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Worksheets

Grade 8 review

Total questions: 80

Worksheet time: 5hrs 15mins

Name
Class
Date
1.
Simplify (c5)(c2)(c2)
a)
c20
b)
c9
c)
c11
d)
3c45
2.
(6x2)(-3x5)
a)
18x7
b)
-18x7
c)
18x7
d)
3x7
3.
a)
a8b13
b)
a2b7
c)
a15b30
4.
(y9)-2
a)
y18
b)
y11
c)
1/y18
d)
y9/2
5.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
6.
Simplify (-7y2)(5y4)
a)
-35y6
b)
-2y6
c)
-35y8
d)
-2y8
7.
Find the difference
(3.8 x 104) - (2 x 103)
a)
1.8 x 104
b)
1.8 x 101
c)
3.6 x 101
d)
3.6 x 104
8.
Multiply using scientific notation.
(2 x 10³) x (1.9 x 10²)
a)
3.8 x 105
b)
3.8 x 102
c)
3.8 x 104
d)
3.8 x 106
9.
What is the simplified version of
a)
3.9 x 106
b)
4 x 1020
c)
4 x 106
d)
3.9 x 1020
10.
Divide:
(6.9 x 107) / (2.3 x 10-3)
a)
3 x 1010
b)
3 x 104
c)
3 x 10-4
d)
3 x 10-11
11.
Write the answer in scientific notation.
7.3 x 105  +   3.7 x 105  =
a)
11.0 x 105
b)
1.1 x 1010
c)
1.10 x 1011
d)
1.1 x 10 6
12.
8v - 4(v + 8) = 8
a)
2
b)
10
c)
4
d)
-4 
13.
2x + 3(5x - 7) = 47
a)
1
b)
2
c)
3
d)
4
14.

Solve

a)

5

b)

2

c)

No Solution

d)

Infinitely Many Solutions

15.
5x - 4 + 2x = 3
a)
1
b)
2
c)
3
d)
4
16.
2x - 3 + 4x = 27
a)
12
b)
4
c)
5
d)
15
17.

The slopes of parallel lines are...

a)

the same

b)

opposite

c)

always different

18.
Find the slope of the line that passes through:
(6,7) and (4,2)
a)
2/5
b)
-5/2
c)
5/2
d)
-1/2
19.
Find the slope of the line that passes through: 
(2, 4) and (6, 12)
a)
1/2
b)
-1/2
c)
2
d)
-2
20.
Given that the slope is  2/3 and the y intercept is -3 what is the equation of the line?
a)
y = 2/3x - 3
b)
y = 2/3x + 3
c)
y = -2/3x - 3
d)
y = -2/3x + 3
21.
Write the equation of the line through the points (4, 5) and (12, 9).
a)
y = 2x - 3
b)
y = 1/2x + 3
c)
y = 1/2x +7
d)
y = 2x - 15
22.
What does 'b" represent in y=mx+b
a)
y-intercept
b)
beans
c)
x-intercept
d)
slope
23.
What does "m" represent in y=mx+b?
a)
y-intercept
b)
slope
c)
macaroni
d)
x-intercept
24.
Identify the slope and y intercept in the equation of the line: y = -1/3x + 1
a)
Slope: 1/3
y-intercept: 1
b)
Slope: 1/3
y-intercept: -1
c)
Slope: -1/3
y-intercept: 1
d)
Slope: -1/3
y-intercept: 0
25.

Write the equation of the line in slope-intercept form with slope m = 4 through the point (-2, 5).

a)

y = 4x - 13

b)

y = 4x + 13

c)

y = 4x - 3

d)

y = 4x + 3

26.
y = -2/3x + 2
y = 3/2x + 9
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
27.

What is the slope of the lline parallel to

y = 2x - 7 ?

