Free Printable Benchmark 3 Review

1.

What equation would show the total number of characters (t) typed by Gabriel in (s) seconds?

a)

t = 10s

b)

t = 12s

c)

60 characters

d)

50 characters

2.

a)

The graph representing the cost of x square feet for a new home in St. Louis is steeper, so it must have a greater slope.

b)

The cost for a square foot in a new home in St. Louis is less than the cost for a square foot in a new home in Tupelo.

c)

The cost for a square foot in a new home in Tupelo is the same as the cost for a square foot in a new home in St. Louis.

d)

The graph representing the cost of x square feet for a new home in Tupelo is steeper, so it must have a greater slope.

3.

a)

A

b)

B

c)

C

d)

D

e)

E

4.

a)

A

b)

B

c)

C

d)

D

e)

E

5.

Based on the graph, which of the following statements area true? Select all that apply.

a)

A.

The line representing the cost of apples has a smaller slope than the line representing the cost of bananas.

b)

B.

The line representing the cost of apples has the same slope as the line representing the cost of bananas.

c)

C.

Do not choose this answer

d)

D.

The cost of a pound of bananas is more than the cost of a pound of apples.

e)

E.

The cost of a pound of bananas is equal to the cost of a pound of apples

6.

Make sure to select an answer for each column.

a)

A

b)

B

c)

C

d)

D

e)

E

7.

Find the slope of the line.

(a)

8.

Which representations have the same slope?

a)

b)

$y=\frac{1}{2}x+5$

c)

$\left(-2,4\right),\ \left(2,6\right)$

d)

9.

Which is the correct graph for the equation?

y=2x+5

a)

b)

c)

d)

10.

Which is the correct graph for the equation?

y=-x+1

a)

b)

c)

d)

11.

Which is the correct graph for the equation?

y=-\frac{3}{4}x-4

a)

b)

c)

d)

12.

Avery, the daring skateboarder, is planning a dramatic entrance at the local skate park. She wants to build a ramp that will launch her into the air with a slope of 3, starting right from the ground. What equation will describe the path of this thrilling ramp?

a)

$y = 3x + 3$

b)

$y = 3x$

c)

$y = x + 3$

d)

$y = 3$

13.

In the bustling city of Mathville, Priya and Oliver, two daring skateboard enthusiasts, are on a mission to design the most thrilling ramp for their local skateboard park. With a slope as steep as 2, their ramp begins its journey 4 feet below the ground level. What equation will represent this adventurous ramp?

a)

$y = 2x - 4$

b)

$y = 2x + 4$

c)

$y = -2x + 4$

d)

$y = 2x$

14.

The slope represents the which of the following ratios?

a)

$m=\frac{\Delta x}{\Delta y}$

b)

$m=\frac{\Delta y}{\Delta x}$

c)

$m=xy$

d)

$m=\Delta y$

15.

Which of the following is the slope formula?

a)

$m=\frac{y_1-x_1}{y_2-x_2}$

b)

$m=\frac{y_2-y_1}{x_2-x_1}$

c)

$m=\frac{x_2-x_1}{y_2-y_1}$

d)

$m=\frac{y_2-x_2}{y_1-x_1}$

16.

-2q + -3 = -2q +8

a)

one solution

b)

no solution

c)

infinite solutions

17.

8p - 1 = 1 + 8p

a)

one solution

b)

no solution

c)

infinite solution

18.

-4n = -7n + 3n

a)

one solution

b)

no solution

c)

infinite solution

19.

You are looking at getting a gym membership. Anytime Fitness charges $20 a month and $4 each visit. Planet Fitness charges $30 a month and $2 each visit. How many visits would it take in one month for both gym memberships to be the same total price?

a)

5 visits

b)

4 visits

c)

6 visits

d)

There is no way it would ever be the same.

20.

Which of the following equations has exactly one solution?

a)

$2x + 3 = 2x + 3$

b)

$x + 5 = 10$

c)

$3x - 3 = 3x + 1$

d)

$4x + 2 = 4x + 2$

21.

