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Edexcel IGCSE Maths

Topic questions Pure mathematics Rearranging formulae

Rearranging formulae

28 questions · 156 marks · about 3 hours

Rearranging formulae questions

TopicRearranging formulae

Edexcel 4MA1 Rearranging formulae 28 questions

Paper 1F June 2025 (R) Foundation tier, Question 23 8 marks

(a)

Expand x(x maths symbol 3)

[1]
(b)
Question 23, shown as an image
[2]
Reveal mark scheme Mark scheme for question 23(b)
(c)

Simplify a6 maths symbol a10

[1]
(d)

Simplify c30 maths symbol c12

[1]
(e)(i)

Factorise y2 maths symbol 10y maths symbol 21

[2]
Reveal mark scheme Mark scheme for question 23(e)(i)
(e)(ii)

Hence, solve y2 maths symbol 10y maths symbol 21 maths symbol 0

[1]
Reveal mark scheme Mark scheme for question 23(e)(ii)

Paper 2F June 2025 Foundation tier, Question 12 5 marks

(a)

Make y the subject of w = 3 y โ€“ d

Diego buys b boxes of crayons and p packets of crayons.

There are 12 crayons in each box. There are 3 crayons in each packet.

Diego buys a total of T crayons.

[2]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Write down a formula for T in terms of b and p

[3]
Reveal mark scheme Mark scheme for question 12(b)

Paper 2F November 2023 Foundation tier, Question 12 6 marks

(a)

Expand x (x + 3)

[1]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Factorise 8p + 10

[1]
(c)

Make e the subject of y = eh โ€’ f

Janya thinks of a whole number. She calls her whole number w Janya writes down this information about her whole number.

[2]
Reveal mark scheme Mark scheme for question 12(c)
(d)

Write down the possible values of w

[2]
Reveal mark scheme Mark scheme for question 12(d)

Paper 1F January 2023 Foundation tier, Question 13 4 marks

p = t โ€“ ac

t = 18 a = โ€“3 c = 5

(a)

Work out the value of p

[2]
Reveal mark scheme Mark scheme for question 13(a)
(b)

Make x the subject of the formula d = 3x + 10

[2]
Reveal mark scheme Mark scheme for question 13(b)

Paper 2F January 2023 (R) Foundation tier, Question 14 7 marks

(a)

Expand x (10 โ€“ x)

[1]
(b)

Factorise 6y + 27

[1]
(c)

Make m the subject of the formula h = fraction + 4

[2]
Reveal mark scheme Mark scheme for question 14(c)
(d)

Solve 7g + 3 = 2g โ€“ 5 Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 14(d)

Paper 1F January 2022 Foundation tier, Question 16, also on the Higher paper 6 marks

(a)

Simplify a7 maths symbol a4

[1]
(b)

Simplify w15 รท w3

[1]
(c)

Simplify (8x5y3)2

[2]
Reveal mark scheme Mark scheme for question 16(c)
(d)

Make t the subject of c = t3 โ€“ 8v

[2]
Reveal mark scheme Mark scheme for question 16(d)

Paper 1H January 2022 Higher tier, Question 1, also on the Foundation paper 6 marks

(a)

Simplify a7 maths symbol a4

[1]
(b)

Simplify w15 รท w3

[1]
(c)

Simplify (8x5y3)2

[2]
Reveal mark scheme Mark scheme for question 1(c)
(d)

Make t the subject of c = t3 โ€“ 8v

[2]
Reveal mark scheme Mark scheme for question 1(d)

Paper 2F January 2022 (R) Foundation tier, Question 15 6 marks

(a)

Solve 5 c = 15

[1]
(b)

Expand x(8 โ€“ x)

T = 5m โ€“ 6n

[1]
(c)

Work out the value of T when m = 4.2 and n = โ€“2.5

[2]
Reveal mark scheme Mark scheme for question 15(c)
(d)

Make g the subject of k = 2g + t

[2]
Reveal mark scheme Mark scheme for question 15(d)

Paper 1H November 2021 Higher tier, Question 17 8 marks

(a)

Factorise 6y2 โ€“ y โ€“ 5

[2]
Reveal mark scheme Mark scheme for question 17(a)
(b)
Question 17, shown as an image
[3]
Reveal mark scheme Mark scheme for question 17(b)
(c)

Express 4x2 โ€“ 8x + 7 in the form a(x + b)2 + c where a, b and c are integers.

[3]
Reveal mark scheme Mark scheme for question 17(c)

Paper 1F January 2021 Foundation tier, Question 12 5 marks

(a)

Expand x (4 โ€“ x)

t = ab โ€“ c

a = 1.5 b = 2.4 c = โ€“5.6

[1]
(b)

Work out the value of t.

