Free Printable Complex Numbers and Rational Exponents Review

1.

Select ALL expressions that are equivalent to $64^{\frac{2}{3}}$

a)

$\left(\sqrt{64}\right)^3$

b)

c)

d)

$4^2$

e)

2.

Select ALL expressions that are equivalent to

64^{\frac{3}{2}}

a)

$8^3$

b)

$512$

c)

$\sqrt{64^3}$

d)

e)

$\left(64^{\frac{1}{3}}\right)^2$

3.

Select ALL expressions that are equivalent to $27^{\frac{2}{3}}$

a)

b)

$3^2$

c)

d)

$9^2$

e)

4.

Select ALL expressions that are equivalent to $729^{\frac{2}{3}}$

a)

b)

c)

$27^2$

d)

$81^2$

e)

$9^2$

5.

How many real solutions does $x^2+8x+20=0$ have?

a)

0 real solutions

b)

1 real solution

c)

2 real solutions

6.

How many real solutions does $x^2+8x-20=0$ have?

a)

0 real solutions

b)

1 real solution

c)

2 real solutions

7.

How many real solutions does $x^2+8x+16=0$ have?

a)

1 real solution

b)

0 real solutions

c)

2 real solutions

8.

How many real solutions does $x^2-6x+9=0$ have?

a)

1 real solution

b)

0 real solutions

c)

2 real solutions

9.

How many real solutions does $x^2-6x+3=0$ have?

a)

0 real solutions

b)

1 real solution

c)

2 real solutions

10.

How many real solutions does $x^2-6x+10=0$ have?

a)

0 real solutions

b)

1 real solution

c)

2 real solutions

11.

Select ALL the solutions to

\left(x-2\right)^2=-16

a)

$2+4i$

b)

$-2+4i$

c)

$2-4i$

d)

$-2-4i$

12.

Select ALL the solutions to $\left(x+2\right)^2=-16$

a)

$2+4i$

b)

$-2+4i$

c)

$2-4i$

d)

$-2-4i$

13.

Select ALL the solutions to $\left(x-4\right)^2=-36$

a)

$4+6i$

b)

$-4+6i$

c)

$4-6i$

d)

$-4+6i$

14.

Select ALL the solutions to $\left(x+4\right)^2=-36$

a)

$4+6i$

b)

$-4+6i$

c)

$4-6i$

d)

$-4-6i$

15.

Let $p=5-2i$ and $q=-3+7i$

Write the sum of

p\ +\ q

expression in the form

a+bi

a)

$2+5i$

b)

$-2-5i$

c)

$2-5i$

d)

$-2+5i$

16.

Let $p=5-2i$ and $q=-3+7i$
Find the difference of $p-q$

a)

$8-9i$

b)

$-8-9i$

c)

$8+9i$

d)

$-8+9i$

17.

Let $p=5-2i$ and $q=-3+7i$
Find the product of $p\cdot q$

a)

$-1+41i$

b)

$-1-41i$

c)

$1-41i$

d)

$1+41i$

18.

Let $k=3-4i$ and $m=-2+9i$
Find the sum of $k+m$

a)

$1+5i$

b)

$-1-5i$

c)

$1-5i$

d)

$-1+5i$

19.

Let $k=3-4i$ and $m=-2+9i$
Find the difference of $k-m$

a)

$5+13i$

b)

$-5-13i$

c)

$5-13i$

d)

$-5+13i$

20.

Let $k=3-4i$ and $m=-2+9i$
Find the product of $k\cdot m$

a)

$30+35i$

b)

$-30-35i$

c)

$30-35i$

d)

$-30+35i$

21.

Find the solution for $\sqrt{2x+1}-4=-1$

a)

4

b)

no solution, a positive square root cannot equal a negative number

c)

-4

d)

1

e)

-1

22.

Find the solution for $\sqrt{2x+1}+4=-1$

a)

4

b)

no solution, a positive square root cannot equal a negative number

c)

-4

d)

1

e)

-1

23.

Find the solution for $\sqrt{2x+1}+4=3$

a)

4

b)

no solution, a positive square root cannot equal a negative number

c)

-4

d)

1

e)

0

24.

Find the solution for $\sqrt{2x+1}+4=-5$

a)

4

b)

no solution, a positive square root cannot equal a negative number

c)

-4

d)

1

e)

0

25.

Find the solution for $\sqrt{2x+1}+4=5$

a)

40

b)

no solution, a positive square root cannot equal a negative number

c)

-40

d)

80

e)

0

26.

Find the solution for $\sqrt{2x+1}-4=3$

a)

24

b)

no solution, a positive square root cannot equal a negative number

c)

-24

d)

1

e)

0

27.

Find an exact solution to the equation

a)

-10

b)

-6

c)

10

d)

6

28.

Find an exact solution to the equation

a)

-64

b)

-4

c)

0

d)

-16

29.

Find an exact solution to the equation

a)

-63

b)

-126

c)

8

d)

-13

30.

Find an exact solution to the equation

a)

-108

b)

108

c)

32

d)

-32

31.

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ What is this formula called?

a)

The quadratic formula

b)

The Pythagorean Theorem

c)

Trig Function for cosine

d)

Baby formula

32.

What is the correct form of the Quadratic Formula?

a)

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

b)

$x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}$

c)

$x=b+\frac{\sqrt{b^2-4ac}}{2a}$

d)

$x=\frac{b\pm\sqrt{b^2-4ac}}{2a}$

e)

$x=\frac{-b\pm\sqrt{b^2+4ac}}{2a}$

33.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

34.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

35.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

36.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

37.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

38.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

39.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

a)

{3, -1}

b)

{4, -4}

c)

{5, -3}

d)

{8, -7}

40.

Solve the following equation by completing the square:
n² = 18n + 40

a)

{11, -11}

b)

{16, 2}

c)

{20, -2}

d)

{10, -4}

41.

Simplify √56

a)

4√14

b)

2√14

c)

2√27

d)

4√7

42.

Simplify √800.

a)

10√8

b)

5√24

c)

12√2

d)

10√2

43.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

44.

Solve by completing the square:
v² + 6v − 59 = 0

a)

{-5 + 5√2, -5 - 5√2}

b)

{5 + 5√2, 5 - 5√2}

c)

{-3 + 2√17, -3 - 2√17}

d)

{3 + 2√17, 3 - 2√17}

Complex Numbers and Rational Exponents Review

Total questions: 44

Worksheet time: 4hrs 40mins

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