Free Printable Practice Makes Perfect

1.

y²-3y

a)

y(y-3)

b)

y² (y-3)

c)

y(1-3)

d)

y² (1-3)

2.

3a² - 9ax

a)

a²(3 - 9x)

b)

3a(a -3x)

c)

3a(a-9x)

d)

a(3a-9x)

3.

x² - 25

a)

(x -5)(x-5)

b)

(x-25)(x+25)

c)

(x+5)(x-5)

d)

(x² +5)(x²-5)

4.

100x² - 121

a)

(50x +11)(50x-11)

b)

(10x - 11)(10x-11)

c)

(10x+11)(10x+11)

d)

(10x+11)(10x-11)

5.

x² +6x+5

a)

(x+2)(x+3)

b)

(x+2)(x-3)

c)

(x+1)(x+5)

d)

(x-1)(x-5)

6.

y²+18y+32

a)

(y+4)(y+8)

b)

(y+ 2)(y+16)

c)

(y+2)(y-16)

d)

(y+1)(y+32)

7.

x²-13x+42

a)

(x-3)(x-14)

b)

(x+6)(x+7)

c)

(x-6)(x-7)

d)

(x-2)(x-21)

8.

a²-7a+12

a)

(a+2)(a+5)

b)

(a+3)(a+4)

c)

(a-2)(a-5)

d)

(a-3)(a-4)

9.

x²+3x-18

a)

(x+6)(x-3)

b)

(x-6)(x+3)

c)

(x-2)(x+9)

d)

(x+2)(x-9)

10.

c²+11c-26

a)

(c-13)(c+2)

b)

(c+13)(c-2)

c)

(c+2)(c+9)

d)

(c+2)(c+13)

11.

x²-3x-54

a)

(x-9)(x-6)

b)

(x+9)(x-6)

c)

(x-9)(x+6)

d)

(x-9)(x+5)

12.

x²-14x-32

a)

(x-16)(x+2)

b)

(x+16)(x-2)

c)

(x-4)(x-8)

d)

(x-2)(x-7)

13.

Factorise x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

14.

Factorise

x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

15.

Factorise

a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

16.

Factorise x² + 13x + 30

a)

(x + 3)(x + 10)

b)

(x + 5)(x + 6)

c)

(x + 2)(x + 15)

d)

(x + 1)(x + 30)

17.

Factorise x² - 2x - 24

a)

(x + 6)(x - 4)

b)

(x + 4)(x - 6)

c)

(x - 4)(x - 6))

d)

(x - 3)(x + 8)

18.

Factorise x² - 16x + 24

a)

(x + 2)(x - 14)

b)

(x - 2)(x - 14)

c)

(x + 14)(x - 2)

d)

(x - 4)(x - 6)

19.

Factorise x² + 13x - 48

a)

(x + 3)(x - 16)

b)

(x + 16)(x - 3)

c)

(x + 4)(x - 12)

d)

(x + 12)(x - 4)

20.

Factorise 2x² - 5x + 2

a)

(2x - 1)(x - 2)

b)

(2x + 1)(x - 2)

c)

(2x - 2)(x - 1)

d)

(2x + 2)(x - 1)

21.

Factorise 3x² - 5x - 2

a)

(3x + 1)(x - 2)

b)

(3x + 2)(x - 1)

c)

(3x - 1)(x + 2)

d)

(3x - 2)(x + 1)

22.

Identify whether the given mathematical statement is correct or not
5 x + 4y = 9xy

a)

CORRECT

b)

NOT CORRECT

23.

The factorisation of 4x + 16 is _______

a)

4(x + 4)

b)

4(x - 4)

c)

x + 4

d)

4x + 4

24.

Identify whether the given mathematical statement is correct or not
(a + 4) (a + 2) = a² + 8

a)

CORRECT

b)

NOT CORRECT

25.

Choose the correct answer:
a² + bc + ab + ac = ______

a)

(a + b) (a + c)

b)

(a + b) (b + c)

c)

(a + c) (b + c)

d)

a (a + b + c)

26.