[2]
Reveal mark scheme Mark scheme for question 12(b)
(c)

Make d the subject of y = dx โ€“ e

[2]
Reveal mark scheme Mark scheme for question 12(c)

Paper 1F January 2021 (R) Foundation tier, Question 21, also on the Higher paper 5 marks

(a)
Question 21, shown as an image
[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Write down the value of g0

[1]
(c)

Factorise x2 โ€“ 11x + 24

[2]
Reveal mark scheme Mark scheme for question 21(c)

Paper 1H January 2021 (R) Higher tier, Question 6, also on the Foundation paper 5 marks

(a)
6 Question 6, shown as an image
[2]
Reveal mark scheme Mark scheme for question 6(a)
(b)

Write down the value of g0

[1]
(c)

Factorise x2 โ€“ 11x + 24

[2]
Reveal mark scheme Mark scheme for question 6(c)

Paper 1F November 2020 (R) Foundation tier, Question 5 8 marks

(a)

Simplify w + w + w + w โ€“ w

[1]
(b)

Simplify 4maths symbolamaths symbol2

[1]
(c)

Simplify fmaths symbol f maths symbolfmaths symbolfmaths symbolf

[1]
(d)

Simplify 4c + 4h + 5c โ€“ 6h

[2]
(e)

Factorise 10d + 15

[1]
(f)

Make t the subject of e = 7t + g

[2]
Reveal mark scheme Mark scheme for question 5(f)

Paper 2F November 2020 Foundation tier, Question 14 5 marks

(a)

Factorise 25 f โ€“ 10

[1]
(b)

Make y the subject of the formula c = 5y โ€“ h

[2]
Reveal mark scheme Mark scheme for question 14(b)
(c)

Solve the inequality 4x + 7 > 2

[2]
Reveal mark scheme Mark scheme for question 14(c)

Paper 1F January 2020 (R) Foundation tier, Question 16, also on the Higher paper 8 marks

(a)

Make a the subject of d = g + 2 ac

[2]
Reveal mark scheme Mark scheme for question 16(a)
(b)

Factorise fully 9e fโˆ’ 12f

[2]
Reveal mark scheme Mark scheme for question 16(b)
(c)

Expand and simplify (x+ 2)(xโˆ’ 5)

[2]
Reveal mark scheme Mark scheme for question 16(c)
(d)
Question 16, shown as an image
[2]
Reveal mark scheme Mark scheme for question 16(d)

Paper 1H January 2020 (R) Higher tier, Question 3, also on the Foundation paper 8 marks

(a)

Make a the subject of d=g+ 2ac

[2]
Reveal mark scheme Mark scheme for question 3(a)
(b)

Factorise fully 9e fโˆ’ 12f

[2]
Reveal mark scheme Mark scheme for question 3(b)
(c)

Expand and simplify (x+ 2)(xโˆ’ 5)

[2]
Reveal mark scheme Mark scheme for question 3(c)
(d)
Question 3, shown as an image
[2]
Reveal mark scheme Mark scheme for question 3(d)

Paper 2F January 2020 Foundation tier, Question 13 7 marks

(a)

Expand x (5 โ€“ x)

[1]
(b)

Factorise 3y โ€“ 21

[1]
(c)

Make p the subject of the formula f = 3p โ€“ d

Sergio buys m boxes of seeds and n packets of seeds.

Each box contains 10 seeds. Each packet contains 6 seeds.

The total number of seeds that Sergio buys is T.

[2]
Reveal mark scheme Mark scheme for question 13(c)
(d)

Write down a formula for T in terms of m and n.

[3]
Reveal mark scheme Mark scheme for question 13(d)

Paper 1H June 2019 (R) Higher tier, Question 18 6 marks

(a)

Expand and simplify (x + 2)(2 x + 3)(x โ€“ 7) Show your working clearly.

[3]
Reveal mark scheme Mark scheme for question 18(a)
(b)
Question 18, shown as an image
[3]
Reveal mark scheme Mark scheme for question 18(b)

Paper 2F June 2018 Foundation tier, Question 18, also on the Higher paper 6 marks

(a)

Make a the subject of the formula M = ac โ€“ bd

[2]
Reveal mark scheme Mark scheme for question 18(a)
(b)

Solve the inequality 5x โ€“ 4 maths symbol 39

[2]
Reveal mark scheme Mark scheme for question 18(b)
(c)

Factorise fully 18e2f3 โ€“ 12e3 f

[2]
Reveal mark scheme Mark scheme for question 18(c)

Paper 2F June 2018 (R) Foundation tier, Question 21 6 marks

(a)

Simplify g7 maths symbol g3

[1]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Simplify (k3)5

[1]
(c)
Question 21, shown as an image
[2]
(d)

Make e the subject of the formula h = 3 e + f

[2]
Reveal mark scheme Mark scheme for question 21(d)

Paper 2H June 2018 Higher tier, Question 1, also on the Foundation paper 6 marks

(a)

Make a the subject of the formula M = ac โ€“ bd

[2]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Solve the inequality 5x โ€“ 4 maths symbol 39

[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)

Factorise fully 18e2f3 โ€“ 12e3 f

[2]
Reveal mark scheme Mark scheme for question 1(c)

Paper 2H June 2018 (R) Higher tier, Question 7 4 marks

Also involves Indices

(a)
Question 7, shown as an image
[2]
Reveal mark scheme Mark scheme for question 7(a)
(b)

Make e the subject of the formula h = 3 e + f

[2]
Reveal mark scheme Mark scheme for question 7(b)

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