Q: Which of the following is the correct formula for the area of a sector of a circle with radius $$r$$ and central angle $$\theta (in $$radians)?

$$A = \frac{1}{2} r^2$ \theta$$

Question 1

Which of the following equations has no real solution?

Accepted Answer

$$x^2 + 4 = 0$

Question 2

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$What is the maximum height reached by the ball?

Accepted Answer

$$16 ft$$

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 4

Given the circle $$x^2$$ + $$y^2 - 6x + 4y = 12$, what is the center of the circle?

Accepted Answer

$$(3, -2)$$

Question 5

Which of the following is the equation of a line parallel to $$y = -2x + 5$$ and passing through the point $$(1, -3)$$?

Accepted Answer

$$y = -2x - 1$$

Question 6

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

Accepted Answer

$$9$$

Question 7

Which of the following is the inverse of $$f(x) = 3x - 4$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 4}{3}$$

Question 8

A population of bacteria triples every 2 hours. If the initial population is $$100$$, which equation models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 100 \cdot 3$$^{t/2}$$

Question 9

Which of the following is equivalent to $$\log_2$ 8$$?

Accepted Answer

$$3$$

Question 10

What is the solution set for $$|2x - 3| \u003c 5$$?

Accepted Answer

$$-1 \u003c x \u003c 4$$

Question 11

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 12

Which of the following is the correct formula for the area of a sector of a circle with radius $$r$$ and central angle $$	heta (in $$radians)?

Accepted Answer

$$A = \frac{1}{2} r^2$ 	heta$$

Question 13

Which of the following statements about the graph of $$y = \sin(x) is $$true?

Accepted Answer

It has a period of $$2\pi$$ and an amplitude of $$1.$$

Question 14

If $$	an(	heta) = \frac{3}{4}$$ and $$	heta is in $$the first quadrant, what is $$\sin(	heta)$$?

Accepted Answer

$$\frac{3}{5}$$

Question 15

Which of the following is a solution to the equation $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 16

What is the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$5$$

Question 17

Which of the following is the correct domain of the function $$f(x) = \ln(x-2)$$?

Accepted Answer

$$x \u003e 2$$

Question 18

If $$\cos(\alpha) = -\frac{1}{2}$$ and $$\alpha is in $$the third quadrant, what is $$\sin(\alpha)$$?

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 19

Which of the following is the correct solution to the equation $$\sqrt{x+5} = x - 1$$?

Accepted Answer

$$x = 2$$

Comprehensive Precalculus Final Exam Study Guide

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