(x + 1) (x + 1) is a factor of ____

a)

x² + 2x + 1

b)

x² - 2x + 1

c)

x² - 1 + 2x

d)

x² + 1 - 2x

27.

Choose the correct answer:
The factors of a⁴ - b⁴ is _____

a)

(a² + b²) (a + b) (a - b)

b)

(a² + b²) (a² + b²)

c)

(a² - b²) (a² - b²)

d)

None of these

28.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

29.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

30.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

31.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

32.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

33.

Factor Completely: 3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

34.

$x^2-x-12=\left(x+p\right)\left(x+q\right)$ . What is the value of $p$ and $q?$

a)

3 , 4

b)

3 , -4

c)

2 , 6

d)

2 , -6

35.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

36.

Factorise:- (m + n)² + (m - n)²

a)

2(m + n)(m - n)

b)

2m² + n²

c)

2(m² + n²)

d)

4mn

37.

Factorise:- 12x³ - 75xy²

a)

3x(4x - 5y)²

b)

3x(2x + 5y)(2x - 5y)

c)

3(4x³ - 15xy²)

d)

3x(2x - 5y)²

38.

$2x^2+5x+3$

a)

(2x+1)(x+3)

b)

(2x+3)(x+1)

c)

(x+1)(3x+2)

d)

(3x+1)(x+3)

39.

Factorise l'expression suivante : $a²-8a+16\ =$

a)

$a-4²$

b)

$a+4²$

c)

$\left(a-4\right)²$

d)

$\left(a+4\right)²$

40.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

41.

Factorise $xy+cy$ fully.

a)

$-y(-c+x)$

b)

$-y(-x+c)$

c)

$y(c+x)$

d)

I don't know 😓

42.

Identify whether the given mathematical statement is correct or not
5 x + 4y = 9xy

a)

CORRECT

b)

NOT CORRECT

43.

The factorisation of 4x + 16 is _______

a)

4(x + 4)

b)

4(x - 4)

c)

x + 4

d)

4x + 4

44.

Identify whether the given mathematical statement is correct or not
(a + 4) (a + 2) = a² + 8

a)

CORRECT

b)

NOT CORRECT

45.

Choose the correct answer:
a² + bc + ab + ac = ______

a)

(a + b) (a + c)

b)

(a + b) (b + c)

c)

(a + c) (b + c)

d)

a (a + b + c)

46.

(x + 1) (x + 1) is a factor of ____

a)

x² + 2x + 1

b)

x² - 2x + 1

c)

x² - 1 + 2x

d)

x² + 1 - 2x

47.

Choose the correct answer:
The factors of a⁴ - b⁴ is _____

a)

(a² + b²) (a + b) (a - b)

b)

(a² + b²) (a² + b²)

c)

(a² - b²) (a² - b²)

d)

None of these

48.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

49.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

50.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

51.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

52.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

53.

Factor Completely: 3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

54.

$x^2-x-12=\left(x+p\right)\left(x+q\right)$ . What is the value of $p$ and $q?$

a)

3 , 4

b)

3 , -4

c)

2 , 6

d)

2 , -6

55.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

56.

The factors of

x^2

+xy+8x+8y are:

a)

(x+y) (x+8)

b)

(2x+y) (x+8)

c)

(x+2y) (x+8)

d)

(x+y) (2x+8)

57.

Factorise:- (m + n)² + (m - n)²

a)

2(m + n)(m - n)

b)

2m² + n²

c)

2(m² + n²)

d)

4mn

58.

Factorise:- 12x³ - 75xy²

a)

3x(4x - 5y)²

b)

3x(2x + 5y)(2x - 5y)

c)

3(4x³ - 15xy²)

d)

3x(2x - 5y)²

59.

$2x^2+5x+3$

a)

(2x+1)(x+3)

b)

(2x+3)(x+1)

c)

(x+1)(3x+2)

d)

(3x+1)(x+3)

60.

