Q: A Ferris wheel has a radius of 30 meters. What is the height above the ground of a seat at an angle $$\theta = \frac{\pi}{3}$$ radians from the lowest point, if the center is 32 meters above the ground?

$$32 + 30 \sin\left(\frac{\pi}{3}\right) = 32 + 30 \times \frac{\sqrt{3}}{2} \approx 58$$ meters

Q: A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 2. $$After how many seconds does the ball reach its maximum height?

$$t = \frac{-b}{2a} = \frac{-10}{2 \times -4.9} \approx 1.02$$ seconds

Q: A car depreciates in value by 15% each year. If the car is currently worth $20,000, what will its value be after 3 years?

$$20,000 \times (0.85)^3$ \approx 12,282$$

Q: A right triangle has an angle $$\theta$$ such that $$\tan(\theta) = 3. $$What is the value of $$\sin(\theta) if$$ $$\theta is in $$the first quadrant?

$$\sin(\theta) = \frac{3}{\sqrt{10}}$$

Question 1

Which of the following equations represents a function whose graph is a parabola opening upwards?

Accepted Answer

$$y = 4x^2$ - 5x + 2$$

Question 2

A chemical reaction's rate can be modeled by the exponential function $$R(t) = 100e$$^{-0.05t}$$, where t$ is time in minutes. What is the rate after 20 minutes?

Accepted Answer

$$R(20) = 100e$$^{-1}$$ \approx 36.79$$

Question 3

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

Accepted Answer

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

Question 4

A population of bacteria doubles every 4 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/4}$$

Question 5

Which of the following is the correct solution to the equation $$\log_3$(x) = 4$$?

Accepted Answer

$$x = 81$$

Question 6

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

Accepted Answer

$$13$$

Question 7

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 8

A Ferris wheel has a radius of 30 meters. What is the height above the ground of a seat at an angle $$	heta = \frac{\pi}{3}$$ radians from the lowest point, if the center is 32 meters above the ground?

Accepted Answer

$$32 + 30 \sin\left(\frac{\pi}{3}ight) = 32 + 30 	imes \frac{\sqrt{3}}{2} \approx 58$$ meters

Question 9

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^3$ - x + 7 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 10

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

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(3) = 9$$

Question 11

A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 2. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = \frac{-b}{2a} = \frac{-10}{2 	imes -4.9} \approx 1.02$$ seconds

Question 12

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

Accepted Answer

$$x = 5$$

Question 13

A car depreciates in value by 15% each year. If the car is currently worth $20,000, what will its value be after 3 years?

Accepted Answer

$$20,000 	imes (0.85)^3$ \approx 12,282$$

Question 14

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

Accepted Answer

$$x \in \mathbb{R}, x 
eq 3$$

Question 15

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

Accepted Answer

$$\cos(	heta) = \frac{4}{5}$$

Question 16

Which of the following is the solution set for $$|2x - 5| = 7$$?

Accepted Answer

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

Question 17

A right triangle has an angle $$	heta$$ such that $$	an(	heta) = 3. $$What is the value of $$\sin(	heta) if$$ $$	heta is in $$the first quadrant?

Accepted Answer

$$\sin(	heta) = \frac{3}{\sqrt{10}}$$

Question 18

Which of the following is the correct equation for the line passing through the points $$(2, 5)$$ and $$(4, 9)$$?

Accepted Answer

$$y = 2x + 1$$

Question 19

If $$f(x) = \sqrt{x - 2}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 2$$

MAT 170 Precalculus Course Structure and Study Guide Overview

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