Free Printable Exam Review 3

1.

Simplify completely. $\sqrt[]{48}$

a)

$4\ \sqrt[]{3}$

b)

$3\ \sqrt[]{4}$

c)

$4\ \sqrt[]{6}$

d)

$6$

2.

Simplify completely. $\sqrt[]{72}$

a)

$6\ \sqrt[]{2}$

b)

$2\ \sqrt[]{36}$

c)

$8\ \sqrt[]{9}$

d)

$3\ \sqrt[]{7}$

3.

Simplify completely. $\sqrt[]{200}$

a)

$10\ \sqrt[]{2}$

b)

$8\ \sqrt[]{5}$

c)

$20\ \sqrt[]{2}$

d)

$10\ \sqrt[]{10}$

4.

Simplify. $\sqrt[]{24}\cdot\sqrt[]{3}$

a)

$3\ \sqrt[]{3}$

b)

$6\ \sqrt[]{2}$

c)

$36\ \sqrt[]{2}$

d)

$8\ \sqrt[]{3}$

5.

Simplify $4\ \sqrt[]{18}\cdot2\ \sqrt[]{6}$

a)

$48\ \sqrt[]{3}$

b)

$72\ \sqrt[]{6}$

c)

$32\ \sqrt[]{3}$

d)

$36\ \sqrt[]{12}$

6.

Simplify:

$2\ \sqrt[]{5}-3\ \sqrt[]{20}$

a)

$-4\ \sqrt[]{5}$

b)

$-1\ \sqrt[]{15}$

c)

$-8\ \sqrt[]{5}$

d)

$8\ \sqrt[]{5}$

7.

Simplify:

$3\ \sqrt[]{54}+3\ \sqrt[]{24}$

a)

$15\ \sqrt[]{6}$

b)

$30\ \sqrt[]{3}$

c)

$39\ \sqrt[]{6}$

d)

$8\ \sqrt[]{18}$

8.

SImplify:

a)

5√6

b)

25√6

c)

√150

d)

10√15

9.

Rationalize the square root.

a)

2

b)

(2√3)/3

c)

6

d)

2√6

10.

Multiply. Be sure to simplify your answer: $6\sqrt{2}\cdot5\sqrt{14}$

a)

$32\sqrt{7}$

b)

$60\sqrt{7}$

c)

$2\sqrt{7}$

d)

$30\sqrt{7}$

11.

Divide. Be sure to simplify your answer: $\frac{\sqrt{20}}{\sqrt{5}}$

a)

$\frac{2\sqrt{5}}{5}$

b)

$\frac{1}{5}$

c)

$4$

d)

$2$

12.

Simplify.

$\frac{\sqrt{8}}{4\sqrt{2}}$

a)

$\frac{1}{2}$

b)

$2$

c)

$\frac{2\sqrt{6}}{3}$

d)

$\frac{3}{10}$

13.

Simplify $\frac{2}{\sqrt{2}}$

a)

$\sqrt{2}$

b)

$\frac{\sqrt{6}}{3}$

c)

$\frac{2\sqrt{3}}{3}$

d)

$\frac{\sqrt{2}}{2}$

14.

Simplify $\frac{8}{\sqrt{6}}$

a)

$\frac{2\sqrt{10}}{5}$

b)

$\frac{\sqrt{30}}{5}$

c)

$\frac{4\sqrt{6}}{3}$

d)

$\frac{\sqrt{6}}{6}$

15.

Simplify $\frac{9}{\sqrt{8}}$

a)

$\frac{\sqrt{6}}{3}$

b)

$\frac{2\sqrt{2}}{9}$

c)

$\frac{\sqrt{6}}{4}$

d)

$\frac{9\sqrt{2}}{4}$

16.

$\frac{10}{\sqrt{12}}$

a)

$\frac{\sqrt{154}}{14}$

b)

$\frac{6\sqrt{33}}{6}$

c)

$\frac{5\sqrt{3}}{3}$

d)

$\frac{\sqrt{14}}{14}$

17.

What should you multiply $\frac{6}{1-\sqrt{5}}$ by to rationalize the denominator?

a)

-4

b)

$1-\sqrt{5}$

c)

$1+\sqrt{5}$

d)

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

18.

What should you multiply $\frac{3\sqrt{2}}{2-\sqrt{7}}$ by to rationalize the denominator?

a)

$2-\sqrt{7}$

b)

$\sqrt{7}$

c)

$2+\sqrt{7}$

d)

$\sqrt{2}$

19.

What would be the first step in rationalizing

$\frac{3+\sqrt{2}}{5-\sqrt{3}}$ ?

a)

$\frac{3+\sqrt{2}}{5-\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}$

b)

$\frac{3+\sqrt{2}}{5-\sqrt{3}}\cdot\frac{5-\sqrt{3}}{5-\sqrt{3}}$

c)

$\frac{3+\sqrt{2}}{5-\sqrt{3}}\cdot\frac{5+\sqrt{3}}{5+\sqrt{3}}$

d)

$\frac{3+\sqrt{2}}{5-\sqrt{3}}\cdot\frac{3-\sqrt{2}}{5+\sqrt{3}}$

20.