−4x − 2y = −12
4x + 8y = −24

a)

(6, -6)

b)

(-6, 6)

c)

(-10, 2)

d)

(2, -10)

22.

x − y = 11
2x + y = 19

a)

(-1, 10)

b)

(30, 19)

c)

(19, 30)

d)

(10, -1)

23.

5x + y = 9
10x − 7y = −18

a)

(4, -11)

b)

(1, 4)

c)

(-1, 14)

d)

(-4, 29)

24.

The √20 is between which two integers?

a)

2 & 3

b)

3 & 4

c)

4 & 5

d)

5 & 6

25.

Which of the following is a perfect square?

a)

24

b)

48

c)

81

d)

110

26.

Order 3π, √ 10 , and 3.25 from greatest to least.

a)

√ 10, 3π, 3.25

b)

√ 10, 3.25, 3π

c)

3π, 3.25, √ 10

d)

3.25, √ 10, 3π

27.

Which represents a rational number?

a)

√110

b)

√324

c)

√65

d)

√80

28.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

29.

Which of the following is rational?

a)

.211232112421125. . . .

b)

π

c)

√25

d)

√12

30.

What is a rational number ?

a)

A rational number is a number that cannot be written as a fraction.

b)

A rational number is a number that can be written as a ratio.

c)

A rational number cannot be a repeating decimal.

d)

A rational number is a never ending never repeating decimal.

31.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

32.

Using exponents, simplify the following expression:

(f^-6)(f¹⁰)

a)

f¹⁶

b)

f⁴

c)

1/f⁴

d)

1/f¹⁶

33.

Rewrite using positive exponents

a)

2⁴

b)

1/2⁴

c)

4²

d)

1/4²

34.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

35.

Which expression is equivalent to the given?

a)

b)

c)

d)

36.

Simplify:

$\frac{3^4\cdot3^5}{3^6}$

a)

$3^{15}$

b)

$3^3$

c)

$\frac{1}{3^3}$

d)

$3^{-3}$

37.

How is Quadrilateral EFGH translated to E'F'G'H'?

a)

6 down

b)

6 down, 1 right

c)

6 down, 3 left

d)

8 down, 1 right

38.

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

a)

A translation 6 units up then a reflection across the y-axis

b)

A Rotation 90 degrees counter-clockwise then a reflection across the x-axis

c)

A Reflection across the x axis then a rotation 90 degrees counterclockwise

d)

A reflection across the y-axis then a rotation 180 degrees

39.

How many degrees was the figure rotated?

a)

90 degrees counterclockwise

b)

180 degrees

c)

270 counterclockwise

40.

Polygon ABCD ≅ polygon PQRS. What is the value of x?

a)

48

b)

49

c)

52

d)

100

41.

If ∆LMK ≅ ∆LMT, then
∠K ≅ ____

a)

T

b)

∠T

c)

∠M

d)

∠L

42.

If ∆LMK ≅ ∆LMT, then
MK= ____

a)

LM

b)

K

c)

MT

d)

LT

43.

A point $A(3, 4)$ is dilated by a scale factor of 2 with the center of dilation at the origin. What are the coordinates of the image of point $A$ after the dilation?

a)

$(6, 8)$

b)

$(1.5, 2)$

c)

$(3, 8)$

d)

$(6, 4)$

44.

A triangle has vertices at $A(1, 2)$ , $B(3, 4)$ , and $C(5, 6)$ . If the triangle is translated by the vector $(2, -1)$ , what are the new coordinates of vertex $B$ ?

a)

$(5, 3)$

b)

$(1, 3)$

c)

$(3, 5)$

d)

$(5, 4)$

45.

A square with vertices at $P(0, 0)$ , $Q(0, 2)$ , $R(2, 2)$ , and $S(2, 0)$ is rotated $90^\circ$ counterclockwise about the origin. What are the new coordinates of vertex $R$ ?

a)

$(-2, 2)$

b)

$(2, 0)$

c)

$(0, 2)$

d)

$(-2, 0)$

46.

What is the rule for the dilation pictured?

a)

(x, y) → (½x, ½y)

b)

(x, y) → (x + 2, y + 2)

c)

(x, y) → (2x, 2y)

d)

(x, y) → (2x, 3y)

47.

