Free Printable 8th Grade WIN Q.3

Worksheets

8th Grade WIN Q.3

Total questions: 140

Worksheet time: 6hrs 51mins

Name

Class

Date

Graph the equation y=-1/2x+4

Write the equation of the graph.

$y=2x+3$

$y=-2x-3$

$y=\frac{1}{2}x+3$

$y=-\frac{1}{2}x-3$

Which pizzeria makes more money?

Pizzeria W

Pizzeria L

They both make the same amount

The graph and the equation represent the speed of two dogs. Milo's speed can be modeled by the equation y=6.5x

Which dog is faster?

Milo

Sawyer

Mika

Nala

Triangles ABC and DEF are similar. The slope of triangle ABC is...

EQUAL TO the slope of triangle DEF.

LESS THAN the slope of triangle DEF.

GREATER THAN the slope of triangle DEF.

What is the meaning of the slope?

The cost to get into the fair is $5

The total cost for the day will increase by $1.75 for every ride you go on.

The cost to get into the fair is $1.75

The total cost for the day will increase by $5 for every ride you go on.

What does the slope mean in the context of the problem?

The cost will increase by $1.40 per topping

The cost will decrease by $1.40 per topping

The cost will increase by $1.90 per topping

The cost will decrease by $1.90 per topping

The graph represents the height of a burning candle. What is the meaning of the slope?

the time it takes to burn the entire candle

the change in the height of the candle each hour it is burning

the different heights of the candle

the original height of the candle

Which of the following angles would NOT be congruent to the measure of $\angle7$ ?

$\angle2$

$\angle3$

$\angle6$

$\angle8$

10.

If the $m\angle7\ =\ 115\degree,$ find the measure of $\angle2.$

$115\degree$

$65\degree$

$180\degree$

Cannot be determined

11.

$\angle1$ and $\angle2$ are ___.

Alternate Interior Angles

Alternate Exterior Angles

Same-side Interior Angles

Corresponding Angles

None of these

12.

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______.

45°

90°

180°

360°

13.

Find the measure of the missing angle.

90^o

10⁰

130^o

50^o

14.

Which triangles are similar to triangle A?

Both

None

15.

Identify the transformation from ABCD to A'B'C'D'.

Translation

Reflection across the y-axis

Reflection across the x-axis

90^o counter clockwise Rotation

16.

Triangle B is rotated 90° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

17.

Describe the transformation shown in the graph.

Reflect over x-axis

Reflect over y-axis

Rotate 270 degrees CCW

Rotate 90 degress CCW

18.

What sequence of transformations will map trapezoid A to its image A'?

Reflection, then translation

Rotation, then translation

Reflection, then rotation

Rotation, then dilation

19.

Which of the statements is true about the graphed triangles?

They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 2.

They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 2.

They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

20.

Identify the sequences of transformations from the red image to the blue image to the green image.

translation then translation

rotation then reflection

rotation then rotation

reflection then translation

21.

Which figure can be transformed into figure L by a 90° rotation clockwise about the origin followed by a translation 2 units down?

Figure J

Figure M

Figure N

Figure P

22.

Enlargement or reduction? Find the scale factor!

It's an enlargement; the scale factor is 3.

It's a reduction; the scale factor is 1/3.

It's a reduction; the scale factor is 1/2.

It's an enlargement; the scale factor is 2.

23.

If a line segment with endpoints $(2, 3)$ and $(4, 5)$ is dilated by a scale factor of $2$ from the origin, what are the coordinates of the image of the endpoint $(4, 5)$ ?

$(8, 10)$

$(6, 7.5)$

$(4, 5)$

$(2, 2.5)$

24.

When talking about figures on a coordinate plane, what does "congruent" mean?

Same shape, same size

Same shape, size changes

Different shape, different size

Same shape, different size

25.

Tell whether the two figures are similar. Explain your reasoning.

Yes, similar because they are the same shape and side lengths are proportional.

No, not similar because they are the same shape, but side lengths are not proportional.

Yes, same shape

No, different sizes

26.

