Q: Which of the following matrices represents a reflection over the $$y-$$axis?

$$\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$$

Question 1

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2$$^{t/3}$$

Question 2

Which of the following is the correct end behavior of the rational function $$f(x) = \frac{2x^3$ + 5}{x^3$ - 4} as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 2$$

Question 3

Which of the following is a complex zero of the polynomial $$f(x) = x^2$ + 4$$?

Accepted Answer

$$x = 2i$$

Question 4

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.9$$ meters

Question 5

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

Accepted Answer

$$3 + \log_2$(x)$$

Question 6

Given $$f(x) = 3x - 2$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$3x^2 - 2$

Question 7

Which of the following describes the vertical asymptote(s) of $$f(x) = \frac{x+1}{x^2$ - 4}$$?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 8

A sinusoidal function modeling daylight hours in a city is $$D(t) = 3\sin\left(\frac{2\pi}{12}t - \frac{\pi}{2}\right) + 12. $$What is the period of this function?

Accepted Answer

$$12$$ months

Question 9

Which of the following is the amplitude of the function $$y = -4\cos(2x)$$?

Accepted Answer

$$4$$

Question 10

If $$\vec{v} = \langle 3, -4 \rangle$$, what is the magnitude $$|\vec{v}|$$?

Accepted Answer

$$5$$

Question 11

Which of the following matrices represents a reflection over the $$y-$$axis?

Accepted Answer

$$\begin{pmatrix} -1 & 0 \ 0 & 1 \end{pmatrix}$$

Question 12

Which conic section is represented by the equation $$x^2$$ + $$y^2 - 6x + 8y + 9 = 0$?

Accepted Answer

Circle

Question 13

A parametric equation for a circle of radius $$r$$ centered at $$(h, k) is$$:

Accepted Answer

$$x = h + r\cos t,\ y = k + r\sin t$$

Question 14

Which of the following is the solution to $$2\sin x = 1$$ for $$x in$$ $$[0, 2\pi)$$?

Accepted Answer

$$x = \frac{\pi}{6},\ \frac{5\pi}{6}$$

Question 15

If $$f(x) = \log_{10}(x)$$ and $$g(x) = 10^x$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$x$$

Question 16

Which of the following best describes the graph of $$y = 	an x$$?

Accepted Answer

It has vertical asymptotes at $$x = \frac{\pi}{2} + n\pi$$, $$n \in \mathbb{Z}$$

Question 17

Which of the following is the correct solution for the system: $$\begin{cases} x + y = 5 \ 2x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2,\ y = 3$$

Question 18

A vector-valued function describes the position of a particle as $$\vec{r}(t) = \langle t^2$, 2t \rangle. $$What is the velocity vector $$\vec{v}(t)$$?

Accepted Answer

$$\langle 2t, 2 \rangle$$

Question 19

Which of the following is the correct transformation for $$y = \sin(x - \frac{\pi}{4}) + 2$$?

Accepted Answer

Shift right $$\frac{\pi}{4}$$ units and up 2 units

Question 20

Which of the following is the correct equivalent representation for $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

AP Precalculus Course Structure and Key Topics: A Study Guide

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