Question 1

Which of the following equations represents a line that passes through the point $$(2, -3)$$ and has a slope of $$4$$?

Accepted Answer

$$y = 4x - 11$$

Question 2

A chemical reaction's temperature $$T (in $$degrees Celsius) is modeled by the function $$T(t) = 20e$$^{0.05t}$$, where t$ is time in minutes. What is the temperature after 10$ minutes, rounded to the nearest degree?

Accepted Answer

$$33$$ degrees

Question 3

Which of the following is the solution set for the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 4

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

Accepted Answer

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

Question 5

Which of the following is the correct factorization of the polynomial $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 6

A medical researcher models the spread of a virus with the function $$N(t) = 1000 \cdot e$$^{0.2t}$$, where N$ is the number of cases and t$ is days since the outbreak. How many cases will there be after 5$ days? (Round to the nearest whole number.)

Accepted Answer

$$2718$$

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

Question 8

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

Accepted Answer

$$x = 32$$

Question 9

A ball is thrown upward from the ground with an initial velocity of $$40 m/s. $$Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -5t^2$ + 40t. At $$what time will the ball reach its maximum height?

Accepted Answer

$$t = 4$$ seconds

Question 10

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 11

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 12

Which of the following is the inverse function of $$f(x) = 3x + 2$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-2}{3}$$

Question 13

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?

Accepted Answer

$$P = 20$$ thousand dollars

Question 14

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

Accepted Answer

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

Question 15

A radioactive substance decays according to $$A(t) = 200e$$^{-0.03t}$$, where A$ is the amount remaining after t$ years. How much remains after 10$ years? (Round to the nearest whole number.)

Accepted Answer

$$149$$

Question 16

Which of the following is the range of the function $$f(x) = x^2$ - 4$$?

Accepted Answer

$$y \geq -4$$

Question 17

If $$f(x) = \sqrt{x+2}$$, for which values of $$x is$$ $$f(x)$$ defined?

Accepted Answer

$$x \geq -2$$

Question 18

A car’s value $$V (in $$dollars) depreciates according to $$V(t) = 25000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after $$3$$ years? (Round to the nearest dollar.)

Accepted Answer

$$15312$$

Question 19

Which of the following is the solution to the equation $$2^{x} = 10$?

Accepted Answer

$$x = \log_2$ 10$$

College Algebra (Precalculus) Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards