Free Printable AP PreCalculus Exam Review

1.

FACTOR THE FOLLOWING:

a)

A

b)

B

c)

C

d)

D

2.

FACTOR THE FOLLOWING:

a)

A

b)

B

c)

C

d)

D

3.

Find the vertical asymptote(s).

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

4.

If $f\left(x\right)=\frac{8x^3-8}{4x^3-2}$ , find $\lim_{x\rightarrow\infty}f\left(x\right)$ .

a)

2

b)

4

c)

8

d)

+∞

5.

What is the solution set of the inequality

$\frac{x\ -3}{x+\ 2}\le0$ ?

a)

$x<-2$

b)

$-2<x\le3$

c)

$x<-2;\ x\ge3$

d)

$-2\le x<3$

6.

On what interval is the average rate of change positive?

a)

(-1,1) & (3,4)

b)

(-3,-2)

c)

(-3, 0) & (2, 4)

d)

(-1, 1) & ( 3, 4)

7.

On which interval is the function increasing at a decreasing rate?

a)

(-∞, -1.5)

b)

(0.3, 2)

c)

(-1.5, 0.3)

d)

(2, 4)

8.

Values of the terms of a geometric sequence $g_n$ are graphed in the figure. Which of the following is an expression for the $n^{th}$ term of the geometric sequence?

a)

$g_n=16\left(-\frac{3}{4}\right)^{n-3}$

b)

$g_n=16\left(\frac{3}{4}\right)^{n-3}$

c)

$g_n=16\left(-\frac{3}{4}\right)^{n+3}$

d)

$g_n=-16\left(\frac{3}{4}\right)^{n-3}$

9.

A quadratic regression was used to develop a model for a given set of data. The figure shows a graph of the residuals of the quadratic regression. Which of the following statements about the quadratic regression is true?

a)

The quadratic model is not appropriate because there are more positive residual values than negative residual values.

b)

The quadratic model is appropriate because none of the residuals fall outside the pattern in the graph of the residuals.

c)

The quadratic model is appropriate because there is a linear pattern in the graph of the residuals.

d)

The quadratic model is not appropriate because there is a clear pattern in the graph of the residuals.

10.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

11.

Which of the following is an equivalent form of $y=6\cdot4^x$ ?

a)

$y=6\cdot2^{3x}$

b)

$y=6\cdot2^{\frac{x}{2}}$

c)

$y=6\cdot16^{\left(\frac{x}{2}\right)}$

d)

$y=3\cdot2^{2x}$

12.

What is the maximum value of the wave y = 10sin(2x - 20) + 25?

a)

10

b)

20

c)

35

d)

30

13.

Which of the following is equivalent to 5sin2x?

a)

$5\left(\sin^2x-\cos^2x\right)$

b)

$10\sin x\cos x$

c)

$5\sin^2x\cdot5\cos^2x$

d)

$5\left(\cos^2x-\sin^2x\right)$

14.

Which of the following would graph one full cycle of $r=5\cos\left(3\theta\right)$ ?

a)

$\left[0,\pi\right]$

b)

$\left[0,2\pi\right]$

c)

$\left[0,\frac{\pi}{2}\right]$

d)

$\left[0,4\pi\right]$

15.

1.Let $k\left(x\right)=\frac{3x^2-4x+12}{x+2}$ . Which of the following statements about the graph of k is correct?

a)

The graph of k has a horizontal asymptote of y = 3.

b)

The graph of k has a slant asymptote of

y = 3x + 2.

c)

The graph of k has a slant asymptote of

y = 3x - 6.

d)

The graph of k has a slant asymptote

y = 3x - 10.

16.

2.The function g is a polynomial with the following end behavior:

$\lim_{x\rightarrow-\infty}g\left(x\right)=-\infty$ and $\lim_{x\rightarrow\infty}g\left(x\right)=-\infty$

Which of the following could be an expression for g(x)?

a)

$-4x^7-3x^3+x-6$

b)

$-3x^6+5x^2+6x-1$

c)

$3x^3+x^2-5x+1$

d)

$2x^4-7x^3+3x^2+1$

17.

3.Let $f(x)=2x^2-3x+1$ and $g(x)=x^2-x+9$ . What are all the intervals for which $f(x)\le g(x)$ ?

a)

[-4, 2]

b)

[-2, 4]

c)

$(-\infty,-4]\ and\ \ [2,\infty)$

d)

$(-\infty,-2]\ and\ [4,\infty)$

18.

4.The graph of the rational function f has a hole at x = 5 and a vertical asymptote at x = -3. Which of the following could be f(x)?

a)

$\frac{x^2-3x-10}{x^2-2x-15}$

b)

$\frac{x^2+5x+6}{x^2-2x-15}$

c)

$\frac{x^2-2x-15}{x^2-3x-10}$

d)

$\frac{x^2+7x+10}{x^2+2x-15}$

19.

5.Selected values of the function $f(x)$ are shown in the table above. Find the average rate of change of $f(x)$ over the interval $[-1,4]$ .

a)

−2

b)

$2$

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

20.

7.The polynomial function $f$ is given by $f(x)=(x+3)^4$ . Find the coefficient of the term containing $x^3$ .

a)

1

b)

12

c)

54

d)

81

21.

8.Selected values of the polynomial $g$ are shown in the table above. Which of the following claim and explanation statements could be true about $g$ ?

a)

The graph of $g$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are positive.

b)

The graph of $g$ could be concave up because the average rates of change over consecutive equal-length input-value intervals are increasing.

c)

The graph of $g$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are negative.

d)

The graph of $g$ could be concave down because the average rates of change over consecutive equal-length input-value intervals are decreasing.