Rewrite $\frac{2}{5+\sqrt[]{3}}$ by rationalizing the denominator.

a)

$\frac{5+\sqrt[]{3}}{11}$

b)

$\frac{5-\sqrt[]{3}}{11}$

c)

$2\left(5+\sqrt[]{3}\right)$

d)

$\frac{2\sqrt[]{3}}{5}$

21.

Calculate the result of the complex number arithmetic: (5 - 2i) * (3 + 4i)

a)

9 - 6i

b)

11 + 2i

c)

15 - 8i

d)

22 + 7i

22.

Perform the following complex number arithmetic: (2 + 3i) + (4 - 5i)

a)

5 - 8i

b)

7 - 3i

c)

3 + 2i

d)

6 - 2i

23.

$\left(3-i\right)\left(2+4i\right)=$

a)

$10+10i$

b)

$1-5i$

c)

$6-4i^2$

d)

$10$

24.

$\left(3-i\right)-\left(2+4i\right)=$

a)

$10+10i$

b)

$1-5i$

c)

$6-4i^2$

d)

$10$

25.

Calculate(Divide, multiply by conjugate):

a)

12/5 − 4/5i

b)

-8/10i − 4/5

c)

-4/5 + 12/5i

d)

12/5 + 4/5i

26.

Add the polynomials:
(3x³+3x²–4x+5) + (x³–2x²+x–4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

27.

Simplify the expression.
(4n⁴-8n+4) - (8n²+4n⁴+1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

28.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

29.

Find the product:

$\left(n^2-4n+5\right)\left(3n^2+3n+3\right)$

a)

$3n^4-12n^2+15$

b)

$3n^4-9n^3+6n^2+3n+15$

c)

$3n^4-15n^3+30n^2-27n+15$

d)

$4n^4+5n^3-8n^2-37n-12$

30.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

31.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

32.

$\left(4x^4-8x^3-3x^2+7x-2\right)\div\left(2x-1\right)$

Use long division to evaluate

a)

$2x^3-3x^2-3x+2$

b)

$2x^3+3x^2+3x+2$

c)

$2x^3-3x^2-3x-2$

d)

$2x^3+2$

33.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

34.

Synthetic Division only uses the ____________ of a polynomial to divide.

a)

Terms

b)

Numbers (coefficients)

c)

Variables

d)

Numbers and letters

35.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

36.

If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.

a)

True

b)

False

c)

Only for the dividend

d)

Only for the divisor

37.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

38.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

39.

Identify the missing term to complete the solution.

(a)

40.

Is this division problem worked correctly? If there is an error, on which line does the FIRST error occur?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

41.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

42.

Factor 2x²+ 4x – 3x – 6 by grouping. Remember to look for Standard Form, then for common factors.

a)

(2x – 3)(x + 2)

b)

2x² + x - 6

c)

(2x + 3)(x - 2)

43.

Factor by grouping:

5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n³+3)(n-2)

c)

(5n²-3)(n-2)

d)

10n(n²-6)

44.

Which of the following expressions are examples of DOTS (Difference of Two perfect Squares)?

a)

$x^2-36$

b)

$x^2+4$

c)

$4x^2-1$

d)

$x^2-196$

e)

$x-100$

45.

Factor completely.
$3x^2-12x$

a)

$3x\left(x^2-4x\right)$

b)

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

c)

$x\left(3x-12\right)$

d)

$3\left(x^2-12\right)$

46.

Factor
x² - 9x + 18.

a)

(x - 3)(x - 6)

b)

(x + 6)(x - 3)

c)

(x - 9)(x - 2)

d)

(x - 6)(x + 3)

47.

Factor
k² - 2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

48.

Factor out GCF first if necessary.

What is the factored form of:

$2x^2-2x-24$

Move the correct answer to each box. Not all answers will be used.

(a) (x+ (b) )(x- (c) )

Choose from the below words

2

3

4

1

6

5

49.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Group

50.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

51.

Factor Completely. $8x^2-200$

a)

$8\left(x+5\right)\left(x-5\right)$

b)

$8\left(x^2-25\right)$

c)

$4\left(2x^2-50\right)$

d)

$4\left(2x+25\right)\left(2x-25\right)$

52.

Factor completely:

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)

53.

Factor completely:

25x²-81

a)

(5x-9)²

b)

(5x+9)(5x-9)

c)

25(x-9)²

d)

(9x+5)(9x-5)

54.

Factor completely:

64x³+125

a)

(4x+5)(16x²-20x+25)

b)

(4x-5)(16x²+20x+25)

c)

(4x-5)(4x²+20x-25)

d)

(4x-5)(4x²+20x+25)

55.

Simplify the Expression

a)

b)

c)

d)

56.

Simplify the Expression

a)

b)

c)

d)

57.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

58.

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

State the values of x which must be excluded to prevent division by zero.

a)

-2 and 5

b)

2 and -5

c)

0, 2, and -5

d)

0, -2, and 5

59.

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

a)

x-5 ;{-2}

b)

$\frac{4x^2}{x-1}$ ;{1}

c)

$\frac{x-1}{4x^2}$ ;{0}

d)

10; {-5}

Exam Review 3

Total questions: 59

Worksheet time: 3hrs 21mins

Similar Resources on Wayground