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Worksheets

Math 8 Examination

Total questions: 155

Worksheet time: 9hrs 32mins

Name
Class
Date
1.

(y-y) = m( x-x)         Which form is the following equation in?

a)

Slope -Intercept Form

b)

Standard Form

c)

Point-Slope Form

d)

Double Intercept Form

2.

y= mx+b Which form is the following equation?

a)

Double Intercept Form

b)

Slope Intercept form

c)

Point-slope form

d)

Standard form

3.

ax + by = c Which form is the following equation?

a)

Standard Form

b)

Double Intercept Form

c)

Slope-intercept Form

d)

Point-Slope Form

4.

xa+ yb= c\frac{x}{a}+\ \frac{y}{b}=\ c  This equation is called?

a)

Standard Form

b)

Double Intercept Form

c)

Slope-Intercept Form

d)

Point-Slope Form

5.

In the equations y = mx + b, m stands for _____, b stands for______

a)

m = x-intercept, b = y intercept

b)

m = slope, b = x-intercept

c)

m = slope, b = y- intercept

d)

m = y -intercept, b = slope

6.

A slope of 2 will be steeper than a slope of 1/2.

a)

True, with a slope of 2 you go up 2 and over 1 and with a slope of 1/2 you go up 1 and over 2.

b)

True, with 2 you go across 2 and up 1and with 1/2 you go across 1 and up 2.

c)

False, with a slope of 2 you go up 2 and over 1 and with a slope of 1/2 you go up 1 and over 2.

d)

False, with 2 you go across 2 and up 1 and with 1/2 you go across 1 and up 2.

7.
Find the slope of the line that passes through
(10, 1) and (5, 2)
a)
1/5
b)
-1/5
c)
5
d)
-5
8.
Find the slope of the line.
a)
Undefined
b)
0
c)
1
d)
-1
9.
Find the slope of the line.
a)
-5/4
b)
5/4
c)
-4/5
d)
4/5
10.
Find the slope of the line.
a)
Undefined
b)
0
c)
1
d)
-1
11.
Find the slope from the table:
a)
-2/5
b)
5/-2
c)
5/2
d)
2/5
12.
Find the slope of the line that passes through the points (2, 4) and (6, 12)
a)
1/2
b)
-1/2
c)
2
d)
-2
13.
Find the slope of the line.
a)
-2
b)
2
c)
-1
d)
1
14.
Which of the following are ways to find the rate of change?
a)
change in y over change in x
b)
rise over run
c)
subtract y coordinates over subtract x coordinates
d)
all of the above
15.
What is the slope of the line y=2x-1
a)
1
b)
2
c)
-1
d)
-2
16.

How would you know if an ordered pairn or a point is a solution to the system of linear equations?

a)

It makes one equation true.

b)

The ordered pair(x, y) satisfies both equations.

c)

It makes both equations false.

d)

It makes one equation true, and the other false.

17.

If a system of linear equations has one solution, what does this mean about the two lines? 

a)

Coincident Lines

b)

Parallel lines

c)

Intersecting Lines

18.

What is the solution of graph shown?

(a)  

19.

How many solutions does the system have?

a)

one solution

b)

no solution

c)

infinitely many solutions

20.

How many solutions does the sytem have?

a)

one solution

b)

no solution

c)

infinitely many solutions

21.

Which of the following system of linear equations is consistent and independent?

a)

3x + y =4

x - y =8

b)

2x + y = -4

y =-2x -5

c)

x+y =6

2x + 2y = 12

d)

3x - 4y =6

6x -8y =5

22.

What type of system of linear equation does 2x −3y = 4 and  4x −6y =02x\ -3y\ =\ 4\ and\ \ 4x\ -6y\ =0  represent?

a)

consitent and independent

b)

inconsistent

c)

consitent and dependent

23.

What type of system of linear equation does 3x − 6y =8 and x +2y =−33x\ -\ 6y\ =8\ and\ x\ +2y\ =-3  represent?

a)

consistent and independent

b)

inconsistent

c)

consistent and dependent

24.

Which of the following systems of linear equations is dependent?

a)

x + y = 7

2y = 14 - 2x

b)

3x + 2y =0

x -2y =5

c)

x = 6

2x -3y = 24

d)

y = 3x + 5

6x - 2y = 8

25.