22.

9.The graph of $f$ is shown above where the labeled points A, B, D, and E represent the x-values where $f$ has a local extremum and the point C represents where the graph of $f$ has a point of inflection. On which of the following intervals is $f$ increasing and the graph of $f$ concave down?

a)

The interval from A to B.

b)

The interval from B to C.

c)

The interval from C to D.

d)

The interval from D to E.

23.

10A. The number of active accounts on the social media app Instagram has grown drastically since 2013. The table above gives the number of active Instagram accounts, in billions, for selected years since 2013. The quadratic function A models the number of active Instagram accounts, in billions, as a function of time t in years since 2013.

The function A can be written in the form $A(t)=ax^2+bx+c$ . What is the equation for $A\left(t\right)$ Choose the correct option.

a)

$A\left(t\right)=0.017226\ x^2+0.075375\ x+0.118392$

b)

$A\left(t\right)=0.075375\ x^2+0.017226\ x+0.118392$

c)

$A\left(t\right)=0.118392\ x^2+0.017226\ x+0.075375$

d)

$A\left(t\right)=\ 0.01722x^2+0.118392x+0.075375$

24.

10B. The number of active accounts on the social media app Instagram has grown drastically since 2013. The table above gives the number of active Instagram accounts, in billions, for selected years since 2013. The quadratic function A models the number of active Instagram accounts, in billions, as a function of time t in years since 2013.

Use the model found in part (i), What is the predicted number of active Instagram accounts for the year 2024 (t=11)?

a)

$3.03188\$ billions

b)

$118392$ Millions

c)

$3.03188\$ millions

d)

$3.03188$

25.

10C. The number of active accounts on the social media app Instagram has grown drastically since 2013. The table above gives the number of active Instagram accounts, in billions, for selected years since 2013. The quadratic function A models the number of active Instagram accounts, in billions, as a function of time t in years since 2013.

What is the value of the residual for the number of Instagram accounts for the year 2017 (t=4)?

a)

$0.00449$

b)

$-0.00449$

c)

$0.07\$

d)

$0.69551$

26.

11.The function g is given by $g(x)=\frac{x^3+8x^2+12x}{x^2+2x-24}$ . What is the domain of g?

a)

all real numbers x where x ≠ 6, x ≠ 4

b)

all real numbers x where x ≠ 0, x ≠ -2

c)

all real numbers x where x ≠ 6, x ≠ 0, x ≠ -2

d)

all real numbers x where x ≠ 6, x ≠ 0, x ≠ -2, x ≠ 4

27.

12.The graph of the polynomial function $p$ is shown above. Which of the following could be an expression for $p$ ?

a)

$-\frac{1}{4}x(x+2)(x-3)$

b)

$-\frac{1}{4}x^2(x-2)(x+3)$

c)

$-\frac{1}{4}x^2(x+2)(x-3)$

d)

$\frac{1}{4}x^2(x+2)(x-3)$

28.

13.The function $f$ is given by $f(x)=x^2(x+3)(x^2+7)$ . Which of the following describes the zeros of $f$ ?

a)

f has exactly three distinct real zeros.

b)

f has exactly seven distinct real zeros.

c)

f has exactly two distinct real zeros and two non-real zeros.

d)

f has exactly three distinct real zeros and two non-real zeros.

29.

14.Determine the least possible degree of $g$ . Show the work that leads to your answer.

a)

0

b)

1

c)

2

d)

3

30.

When is a function considered positive?

a)

When its y values are below the x-axis

b)

When its y values are above the x-axis

c)

When its y values are getting smaller

d)

When its y values are getting larger

31.

Use the graph of f below for this problem. How many points of inflection does the graph of f have?

a)

1

b)

2

c)

3

d)

4

32.

Over which interval is the graph of f(x) both decreasing and concave up?

a)

(B, C)

b)

(D, E)

c)

(C, D)

d)

(H, I)

33.

Which of the following scenarios would best represent the graph shown?

a)

Jackson ran to try and catch a bus at a stop near his house. He waited two minutes at the stop but realized he had missed the bus. So he slowly walked home.

b)

Wesley walked to the end of his driveway to get the newspaper and then turned to walk back inside at the same constant rate.

c)

Ben walked to a gas station close to his home to get a soda. He talked to some friends at the gas station for a few minutes. His mom called and told him to get home to do his Precal HW. The friend drove Ben back home. Luckily he got home faster in the car than when he walked.

d)

Jenny and her friend took the escalator to the 2nd story of the mall, shopped there for a while, and took the escalator back down.

34.

Over what intervals is the average rate of change decreasing?

a)

(-∞, 1)

b)

(0, 2)

c)

(-1, ∞)

d)

(-∞, 2)

35.

Let s(x) give the total snowfall, in inches, x hours from the start of the snowstorm. Which expression can be used to find the average rate at which snow fell between 2 and 5 hours after the start of the snowstorm?

a)

$\frac{s\left(5\right)\ -\ s\left(2\right)}{3}$

b)

$\frac{s\left(5\right)\ +\ s\left(2\right)}{3}$

c)

$\frac{s\left(2\right)\ -\ s\left(5\right)}{3}$

d)

$\frac{s\left(2\right)\ +\ s\left(5\right)}{3}$

AP PreCalculus Exam Review

Total questions: 35

Worksheet time: 4hrs 12mins

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