Question 1

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

Accepted Answer

Question 2

A biologist models the population of a bacteria culture with the exponential function $$P(t) = 500e$$^{0.3t}$$, where t$ is in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 500e$$^{1.5}$$ \approx 2240$$

Question 3

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

Accepted Answer

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

Question 4

A pharmacist needs to mix a 10% saline solution with a 30% saline solution to obtain 100 mL of a 20% solution. How many mL of the 10% solution should be used?

Accepted Answer

$$50 mL$$

Question 5

Simplify the expression $$\dfrac{2x^2$ - 8x}{4x}$$ for $$x 
eq 0.$$

Accepted Answer

$$\dfrac{x - 4}{2}$$

Question 6

Which of the following is the solution set for $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6$$ and $$x = -1$$

Question 7

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$P(4) = 8$$ thousand dollars, at $$x = 4$$ thousand units

Question 8

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

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

Question 9

If $$f(x) = 3x^2$ - 2x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 19$$

Question 10

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x^2$ - 4}$$?

Accepted Answer

$$x 
eq 2$$ and $$x 
eq -2$$

Question 11

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 20 years?

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 36.8$$

Question 12

Which of the following is the correct simplification of $$\sqrt{50} + \sqrt{18}$$?

Accepted Answer

Question 13

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = 22.4$$ meters

Question 14

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 15

Simplify the rational expression $$\dfrac{x^2$ - 4}{x^2$ - 2x}$$ for $$x 
eq 0, x 
eq 2.$$

Accepted Answer

$$\dfrac{x + 2}{x}$$

Question 16

A car’s value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

Accepted Answer

$$V(3) = 20000(0.85)^3$ \approx 12251$$

Question 17

Which of the following is the correct solution to $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 18

If $$f(x) = \dfrac{1}{x}$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = \dfrac{1}{4}$$

Question 19

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

Accepted Answer

$$x \u003c 12$$

College Algebra (MATH 1000) Syllabus and Topic Outline Study Guide

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