Line segment AB is reflected across the y-axis to form segment CD. Then, segment CD is rotated 180 degrees clockwise to form segment EF. Which statement is TRUE about this transformation?

Line segment EF is the same length as line segment AB.

Line segment EF is longer than line segment CD.

Line segment EF is shorter than line segment AB.

Line segment CD is shorter than line segment AB.

27.

What is NOT true for congruent triangles?

Corresponding angles are congruent

Corresponding sides are congruent

Same shape but different size

The sum of the angles is still 180 degrees

28.

What does congruent mean?

corresponding sides and angles are congruent

corresponding sides are proportional and corresponding angles are congruent

sames shape

neither sides or angles are congruent

29.

As it relates to geometry, what does it mean for figures to be similar?

corresponding sides are proportional and corresponding angles are congruent

corresponding sides and angles are congruent

angles are similar, and side lengths are the same, producing a figure that looks very close to another one.

neither sides or angles are congruent

30.

Use the congruence statement to answer the question.

31.

If two figures are similar, the corresponding sides are ______________.

equal

congruent

proportional

none of these

32.

What is the first step in solving this equation?

2x + 3 - 5x = 15x - 10

parentheses

combine like terms

add 10

move the 2x

33.

What is the first step you should take to solve this equation:

3\left(x-2\right)=2x+7

Add 2 to both sides

Use distributive property to get rid of the parentheses

Isolate the variable on one side

Subtract 7 from both sides

34.

Jacob solved the following equation using the steps shown.

Step 1 5x + 9 = 2x - 3

Step 2 3x + 9 = -3

Step 3 3x = -12

Step 4 x = -4

What operation did he perform to get from Step 1 to Step 2?

Subtracted 2x from both sides of the equation

Subtracted 9 from both sides of the equation

Multiplied both sides of the equation by 3

Added -3 to both sides of the equation

35.

What would be the best first step to solve this equation:

11-3x=44

Add 3 to both sides

Add 11 to both sides

Subtract 11 from both sides

Divide by 3 on both sides

36.

What would be the best next step in solving this equation:

1+4n=10-14n

Subtract 14n from both sides

Add 14n to both sides

Add 10 to both sides

37.

What is the definition of no solution?

no matter what constant is substituted in for the variable, the equation is ALWAYS true

no matter what constant is substituted in for the variable, the equation will NEVER be true

only this ONE solution will make the equation true

38.

What is the definition of one solution?

no matter what constant is substituted in for the variable, the equation is ALWAYS true

no matter what constant is substituted in for the variable, the equation will NEVER be true

only this ONE solution will make the equation true

39.

What is the definition of infinite solutions?

no matter what constant is substituted in for the variable, the equation is ALWAYS true

no matter what constant is substituted in for the variable, the equation will NEVER be true

only this ONE solution will make the equation true

40.

9y+8=9y-8

No Solution

One Solution

Infinite Solution

41.

What is the solution to the equations?

one solution

no solution

infinite solutions

none of these

42.

3(x-8)=3x-24

No Solution

One Solution

Infinite Solutions

43.

-10y-6 = -10y-6

No Solution

One Solution

Infinite Solutions

44.

Does the following equation have one solution, no solutions, or infinitely many solutions?

5x + 4 = 2x + 4

One

None

Infinite

This cannot be determined

45.

Does the following equation have one solution, no solutions, or infinitely many solutions?

4 - 3x = -3(x - 5) - 7

One

None

Infinite

This cannot be determined

46.

Ben ordered 20 total items consisting of pizza and sodas. A pizza is $10, a soda is $2, and he spent a total of $72. Which system models this scenario?

10P + 2S = 20
P + S = 72

P + S = 20
2P + 10S = 72

P + S = 20
10P + 2S = 72

47.

Uncle Freddy rented a total of 12 movies and games. A movie rents for $3 and a game rents for $4.50, for a total of $42. Which system models this scenario?

3M + 4.50G = 42
M + G = 12

3M + 4.50G = 12
M + G = 42

M + G = 12
4.50M + 3G = 42

48.

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. which would be the correct representation of the 2 variables?

t: # of tacos
m: # of glasses of milk

t: Cost of each taco
m: Cost of each glass of milk

t: total cost
m: # of food items

t: Cost of each glass of milk
m: Cost of each taco

49.

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. which system of equations represents this scenario?

1t + 1m = 2.10

2t + 3m = 5.15

1t + 1m = 5.15

2t + 3m = 2.10

1t + 1m = 2.10

1t + 3m = 5.15

2t + 1m = 2.10

t + m = 5.15

50.

A gym charges a one-time registration fee as well as a monthly fee. The cost of joining the gym for 4 months is $370, and the cost of joining for 6 months is $530. Write a system of equations to find the registration fee and monthly fee. m= months; r = registration fee.

r - 4m = 370
r - 6m = 530

r + 4m = 370
r + 6m = 530

m + 4r = 370
m + 6r = 530

m - 4r = 370
m - 6r = 530

51.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

3x + 2y = 315
2x + 4y = 450

3x + 2y = 450
2x + 4y = 315

2x + 2y = 315
3x + 4y = 450

52.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

1.5x+0.5y=78.5
x+y=87

1.5x+0.5y=78.5
1.5x+0.5y=87

x+y=78.5
1.5x+0.5y=87

x+y=78.5
x+y=87

53.

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

1s + 3c = 38
2s + 3c = 52

3s + 1c = 38
3s + 2c = 52

s + c = 38
s + c = 52

3s + 3c = 38
1s + 2c = 52

54.

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

x + y = 1550
y = 4x

x + y = 1550
y = x + 4

y - x = 1550
y = 4x

y = 1550 + x
y = x + 4

55.

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

10c + 5d = 14.25
5c + 10d = 16.50

10c + 5d = 16.50
5c + 10d = 14.25

c + d = 10
5c + 10d = 16.50

c + d = 5
5c + 10d = 16.50

56.

Simplify the expression:
c⁴⋅c³=

^c12

c⁴⁺³

c⁷

57.

Simplify the expression: 3x²⋅x²=

3x²⁺²

3x⁴

58.

(2⁸)²

2¹⁶

2¹⁰

2⁶

2⁴

59.

Simplify 4^-2=

1/16

-16

1/4

-42

60.

x^-3

-x³

1 / x³

1 / x^-3

-x^-3

61.

Anything raised to a power of zero is always:

itself

negative

62.

8⁷ ⁄ 8²

8⁵

8⁹

8¹⁴

1⁵

63.

(2⁸)²

2¹⁶

2¹⁰

2⁶

2⁴

64.

m ⋅ m⁵⋅ m⁶

m³⁰

m¹²

12m

mm¹¹

65.

m⁴

m⁶

m¹⁰

1/m⁶

66.

What is another way to write 5³

3 x 3 x 3

3 x 3 x 3 x 3 x 3

5 + 5 + 5 + 5 + 5

5 x 5 x 5

67.

Solve $x^2=25$

-5

12.5

5,-5

12.5,-12.5

68.

Solve $x^3=64$

-4

4,-4

69.

Solve $x^3=-64$

-4

4,-4

70.

Solve $x^2=-100$

-50

No solution

-10

71.

solve $x^2=400$

200

100, 100

-20,20

72.

1/3

73.

To square a number, multiply it by ________.

itself

two

three

four

74.

The area of a square painting is 81 $cm^2$ . What is the length of one side?

-9

40.5

-40.5

75.

Solve for p when $p^2=100$

$\pm10$

$\pm1,000$

1,000

76.

A cube with side length s has a volume of 512 cubic units. What is the length of one side?

77.

A square poster has an area of 81 square inches. What is the length of each side of the square?

3 inches

9 inches

20.25 inches

40.5 inches

78.

This symbol is called

cube root

square root

checkmark

triple check

79.

solve this equation

$x^2=60$

$x\approx\pm\ 7.7$

undefined

x=30

$x\approx\pm\ 9.2$

80.

