Question 1

Which of the following is the correct domain of the function $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

$$x \geq 2.5$$

Question 2

A ball is thrown upward from the top of a 50-meter building with an initial velocity of 20 m/s. Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 50. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 3

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

Accepted Answer

Question 4

Given the function $$f(x) = x^2$ - 4x + 3$$, which of the following represents the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 5

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 6

A population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 2$$^{t/3}$$

Question 7

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

Accepted Answer

$$x = 32$$

Question 8

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

Accepted Answer

$$9$$

Question 9

Which of the following transformations will reflect the graph of $$y = f(x)$$ over the $$y-$$axis?

Accepted Answer

$$y = f(-x)$$

Question 10

A right triangle has legs of length $$5$$ and $$12. $$What is the length of the hypotenuse?

Accepted Answer

$$13$$

Question 11

Which of the following is the sum of the first $$n$$ terms of a geometric sequence with first term $$a$$ and common ratio $$r ($$where $$r 
eq 1$$)?

Accepted Answer

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

Question 12

Which of the following is the correct expression for the binomial expansion of $$(x + y)^3$?

Accepted Answer

$$x^3$$ + $$3x^2y$$ + $$3xy^2$$ + $$y^3$$

Question 13

If $$\sin(	heta) = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos(	heta)$$?

Accepted Answer

$$\frac{4}{5}$$

Question 14

Which of the following is the period of the function $$f(x) = 2 \sin(3x)$$?

Accepted Answer

$$\frac{2\pi}{3}$$

Question 15

Solve for $$x$$: $$2^{x+1} = 16$.

Accepted Answer

$$x = 3$$

Question 16

Which of the following is the correct equation for the tangent line to $$y = x^2$ at x = 1$?

Accepted Answer

$$y = 2x - 1$$

Question 17

If $$f(x) = \frac{1}{x}$$, which of the following statements is true?

Accepted Answer

$$f is $$undefined at $$x = 0$$

Question 18

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

Accepted Answer

$$(4, 3)$$

Question 19

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-kt}$$. If the half-life is 10 years, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 2}{10}$$

Precalculus Course Overview and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards