Free Printable F2 Chapter2 Factorisation and Algebraic Fraction

1.

Simplify.

(5x + 2) – 3(x – 5)

a)

2x − 3

b)

2x + 17

c)

2x + 7

d)

4x – 3

2.

Factorise 9m² −25

a)

(3m − 5)(3m – 5)

b)

(3m + 5)(3m – 5)

c)

(3m + 5)(5 + 3m)

d)

(3m + 5)(5 − 3m)

3.

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

a)

$\frac{x}{20}$

b)

$-\frac{x}{20}$

c)

$20x$

d)

$-20x$

4.

Factorise.

6a + 21a²

a)

3a(6a + 21a²)

b)

3a(2a + 7a)

c)

3a(2 + 7a)

d)

3a(2 + 21a)

5.

Expand.

3(2x − 5)

a)

6x − 5

b)

6x + 5

c)

6x − 15

d)

6x + 15

6.

Expand.

(p + q)(p − q) + p(p + q)

a)

−q² + pq

b)

p² – q² + pq

c)

2p² + pq – q²

d)

2p² – q² + 2pq

7.

Expand.

(4p − 3)²

a)

4p² − 9

b)

16p² – 9

c)

16p² – 24p + 9

d)

16p² + 24p − 9

8.

Factorise.

$6y^2-7y-3$

a)

(−3y – 1)(2y – 3)

b)

(3y + 1)(2y – 3)

c)

(6y – 2)(y + 2)

d)

(6y + 2)(y – 2)

9.

Simplify.

$\frac{3x^2+9x}{2x+10}\div\frac{3x}{x+5}$

a)

$\frac{x}{2}$

b)

$\frac{x+3}{2}$

c)

$\frac{3}{2}x$

d)

$\frac{2}{x+3}$

10.

What is the highest common factor (HCF) for terms 8p²k and 20pk²?

a)

4

b)

4p

c)

4pk

d)

4p²k²

11.

Simplify.

$\frac{9x^2-1}{6x+2}$

a)

$\frac{3x}{2}$

b)

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

c)

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

d)

$\frac{3x+1}{6x}$

12.

Factorise.

3x² – 48

a)

3(x + 2)(x – 2)

b)

3(x − 4)(x + 4)

c)

3(x − 2)(x + 4)

d)

3(x + 1)(x – 4)

13.

Divide and Simplify $\frac{6}{k-4}\div\frac{k+6}{k^2+2k-24}$

a)

$\frac{9}{k-4}$

b)

$\frac{k+7}{8}$

c)

$6$

d)

$k-3$

14.

Factorise ab+bc+pq+pr.

a)

a(b+c) + p(q+r)

b)

b(a+c) + p(q+r)

c)

b(a+b) + p(q+r)

d)

b(a+c) + q(p+r)

15.

Simplify $\frac{4}{rs}-\frac{2}{s}$

a)

$\frac{4-2r}{rs}$

b)

$\frac{4r-2}{rs}$

c)

$\frac{4-2s}{rs}$

d)

$\frac{4s-2}{rs}$

16.

Simplify $\frac{2p+4}{p^2-4}$

a)

$\frac{2}{p-2}$

b)

$\frac{p}{p-2}$

c)

$\frac{2}{2-p}$

d)

$\frac{p}{p-2}$

17.

Expand $(2x+5y)(3x-y)$ .

a)

$6x^2-13xy-5y^2$

b)

$6x^2+13xy-5y^2$

c)

$6x^2+17xy-5y^2$

d)

$6x^2+13xy+5y^2$

18.

Choose the correct answer:
$a^2+ab+ac+bc$

a)

(a + b) (a + c)

b)

(a + b) (b + c)

c)

(a + c) (b + c)

d)

a (a + b + c)

19.

Factorise $a^2-4a$

a)

$a-4$

b)

$-3a$

c)

$a\left(a-4\right)$

d)

$3a^2$

20.

Expand $3x(3y+2z)+4x(5y+2z)$ .

a)

$x(29y+14z^2)$

b)

$z(14x+29yx)$

c)

$29x^2y+14xz^2$

d)

$x\left(29y+14z\right)$

21.

Expand $2(2x+1)(3x-2)$ .

a)

$12x^2+14x+4$

b)

$12x^2+2x+4$

c)

$12x^2-2x-4$

d)

$12x^2-14x-4$

22.

$Simplify\ \frac{2u+6}{u^2-9}\ \div\ \frac{u+3}{u-3}$

a)

$\frac{2u}{u+3}$

b)

$\frac{2}{u+27}$

c)

$\frac{2}{u+3}$

d)

$\frac{2}{u^2+3}$

23.

$Express\ \frac{2g-9}{8h}\ -\ \frac{3\ +4g}{4g}\ in\ its\ simplest\ form$

a)

$\frac{6g\ -15}{8h}$

b)

$\frac{-6g\ +15}{8h}$

c)

$\frac{-6g\ -15}{-8h}$

d)

$\frac{-6g\ -15}{8h}$

24.

Express $\frac{3s^2-5}{s}-\frac{2s+9}{7}$ as a single fraction in its simplest form

a)

$\frac{19s^2-9s-35}{7s}$

b)

$\frac{19s^2-9s-35}{s}$

c)

$\frac{3s^2-2s-14}{s}$

d)

$\frac{3s^2-2s+4}{s}$

25.

Simplify $\frac{3x-3y}{x+y}\times\frac{2x\ +2y}{6x}$

a)

$\frac{x+y}{x}$

b)

$\frac{x+y}{y}$

c)

$\frac{x-y}{x}$

d)

$\frac{x-y}{y}$

26.

Simplify: $\frac{4x^2-36}{x^2+10x+21}$

a)

$\frac{4\left(x-3\right)}{x-7}$

b)

$\frac{4\left(x+3\right)}{x+7}$

c)

$4\left(x+3\right)\left(x-7\right)$

d)

$\frac{4\left(x-3\right)}{x+7}$

27.

Simplify the following.

$\frac{6t}{5}\div\frac{3}{4t}$

a)

$\frac{8t^2}{5}$

b)

$\frac{18t}{20t}$

c)

$\frac{9t}{10t}$

d)

$\frac{10t}{8}$

28.

$\frac{3p-4}{p^2-4}-\frac{3p-6}{p^2-4}$

a)

$\frac{2}{p^2-4}$

b)

$\frac{26p-26+3p^3-9p^2}{2p^2-10p+8}$

c)

$\frac{3p-7}{p^2-5p+4}$

d)

$\frac{30p-26+p^3-10p^2}{2p^2-10p+8}$

29.

The area, A of trapezium ABCD is given by the formula

A = $\frac{1}{2}$ (a + b)h.
Which of the following is true?

a)

h is the length of AB

b)

h is the length of DC

c)

a is the length of AB

d)

b is the length of DC

30.

Diagram shows a trapezium. state the formula of the area of the trapezium.

a)

$\frac{1}{2}\times\left(p+r\right)\times9$

b)

$9\times r$

c)

$9\times r\times p$

d)

$\frac{1}{2}\times9\times p\times r$

31.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

32.

Simplify $\frac{8x^3y^4}{5x^4y}\div\frac{4y^2}{15x^2y}$

a)

$\frac{6y^4}{x^3}$ .

b)

$\frac{12x}{y^2}$

c)

$6xy^2$

d)

$\frac{32y^4}{75x^3}$

33.

Factorise completely : 2x²- 50

a)

2( x - 5 )²

b)

2( x + 5 )( x - 5)

c)

(2x + 5)(2x - 5)

d)

(2x + 5)(x - 5)

34.

What value should be in each box if you need to factorize
$x^2-8x+16$ ?

a)

$p=x^2,\ q=+8x,\ r=+16$

b)

$p=x^2,\ q=+16,\ r=+8x$

c)

$p=x^2,\ q=+16,\ r=-8x$

d)

$p=x^2,\ q=-8x,\ r=+16$

35.

Express $\frac{2h+3k}{15hk}\div\frac{6h+4k}{25k^2}$ as a single fraction in its simplest form.

a)

$\frac{5k}{6h}$

b)

$\frac{5\left(2h\ +\ 3k\right)}{6\left(3h\ +\ 2k\right)}$

c)

$\frac{5k\left(2h\ +\ 3k\right)}{2h\left(3h\ +\ 2k\right)}$

d)

$\frac{5k\left(2h\ +\ 3k\right)}{6h\left(3h\ +\ 2k\right)}$

36.

Simplify $\frac{3x-3y}{x+y}\times\frac{2x\ +2y}{6x}$

a)

$\frac{x+y}{x}$

b)

$\frac{x+y}{y}$

c)

$\frac{x-y}{x}$

d)

$\frac{x-y}{y}$

37.

Below are the factors of 3ab, except...

a)

$ab$

b)

1

c)

$a^2$

d)

$3b$

38.

What is the highest common factor (HCF) for terms 8p²k and 20pk²?

a)

4

b)

4p

c)

4pk

d)

4p²k²

39.

Simplify.

(3p – 1)(p + 2) – 5p

a)

3p² + 2

b)

3p² − 2

c)

3p² − 10p + 2

d)

3p² − 10p − 2

40.

Factorise.

3x² – 48

a)

3(x + 2)(x – 2)

b)

3(x − 4)(x + 4)

c)

3(x − 2)(x + 4)

d)

3(x + 1)(x – 4)

F2 Chapter2 Factorisation and Algebraic Fraction

Total questions: 40

Worksheet time: 2hrs 57mins

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