Free Printable Math 3 Fall Final Review

1.

Solve the equation for x: $\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

2.

Solve for x: $\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}$

a)

x = 5

b)

x = $\frac{4}{5}$

c)

x = 1

d)

x = - 4

3.

Multiply & Simplify:
$\frac{x^3-9x}{x^2+10x+21}\cdot\frac{x^2+7x}{x^2+5x-24}$

a)

$\frac{2x}{x+8}$

b)

$\frac{x^2}{x+8}$

c)

$\frac{x}{x+4}$

d)

$\frac{x^2\left(x-9\right)}{x+8}$

4.

Simplify:

$\frac{3}{x+4}+\frac{2}{x-2}$

a)

$\frac{5x+2}{\left(x+4\right)\left(x-2\right)}$

b)

$\frac{3x-6}{\left(x-2\right)\left(x+4\right)}$

c)

$\frac{5x-10}{\left(x-2\right)\left(x+4\right)}$

d)

$\frac{6x+24}{\left(x-2\right)\left(x+4\right)}$

5.

Simplify

$\frac{2x+2}{x+2}\div\frac{4x^2+8x+4}{12x+12}$

a)

$\frac{1}{40x}$

b)

$-\frac{3}{2\left(x-6\right)}$

c)

$\frac{6}{x+2}$

d)

$\frac{3}{5x}$

6.

What is the DOMAIN?

a)

$\left(-\infty,-3\right)U\left(-3,\infty\right)$

b)

$\left(-\infty,1\right)U\left(1,\infty\right)$

c)

$\left(-\infty,-3\right)U\ \left(-3,\ 1\right)\ U\left(1,\infty\right)$

d)

All Real Numbers

7.

Which graph matches the function?

a)

A

b)

B

c)

C

d)

D

8.

Which graph matches the function?

a)

A

b)

B

c)

C

d)

D

9.

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

a)

48 minutes

b)

50 minutes

c)

24 minutes

d)

12 minutes

10.

List the potential real zeros of:
f(x) = 5x³ - x² + 3

a)

±1/5, ±3/5, ±1, ±3

b)

±1/3, ±5/3, ±1, ±5

c)

±1/5, ±3/5, ±1, ±3, ±5

d)

±1/5, ±1/3, ±1, ±3, ±5

11.

Given the roots, which roots are missing: -7i, 3√2, _____, ______

a)

-7i, 3√2,

b)

-7i, -3√2,

c)

7i, 3√2,

d)

7i, -3√2,

12.

Which of the following would be the correct factored form with roots 2, 5i, and 6?

a)

(x-6)(x-2)(x+5i)(x-5i)

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

(x+6)(x+2)(x-5i)

13.

Find all zeroes given a factor of (x+3).

y = 2x³+ 5x²- 6x - 9

a)

-1,-3,-3

b)

-1,-3,3/2

c)

3,3,3

d)

-3,2/3,-1

14.

Given the function
$f\left(x\right)=-x^5-5x^4+12x^3-60x^2+27x\ +135$
which of the following is NOT a possible combination of roots?

a)

5 real, 0 imaginary

b)

4 real, 1 imaginary

c)

3 real, 2 imaginary

d)

1 real, 4 imaginary

15.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

16.

Which of the following correctly identifies the End Behavior?

a)

b)

c)

d)

17.

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

18.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

19.

Which of the following is the function shown in the graph?

a)

f(x)= -√(x+4) -2

b)

f(x)= √(x-4) -2

c)

f(x)= -√(x-4) -2

d)

f(x)= √(x+4) +2

20.

What are the transformations of this functions compared to the parent function?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

21.

Which function matches the graph?

a)

A

f(x) = ∛(x + 3) + 2

b)

B

f(x) = − ∛(x - 3) + 2

c)

C

f(x) = ∛(x - 3) + 2

d)

D

f(x) = ∛(x - 2) + 3

22.

a)

5

b)

4

c)

41

d)

82

23.

a)

5

b)

33

c)

85

d)

21

24.

What is the value of x in the equation (2x + 1)^1/3 + 3 = 6

a)

1

b)

13

c)

4

d)

16

e)

None

25.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

26.

What are the restricted values?

a)

x = - 3 and x = 4

b)

x = 3 and x = - 4

c)

x = 3 only

d)

x = - 4 only

27.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

28.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3,±9

c)

±1,±3±9,±1/2,±3/2,±9/2

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

29.

The horizontal asymptote equals zero when:

a)

the degree of the numerator and denominator are equal

b)

the degree of the numerator is less than the degree of the denominator

c)

the degree of the numerator is greater than the degree of the denominator

d)

the numerator equals zero

30.

$g\left(x\right)=\frac{x^2+4x-21}{x^2-49}$

Find the hole, if one exists.

a)

$no\ hole\ exists$

b)

$\left(3,-4\right)$

c)

$\left(7,4\right)$

d)

$\left(-7,\frac{5}{7}\right)$

31.

What is/are the decreasing interval(s) for the function shown?

a)

$\left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

b)

$\left(-\infty,\ 1\right)\ and\ \left(8,\ \infty\right)$

c)

$\left(-\infty,1\right),\ \left(-3,\ 1\right)\ and\ \left(8,\ \infty\right)$

d)

$\left(-\infty,\ 1\right),\ \left(2,\ 4\right)\ and\ \left(8,\ \infty\right)$

32.

Solve using Long Division.

27x^3+9x^2-3x-10\ \div3x-2

a)

$9x^4+5$

b)

$9x^2+9x+5$

c)

$9x^2-9x+5$

d)

$9x^2-9x$

33.

Simplify. Your final answer should have positive exponents only.

$\left(\frac{25x^2y^3}{75x^{7y^0}}\right)^4$

a)

$\frac{3y^{12}}{x^{20}}$

b)

$\frac{y^{12}}{3x^{20}}$

c)

$3^4x^{-20}y^{12}$

d)

$\frac{y^{12}}{3^4x^{20}}$

Math 3 Fall Final Review

Total questions: 33

Worksheet time: 3hrs 45mins

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