(a)  

28.
The following represents slopes of two lines.  Which answer choice describes the two lines?
m = 3/4 and m = 4/3
a)
Parallel
b)
Perpendicular
c)
Neither
29.
y = 3x +2
y = 3x - 3
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
d)
The same line
30.
What is the slope of a line perpendicular to a line with slope -6/5 ?
a)
-6/5
b)
-5/6
c)
5/6
d)
-4/3
31.

-6x + y = 2

y = 6x - 5

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

32.

What is the solution to the system of equations?

a)

(2, -2)

b)

(2, 2)

c)

No Solution

d)

(-2, -2)

33.

What is the solution to the system?

a)

(-1, 3)

b)

(-3, 1)

c)

(3, -1)

d)

(-3, -1)

34.

What is the solution to the system of equations?

a)

No Solution

b)

Infinitely Many Solutions

c)

(7, -2)

d)

(-5, -5)

35.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
36.
Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8 
a)
(5, 8)
b)
(5, -8)
c)
(-5, -18)
d)
(-5, 8)
37.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
38.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
39.
Find the length of the missing side. 
a)
17 cm
b)
22 cm
c)
15 cm
d)
13 cm
40.
Find the length of the missing side. 
a)
20 in.
b)
68 in.
c)
16 in.
d)
80 in.
41.
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?
a)
210 m
b)
180 m
c)
150 m
d)
79 m
42.
Find h
a)
35.60
b)
35.00
c)
35.71
d)
61.03
43.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
44.
You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?
a)
25 feet
b)
26 feet
c)
27 feet
d)
28 feet
45.
Find the missing side
a)
36
b)
76.8
c)
12
d)
40
46.

(4x3-5x2+3x)+(-2x3-x2+6x)

a)

2x3-6x2-9x

b)

2x3+6x2+9x

c)

-2x3-6x2+9x

d)

2x3-6x2+9x

e)

None of these

47.

Add the following polynomials

(x³-6x²+3)+(3x³+4x-1)

a)

4x³-2x²+2

b)

4x³-6x²+4x+2

c)

-2x³+2x+2

d)

4x³-2x²-2

e)

None of these

48.

(3x2+xy-5y2) + (2x2-xy+3y2)

a)

5x2-2xy+8y2

b)

5x2-2y2

c)

5x2+2y2

d)

5x2+2xy-8y2

e)

None of these

49.

Add the polynomials.

(2xy - 3x2 + 4y - 5) + (-3xy + 4y2 - 3y + 8)

a)

-1xy - 3x2 + 4y2 + 1y + 3

b)

-1xy + 1x2 + 1y + 3

c)

-1xy + 1y2 + 1y + 3

d)

1xy + 3x2 + 4y2 + 1y + 3

e)

None of these

50.

(2x + 5y - z) + (-6x - 4y + 7z)

a)

-4x2 +6y2 + 6z2

b)

4x + y + 6z

c)

-4x2 - y2 + 6z2

d)

-4x + y + 6z

e)

None of these

51.
Add or Subtract to Simplify:
(4x2+ x) - (x2+ 2x)
a)
3x2 - x
b)
4x2 + 2x
c)
3x2 + 3x
d)
3x2 + 2x
52.
Add or Subtract to Simplify:
(x5 + x3) - (6x - x3 + 6x5)
a)
-5x5 + 2x3 - 6x
b)
7x5 - 6x
c)
-5x3 + 2x2 - 6x
d)
-5x5 - 6x
53.
Add or Subtract to Simplify:
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
a)
4b4 - 2b3 + 7
b)
5b4 - 2b3 + 4
c)
b4 - 2b3 + 7
d)
5b4 - 2b3 + 7
54.
6v(2v + 3) 
a)
12v+18
b)
15v2 + 8v
c)
12v2 + 18v
d)
12v2 + 18v2
55.
(2n + 2)(6n + 1)
a)
12n + 2
b)
12n2 + 2
c)
12n2 + 12n + 2
d)
12n2 + 14n + 2
56.
(x+10)(x-10)
a)
x2  - 100
b)
x2 + 100
c)
x2 + 20x - 100
d)
x2 -20x + 100
57.