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

a)

Coincident Lines

b)

Parallel lines

c)

Intersecting Lines

26.
The solution to a system of equations is any ordered pair that makes both equations true. 
a)
TRUE
b)
FALSE
27.
What is the solution? 
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
28.
This system has _____ solutions
a)
0
b)
1
c)
2
d)
Infinitely many
29.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
30.

What variable do you eliminate, and what do you multiply the equation(s) by?

5x + y = 9

10x − 7y = −18

a)

You eliminate x, and multiply the top equation by 11

b)

You eliminate y, and multiply the top equation by 7

31.
Solve the system given:
3x - y = 7
2x + y = 3
a)
(-1,2)
b)
(5,4)
c)
(4,5)
d)
(2,-1)
32.
If the solution is infinitely many the lines will ________?
a)
intersect at exactly one point
b)
be parallel
c)
overlap each other
d)
never exist
33.

Solve the following system using any method.

3x + 2y = 16

7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

34.

Solve the following system using any method.

y = 2x + 1

y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

35.
Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 
a)
y = 9.65 + x
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
36.

Mrs. Fox invested $7500. Part of her money went into a 6% investment and the rest went into an 8% investment. Find the amount she invested at 8% if the total yearly income is $590.

(a)  

37.

Mr. Hawgood invested a sum of money. Half his money went into a 5% bond, a third of his money went into a 6% bond, and the rest went into a 3% bond. His total annual income was $300. How much did he invest in all?

(a)  

38.

Mr. Ellison invested a sum of money at 6%. He invested $200 more than this sum at 4%. If the annual incomes from both investments were the same, how much did he invest in the 4% account?

(a)  

39.

Mrs. Lamm invested $7500 in two businesses. The first business made a 5% profit, and the other had a 2% loss. Her net profit for the year was $130. Find the amount invested in the 2% account.

(a)  

40.

Mr. Fullwood invested $6000, part at 8% and the rest at 7%. The income from the 8% investment exceeded twice the income from the 7% investment by $40. How much did he invest at 8%?

(a)  

41.

What is the solution to the system of equations?

y = 3x - 8

y = 4 - x

a)

(3, 1)

b)

(1, 3)

c)

(-3, 1)

d)

(3, -1)

42.
Solve:
x = -3y - 17
2x + 3y = -7
a)
(1, -20)
b)
(3, 0)
c)
(-5, -2)
d)
(10 , -9)
43.
Solve the system of equations using substitution:
-4x + 4y = 8
y = -2x - 10
a)
(-4, -2)
b)
(12, -34)
c)
(4, -18)
d)
(-2, -6)
44.

Solve using Elimination method.


-3x - 9y = 15

x +3y = - 5

a)

Infinitely Many Solutions

b)

No Solution

c)

(0,0)

d)

(15,0)

e)

(3,9)

45.
Solve the system:
x + 6y = 17
x - 3y = 8
a)
(5, 2)
b)
(11, 1)
c)
(1, 11)
d)
no solution
46.
What is the correct equation in 
Slope-Intercept Form?
(y = mx +b)
a)
y = 1/3x - 1
b)
y = 1/4x -1
c)
y = -1/3x +1
d)
y = -1/4x + 1 
47.
What is the correct equation in 
Slope-Intercept Form?
(y = mx +b)
a)
y = x
b)
y = x + 1
c)
y = -x 
d)
y = -x + 1
48.
What is the correct equation in 
Slope-Intercept Form?
(y = mx +b)
a)
y = 3x - 3
b)
y = 3x - 1
c)
y = -3x - 3
d)
y = -3x - 1 
49.
What is the correct equation in 
Slope-Intercept Form?
(y = mx +b)
a)
x = 4
b)
y = 4 
50.
What is the correct equation?
a)
x = 5
b)
y = 5
c)
x = - 5
d)
y = -5 
51.
What is the correct equation in
Slope-Intercept Form?
(y = mx +b)
a)
y = -1/3x + 3
b)
y = 1/3x - 3
c)
y = -1/3x - 3
d)
y = 1/3x + 3 
52.

