Free Printable Final Exam Review

1.

Name the polynomial by degree and number of terms:

-7x²

a)

quadratic monomial

b)

linear binomial

c)

quadratic trinomial

d)

quartic monomial

2.

What is the standard form of the polynomial,
9x² + 5x + 27 + 2x³

a)

27 + 5x + 9x² + 2x³

b)

9x² + 5x + 2x³ + 27

c)

9x² + 5x + 27 + 2x³

d)

2x³ + 9x² + 5x + 27

3.

a)

A

b)

B

c)

C

d)

D

4.

Name the polynomial by degree and number of terms:

2m² - 5m

a)

quadratic trinomial

b)

quintic binomial

c)

quadratic binomial

d)

constant binomial

5.

6v(2v + 3)

a)

12v+18

b)

15v² + 8v

c)

12v² + 18v

d)

12v² + 18v²

6.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

7.

(4a + 2)(6a² − a + 2)

a)

24a³ + 16a² + 6a + 4

b)

24a³ + 8a² + 10a + 4

c)

24a³ + 8a² + 6a + 4

d)

24a³ - 8a² - 6a + 4

8.

Select the correct expansion of

(1 + 4x)³

a)

1 + 12x + 12x² + 4x³

b)

1 + 12x + 48x² + 64x³

c)

1 + 3x + 3x² + x³

d)

1 + 4x + 16x² + 64x³

9.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

10.

Divide using long division. $\left(9x^3-18x^2-x+2\right)\div\left(3x+1\right)$

a)

$3x^2+7x-14$

b)

$3x^2-7x-2$

c)

$3x^2-7x+14$

d)

$3x^2-7x+2$

11.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

12.

Divide using synthetic division
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

13.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

a)

±1, ±5, ±1/2, ±5/2

b)

±1, ±2, ±5, ±1/2, ±5/2

c)

±1, ±5

d)

±1, ±2, ±5, ±1/2, ±5/2, ±2/5

14.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

15.

Is (x-7) a factor of (x²-5x+14)?

a)

Yes

b)

No

16.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

17.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

18.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

19.

a)

A.

b)

B.

c)

C.

d)

D.

20.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

21.

How many solutions will this quadratic equation x²+8x+16 has?

a)

2 real solutions

b)

2 imaginary solution

c)

1 solution

d)

3 solutions

22.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and
x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and
x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and
x→∞, y→⁻∞

23.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and x→∞, y→⁻∞

b)

x → ∞, y→ ∞ and x→⁻∞, y→∞

c)

x → ∞, y→ ∞ and x→⁻∞, y→ 0

d)

x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞

24.

Determine the end behavior of the graph of
f(x) = 3x⁴ + 2x - 5
Note: f(x)=y

a)

As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.

b)

As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.

c)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.

d)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.

25.

Find the excluded value(s).

a)

a = 0

b)

a = 10

c)

a = 1

d)

a = -1

26.

Find the excluded value(s).

a)

n = 0

b)

n = 24

c)

n = -24

d)

n can be any real number

27.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

28.

Reduce, or simplify

the rational expression.

a)

( x + 5 )( x - 5 ) / ( x + 5 )( x - 2 )

b)

( x - 5 ) / ( x - 2 )

c)

( x + 5 ) / ( x - 2 )

d)

-25 / ( 3x - 10 )

29.

a)

A

b)

B

c)

C

d)

D

30.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

31.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

32.

Rewrite in exponential form.

a)

A

b)

B

c)

C

d)

D

33.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

34.

Sovle for x:

5^{-3x - 1} = 25

a)

x = 1

b)

x = -4

c)

x = -3

d)

x = -1

35.

Condense

a)

log xyz³

b)

log (xy/z³)

c)

log x + log y + log z³

d)

log x³y³z³

36.

Expand the Logarithm

a)

A

b)

B

c)

C

d)

D

37.

Solve the equation for x.

a)

32

b)

25

c)

1.66

d)

512

Final Exam Review

Total questions: 37

Worksheet time: 1hrs 14mins

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