Free Printable Benchmark Study Set (Gr8)

1.

Which of the following is rational?

a)

.211232112421125. . . .

b)

π

c)

√25

d)

√12

2.

Simplify the expression:
(a⁵)(a⁴)

a)

a²⁰

b)

a⁹

c)

a¹

3.

a)

7/50

b)

14/9

c)

7/45

d)

14/99

4.

Which number is a rational number ?

a)

1/4

b)

π

c)

√3

d)

∛25

5.

The √98 falls between what two numbers on a number line?

a)

10 and 11

b)

11 and 12

c)

9 and 10

d)

90 and 100

6.

How many times larger is 8 x 10⁹than 2 x 10³?

a)

6,000,000 times

b)

6,000 times

c)

4,000 times

d)

4,000,000 times

7.

Which of the following is correct scientific notation?

a)

20.35 x 10⁴

b)

.2035 x 10⁴

c)

2035⁴

d)

2.035 x10⁴

8.

Congruent geometric figures have the:

a)

Same size

b)

Sides Equal

c)

Same Size and Same Shape

d)

Angles Equal

9.

Is the picture being reflected in the y-axis or x-axis?

a)

y-axis

b)

x-axis

10.

What is the algebraic notation of a figure is Translated 9 units right and 3 units down?

a)

(x, y) --> (x - 9, y + 3)

b)

(x, y) --> (x + 9, y - 3)

c)

(x, y) --> (x + 3, y - 9)

d)

(x, y) --> (9x, 3y)

11.

Rotate the point (-3,-4) around the origin 180 degrees. State the image of the point.

a)

(-4,-3)

b)

(-4,3)

c)

(4,-3)

d)

(3,4)

12.

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

a)

A

b)

B

c)

C

d)

D

13.

Determine how to translate triangle A'B'C' to triangle ABC.

a)

(x+2, y-5)

b)

(x+2, y-9)

c)

(x-2, y-9)

14.

Find K' if the figure is reflected across the x-axis

a)

(4, 1))

b)

(-1, -4)

c)

(1, -4)

d)

(1, 4)

15.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

16.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

17.

a)

x¹²

b)

x^-12

c)

x²

d)

x^-2

18.

Write 7.113 x 10⁷ in standard form.

a)

71,130,00

b)

7,113,000

c)

0.0000007113

d)

7,113

19.

Write 0.00000707 in scientific notation.

a)

7.07 x 10^-6

b)

7.07 x 10⁶

c)

707 x 10⁸

d)

707 x 10^-8

20.

(2 x 10⁹)(4 x 10^-4)

a)

8 x 10¹³

b)

8 x 10³⁶

c)

8 x 10⁵

d)

8 x 10^-36

21.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

22.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

23.

Simplify
x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

24.

Which number is NOT a perfect square?

a)

196

b)

169

c)

121

d)

132

25.

(5x10¹⁰) x (3x10⁷)

a)

15x10¹⁷

b)

1.5x10¹⁷

c)

1.5x10¹⁸

d)

1.5x9¹⁷

26.

(5 x 10⁶)(5 x 10⁷)

a)

2.5 x 10¹²

b)

2.5 x 10¹⁴

c)

25 x 10¹²

d)

25 x 10¹³

27.

Solve:
(6 x 10⁶) / (2 x 10³)

a)

12 x 10³

b)

3 x 10⁹

c)

1.2 x 10⁴

d)

3 x 10³

28.

What kind of number is π ?

a)

rational

b)

irrational

c)

whole

d)

integer

29.

Which number is NOT an integer?

a)

0

b)

45

c)

-19

d)

12.3

30.

Choose all the numbers below that are irrational.

a)

$3\pi$

b)

$\sqrt{25}$

c)

$\sqrt{27}$

d)

$\frac{3}{4}$

e)

$7.82367653289...$

31.

Irrational numbers are numbers that cannot be made into:

a)

Pi

b)

Square Roots

c)

Fractions

d)

Non-terminating Decimals

32.

Choose all the numbers below that are perfect squares.

a)

4

b)

19

c)

36

d)

40

e)

100

33.

