factorization of $x^2 + 6x + 9$?

Accepted Answer

$(x + 3)^2$

Question 18

A population model is given by $n^2 - 16 = 0$. What are the possible population sizes $n$?

Accepted Answer

$n = 4$ or $n = -4$

Question 19

Which of the following is the correct solution for $x$ in $x^2 - 2x = 0$?

Accepted Answer

$x = 0$ or $x = 2$

Key Precalculus Concepts: Properties of Inequality, Quadratic Equations, and Factoring

Study Guide - Practice Questions

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