Question 1

Which of the following is the correct solution to the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 2

A chemist needs to prepare a solution by mixing two liquids. The equation $$\frac{1}{x} + \frac{1}{x+2} = \frac{3}{4}$$ models the relationship between the volumes. What is the value of $$x$$?

Accepted Answer

Question 3

Which of the following is the correct graph for the equation $$y = -2x + 5$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$5$$

Question 4

Solve the inequality $$|3x - 4| \leq 8.$$

Accepted Answer

$$-\frac{4}{3} \leq x \leq 4$$

Question 5

Which of the following is the inverse of the function $$f(x) = 2x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-7}{2}$$

Question 6

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2$$^{t/3}$$

Question 7

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 1)$$

Question 8

Which of the following is the correct formula for the circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 9

Solve for $$x$$: $$\log_2$(x) = 5.$$

Accepted Answer

$$x = 32$$

Question 10

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R = 50 + 20\ln(x)$$, where $$x is $$the number of years since opening. What is the revenue after 3 years? (Round to the nearest dollar.)

Accepted Answer

$$R \approx 71$$

Question 11

Which of the following is the solution to the rational equation $$\frac{x}{x-2} = 3$$?

Accepted Answer

$$x = 3$$

Question 12

Which conic section is represented by the equation $$x^2$$ - $$4y^2 = 16$?

Accepted Answer

Hyperbola

Question 13

A medical researcher models the decay of a drug in the bloodstream with $$C = 100e$$^{-0.2t}$$, where C$ is the concentration and t$ is time in hours. What is the concentration after 5 hours? (Round to the nearest integer.)

Accepted Answer

$$C \approx 37$$

Question 14

Which of the following is the solution set for the inequality $$2x + 5 \u003e 11$$?

Accepted Answer

$$x \u003e 3$$

Question 15

If $$f(x) = x^2$ - 4x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 16

Which of the following is the correct solution to $$\sqrt{x+5} = x - 1$$?

Accepted Answer

$$x = 5$$

Question 17

A business’s profit $$P is $$given by $$P = 3x^2$ - 12x + 9$$, where $$x is $$the number of units sold. How many units must be sold to maximize profit?

Accepted Answer

$$x = 2$$

Question 18

Which of the following is the correct solution to the system of inequalities $$y \u003e 2x - 1$$ and $$y \u003c -x + 4$$?

Accepted Answer

The region above $$y = 2x - 1$$ and below $$y = -x + 4$$

College Algebra Syllabus and Course Guide – BPCC

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