Two objects that are the same shape but not the same size are _______.

a)

Congruent

b)

Vertical

c)

Similar

d)

Complementary

48.

Suppose a rectangle undergoes a reflection across the x-axis and a translation 5 units down. Which of the statements is true?

a)

The resulting rectangle will be congruent to the original rectangle regardless of the order of the rotation and the translation.

b)

The resulting rectangle will be congruent to the original rectangle only if the rotation occurs before the translation.

c)

The resulting rectangle will be congruent to the original rectangle only if the translation occurs before the rotation.

d)

The resulting rectangle will not be congruent to the original rectangle regardless of the order of the rotation and the translation.

49.

$\angle1\ and\ \angle8$ are what type of angles?

a)

corresponding angles

b)

adjacent angles

c)

alternate interior angles

d)

alternate exterior angles

50.

$\angle7\ and\ \angle8$ are _______ angles

a)

opposite

b)

adajacent

c)

vertical

d)

alternate

51.

$\angle5\ and\ \angle6$ are ______ angles

a)

opposite

b)

adjacent

c)

vertical

d)

congruent

e)

supplementary

52.

$\angle7\ and\ \angle8$ are _______ angles

a)

opposite

b)

adajacent

c)

vertical

d)

alternate

53.

Lines s and t are parallel and are intersected by transversal u.

What is the value of x?

a)

6

b)

8

c)

15

d)

22

54.

What is the measure of angle M? Numerical answer only, no words, spaces or other symbol.

(a)

55.

Durham and Chapel Hill are 14 miles apart. Chapel Hill and Raleigh are 28 miles part. Raleigh and Durham are 25 miles part. Do these three cities form a right triangle?

a)

Yes they form a right triangle

b)

No they do not form a right triangle

56.

Zoe is walking to Peter’s house. Zoe walks 4 blocks north to school to find her missing water bottle. She then walks 3 blocks west to Peter’s house. On the way home, Zoe walks straight home from Peter’s house. How many blocks shorter was Zoe’s walk home?

a)

5

b)

4

c)

2

d)

7

57.

Solve for x.

$\frac{x}{4}-5=3$

a)

x = -2

b)

x = 8

c)

x = 32

d)

x = 24

58.

What is the value of a in the formula, $a^2 + b^2 = c^2$ ?

a)

$a=\sqrt{c^2-b^2}$

b)

$a=\sqrt{c^2+b^2}$

c)

$a=c^2+b^2$

d)

$a=c^2-b^2$

59.

Which are NOT the dimensions of a right triangle?

a)

3in, 4in, 5in

b)

7in, 10in, 16in

c)

11in, 60in, 61in

d)

12in, 35in, 37in

60.

Which of the following are NOT measures of the sides of a right triangle?

a)

3cm, 4cm, 5cm

b)

5cm, 12cm, 13cm

c)

8cm, 15cm, 17cm

d)

10cm, 24cm, 35cm

61.

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

62.

To get from one side of the pond to the other you must walk 34 meters south and 41 meters east. To the nearest meter, how many less meters would it take if it were possible to go directly across the pond.

a)

53

b)

22

c)

75

d)

9

63.

a)

A

b)

B

c)

C

d)

D

64.

Find the distance.

a)

7.1

b)

7.8

c)

8.7

d)

8.9

65.

What is the distance between (-5, 3) and (4, -5)

a)

Square root of -145

b)

Square root of 145

c)

145

d)

-145

66.

Find the volume

a)

40π m³

b)

160π m³

c)

400π m³

d)

100π m³

67.

A funnel in the shape of a cone is used to hold water in the town of Hicksville, KY. The height of the cone tower is 12m with a diameter of 6m, what is the volume?

a)

108π m³

b)

144π m³

c)

36π m³

d)

432π m³

68.

A globe in a brass stand has an approximate volume of 33,510.32 in³, what is its radius length?

a)

10 in.

b)

15 in.

c)

40 in.

d)

20 in.

69.

Find the volume.

a)

255π cm³

b)

240π cm³

c)

15π cm³

d)

200 cm³

Benchmark 3 Review

Total questions: 69

Worksheet time: 2hrs 20mins

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