Free Printable Solving Complex Expressions

1.

Solve
4m² - 100 = 0

a)

m=25, -25

b)

m=96

c)

m=5, -5

d)

m=-96

2.

Solve
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

3.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

4.

Solve by taking square roots:
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solution

5.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

6.

Convert x²-6x+9 to factored form and identify the solution.

a)

(x-3)(x-3); x=3

b)

(x+3)(x+3); x=-3

c)

(x+4)(x+2); x=-4, -2

d)

Not factorable

7.

Convert x²-9x+20 to factored form and solve.

a)

(x-10)(x+2); x=-2, 10

b)

(x+4)(x+5); x=-5, -4

c)

(x-4)(x-5); x=4, 5

d)

Not factorable

8.

Solve:
X² - 3 =6X + 10

a)

X = 7, -1

b)

X = -7, 1

c)

X = -7, -1

d)

No Solution

9.

What is the degree of every Quadratic Equation?

a)

1

b)

2

c)

3

d)

4

10.

What is the greatest number of solutions that a Quadratic Equation can have?

a)

0

b)

1

c)

2

d)

3

11.

What are the solutions?

a)

-2, 1

b)

1, 2

c)

-1,2

d)

0,-4

12.

Use the Quadratic Formula to solve the Quadratic Equation.
x² + 5x - 36

a)

-9, 1

b)

-9, 4

c)

9, 4

d)

9, -4

13.

Look at the graph of f(x) on the left. What is the axis of symmetry?

a)

$\left(2,3\right)$

b)

$x=2$

c)

$y=3$

d)

$\left(3,2\right)$

14.

Look at the graph of f(x) on the left. What is the vertex?

a)

$\left(2,3\right)$

b)

$\left(1,4\right)$

c)

$\left(3,4\right)$

d)

$\left(3,2\right)$

15.

Given the parabola $y=x^2+6x$ , what is the y-intercept?

a)

$\left(6,0\right)$

b)

$\left(1,0\right)$

c)

$\left(-3,-9\right)$

d)

$\left(0,0\right)$

16.

What is the vertex of the parabola $y=x^2+6x$ ?

Hint: Use the vertex form you created to find the vertex.

(a)

17.

Will the parabola $y=x^2+6x$ have a maximum or minimum?

(Will the parabola open up or down)

a)

Maximum

b)

Minimum

18.

What is the vertex of the parabola $y=\left(x+7\right)^2-9$ ?

a)

$\left(-7,-9\right)$

b)

$\left(-9,\ 7\right)$

c)

$\left(7,\ -9\right)$

19.

Distribute the following equation. $\left(3x-1\right)\left(3x+1\right)$

a)

$6x^2-1$

b)

$9x^2+6x-1$

c)

$9x^2-1$

d)

$6x^2+6x-1$

20.

Factor the quadratic

$27m^2-90m+72$

a)

$\left(m-2\right)\left(3m-4\right)$

b)

$9\left(m-2\right)\left(3m-4\right)$

c)

$\left(3m-2\right)\left(m-4\right)$

d)

$9\left(3m-2\right)\left(m-4\right)$

21.

Simplify the following radical: √24

a)

2√6

b)

4√6

c)

2√12

d)

3√8

22.

Simplify the following radical: √300

a)

3√10

b)

2√150

c)

100√3

d)

10√3

23.

Simplify the following radical: √150

a)

5√15

b)

5√2

c)

5√6

d)

15√5

24.

Simplify 4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

25.

Simplify the following radical: 2√24

a)

4√6

b)

2√6

c)

24√2

d)

4√4

26.

a)

7√3

b)

Can't Simplify

c)

6√15

d)

6√3

27.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

28.

Add: 4√7 - 10 √7 + 7√7

a)

-6√7

b)

14√7

c)

-3√14

d)

√7

29.

Simplify: 2√40 - 3√10

a)

5√10

b)

√10

c)

-√30

30.

2√5 - √5 + 4√5 + √3

a)

6√5 + √3

b)

5√5 + √3

c)

6√5

d)

6√3

31.

Simplify:

a)

8x⁹

b)

8x³

c)

8x⁴√x

d)

8x³√x

32.

a)

A

b)

B

c)

C

d)

D

33.

5√48x²

a)

10x√3

b)

15x√3

c)

20x√3

d)

25x√3

34.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

35.

$\sqrt{45x^4y^7}$

a)

$3x²y³\sqrt{5}$

b)

$9x²y³\sqrt{5y}$

c)

$3x²y³\sqrt{5y}$

d)

$3x⁴y⁷$

36.

Simplify the radical... $\sqrt{20a²b⁴}$

a)

$2ab²\sqrt{5}$

b)

$4ab²\sqrt{5}$

c)

$5ab²\sqrt{2}$

d)

$2a²b²\sqrt{5}$

37.

When using the (a) rule, you multiply the exponents.

38.

Simplify this exponential equation.

$9b^8\times3b^5$

a)

$12b^{13}$

b)

$3b^9$

c)

$9b^5$

d)

$27b^{13}$

39.

Simplify the exponential expression

$\frac{j^6k^5}{j^2k^3}$

a)

$j^{\ 8}k^{\ 8}$

b)

$j^{\ 4}k^{\ 2}$

c)

jk

40.

Simplify the exponential expression.

$\left(2\times3\right)^3$

a)

$6^3$

b)

18

c)

$2^3\times3^3$

41.

Simplify the exponential expression.

$\frac{x^2y^{10}}{xy^8}$

a)

xy

b)

$x^2y^2$

c)

$xy^2$

42.

a)

A

b)

B

c)

C

d)

D

43.

a)

F

b)

G

c)

H

d)

J

44.

a)

F

b)

G

c)

H

d)

J

45.

a)

F

b)

G

c)

H

d)

J

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

F

b)

G

c)

H

d)

J

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

F

b)

G

c)

H

d)

J

50.

a)

F

b)

G

c)

H

d)

J

51.

Who's this Simpsons character?

a)

Maggie

b)

Marge

c)

Lisa

d)

Bart

52.

Who's this Simpsons character?

a)

Maggie

b)

Marge

c)

Lisa

d)

Homer

53.

Who's this Simpsons character?

a)

Bart

b)

Homer

c)

Moe

d)

Flanders

54.

Where do The Simpsons live?

a)

Growfield

b)

Springfield

c)

Europe

d)

Simpsonsland

55.

Where does Homer work Simpsons?

a)

He works in a bar.

b)

He works in a supermarket.

c)

He works in a nuclear power plant

d)

He doesn't work anywhere.

56.

Sideshow Bob hates ____________

a)

Homer

b)

Bart

c)

Lisa

d)

Marge

57.

What grade is Bart Simpson in?

a)

3rd

b)

5th

c)

4th

d)

Freshman

58.

What is the name of Ned's Left-Handed Store in the Simpsons?

a)

Lefty's

b)

The Leftorium

c)

Ned's Left-Handed Store

d)

Left Turn

59.

Jebediah Springfield founded the town in:

a)

1796

b)

1987

c)

1989

d)

1769

60.

Bart Simpson is allergic to:

a)

Glow in the dark monster make-up

b)

Pumpkin

c)

Santa's Little Helper

d)

Nuts

Solving Complex Expressions

Total questions: 60

Worksheet time: 3hrs 22mins

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