Free Printable 6th Grade Benchmark

1.

What is the greatest common Factor between 30 and 45?

a)

1

b)

15

c)

3

d)

5

2.

Find the GCF of each set of numbers.
50, 40

a)

5

b)

2

c)

10

d)

8

3.

Find the LCM of each set of numbers.
8, 12

a)

48

b)

24

c)

76

d)

96

4.

What is the LCM of 7 and 8?

a)

7

b)

8

c)

42

d)

56

5.

What is the least common multiple (LCM) of 4 and 10?

a)

4

b)

40

c)

15

d)

20

6.

What is the greatest common Factor between 28 and 35?

a)

1

b)

14

c)

7

d)

5

7.

Which of the following is a rational number? Select all answers that apply.

a)

$-51$

b)

$3.75$

c)

$4$

d)

$2\ \frac{1}{2}$

8.

The math teacher wrote the following rational numbers on the board:

5

,

-5\ \frac{1}{2}

,

5.3

,

-4\ \frac{5}{16}

Which list shows these numbers in order from greatest to least?

a)

$5.3$ , $5$ , $-4\ \frac{5}{16}$ , $-5\ \frac{1}{2}$

b)

$-5\ \frac{1}{2}$ , $5$ , $5.3$ , $-4\ \frac{5}{16}$

c)

$-5\ \frac{1}{2}$ , $-4\ \frac{5}{16}$ , $5$ , $5.3$

d)

$5$ , $-5\ \frac{1}{2}$ , $5.3$ $-4\ \frac{5}{16}$

9.

Is -5.4 less than -3.4 and 1.6?

a)

True

b)

False

10.

$112\ \div\ \frac{4}{3}$

(a)

11.

Find the sum of the teams' golf scores.

(a)

12.

What is the value of $\frac{4}{15}\div\frac{2}{3}$ ?

a)

$\frac{8}{45}$

b)

$\frac{14}{15}$

c)

$\frac{5}{2}$

d)

$\frac{2}{5}$

13.

A town received 0.95 in. of rain. Which fraction is equivalent to this amount of rain in inches?

a)

$\frac{19}{50}in.$

b)

$\frac{19}{20}in.$

c)

$\frac{95}{10}in.$

d)

$\frac{9}{5}in.$

14.

17 - 5 · 3

a)

2

b)

36

c)

3

d)

35

15.

15 + 7 × 2 – 11 + 35=

a)

38

b)

251

c)

53

d)

50

16.

Solve the following:
(2 + 7 - 1) ÷ 2²

a)

16

b)

2

c)

72.25

d)

8.75

17.

40 - 2⁴ + 8

a)

40

b)

32

c)

24

d)

42

18.

-3(-5) - 16

a)

-8

b)

24

c)

-24

d)

-1

19.

Find and explain the error.
5 - 3 + 2
5 - 5
0

a)

There is no error.

b)

Addition was done first and you should have subtracted first

c)

There is a subtraction error

20.

Solve the following:
3 + 27 ÷ (-3)

a)

-6

b)

-10

c)

10

d)

-12

21.

2 + (9²- 4)

a)

16

b)

77

c)

79

22.

Simplify the following:
-8 + (15 - 3) ÷ 4

a)

-5

b)

1

c)

-11

d)

11

23.

-56 ÷ (-7) - (-3)

a)

5

b)

11

c)

-5

24.

Solve the following:
5 - 6² ÷ 4 - 3

a)

1

b)

-10.75

c)

-31

d)

-7

25.

Solve the following:
-2 ⋅ (3 + 8 ÷ 4)²

a)

-16

b)

1.375

c)

4

d)

-50

26.

−⅓ x −½ x ⅓ =

a)

1/8

b)

-1/8

c)

1/18

d)

-1/18

27.

$-1-3\frac{1}{5}\times-\frac{3}{2}$

(a)

28.

$2\frac{4}{5}+3\frac{3}{4}\div-2\frac{1}{2}$

(a)

29.

$\frac{7}{4}\left(2\frac{1}{2}+\frac{1}{5}\right)$

(a)

30.

$-6+3\frac{5}{6}--\frac{3}{2}$

(a)

31.

$\frac{1}{2}\div-\frac{2}{3}-\frac{7}{5}$

(a)

32.

$-1>x$

a)

b)

c)

d)

33.

$x\ge-6$

a)

b)

c)

d)

34.

Solve: 4 = 2(x + 3)

a)

1/2

b)

7/2

c)

-1

d)

5

35.

Solve: 6z + 3 -4z = 9

a)

z = 3

b)

z = 60

c)

z = 30

d)

z = 1

36.

The variable, k, is being divided by 11. How should you isolate the variable?

$16=\frac{k}{11}$

a)

Divide both sides by 11

b)

Multiply both sides by 11.

c)

Add 11 to both sides.

d)

Subtract 11 to both sides.

37.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

38.

Which figure shows the inequality x > -4?

a)

Figure 1

b)

Figure 2

c)

Figure 3

d)

Figure 4

39.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

40.

$4\left(x+3\right)>-24$

a)

x > -9

b)

x < 9

c)

x < -12

d)

x > 4

41.

Select all possible solutions

a)

-25

b)

0

c)

15

d)

-10

e)

-15

42.

a)

b)

c)

d)

43.

