Question 1

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

Accepted Answer

All real numbers except $$x = 3$$

Question 2

A biologist models the population of a species using the function $$P(t) = 500e$$^{0.03t}$$, where t$ is time in years. What is the population after 10 years?

Accepted Answer

$$P(10) = 500e$$^{0.3}$$ \approx 674$$

Question 3

Which of the following is the correct inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-5}{2}$$

Question 4

A medication's concentration in the bloodstream is modeled by $$C(t) = 100e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 100e$$^{-1}$$ \approx 36.8$$

Question 5

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

Accepted Answer

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

Question 6

A company’s profit $$P(x) in $$thousands of dollars is modeled by $$P(x) = -2x^2$ + 40x - 100$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$P(10) = -2(10)^2$ + 40(10) - 100 = 100$$

Question 7

Which of the following is the correct solution to the equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 8

A radioactive substance decays according to $$A(t) = 200e$$^{-0.05t}$$. How long will it take for the substance to decay to half its original amount?

Accepted Answer

$$t = \dfrac{\ln(0.5)}{-0.05} \approx 13.86$$

Question 9

Which of the following is the correct equation for the line passing through $$(1,2)$$ with slope $$-3$$?

Accepted Answer

$$y - 2 = -3(x - 1)$$

Question 10

A car’s value $$V$$ depreciates according to $$V(t) = 20,000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

Accepted Answer

$$V(3) = 20,000(0.85)^3$ \approx 12,281$$

Question 11

Which of the following is the correct solution to $$\log_{2}(x) = 4$$?

Accepted Answer

$$x = 16$$

Question 12

A projectile is launched from the ground and its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t. $$What is the maximum height reached?

Accepted Answer

$$h(2.04) = -4.9(2.04)^2$ + 20(2.04) \approx 20.4$$

Question 13

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

Accepted Answer

$$(x-3)(x+3)$$

Question 14

A bacteria culture grows according to $$N(t) = 1000 \cdot 2$$^{t}$$, where t$ is in hours. How many bacteria will there be after 5 hours?

Accepted Answer

$$N(5) = 1000 \cdot 2$$^{5}$$ = 32,000$$

Question 15

Which of the following is the correct solution to $$x^2 - 4x + 3 = 0$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 16

A city’s population is modeled by $$P(t) = 50,000(1.02)^t$$, where $$t is $$the number of years since 2020. What is the population in 2025?

Accepted Answer

$$P(5) = 50,000(1.02)^5$ \approx 55,204$$

Question 17

Which of the following is the correct solution to $$\sin(x) = 0.5$$ for $$x in$$ $$[0, 2\pi]$$?

Accepted Answer

$$x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Question 18

A right triangle has legs of length $$6$$ and $$8. $$What is the length of the hypotenuse?

Accepted Answer

$$\sqrt{6^2$ + 8^2$} = 10$$

Question 19

Which of the following is the correct solution to $$\cos(x) = 0$$ for $$x in$$ $$[0, 2\pi]$$?

Accepted Answer

$$x = \dfrac{\pi}{2}, \dfrac{3\pi}{2}$$

2023 Fall Precalculus Syllabus and Course Structure

Study Guide - Practice Questions

Study Guide - Flashcards