Bob has $150 in his savings account and saves $40 per month.

a)

y=150 + 40

b)

y=40x + 150

c)

y=150x + 40

53.
 In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.
a)
y = 20x + 5
b)
y = 5x +20
54.
Bob has $150 in his savings account and saves $40 per month.  Which equation represents the amount Bob has in his account after x months?
a)
y = 150 + 40
b)
y = 40x + 150
c)
y = 150x + 40
55.

A T-shirt design company charges your team a startup fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.

a)

The additional fee of $8.

b)

The starting fee of $25.

c)

The additional fee of $25.

d)

The starting fee of $8.

56.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
57.
Make this negative exponent positive.
9-3
a)
93
b)
1/9-3
c)
1/93
d)
729
58.
According to exponent rules, when we multiply the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
59.
According to exponent rules, when we divide the same base we _______ the exponents.
a)
Multiply
b)
Add
c)
Divide
d)
Subtract
60.
How do you write
5⋅5⋅5⋅5⋅5⋅5⋅5
with an exponent?
a)
57
b)
56
c)
75
d)
5
61.
Simplify:
b2 ⋅ b4
a)
b8
b)
b6
c)
b2
d)
2b6
62.
Simplify:
(x5)4
a)
x9
b)
x20
c)
x
d)
x54
63.
(x3y)6
a)
2x18y6
b)
x18y6
c)
x3y6
d)
x3y6
64.
Simplify (-1/2)0
a)
1
b)
0
c)
-1
d)
-2
65.
Simplify the following expression: 
xy-7
a)
xy7
b)
x/y7
c)
x7/y
d)
x7y
66.
According to exponent rules, when we raise the power to a power we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
67.
n²⋅n⁴⋅n⁵
a)
n¹¹
b)
n⁴⁰
c)
n¹³
d)
n²²
68.
Multiply
a)
100
b)
101
c)
10-2
d)
1/100
69.
a)
6-2
b)
1/62
c)
1/36
d)
All of the above
70.
a)
49
b)
444
c)
421
d)
415
71.
a)
0
b)
3
c)
1
d)
-1
72.
a)
w
b)
w-1= 1/w
c)
-w
d)
w17
73.
a)
a7
b)
a10
c)
a3
d)
a-3
74.
a)
2560
b)
2517
c)
560
d)
517
75.
a)
1
b)
60
c)
36/36
d)
all of the above
76.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

13xyz

b)

13x2y2z2

77.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

-18x2y2z2

b)

-2x2y2z2

78.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

-11a2b2c

b)

-5a2b2c

79.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

-17x2y2z2

b)

-7x2y2z2

80.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

26mn

b)

26m2n2

81.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

12y5

b)

12y7

82.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

15xy4z2

b)

-8xy4z2

83.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

27m2n4

b)

27mn2

84.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

20x5

b)

-20x5

85.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

9p3q3

b)

9p2q

86.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

6a4

b)

6a5

87.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

12m5\frac{12}{m^5}

b)

12m512m^5

88.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

-8m4n3o2

b)

-8mno

89.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

-3r3s

b)

-3r3

90.

Perform the indicated operation on polynomials.

Choose your answer below.

a)

15x4yz3\frac{15x^4y^{ }}{z^3}

b)

15x4z3y\frac{15x^4z^3}{y}

91.

What is a Rectangular Coordinate System?

a)

It is a coordinate system that is used for naming points in a plane.

b)

It is a coordinate system that is used for graphing linear functions.

c)

It is a coordinate system that is used to determine the location of a point by using a single number.

d)

It is a coordinate system that is composed of two perpendicular number lines that meet at a point of origin.

92.

How many quadrants does a Rectangular Coordinate System have?

a)

2

b)

4

c)

6

d)

8

93.

Which among these mathematicians was the Cartesian Plane named after?

a)

Euclid

b)

Pythagoras

c)

Rene Descartes

d)

Blaise Pascal

94.

What do you call the vertical number line in the Cartesian plane?

a)

y-axis

b)

x-axis

c)

origin

d)

quadrant

95.

Rectangular Coordinates System is also called as _______.

a)

Origin

b)

Cartesian Plane

c)

Abscissa

d)

Ordinate

96.

For the coordinates of the point in quadrant IV, the x value and y value are always _____ and ______, respectively.

a)

negative, positive

b)

negative, negative

c)

positive, negative

d)

positive, positive

97.

