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 $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

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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