(4x - 1)(5x−2)

a)

20x2 + 3x − 2

b)

20x2 − 11x + 5

c)

20x2 − 13x + 2

d)

20x2 − 3x − 2

58.
Simplify:
2x ( -2x -3)
a)
-4x - 3
b)
x2 - 3
c)
-4x2 - 6x
d)
-4x - 6
59.
(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
60.
a)
This is correct
b)
This is incorrect
61.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
a)
0
b)
2x-10
c)
-2x-10
d)
2x+10
62.
What is the proper way to write the answer for the following problem? 
a)
2x3-x2-25x-12
b)
2x4-x3-25x2-12x+0
63.

What is the remainder when you divide
(2x3−5x−7) by (x+2)\left(2x^3-5x-7\right)\ by\ \left(x+2\right)  ?

a)

-9

b)

11

c)

-13

d)

-1

64.

Solve using long division. (x2+2x − 63)÷(x+9)\left(x^2+2x\ -\ 63\right)\div\left(x+9\right)  

a)

x−7x-7  

b)

x2−7x^2-7  

c)

x+7x+7  

d)

x2+3x−54x^2+3x-54  

65.
Use 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
66.
Divide using synthetic division 
(2x³ + 4x² - 5) by (x + 3).
a)
2x² + 2x - 4  R(-12)
b)
2x² - 2x + 6  R(-23)
c)
2x² - 2x + 8  R(-20)
d)
2x² - 4x + 1  R0
67.
Factor the Trinomial:
x2 - 8x + 15
a)
(x + 5) ( x + 3)
b)
(x - 5) (x - 3)
c)
(x + 15) (x - 1)
d)
(x - 7) (x - 8)
68.
Factor
x2 + 12x + 36
a)
(x + 6)(x +6)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 6)(x - 6)
69.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
70.
Factor
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
71.
Factor
x2 -16x + 48
a)
(x - 12)(x - 4)
b)
(x + 6)(x - 8)
c)
(x + 12)(x - 4)
d)
(x -16)(x - 3)
72.
Factor by using GCF:
8n3 + 2n2
a)
2n2(4n-1)
b)
2n2(4n + 1)
c)
n2(8n+2)
d)
3n(4n+1)
73.
Factor by using GCF:
10x2 + 15x-5
a)
25(10x3+45x-15)
b)
5(2x3 + 3x2-x)
c)
x(10x3+15x-5)
d)
5(2x2+3x-1)
74.

36a2+24a36a^2+24a  

Factor:

a)

12a(3a+2)12a\left(3a+2\right)  

b)

a(36a+24)a\left(36a+24\right)  

c)

12(3a2+2a)12\left(3a^2+2a\right)  

d)

a2(36+24a)a^2\left(36+24a\right)  

75.

Factor:
81m+48mn81m+48mn  

a)

3m(27+16n)3m\left(27+16n\right)  

b)

m(81+48n)m\left(81+48n\right)  

c)

3(27+16n)3\left(27+16n\right)  

d)

mn(81+48n)mn\left(81+48n\right)  

76.

x2 - 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Unfactorable

77.

x4 - 16

a)

( 2x - 4) ( 2x + 4)

b)

( x2 - 4) ( x2 + 4)

c)

( x2 - 8) ( x2 + 8)

d)

( x - 4) ( x + 4)

78.

x2 + 81

HINT: Look at the sign.

a)

Unfactorable

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

79.

9x2 - 49y6

a)

( 3x + 7y3) (3x + 7y3)

b)

( 3x - 7y3) (3x + 7y3)

c)

( 3x - 7y3) (3x - 7y3)

d)

Unfactorable

80.

Factor completely.

x2 - 144

a)

( x - 12 ) 2

b)

( x - 12 ) ( x - 12 )

c)

( x + 12 ) ( x + 12 )

d)

( x + 12 ) ( x - 12 )

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