Free Printable PreCalculus Fall Term Final Review

1.

Which values of x make the expression undefined?

a)

5, 2

b)

-5, -2

c)

10, 1

d)

-10, -1

2.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

3.

If you factor 6x²+7x - 3 , one of the factors is

a)

(2x - 7)

b)

(2x + 3)

c)

(2x - 1)

d)

(2x + 1)

4.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

5.

What is f(2)?

a)

0

b)

1

c)

2

d)

-1

6.

Write a 4th degree polynomial function with:
*a positive leading coefficient
*zeros: 9, 3, -2, 0

a)

y = x(x - 9)(x - 3)(x + 2)

b)

y = x(x + 9)(x + 3)(x - 2)

c)

y = -x(x - 9)(x - 3)(x + 2)

d)

y = -x(x + 9)(x + 3)(x - 2)

7.

a)

y = x(x - 3)(x - 2)

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

8.

What is the y-intercept?
f(x) = -x⁴ + x³ + 5x² + x + 6

a)

-1

b)

1

c)

5

d)

6

9.

Is the leading coefficient positive or negative

a)

positive

b)

negative

10.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

11.

Find the vertical asymptote.
x²-2x-8
__________
3x-2

a)

y=2/3

b)

x=3/2

c)

x= 2/3

d)

x=1/3

12.

What are the asymptotes?

a)

x=-3, y=1

b)

x=3, y =1

c)

x=-3, y =-1

d)

x=3 y=-1

13.

What is the horizontal asymptote to this function?

a)

y = 4

b)

y = 0

c)

y = -2

d)

y =1

14.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

15.

What is/are the x-intercepts of this graph?

a)

(-2,0) and (2,0)

b)

(-2,0)

c)

(3,0)

d)

(2,0) and (3,0

16.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

17.

Find the oblique asymptote.

a)

y = 3x - 12

b)

y = x + 5

c)

y = 3x - 5

d)

y = 3x - 7

18.

Given f(x) = 2x and g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

19.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

20.

Which piecewise function corresponds to this graph?

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

21.

What is the factored form of x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

22.

Find the missing value "c" to complete the square.

x² + 6x + ____

a)

9

b)

12

c)

36

d)

- 9

23.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

24.

Solve. x² = √-36

a)

x = ± 6

b)

x = 6i

c)

x = ± 6i

d)

x = i√6

25.

Solve.
x² +12 = 5

a)

x = ± 49

b)

x = ± i√7

c)

x = ± √7

d)

x = ± 3.5i

26.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

27.

Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8

a)

(5, 8)

b)

(5, -8)

c)

(-5, -18)

d)

(-5, 8)

28.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

29.

An MLB stadium sells three types of tickets. Reserved tickets are sold for $20 each, field level tickets are sold for $50 each, and box seat tickets are sold for $100 each. You purchase 10 total tickets for $370. You have twice as many reserved tickets as field level tickets. Set up the system using the variables

x: reserved

y: field-level

z: box seats

a)

$x+y+z=370$
$20x+50y+z=100$
$2x=y$

b)

x+y+z=10

20x+50y+100z=370

x=2y

c)

$2x+y+z=370$
$20x+50y+100z=2$
$2z=x$

30.

$8x+3y+7z=7$

2y+3z=-4

4y=-20

Solve for z

a)

z = -5

b)

z = 2

c)

z = -14/3

d)

z = 5

31.

$2x+y-2z=12$
$3x-y-4z=26$
$x+3y+z=0$

Solve the system

a)

(-4, 10, 2)

b)

(10, -4, 2)

c)

(10, 4, -2)

d)

(4, -10, -2)

32.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

33.

$x^5+3x^2-4x+120$ has how many total possible positive real solutions?

a)

4

b)

3

c)

2

d)

1

e)

0

PreCalculus Fall Term Final Review

Total questions: 33

Worksheet time: 52mins

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