Question 1

A ball is thrown upward from the top of a 50-meter building with an initial velocity of 20 m/s. The height $$h(t) in $$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

$$t = 2.04$$

Question 2

Which of the following is the correct equation for the horizontal asymptote of the function $$f(x) = \frac{3x^2$ + 2}{2x^2$ - 5}$$?

Accepted Answer

$$y = \frac{3}{2}$$

Question 3

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 4

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

Accepted Answer

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

Question 5

A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?

Accepted Answer

$$25$$

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Which of the following is equivalent to $$\sin^2$(x) + \cos^2$(x)$$?

Accepted Answer

$$1$$

Question 9

A chemical reaction follows the law $$C(t) = 100e$$^{-0.05t}$$, where C$ is the concentration in mg/L after t$ minutes. What is the concentration after 20 minutes?

Accepted Answer

$$36.79 mg/L$$

Question 10

Which of the following is the correct formula for the Law of Cosines for a triangle with sides $$a$$, $$b$$, $$c$$ and angle $$C$$ opposite side $$c$$?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$\cos C$$

Question 11

Which of the following is the solution set for the equation $$2^x = 16$$?

Accepted Answer

$$x = 4$$

Question 12

Given the function $$f(x) = x^2$ - 6x + 8$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 13

A Ferris wheel has a radius of 20 meters and makes one complete revolution every 60 seconds. If a passenger starts at the lowest point, what is their height above the ground after 15 seconds, assuming the center is 22 meters above the ground?

Accepted Answer

$$42$$ meters

Question 14

Which of the following is the correct sum formula for sine?

Accepted Answer

$$\sin(x + y) = \sin x \cos y + \cos x \sin y$$

Question 15

If $$	an x = 3$$ and $$x is in $$Quadrant III, what is $$\sin x$$?

Accepted Answer

$$-\frac{3}{\sqrt{10}}$$

Question 16

Which of the following is the correct equation for a parabola with vertex at $$(0,0)$$ and focus at $$(0,2)$$?

Accepted Answer

$$x^2 = 8y$

Question 17

A system of equations is given by $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 18

Which of the following is the correct form of the equation for an ellipse centered at the origin with major axis along the $$x-$$axis, $$a \u003e b$$?

Accepted Answer

$$\frac{x^2$}{a^2$} + \frac{y^2$}{b^2$} = 1$$

Question 19

If $$f(x) = \log_2$(x-1)$$, what is the domain of $$f$$?

Accepted Answer

$$x \u003e 1$$

Precalculus Study Guide: Functions, Trigonometry, and Analytic Geometry

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