Free Printable AP PreCal Review Units 1-3A

1.

NO CALCULATOR:

$f\left(x\right)=\frac{x^3+3x^2-10x}{x^2-25}$

Select all vertical asymptote(s).

a)

x=2

b)

x=0

c)

x=5

d)

x=-5

2.

The function g(x) is the result of applying the following transformations to f(x):

reflection over the y-axis, horizontal translation -3 and vertical dilation 2.

a)

g(x)=f(-2x-3)

b)

g(x)=2f(-x+3)

c)

g(x)=-2f(x+3)

d)

g(x)=2f(-x-3)

3.

Find the coefficient of the term containing x²in the expansion of (4x-3)⁵.

a)

5760

b)

-4320

c)

-3840

d)

1620

4.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?

a)

200

b)

150

c)

300

d)

75

5.

Which one of the following functions is even?

a)

f(x) = x⁴ + x³

b)

g(x) = x⁴ + x²

c)

h(x) = x⁵ + x³

d)

k(x) = x³ + x

6.

The function shown in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

7.

Find the point(s) of inflection (if it exists) of the graphed function.

a)

No point of inflection

b)

Points 3 and 5

c)

Points 1, 3, 5 and 7

d)

Points 1, 2, 3, 4, 5, 6 and 7

e)

Points 2, 4 and 6

8.

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)

$16x^2-1$

9.

What transformations have happened to f(x) = 2^x if the new equation is
g(x) = -2^(x+3) -6

a)

It stayed the same

b)

reflects, up 3, left 6

c)

reflects over y-axis, right 3, down 6

d)

reflects over x-axis, left 3, down 6

10.

Write the function for the following table:

a)

f(x)=1(3)^x

b)

$f(x)=3(3)^x$

c)

$f(x)=3x+3$

11.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

12.

What is the amplitude of the graph?

a)

3

b)

2

c)

-3

d)

-2

13.

What is the midline of the graph?

a)

$y=-1$

b)

$y=1$

c)

$y=2$

d)

$y=-2$

14.

What is the period of $f\left(x\right)=2\cos\left(4x+8\right)-5$

a)

$\frac{\pi}{3}$

b)

$6\pi$

c)

$\frac{2\pi}{3}$

d)

$\frac{\pi}{2}$

15.

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function:
$y=19+6\sin\left(\frac{π}{12}(x–11)\right)$
where y is the temperature (ºC) and x is the time in hours past midnight. What are the minimum and maximum temperatures in the office?

a)

min: 13ºC

max: 25ºC

b)

min: 17ºC

max: 23ºC

c)

min: 5ºC

max: 17ºC

d)

min: 8ºC

max: 30ºC

16.

Given function $f\left(x\right)=a\cos\left(bx\right)$ , what is the value of 𝑎 and 𝑏 if function has a period of 4𝜋 and an amplitude of 10,

a)

period: $\frac{1}{2}$

amplitude: 10

b)

period: $2$

amplitude: 10

c)

period: $\frac{1}{2}$

amplitude: $\frac{1}{10}$

d)

period: $2$

amplitude: $\frac{1}{10}$

17.

Which of the following functions is an equivalent form of the function $h$ defined by $h\left(x\right)=100\cdot9^x$ ?

a)

$h\left(x\right)=10\cdot3^{2x}$

b)

$h\left(x\right)=100\cdot9^{2x}$

c)

$h\left(x\right)=100\cdot3^{2x}$

d)

$h\left(x\right)=100\cdot3^{\left(\frac{x}{2}\right)}$

18.

From 2011 – 2015, the number of electric vehicles purchased in Norway grew exponentially. The percent of all new vehicles purchased that were electric is modeled by the function $E$ , which increased by $96.8\%$ each year. In 2011 ( $t=0$ ), $1.6\%$ of all new cars purchased in Norway were electric. If $t$ is measured in months, which of the following is an expression for $E\left(t\right)$ ? (Note: There are twelve months in one year.)

a)

$1.6\left(0.968\right)^{\left(\frac{t}{12}\right)}$

b)

$1.6\left(0.968\right)^{12t}$

c)

$1.6\left(1.968\right)^{\left(\frac{t}{12}\right)}$

d)

$1.6\left(1.968\right)^{12t}$

19.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

20.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

21.

tan (-π)

a)

undefined

b)

0

c)

1

d)

-1

22.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

23.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

24.

What quadrant is -2π/3 in?

a)

I

b)

II

c)

III

d)

IV

25.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

26.

Q: Mary’s father has 5 daughters – Nana, Nene, Nini, Nono. What is the fifth daughter's name?

a)

Nunu

b)

Dazlyn

c)

Mary

d)

Janet

27.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

AP PreCal Review Units 1-3A

Total questions: 27

Worksheet time: 1hrs 6mins

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