Factorise l'expression suivante : $a²-8a+16\ =$

a)

$a-4²$

b)

$a+4²$

c)

$\left(a-4\right)²$

d)

$\left(a+4\right)²$

61.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

62.

Factorise $xy+cy$ fully.

a)

$-y(-c+x)$

b)

$-y(-x+c)$

c)

$y(c+x)$

d)

I don't know 😓

63.

A prime number...

a)

has one factor.

b)

has more than 2 factors.

c)

has 100 factors.

d)

has exactly 2 factors: 1 and the itself.

64.

All of these are prime except

a)

3

b)

9

c)

2

d)

13

65.

Which list contains all prime numbers?

a)

2, 3, 5, 7, 11

b)

2, 3, 5, 7, 9

c)

2, 4, 5, 7, 11

d)

2, 3, 5, 7, 12

66.

Which of the following is NOT prime?

a)

29

b)

23

c)

17

d)

39

67.

2 x 2 x 2 is the prime factorization of...

a)

6

b)

12

c)

22

d)

8

68.

Find the prime factorization of 12 ?

a)

2 x 6

b)

2 + 2 + 2 + 2 + 2 + 2

c)

2²x 3

d)

1 x 2²x 3

69.

Write 54 as a product of its prime factors.

a)

2x2x3x3

b)

2x3x3x3

c)

2x3x9

d)

6x9

70.

Write 28 as a product of its prime factors.

a)

2x2x7

b)

4x7

71.

Write 64 as a product of its prime factors.

a)

8x8

b)

4x4x4

c)

2x2x2x2x2x2

d)

2x2x4x4

72.

210 written as a product of its prime factors is 2x3x5x7.

a)

True

b)

False

73.

Which of the following shows the prime factorization of 24?

a)

2 × 2 × 2 × 3 × 3

b)

2 × 2 × 2 × 3

c)

2 × 2 × 2 × 2 × 3

d)

2 × 2 × 3 × 3

74.

Which of the following shows the prime factorization of 27?

a)

2 x 2 x 3

b)

2 x 3 x 5

c)

3 x 3 x 3

d)

2 x 3 x 3

75.

Which of the following shows the prime factorization of 32?

a)

2 × 2 × 2 × 2 × 2

b)

2 × 2 × 2 × 3 × 2

c)

2 × 2 × 3 × 3 × 2

d)

2 × 3 × 3 × 3 × 2

76.

Which of the following shows the prime factorization of 36?

a)

2 × 2 × 2 × 2

b)

2 × 2 × 2 × 3

c)

2 × 3 × 3 × 3

d)

2 × 2 × 3 × 3

77.

Which of the following shows the prime factorization of 48?

a)

1 × 2 × 2 × 2 × 2

b)

2 × 2 × 2 × 2 × 3

c)

2 × 2 × 2 × 3 × 3

d)

2 × 2 × 3 × 3 × 3

78.

Which of the following shows the prime factorization of 50?

a)

2 x 5 x 5

b)

2 x 2 x 5

c)

2 x 5 x 5 x 5

d)

2 x 2 x 2 x 5

79.

Which of the following shows the prime factorization of 54?

a)

2 x 3 x 3

b)

2 x 2 x 3

c)

2 x 3 x 3 x 3

d)

2 x 2 x 2 x 3

80.

Which of the following shows the prime factorization of 60?

a)

2 x 3 x 3 x 5

b)

2 x 2 x 3 x 5

c)

2 x 2 x 3 x 7

d)

2 x 3 x 5 x 5

81.

Which of the following shows the prime factorization of 64?

a)

2 x 2 x 2 x 2 x 2

b)

2 x 2 x 2 x 2 x 2 x 2 x 2

c)

3 x 3 x 3 x 3 x 3 x 3

d)

2 x 2 x 2 x 2 x 2 x 2

82.

Which of the following shows the prime factorization of 84?

a)

2 x 2 x 3 x 7

b)

2 x 3 x 3 x 7

c)

2 x 3 x 7 x 7

d)

2 x 3 x 7

83.

What number is never allowed in a factor tree?

a)

13 (it's bad luck!)

b)

1

c)

8675309

d)

2

84.

