Question 1

A biologist is tracking the movement of a tagged animal. On Monday, the animal is at $(2, 3)$, and on Friday, it is at $(6, 11)$. What is the distance the animal traveled, assuming a straight path?

Accepted Answer

$\sqrt{80}$

Question 2

A medical researcher models the spread of a virus using $f(x) = \sqrt{x - 5}$. What is the domain of this function?

Accepted Answer

$x \geq 5$

Question 3

A city planner wants to find the midpoint between two locations: $(-4, 5)$ and $(2, -1)$. What are the coordinates of the midpoint?

Accepted Answer

$(-1, 2)$

Question 4

A line passes through the point $(1, 4)$ and has a slope of $3$. Which of the following is the correct equation for this line?

Accepted Answer

$y = 3x + 1$

Question 5

Solve the absolute value equation $|x - 3| = 7$ for $x$. Which set contains all solutions?

Accepted Answer

$\{10, -4\}$

Question 6

A circular park has the equation $(x - 2)^2 + (y + 1)^2 = 9$. What is the center and radius of the park?

Accepted Answer

Center: $(2, -1)$, Radius: $3$

Question 7

A chemist measures the rate of change in concentration using $f(x) = x^2$ from $x = 1$ to $x = 3$. What is the average rate of change?

Accepted Answer

$4$

Question 8

A line passes through $(-2, 5)$ and $(4, -1)$. What is the slope of the line?

Question 9

A line is parallel to $y = 2x - 3$ and passes through $(0, 5)$. What is its equation?

Accepted Answer

$y = 2x + 5$

Question 10

Solve $2|x + 4| = 10$ for $x$. Which set contains all solutions?

Accepted Answer

$\{1, -9\}$

Question 11

A student is asked to find the difference quotient for $f(x) = x^2$ at $x$ with increment $h$. What is the simplified form?

Accepted Answer

$2x + h$

Question 12

A line is perpendicular to $y = -\frac{1}{2}x + 4$ and passes through $(2, 3)$. What is the slope of the perpendicular line?

Accepted Answer

$2$

Question 13

A rational function $f(x) = \frac{1}{x - 2}$ models a chemical reaction rate. What is the domain of $f(x)$?

Accepted Answer

$x 
eq 2$

Question 14

If $|x - 5| < 3$, what is the solution set for $x$?

Accepted Answer

$2 < x < 8$

Question 15

A circle has equation $(x + 3)^2 + (y - 2)^2 = 16$. What is the radius?

Accepted Answer

$4$

Question 16

A line passes through $(0, 0)$ and $(5, 10)$. What is its slope?

Accepted Answer

$2$

Question 17

A function $f(x) = \sqrt{9 - x}$ is used to model a physical process. What is the domain of $f(x)$?

Accepted Answer

$x \leq 9$

Question 18

A line passes through $(2, -3)$ and is perpendicular to $y = 4x + 1$. What is the slope of the new line?

Accepted Answer

$-\frac{1}{4}$

Question 19

A business tracks profit using $f(x) = 5x - 2$. What is the average rate of change from $x = 2$ to $x = 6$?

Accepted Answer

$5$

Question 20

A student solves the inequality $-2x > 6$. What is the correct solution?

Accepted Answer

$x < -3$

College Algebra: Core Concepts and Practice for Test 1

Study Guide - Practice Questions

Study Guide - Flashcards