Q: Which of the following is the correct formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Q: Which of the following is the correct formula for the midpoint between two points $(x_1, y_1)$ and $(x_2, y_2)$?

$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Question 1

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

Accepted Answer

$-5$

Question 2

Simplify the following expression using the order of operations: $3^2 + 4 	imes 2 - (6 \div 3)$

Accepted Answer

$17$

Question 3

A chemist mixes two solutions, one with a concentration of $x$ grams per liter and another with $y$ grams per liter. If the total mixture is $10$ liters and the chemist wants the final concentration to be $8$ grams per liter, which equation represents this scenario?

Accepted Answer

$\frac{10x + 10y}{10} = 8$

Question 4

Given the points $A(2, 3)$ and $B(6, 11)$, what is the slope of the line passing through these points?

Accepted Answer

$2$

Question 5

Which of the following is the correct vertex form of a quadratic equation?

Accepted Answer

$y = a(x - h)^2 + k$

Question 6

A ball is thrown upward from the ground with a velocity such that its height $h$ (in meters) after $t$ seconds is given by $h = -5t^2 + 20t$. What is the maximum height reached by the ball?

Accepted Answer

$25$ meters

Question 7

Which of the following best describes the solution set for the inequality $2x - 5 < 7$?

Accepted Answer

$x < 6$

Question 8

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

Accepted Answer

$10$

Question 9

Which of the following is the correct formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Question 10

A line has the equation $y = -\frac{1}{2}x + 4$. What is the slope of a line perpendicular to this line?

Accepted Answer

$2$

Question 11

Which of the following is the correct solution to the equation $|2x - 3| = 7$?

Accepted Answer

$x = 5$ or $x = -2$

Question 12

A quadratic function models the height of a projectile. If the function is $h(t) = -16t^2 + 32t + 5$, what is the time at which the projectile reaches its maximum height?

Accepted Answer

$t = 1$

Question 13

Which of the following is the correct formula for the midpoint between two points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Question 14

Which of the following describes the domain of the function $f(x) = \sqrt{x - 3}$?

Accepted Answer

$x \geq 3$

Question 15

If the quadratic equation $x^2 - 6x + 9 = 0$ is solved, what are the solutions?

Accepted Answer

$x = 3$

Question 16

A company models its profit $P$ (in thousands of dollars) as $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum profit the company can achieve?

Accepted Answer

$26$ thousand dollars

Question 17

Which of the following is the correct transformation for the graph of $y = x^2$ shifted 3 units to the right and 2 units up?

Accepted Answer

$y = (x - 3)^2 + 2$

Question 18

Which of the following is the correct formula for the axis of symmetry of the quadratic $y = ax^2 + bx + c$?

Accepted Answer

$x = -\frac{b}{2a}$

Question 19

A biologist is studying the population of a species modeled by $P(t) = 1000 - 50t^2$, where $t$ is the number of years since the study began. After how many years will the population reach zero?

Accepted Answer

$t = 10$

Question 20

Which of the following is the correct solution to the inequality $|x - 4| \leq 3$?

Accepted Answer

$1 \leq x \leq 7$

College Algebra: Core Concepts and Applications Study Guide

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