Select all of the prime numbers.

a)

0

b)

19

c)

31

d)

47

e)

51

85.

What is a prime factorization

a)

A whole number written as a doge emoji

b)

A whole number written as a novel

c)

A whole number written as a merchandise product

d)

A whole number written as a product of prime factors

86.

Which of the following is a prime number?

a)

2

b)

12

c)

22

d)

32

87.

All odd numbers are prime

a)

True

b)

False

88.

Identify a factor of 40

a)

6

b)

7

c)

8

d)

9

89.

Identify a factor of 60

a)

12

b)

7

c)

8

d)

9

90.

Identify a factor of 28

a)

5

b)

7

c)

8

d)

6

91.

Identify a factor of 16

a)

5

b)

7

c)

8

d)

6

92.

Identify a factor of 54

a)

8

b)

11

c)

9

d)

12

93.

Which value is not a factor of 12...

a)

1

b)

2

c)

4

d)

5

94.

Which value is not a factor of 20...

a)

10

b)

4

c)

6

d)

5

95.

Which value is not a factor of 24...

a)

3

b)

8

c)

6

d)

7

96.

Which value is not a factor of 30...

a)

3

b)

8

c)

6

d)

5

97.

Which value is not a factor of 48...

a)

12

b)

8

c)

6

d)

7

98.

Which value is not a factor of 42...

a)

14

b)

8

c)

6

d)

7

99.

Identify all the factors of 20....

a)

4

b)

5

c)

6

d)

8

100.

Identify all the factors of 30....

a)

1

b)

6

c)

4

d)

15

101.

Identify all the factors of 32....

a)

4

b)

6

c)

8

d)

12

102.

Identify all the factors of 36....

a)

3

b)

6

c)

9

d)

12

103.

Identify all the factors of 40....

a)

6

b)

12

c)

9

d)

8

104.

Identify all the factors of 48....

a)

6

b)

12

c)

16

d)

8

105.

Identify all the factors of 60....

a)

4

b)

12

c)

15

d)

8

106.

Identify the correct list for all the factors 16....

a)

1, 2, 4, 8, 16

b)

1, 2, 8, 16

c)

1, 4, 8, 16

d)

1, 2, 4, 6, 8, 16

107.

Identify the correct list for all the factors 12....

a)

1, 2, 3, 4, 6, 12

b)

1, 2, 3, 5, 6, 12

c)

1, 2, 3, 4, 8, 12

d)

1, 2, 3, 6, 12

108.

Identify the correct list for all the factors 10....

a)

1, 2, 5, 10

b)

1, 2, 4, 5, 10

c)

1, 2, 10

d)

1, 2, 4, 10

109.

Find the HCF of 12 and 16...

a)

2

b)

4

c)

6

d)

8

110.

Find the HCF of 8 and 24 ...

a)

2

b)

4

c)

6

d)

8

111.

Find the HCF of 20 and 24

a)

6

b)

4

c)

5

d)

12

112.

Find the HCF of 30 and 25

a)

5

b)

6

c)

10

d)

15

113.

Find the GCF of 64 and 144

a)

8

b)

6

c)

16

d)

2

114.

Find the LCM of 42 and 66

a)

2772

b)

6

c)

462

d)

132

115.

Find the LCM of 18 and 24

a)

6

b)

72

c)

24

d)

5

116.

Find the LCM of each set of numbers.
3, 5

a)

15

b)

20

c)

30

d)

33

117.

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

a)

4

b)

40

c)

15

d)

20

118.

What is the least common multiple (LCM) of 8 and 5?

a)

50

b)

40

c)

5

d)

8

119.

GCF of 12 and 18

a)

3

b)

4

c)

6

d)

2

120.

List all the factors of 12

a)

1, 2, 3, 4, 6, 12

b)

1, 2, 4, 12

c)

1, 12

d)

1, 2, 3, 4, 5, 6, 12

Practice Makes Perfect

Total questions: 120

Worksheet time: 3600secs

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