Sec 3 G1 Maths Factorisation and formulae worksheet with answers

A free Sec 3 G1 Maths worksheet on factorisation and formulae: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 3 G1 Maths worksheet: Factorisation and formulae

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

(a)Factorise

x^{2} - 9x + 14

Answer (a)[1]

(b)Factorise

x^{2} - 9x + 8

Answer (b)[1]

(a)The distance travelled is given by

s = ut + \dfrac{1}{2}at^2

. Find the value of

s

when

u = -5

t = 6

and

a = 10

Answer (a)[1]

(b)The perimeter of a rectangle is given by

P = 2(l + b)

. Find the value of

b

when

P = 34

and

l = 13

Answer (b)[2]

(a)Make

x

the subject of

y = -3x - 4

Answer (a)[1]

(b)Make

x

the subject of

y = \dfrac{5x + 1}{3}

Answer (b)[2]

(a)The perimeter of a rectangle is given by

P = 2(l + b)

. Find the value of

P

when

l = 6

and

b = 8

Answer (a)[1]

(b)The perimeter of a rectangle is given by

P = 2(l + b)

. Find the value of

l

when

P = 52

and

b = 13

Answer (b)[2]

(a)The formula

v = u + at

gives the speed of a moving object. Find the value of

v

when

u = 5

a = 6

and

t = 3

Answer (a)[1]

(b)The perimeter of a rectangle is given by

P = 2(l + b)

. Find the value of

l

when

P = 18

and

b = 6

Answer (b)[2]

(a)Factorise

15x + 9y

completely.

Answer (a)[2]

(b)Factorise

45x + 72y

completely.

Answer (b)[2]

Section B

(a)(i)Factorise

x^{2} - 11x + 30

Answer (a)(i)[1]

(a)(ii)Factorise

x^{2} - 10x + 16

Answer (a)(ii)[1]

(b)(i)Make

x

the subject of

y = -3x + 4

Answer (b)(i)[1]

(b)(ii)Make

x

the subject of

y = \dfrac{3x - 1}{4}

Answer (b)(ii)[2]

(a)(i)The distance travelled is given by

s = ut + \dfrac{1}{2}at^2

. Find the value of

s

when

u = -4

t = 9

and

a = 2

Answer (a)(i)[1]

(a)(ii)The perimeter of a rectangle is given by

P = 2(l + b)

. Find the value of

b

when

P = 44

and

l = 11

Answer (a)(ii)[2]

(b)(i)Factorise

9x + 9

completely.

Answer (b)(i)[2]

(b)(ii)Factorise

3x - 27

completely.

Answer (b)(ii)[2]

END OF PAPER

Answers and worked solutions

Question 1

(a)Answer:

(x-7)(x-2)

[1]

(x-7)(x-2)

(b)Answer:

(x-8)(x-1)

[1]

(x-8)(x-1)

Question 2

(a)Answer:

s = 150

[1]

s = (-5) \times 6 + \dfrac{1}{2} \times 10 \times 6^2

s = 150

(b)Answer:

b = 4

[2]

34 = 2(13 + b)

2b = 8

b = 4

Question 3

(a)Answer:

x = \dfrac{y + 4}{-3}

[1]

y + 4 = -3x

x = \dfrac{y + 4}{-3}

(b)Answer:

x = \dfrac{3y - 1}{5}

[2]

3y = 5x + 1

3y - 1 = 5x

x = \dfrac{3y - 1}{5}

Question 4

(a)Answer:

P = 28

[1]

P = 2(6 + 8)

P = 28

(b)Answer:

l = 13

[2]

52 = 2(l + 13)

2l = 26

l = 13

Question 5

(a)Answer:

v = 23

[1]

v = 5 + 6 \times 3

v = 23

(b)Answer:

l = 3

[2]

18 = 2(l + 6)

2l = 6

l = 3

Question 6

(a)Answer:

3(5x + 3y) = 15x + 9y

✓[2]

\text{HCF of } 15 \text{ and } 9 =

3

No letter is in every term.

15x + 9y = 3(5x + 3y)

3(5x + 3y) = 15x + 9y

✓

(b)Answer:

9(5x + 8y) = 45x + 72y

✓[2]

\text{HCF of } 45 \text{ and } 72 =

9

No letter is in every term.