Solve this equation

s^3\ =\ 48

$s\approx3.6$

$s=24$

$s\approx6.9$

81.

Convert the following number to Standard Notation:

$2.5\times10^3$

2,500

25,000

2.500

0.0025

82.

Convert the following number to Standard Notation:

$4\times10^5$

0.40000

40,000

400,000

0.00004

83.

Write 0.00000707 in scientific notation.

7.07 x 10^-6

7.07 x 10⁶

707 x 10⁸

707 x 10^-8

84.

Write 7.8 x 10^-3in standard form.

0.0078

7,800

0.078

85.

Write 2.08 x 10²in standard form.

208

0.0208

20,800

0.208

86.

Which of the following is correct scientific notation?

20.35 x 10⁴

.2035 x 10⁴

2035⁴

2.035 x10⁴

87.

Change from standard form to scientific notation: 0.004078

4.078 x 10^-3

4.078 x 10³

40.78 x 10^-4

.4078 x 10^-2

88.

The factor multiplied by a power of 10 in scientific notation needs to be greater than or equal to one but less than ___________?

100

1,000

89.

How do you write
8.317 x 10⁶in standard form?

8, 371, 000

83, 170, 000

837, 100

8, 317, 000

90.

$3.46×10^2$

0.0346

3.46

24,600

346

91.

Is this written in scientific notation?

Yes, it is in scientific notation!

No, it's not in scientific notation.

92.

How would you write 0.0005 in scientific notation?

50 x 10⁵

5 x 10^-4

5 x 10³

.5 x 10³

93.

How do you write
1001
in scientific notation?

1.0001 x 10⁴

1.01 x 10⁵

1.001 x 10³

10.1 x 10³

94.

How would you write 4.3756 x 10⁴in standard form?

437,560,000

0.00043756

43,756

4,3756

95.

Convert to scientific notation:

520,000,000

52 x 10⁷

5.2 x 10^-7

5.2 x 10⁸

0.52 x 10⁹

96.

Add the scientific notation:

(6.2 x 10²) + (9.7 x 10⁰)

.6297 x 10²

6.297 x 10⁰

6.297 x 10³

6.297 x 10²

97.

Add with scientific notation.

(5.2 x 10⁷) + (3.01 x 10⁴)

5.20301 x 10¹¹

.520301 x 10⁷

5.20301 x 10⁷

5.20301 x 10⁸

98.

Subtract with scientific notation.

-3.936 x 10⁸

3.936 x 10⁸

3.936 x 10⁷

3.936 x ⁻²

99.

Divide the scientific notation:

(6.9 x 10⁷) / (2.3 x 10^-3)

3 x 10¹⁰

3 x 10⁴

3 x 10^-4

3 x 10^-11

100.

Divide the scientific notation:

5.2 x 10¹³ / 1.5 x 10⁷

3.9 x 10⁶

4 x 10²⁰

3.4 x 10⁶

3.9 x 10²⁰

101.

Multiply the scientific notation:

(9.4 x 10⁶)(3.2 x 10⁵)

30.08 x 10¹¹

3.8 x 10¹

3.008 x 10¹²

2.9375 x 10¹

102.

Multiply the scientific notation:

(9.6×10^-8)(2×10^-15)

1.92×10^-22

19.2×10^-23

1.92×10^-24

19.2×10^-25

103.

Is this mapping a function or not a function?

Function

Not a Function

104.

Is this set of ordered pairs a function or not a function?

Function

Not a Function

105.

Is this graph a function or not a function?

Function

Not a Function

106.

Which graph does NOT pass the vertical line test?

Graph 1

Graph 2

Graph 3

Graph 4

107.

Which set of values is a function?

(9,5) (10,5) (9,-5) (10,-5)

(3,4) (4,-3) (7,4) (3, 8)

(6,-5) (7, -3) (8, -1) (9, 1)

(2, -2) (5, 9) (5, -7) (1, 4)

108.

Function

Not a Function

109.

Is the relation a function? Why.

