Q: Which of the following is a correct application of the Fundamental Theorem of Algebra?

A polynomial of degree $n$ has exactly $n$ complex roots, counting multiplicities.

Q: Which of the following best describes the graph of $y = \log_2(x)$?

It passes through $(1, 0)$ and increases slowly for large $x$.

Question 1

Which of the following best describes the primary focus of Pre-Calculus Algebra as outlined in the syllabus?

Accepted Answer

To develop skills in solving equations, inequalities, and modeling functions with and without technology.

Question 2

A student is asked to solve the equation $|2x - 5| = 9$. Which of the following is the correct set of solutions?

Accepted Answer

$x = 7,\ x = -2$

Question 3

Which of the following is NOT a recommended tool or material for this Pre-Calculus Algebra course?

Accepted Answer

Scientific calculator without graphing capabilities

Question 4

Given the quadratic function $f(x) = -2x^2 + 8x - 3$, what is the vertex of the parabola?

Accepted Answer

$(2, 5)$

Question 5

A real-world scenario: A company models its profit $P$ (in thousands of dollars) as $P(x) = -3x^2 + 18x - 12$, where $x$ is the number of units sold (in hundreds). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $24$ thousand dollars at $x = 3$ hundred units.

Question 6

Which of the following statements about academic honesty in this course is TRUE?

Accepted Answer

Using unauthorized resources on tests is considered academic dishonesty.

Question 7

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

Accepted Answer

$f(g(2)) = 2 	imes 1 + 1 = 3$

Question 8

Which of the following best describes the solution set for the inequality $x^2 - 4x + 3 < 0$?

Accepted Answer

$1 < x < 3$

Question 9

A student is using the distance formula to find the distance between the points $(2, -1)$ and $(5, 3)$. Which of the following is the correct answer?

Accepted Answer

$5$

Question 10

Which of the following is a correct application of the Fundamental Theorem of Algebra?

Accepted Answer

A polynomial of degree $n$ has exactly $n$ complex roots, counting multiplicities.

Question 11

Given the exponential function $f(x) = 3 \cdot 2^x$, what is $f(4)$?

Accepted Answer

$48$

Question 12

Which of the following best describes the graph of $y = \log_2(x)$?

Accepted Answer

It passes through $(1, 0)$ and increases slowly for large $x$.

Question 13

A system of equations is given by $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$. What is the solution $(x, y)$?

Accepted Answer

$(2, 1)$

Question 14

Which of the following is the correct inverse of the function $f(x) = 5x - 7$?

Accepted Answer

$f^{-1}(x) = \frac{x + 7}{5}$

Question 15

A radioactive substance decays according to $A(t) = 100e^{-0.05t}$, where $A$ is the amount remaining after $t$ years. How much remains after $10$ years?

Accepted Answer

$60.65$

Question 16

Which of the following is a correct interpretation of the solution to the equation $\log_{10}(x) = 2$?

Accepted Answer

$x = 100$

Question 17

If $f(x) = x^2 - 4$ and $g(x) = x + 2$, what is $f(g(3))$?

Accepted Answer

$21$

Question 18

Which of the following is the correct solution to the rational equation $\frac{2}{x} = 4$?

Accepted Answer

$x = 0.5$

Question 19

A student is asked to solve the system using matrices: $\begin{cases} x + 2y = 5 \ 3x - y = 4 \end{cases}$. What is the solution $(x, y)$?

Accepted Answer

$(2, 1.5)$

Question 20

Which of the following best describes the domain of the function $f(x) = \sqrt{x - 2}$?

Accepted Answer

$x \geq 2$

Pre-Calculus Algebra (MAT-171) Syllabus and Course Structure Overview

Study Guide - Practice Questions

Study Guide - Flashcards