What do you call the horizontal number line in the Cartesian plane?

a)

y-axis

b)

x-axis

c)

origin

d)

quadrant

98.

In the quadrant l, the values of x and y are always ____, and _____, respectively.

a)

positive, positive

b)

positive, negative

c)

Negative, negative

d)

Negative, positive

99.

The point of intersection of the the horizontal and vertical number lines is called _____.

a)

y-axis

b)

x-axis

c)

origin

d)

quadrant

100.

The point (9, −1) is an example of______.

a)

fractions

b)

numbers

c)

labels

d)

ordered pair

101.

Point (−7, −5) is located in which quadrant?

a)

I

b)

II

c)

III

d)

IV

102.

The coordinates for the origin in the coordinate plane are________?

a)

(0,1)

b)

(0,0)

c)

(1,1)

d)

(1,0)

103.

When plotting the point (−8,1), which describes the movement along the x-axis and y-axis in the correct order?

a)

8 units right then 1 unit up

b)

8 units down then 1 unit left

c)

8 units left then 1 unit up

d)

8 units up then 1 unit right

104.

Which of the following is true about point (5, 5)?

a)

It lies in x-axis

b)

It lies in y-axis

c)

It lies in Quadrant I

d)

It lies in Quadrant II

105.

In which quadrant is point A located?

a)

I

b)

II

c)

III

d)

IV

106.

Where is point F located?

a)

(7,-5)

b)

(7,5)

c)

(-7,5)

d)

(-7,-5)

107.

The point (-12,-10) is located in which quadrant?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

108.

Samantha is going to draw a rectangle on this grid. Give the co-ordinates of the fourth point on her rectangle.

a)

(-6, 4)

b)

(4, -6)

c)

(4, 6)

d)

(-4, -7)

109.

Point M is at (-5,4). How far is M from the x axis?

a)

4

b)

5

c)

-4

d)

-5

110.

Where is T?

a)

(3,2)

b)

(-3,2)

c)

(-2,-3)

d)

(-3, -2)

111.
What is the Domain?
a)
{-3, -1, 1, 3, 5, 7, 9}
b)
{-3, -2, -1, 0, 1, 2, 3}
c)
-3 ≤ x ≤ 3
d)
-3 ≤ x ≤ 9
112.
What is the Range?
a)
{-3, -1, 1, 3, 5, 7, 9}
b)
{-3, -2, -1, 0, 1, 2, 3}
c)
-3 ≤ x ≤ 3
d)
-3 ≤ x ≤ 9
113.
Does this table represent a function?
a)
Yes!
b)
No!
c)
I Don't Know
114.
Is this graph a function? (Vertical Line test)
a)
Yes
b)
No
c)
I Don't Know
115.
State the domain of the given relation:
a)
{2, 3, 7}
b)
{1, 4}
c)
{1, 2, 3, 4, 7}
116.
State the range of the given relation.
a)
{2, 3, 7}
b)
{1, 4}
c)
{1, 2, 3, 4, 7}
117.
Which graph does NOT pass the vertical line test?
a)
Graph 1
b)
Graph 2
c)
Graph 3
d)
Graph 4
118.

Which is the set of all y-values or the outputs?

a)

Domain

b)

Range

c)

Relation

d)

Function

119.

What is the domain of a relation?

a)

the set of all x-values

b)

the set of all y-values

120.
a)

{-2, 3, 7}

b)

[-2, 7]

c)

{1, 2, 3, 4}

d)

[1, 4]

121.
A relation is shown below:
{(2, 140), (5, 350), (14, 960)}
What is the domain of the relation?
a)
{2, 5, 14}
b)
{140, 350, 960}
c)
{all whole numbers from 2 to 14}
d)
{all whole numbers from 140 to 960}
122.

State the domain of the following relation:


{(1, 5), (3, 7), (6, 8), (8, 9), (3, 4)}

a)

{4, 5, 7, 8, 9}

b)

{1, 3, 6, 8}

c)

(1,5)

d)

{(1, 5), (3, 7), (6, 8), (8, 9), (3, 4)}

123.

