Question 1

Which of the following is the correct simplification of the expression $$\displaystyle (2x$$^{-3}$$y^2)^2$?

Accepted Answer

$$\displaystyle 4x$$^{-6}$$y^4$

Question 2

A company’s profit $$P (in $$thousands of dollars) after $$x$$ months is modeled by the function $$P(x) = -2x^2$ + 12x - 8. $$What is the maximum profit, and after how many months does it occur?

Accepted Answer

Maximum profit is $$16$$ thousand dollars after $$3$$ months.

Question 3

Which of the following is equivalent to $$\displaystyle \sqrt[3]{x^4$}$$ expressed using rational exponents?

Accepted Answer

$$\displaystyle x$$^{4/3}$$

Question 4

Given the function $$f(x) = \dfrac{2x+1}{x-3}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 3$$

Question 5

Solve the equation $$|2x - 5| = 9.$$

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 6

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x-4)(x-5)$$

Question 7

A biologist models the population of a bacteria culture by $$P(t) = 500e$$^{0.3t}$$, where t$ is in hours. How long will it take for the population to double?

Accepted Answer

$$\displaystyle t = \frac{\ln 2}{0.3}$$ hours

Question 8

Which of the following is the inverse of the function $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+7}{3}$$

Question 9

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

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

Question 10

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 11

Which of the following is the correct solution to the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 12

Write $$\log_2$ 16 as an $$exponential equation.

Accepted Answer

$$2^x = 16$$

Question 13

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

Accepted Answer

$$9$$

Question 14

Which of the following is the correct sum of $$\dfrac{2}{x} + \dfrac{3}{x+1}$$?

Accepted Answer

$$\dfrac{2(x+1) + 3x}{x(x+1)}$$

Question 15

A line passes through the points $$(1,2)$$ and $$(3,8). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 3x - 1$$

Question 16

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 5 = 0$?

Accepted Answer

$$x = 1 or$$ $$x = 5$$

Question 17

Which of the following is the correct simplification of $$\dfrac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

$$\dfrac{(x+3)}{(x-3)}$$

Question 18

If $$\log_5$(x) = 3$$, what is the value of $$x$$?

Accepted Answer

$$125$$

Question 19

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

Accepted Answer

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

Question 20

A chemist mixes two solutions: one with 30% acid and one with 50% acid. How many liters of each should be mixed to obtain 10 liters of a 40% acid solution?

Accepted Answer

5 liters of each solution

College Algebra Syllabus and Course Overview – MAT 1314

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