Yes, because the x-value 11 has two y-values pair with it.

Yes, because each x-value has only one y-value paired with it.

No, because the x-value 11 has two y-values pair with it.

No, because each x-value has only one y-value paired with it.

110.

Which linear function has the greatest initial value?

Function A

Function B

Function C

I don't have a clue

111.

Which linear function has the greatest rate of change?

Function A

Function B

Function C

I don't have a clue

112.

Is the graph pictured a linear or nonlinear function?

Linear

Nonlinear

113.

Is the equation linear or nonlinear?

Linear

Nonlinear

114.

Is the table linear or nonlinear?

Linear

Nonlinear

115.

Determine if the graph is linear or nonlinear.

Linear

Nonlinear

116.

Nancy can type 50 words per minute. Look at the table below to write an equation that matches the data.

m=50 + w

w= 50m

w= 50 + m

m= 50 - w

117.

What is the algebraic equation for this table?

y = x + 3

y = 3x

y = x ÷ 3

y = x - 3

118.

Write the equation that created this table.

y = 3x - 9

y = 3x + 3

y = -3x + 3

y = 6x + 5

119.

Write a linear equation in the form of y=mx+b

y = 2x + 3

y = -2x + 3

y = 2x -3

y = 3x - 4

120.

The graph shows the speed of Mr. Sam driving to work. Which section shows Mr. Sam driving on the interstate?

a. - his rate of change is the steepest

b. - he's going the fastest here

g. - steep rate of change and not for a long time

d. - shortest amount of time

f. - he's going fast here

121.

The graph shows Mrs. Smith's distance from home as she drives to work. Which section of graph and description match?

Section A: Mrs. Smith leaves home, first driving slowly and then speeding up.

Section B: Mrs. Smith continues driving at a constant speed.

Section C: Mrs. Smith forgot her lunch and had to return home to get it.

Section D: Mrs. Smith drives to work, making a stop along the way.

122.

Choose the the graph that best depicts a man taking a ride on a ferris wheel.

123.

A train increases it's speed. It then travels at a constant speed.

A train decreases it speed. It then travels at a constant speed.

A train is going a constant speed. It then decreases it speed until it stops.

124.

The graph shows the speed of Mr. Sam driving to work. Which section shows Mr. Sam stopped in traffic?

125.

The graph shows Timmy's distance he is as he leaves school one afternoon. What happens in section D?

Timmy is walking back to school because he forgot his math book.

Timmy is talking to a friend and not walking.

Timmy is walking all the way home.

Timmy is dancing in the street.

126.

Level 2

Solve for the value of y

127.

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

65 miles

89 miles

45.4 miles

We don't have enough information.

128.

Is this a right triangle?

Yes

129.

The Pythagorean Theorem ONLY works on which triangle?

obtuse

scalene

isosceles

right

130.

What is the measurement of the missing side length?

131.

A triangle has a leg that's 7 units long and a hypotenuse that's 18 units long. What is the measurement of the missing side?

16.6

15.4

17.9

14.6

132.

_{^{Find the missing side}}

17.66

312

133.

Find the distance between these 2 points.

5.8

6.3

8.1

134.

Find the distance.

9.7

10.7

11.7

12.7

135.

What is the distance between the two points?

6.3

6.5

6.7

136.

What is the distance between the two points?

4.5 units

5.1 units

3.2 units

6.4 units

137.

Find the length of the red line AD...

Round your answer to 1 decimal place

5.8 cm

5.9 cm

4.0 cm

4.1 cm

138.

Find the length of BH in the shape pictured below, giving your answer to 3 significant figures.

(a)

139.

What is the approximate length of the blue segment?

8.367

3.741

140.

Doug and his dog Burt are deciding which way they will walk to a friend's house. How much longer is their walk if they take the blue path (L shape) than if they take the pink path (straight path)?

8.06 blocks

11 blocks

19.06 blocks

2.94 blocks

100 %

8th Grade WIN Q.3

Total questions: 140

Worksheet time: 6hrs 51mins

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