Q: A car's value depreciates by 15% each year. If the initial value is $$V_0 = 20$$,000$$, what is the value after 2 years?

$$V = 20,000 \times (0.85)^2$ = 14,450$$

Q: Which of the following is the correct solution to $$\sin(\theta) = 0.5$$ for $$0 \leq \theta \u003c 2\pi$$?

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

Question 1

Which of the following is the correct definition of a rational expression?

Accepted Answer

An expression that can be written as the ratio of two polynomials.

Question 2

A student is solving the inequality $$2x^2 - 5x + 3$$ \u003c 0$$. Which of the following steps is correct for finding the solution set?

Accepted Answer

Factor the quadratic and test intervals between the roots.

Question 3

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

Accepted Answer

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

Question 4

A chemical reaction is modeled by the exponential function $$C(t) = 5e$$^{-0.2t}$$, where C$ is the concentration in mol/L and t$ is time in hours. What is the concentration after 3 hours?

Accepted Answer

$$C(3) = 5e$$^{-0.6}$$ \approx 2.74$$ mol/L

Question 5

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

Accepted Answer

$$x = 32$$

Question 6

A medical dosage is calculated using the formula $$D = \dfrac{mg}{kg} 	imes W$$, where $$W is $$the patient's weight in kg. If the recommended dosage is $$2 \dfrac{mg}{kg}$$ and the patient weighs 70 kg, what is the total dosage?

Accepted Answer

$$140 mg$$

Question 7

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

Accepted Answer

$$x = 5, y = 2$$

Question 8

A population of bacteria doubles every 4 hours. If the initial population is 500, what will the population be after 12 hours?

Accepted Answer

$$500 	imes 2^3$ = 4000$$

Question 9

Which of the following is the correct expression for the sum of a geometric series with first term $$a$$ and common ratio $$r$$ for $$n$$ terms?

Accepted Answer

$$S_n = a \dfrac{1 - r^n}{1 - r}$$

Question 10

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

Accepted Answer

$$10 cm$$

Question 11

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

Accepted Answer

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

Question 12

A car's value depreciates by 15% each year. If the initial value is $$V_0 = 20$$,000$$, what is the value after 2 years?

Accepted Answer

$$V = 20,000 	imes (0.85)^2$ = 14,450$$

Question 13

Which of the following is the correct solution to $$\sin(	heta) = 0.5$$ for $$0 \leq 	heta \u003c 2\pi$$?

Accepted Answer

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

Question 14

A student is asked to solve $$x^2 - 4x + 4 = 0$. What is the correct solution?

Accepted Answer

$$x = 2$$

Question 15

Which of the following is the correct formula for the area of a circle with radius $$r$$?

Accepted Answer

$$A = \pi r^2$

Question 16

A student is analyzing the function $$f(x) = x^3$ - 6x^2$ + 9x. $$What is the $$x-$$coordinate of the local minimum?

Accepted Answer

$$x = 3$$

Question 17

Which of the following is the correct solution to $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6, x = -1$$

Question 18

A student is asked to find the sum $$\sum_{k=1}^{4} (2k + 1). $$What is the correct answer?

Accepted Answer

$$21$$

Question 19

Which of the following is the correct solution to the equation $$e^{2x} = 7$?

Accepted Answer

$$x = \dfrac{1}{2} \ln 7$$

Precalculus Syllabus: Algebra & Trigonometry Course Structure, Policies, and Learning Outcomes

Study Guide - Practice Questions

Study Guide - Flashcards