Find the domain of the relation R = {(1, 2), (2, 3), (3, 4)}.

a)

{1, 3, 4}

b)

{2, 3, 4}

c)

{1, 2, 4}

d)

{1, 2, 3}

124.
What is the range of the table?
a)
{-4, 0, 1, 3}
b)
{-2, 0, 2, 3}
c)
{-4, -2, 0, 1, 2, 3}
d)
{ (0, 0), (2, -4), (3, 3), (-2, 1) }
125.

Which table represents y as a function of x?

a)

Table 1

b)

Table 2

126.

What is a Linear equation

a)

Equation with degree 1

b)

Equation with degree 3

c)

Equation with degree 7

d)

Equation with degree 2

127.

How many solutions does a Linear equation in two variable would have?

a)

Only one

b)

Two solutions

c)

Five solutions

d)

Infinity

128.

Which of these equation proves that x=5, y=18?

a)

3x-y=2

b)

y-x=0

c)

3y-5x=29

d)

2x-5y=18

129.

The solution of equation x - 2y = 4 is

a)

(0,2)

b)

(2,0)

c)

(4,0)

d)

(1,1)

130.

Find the value of a, if x=1, y=2 is a solution of 4x+8y=a

a)

a=0

b)

a=9

c)

a=16

d)

a=20

131.

The graph of x=3 is a line

a)

Parallel to the x-axis

b)

Parallel to y-axis

c)

Data not enough

132.

The general form of linear equation in two variable is

a)

ax+bx+c=0

b)

ax+by+c=1

c)

ax+bx+c=1

d)

ax+by+c=0

133.

Find the solution of 3x-6y=(-48)

a)

2,0

b)

5,3

c)

0,8

d)

2,3

134.

An equation of the type _____________ represents a line passing through the orign

a)

x = a

b)

y = mx

c)

y = a

d)

None of the above

135.

Find the solutions of x + 2y = 6
[ more than one option ]

a)

(2,2)

b)

(0,3)

c)

(5,4)

d)

(4,1)

e)

(3,2)

136.

Solve for x:

x − 5 = 7

a)

x = 2

b)

x = −2

c)

x = 12

d)

x = −7/5

137.

Solve for x:

5x = −35

a)

x = −40

b)

x = −7

c)

x = 7

d)

x = −30

138.

Solve:

-4x = 24

a)

20

b)

−20

c)

6

d)

−6

139.
Solve for x:
a)
x = 20
b)
x = 7
c)
x = 10
d)
x = 3
140.

Solve  43x=20\frac{4}{3}x=20  

a)

x = 15

b)

x =  26 2326\ \frac{2}{3}  

c)

x = 10

d)

x = 20

141.

Solve for x:

2x + 5 = 12

a)

7

b)

3

c)

7/2

d)

17/2

142.

Solve for x:

10 = 3x − 12

a)

22/3

b)

2/3

c)

10/9

d)

8

143.

Solve for x:

9x + 2 = 5

a)

1/3

b)

3

c)

3/7

d)

1

144.

Solve for x:

7 − 5x = 12

a)

1

b)

−6

c)

−1

d)

6

145.

Solve for x:

12 = 15x − 18

a)

1

b)

−2

c)

−1

d)

2

146.

Solve for v.

a)

60

b)

−3

c)

15

d)

3

147.

Solve the equation

a)

6

b)

−6

c)

2

d)

−2

148.

Solve for x:

6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

149.

Solve for x:

4x + 1 = 7x − 5

a)

−1

b)

2

c)

6/11

d)

8

150.

Solve for x:

2 − 4x = 3x − 12

a)

2

b)

−14

c)

10

d)

−2

151.

Solve for x:

7 + 11x = x + 12

a)

−1/2

b)

2

c)

−2

d)

1/2

152.

Solve for x:

5 + 3x = 8x − 15

a)

10

b)

4

c)

2

d)

20/11

153.

Solve for x:

15x + 40 = 5x − 10

a)

3

b)

−3

c)

−5

d)

5

154.

Solve for x:

2(3x + 4) + 2 = 4 + 3x

a)

2

b)

-2/3

c)

10

d)

-2

155.

4(x + 8) − 4 = 34 − 2x

a)

x = 1

b)

x = 2

c)

x = 3

d)

x = 4

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