You must be at least 16 years old to have a driver’s license.

a)

d > 16

b)

d < 16

c)

d > 16

d)

d < 16

e)

d = 16

44.

You must be older than 12 years old to ride the go-karts.

a)

a > 12

b)

a < 12

c)

a > 12

d)

a < 12

e)

a = 12

45.

Swim practice will be no more than 35 laps.

a)

L > 35

b)

L < 35

c)

L > 35

d)

L < 35

e)

L = 35

46.

More than 800 fans attended the opening soccer game.

a)

f > 800

b)

f < 800

c)

f > 800

d)

f < 800

e)

f = 800

47.

Mrs. Smith is 42 years old.

a)

m > 42

b)

m < 42

c)

m > 42

d)

m < 42

e)

m = 42

48.

The occupancy of the room must be less than 437 people.

a)

p > 437

b)

p < 437

c)

p > 437

d)

p < 437

e)

p = 437

49.

To use one stamp, your letter must be under 3.5 ounces.

a)

L > 3.5

b)

L < 3.5

c)

L > 3.5

d)

L < 3.5

e)

L = 3.5

50.

It is not safe to use a light bulb of more than 60 watts in this light fixture.

a)

w > 60

b)

w < 60

c)

w > 60

d)

w < 60

e)

w = 60

51.

The maximum amount of weight that an elevator can hold is 2,000 pounds.

a)

p > 2,000

b)

p < 2,000

c)

p > 2,000

d)

p < 2,000

e)

p = 2,000

52.

Charity needs to get a score of higher than 89 to get an A on her next math test.

a)

s > 89

b)

s < 89

c)

s > 89

d)

s < 89

e)

s = 89

53.

The box was at least 20 pounds.

a)

b > 20

b)

b < 20

c)

b > 20

d)

b < 20

e)

b = 20

54.

Children under 3 years old get into the park for free.

a)

c > 3

b)

c < 3

c)

c > 3

d)

c < 3

e)

c = 3

55.

In order to qualify for free shipping, you must spend a minimum of $25 at Amazon.

a)

s > 25

b)

s < 25

c)

s > 25

d)

s < 25

e)

s = 25

56.

The bookshelf can only be 7 1/2 feet tall.

a)

d > 7 1/2

b)

d < 7 1/2

c)

d > 7 1/2

d)

d < 7 1/2

e)

d = 7 1/2

57.

Your essay must be over 200 words.

a)

w > 200

b)

w < 200

c)

w > 200

d)

w < 200

e)

w = 200

58.

Simplify by combining like terms:
5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

59.

3x-5x

a)

2x

b)

8x

c)

-2x

d)

15x²

60.

Like terms have the same _____ and the same _____.

a)

variables and numbers

b)

signs and numbers

c)

variables and exponents

d)

variables and signs

61.

How many terms does this expression have?
3x + 5y - 17 - 2y + x

a)

3

b)

-17

c)

5

d)

1

62.

Simplify by combining like terms.
m + 9 - 4m

a)

5m

b)

m + 5m

c)

-3m + 9

d)

4m

63.

How many terms does this expression have?
-18y + 7yz - 4z

a)

-18

b)

3

c)

7

d)

-4

64.

Which expression is equivalent to the expression $-3\left(4x-2\right)-2x?$

a)

$-8x$

b)

$-16x$

c)

$-14x-2$

d)

$-14x+6$

65.

Which expression is equivalent to $7a-8-12a+4?$

a)

$-9a$

b)

$31a$

c)

$-5a-4$

d)

$19a+12$

66.

Expand using the distributive property

-2(3x + 4y + 1)

a)

-6x + 8y + 2

b)

-6x - 8y + 2

c)

-6x - 8y - 1

d)

-6x - 8y - 2

67.

How many terms does this expression have?
3x + 5y - 17 - 2y + x

a)

3

b)

-17

c)

5

d)

1

68.

n -10 +9n -3=

a)

9n - 3

b)

9n - 3

c)

10n + 13

d)

10n -13

69.

Factor out the GCF and rewrite the polynomial: 10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

70.

What is the GCF? 2x²-4x+8

a)

2x

b)

2

c)

x

d)

1

71.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

72.

What is the GCF? 3x²-2x

a)

3

b)

3x

c)

x

d)

2

73.

Factor out the GCF and rewrite the polynomial: x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

74.

Factor out the GCF and rewrite the polynomial: 8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

75.

Factor out the GCF and rewrite the polynomial: 56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

76.

Factor out the GCF and rewrite the polynomial: 2n³+16n+12

a)

2n(n³+24n+6)

b)

2(n³+8n+6)

c)

2n(n³+8n+6)

d)

3(n³+8n+6)

77.

Factor out the GCF and rewrite the polynomial

3x³ + 9x

a)

3x (x²+ 3)

b)

3x ( x³ + 9)

c)

x (3x² + 9)

d)

3x (x³ + 3x)

78.

Factor out the GCF and rewrite the polynomial

18x³ + 81x - 27

a)

9x (2x² + 9x - 3)

b)

3 (6x³ + 27x - 9)

c)

9 (2x³ + 9x - 3)

d)

9 (2x² + 9x - 3)

6th Grade Benchmark

Total questions: 78

Worksheet time: 4hrs 54mins

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