45x + 72y = 9(5x + 8y)

9(5x + 8y) = 45x + 72y

✓

Question 7

(a)(i)Answer:

(x-6)(x-5)

[1]

(x-6)(x-5)

(a)(ii)Answer:

(x-8)(x-2)

[1]

(x-8)(x-2)

(b)(i)Answer:

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

[1]

y - 4 = -3x

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

(b)(ii)Answer:

x = \dfrac{4y + 1}{3}

[2]

4y = 3x - 1

4y + 1 = 3x

x = \dfrac{4y + 1}{3}

Question 8

(a)(i)Answer:

s = 45

[1]

s = (-4) \times 9 + \dfrac{1}{2} \times 2 \times 9^2

s = 45

(a)(ii)Answer:

b = 11

[2]

44 = 2(11 + b)

2b = 22

b = 11

(b)(i)Answer:

9(x + 1) = 9x + 9

✓[2]

\text{HCF of } 9 \text{ and } 9 =

9

No letter is in every term.

9x + 9 = 9(x + 1)

9(x + 1) = 9x + 9

✓

(b)(ii)Answer:

3(x - 9) = 3x - 27

✓[2]

\text{HCF of } 3 \text{ and } 27 =

3

No letter is in every term.

3x - 27 = 3(x - 9)

3(x - 9) = 3x - 27

✓

Sec 3 G1 Maths Factorisation and formulae worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)(i)Factorise

x^{2} - 11x + 30

Answer (a)(i)[1]

(a)(ii)Factorise

x^{2} - 10x + 16

Answer (a)(ii)[1]

(b)(i)Make

x

the subject of

y = -3x + 4

Answer (b)(i)[1]

(b)(ii)Make

x

the subject of

y = \dfrac{3x - 1}{4}

Answer (b)(ii)[2]

Answers and worked solutions

Question 1

(a)Answer:

(x-7)(x-2)

[1]

(x-7)(x-2)

(b)Answer:

(x-8)(x-1)

[1]

(x-8)(x-1)

Question 2

(a)Answer:

s = 150

[1]

s = (-5) \times 6 + \dfrac{1}{2} \times 10 \times 6^2

s = 150

(b)Answer:

b = 4

[2]

34 = 2(13 + b)

2b = 8

b = 4

Question 3

(a)Answer:

x = \dfrac{y + 4}{-3}

[1]

y + 4 = -3x

x = \dfrac{y + 4}{-3}

(b)Answer:

x = \dfrac{3y - 1}{5}

[2]

3y = 5x + 1

3y - 1 = 5x

x = \dfrac{3y - 1}{5}

Question 4

(a)Answer:

P = 28

[1]

P = 2(6 + 8)

P = 28

(b)Answer:

l = 13

[2]

52 = 2(l + 13)

2l = 26

l = 13

Question 5

(a)Answer:

v = 23

[1]

v = 5 + 6 \times 3

v = 23

(b)Answer:

l = 3

[2]

18 = 2(l + 6)

2l = 6

l = 3

Question 6

(a)Answer:

3(5x + 3y) = 15x + 9y

✓[2]

\text{HCF of } 15 \text{ and } 9 =

3

No letter is in every term.

15x + 9y = 3(5x + 3y)

3(5x + 3y) = 15x + 9y

✓

(b)Answer:

9(5x + 8y) = 45x + 72y

✓[2]

\text{HCF of } 45 \text{ and } 72 =

9

No letter is in every term.

45x + 72y = 9(5x + 8y)

9(5x + 8y) = 45x + 72y

✓

Question 7

(a)(i)Answer:

(x-6)(x-5)

[1]

(x-6)(x-5)

(a)(ii)Answer:

(x-8)(x-2)

[1]

(x-8)(x-2)

(b)(i)Answer:

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

[1]

y - 4 = -3x

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

(b)(ii)Answer:

x = \dfrac{4y + 1}{3}

[2]

4y = 3x - 1

4y + 1 = 3x

x = \dfrac{4y + 1}{3}

Question 8

(a)(i)Answer:

s = 45

[1]

s = (-4) \times 9 + \dfrac{1}{2} \times 2 \times 9^2

s = 45

(a)(ii)Answer:

b = 11

[2]

44 = 2(11 + b)

2b = 22

b = 11

(b)(i)Answer:

9(x + 1) = 9x + 9

✓[2]

\text{HCF of } 9 \text{ and } 9 =

9

No letter is in every term.

9x + 9 = 9(x + 1)

9(x + 1) = 9x + 9

✓

(b)(ii)Answer:

3(x - 9) = 3x - 27

✓[2]

\text{HCF of } 3 \text{ and } 27 =

3

No letter is in every term.

3x - 27 = 3(x - 9)

3(x - 9) = 3x - 27

✓