Which number below is irrational?

a)

$2\sqrt{7}$

b)

$2\sqrt{9}$

c)

$2\sqrt{25}$

d)

$2\sqrt{36}$

34.

What is the side length of a square that has an area of 36?

a)

9

b)

18

c)

6

d)

1296

35.

What is the side length of a square that has an area of 121?

a)

11

b)

60.5

c)

30.25

d)

14641

36.

Which of the following in NOT a perfect square?

a)

49

b)

81

c)

111

d)

144

37.

(-6)²

a)

12

b)

-12

c)

-36

d)

36

38.

A cube has the volume of 8in³. What are the side lengths?

a)

64in

b)

2in

c)

4in

d)

16in

39.

A cube has the volume of 343in³. What are the side lengths?

a)

7in

b)

6in

c)

8in

d)

13in

40.

$9^2=18$ True or false?

a)

True

b)

False

41.

$-\sqrt{144}$

a)

12

b)

-12

c)

-72

d)

no real number solutoin

42.

$\sqrt{-144}$

a)

12

b)

-12

c)

-72

d)

no real number solutoin

43.

Simplify:

$5\left(3\right)^2$

(a)

44.

Simplify:

$4\left(2\right)^3$

(a)

45.

$5^3$

(a)

46.

$3^3$

(a)

47.

What is the cube root of 27?

(a)

48.

What is the cube root of 8?

(a)

49.

Simplify: $-4^3$

(a)

50.

Simplify: $\left(-4\right)^3$

(a)

51.

$\sqrt{121}$

(a)

52.

$\sqrt{64}$

(a)

53.

$\sqrt{81}$

(a)

54.

$\sqrt{16}$

(a)

55.

Simplify: $\left(\sqrt[]{11}\right)^2$

(a)

56.

Simplify: $\left(\sqrt[]{59}\right)^2$

(a)

57.

Simplify: $\left(\sqrt[]{150}\right)^2$

(a)

58.

Simplify: $\left(\sqrt[3]{17}\right)^3$

(a)

59.

Simplify: $\left(\sqrt[3]{73}\right)^3$

(a)

60.

Does the transformation shown preserve congruence and/or orientation?

a)

Congruence yes, Orientation yes

b)

Congruence No, Orientation No

c)

Congruence No, Orientation yes

d)

Congruence Yes, Orientation No

61.

Which of the following are congruence transformations?

a)

Rotations

b)

Translations

c)

Reflections

d)

All Three

62.

If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be?

a)

(-5, 5)

b)

(-3, 5)

c)

(-5, 3)

d)

(-3, 3)

63.

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

a)

A

b)

B

c)

C

d)

D

64.

Rotate the point (7,8) around the origin 90 degrees counterclockwise.
State the image of the point.

a)

(-7,-8)

b)

(8,-7)

c)

(-8,7)

d)

(8,7)

65.

Rotate the point (-5,8) around the origin 270 degrees counterclockwise. State the image of the point.

a)

(-8,5)

b)

(8,-5)

c)

(8,5)

d)

(5,-8)

66.

Reflect the point: (10, 6) over the y-axis. (Try to remember the rule and not use a coordinate plane!)

a)

(-10, 6)

b)

(10, -6)

c)

(10, 6)

d)

(-10, -6)

67.

How is the blue triangle rotated to the red triangle?

a)

90 clockwise

b)

90 counter-clockwise

c)

180 clockwise

68.

State the line of reflection.

a)

Reflection across y-axis

b)

Reflection across x-axis

c)

Reflection across x = 1

d)

Reflection across y = 1

69.

Change from standard form to scientific notation: 12,000,000

a)

12.0 x 10⁷

b)

0.12 x 10⁷

c)

1.2 x 10⁶

d)

1.2 x 10⁷

70.

Write this number in standard form: 7.7 x 10⁹

a)

7,700,000,000

b)

7,700,000

c)

7,000,000.000

d)

70,000,000,000

Benchmark Study Set (Gr8)

Total questions: 70

Worksheet time: 5hrs 30mins

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