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Edexcel IGCSE Maths

Topic questions Pure mathematics Indices

Indices

80 questions · 374 marks · about 7.5 hours

Indices questions

Edexcel 4MA1 Indices 80 questions

Paper 1F June 2025 Foundation tier, Question 21, also on the Higher paper 4 marks

x5 × x7 = xm

(a)

Find the value of m

y8 ÷ y3 = yn

[1]
(b)

Find the value of n

[1]
(c)

Simplify fully (5a4r2)3

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

Paper 1H June 2025 Higher tier, Question 4, also on the Foundation paper 4 marks

x5 maths symbol x7 = xm

(a)

Find the value of m

y8 ÷ y3 = yn

[1]
(b)

Find the value of n

[1]
(c)

Simplify fully (5a4r2)3

[2]
Reveal mark scheme Mark scheme for question 4(c)

Paper 1H June 2025 (R) Higher tier, Question 8 5 marks

(a)

Simplify a6 maths symbol a10

[1]
(b)

Simplify c30 maths symbol c12

[1]
(c)(i)

Factorise y2 maths symbol 10y maths symbol 21

[2]
Reveal mark scheme Mark scheme for question 8(c)(i)
(c)(ii)

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

[1]
Reveal mark scheme Mark scheme for question 8(c)(ii)

Paper 2F June 2025 (R) Foundation tier, Question 22 5 marks

(a)

Write down the value of 50

Question 22, shown as an image
[1]
(b)

Find the value of k

[2]
Reveal mark scheme Mark scheme for question 22(b)
(c)

Simplify fully maths symbol2d4e5 maths symbol3

[2]
Reveal mark scheme Mark scheme for question 22(c)

Paper 1F November 2024 Foundation tier, Question 5 7 marks

(a)

Simplify 8d maths symbol 4d maths symbol 7d

[1]
(b)

Simplify m maths symbol 10 p

[1]
(c)

Solve x maths symbol 5 maths symbol maths symbol19

[1]
(d)
Question 5, shown as an image
[1]
(e)

Simplify a maths symbol a maths symbol a maths symbol a

k maths symbol 8 and n = 12

[1]
(f)

Work out the value of 9k maths symbol 4n

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

Paper 1F November 2024 Foundation tier, Question 20 6 marks

(a)

Simplify maths symbol p3 maths symbol5

[1]
(b)

Expand and simplify 2nmaths symbol4n maths symbol 3maths symbol maths symbol nmaths symboln maths symbol 4maths symbol

[2]
Reveal mark scheme Mark scheme for question 20(b)
(c)
Question 20, shown as an image

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 20(c)

Paper 1H June 2024 Higher tier, Question 10 4 marks

(a)

Simplify (2p)0 where p maths symbol 0

y9maths symboly–3 = yn

[1]
(b)

Find the value of n

[1]
(c)

Simplify fully (5a4c2)3

[2]
Reveal mark scheme Mark scheme for question 10(c)

Paper 1H June 2024 (R) Higher tier, Question 11 4 marks

A maths symbol 25 maths symbol 5 maths symbol 72 B maths symbol 23 maths symbol 53 maths symbol 74

(a)

Write down the highest common factor (HCF) of 5A and 2B Give your answer as a product of prime factors.

A maths symbol 25 maths symbol 5 maths symbol 72 B maths symbol 23 maths symbol 53 maths symbol 74

[2]
Reveal mark scheme Mark scheme for question 11(a)
(b)

Work out the value of maths symbol ABmaths symbol2 Give your answer as a product of prime factors.

[2]
Reveal mark scheme Mark scheme for question 11(b)

Paper 2F June 2024 (R) Foundation tier, Question 6 5 marks

(a)

Find the value of 3.42

[1]
(b)

Find the cube root of 373 248

[1]
(c)

Write 7 maths symbol 7 maths symbol 7 maths symbol 7 maths symbol 7 maths symbol 7 as a single power of 7

[1]
(d)

Write one set of brackets in each calculation to make the answer correct.

(d)(i)

5 + 3 × 2 = 16

[1]
(d)(ii)

10 − 8 − 10 − 6 ÷ 2 = 0

[1]

Paper 2H November 2023 Higher tier, Question 4 8 marks

(a)
4 Question 4, shown as an image

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 4(a)
(b)

Simplify h15 maths symbol h3

[1]
(c)

Simplify fully maths symbol2g3k5 maths symbol4

[2]
(d)
Question 4, shown as an image

work out the value of n

[2]
Reveal mark scheme Mark scheme for question 4(d)

Paper 2H November 2023 Higher tier, Question 12 4 marks

27 maths symbol 45 maths symbol 4x

(a)

Calculate the value of x

[2]
Reveal mark scheme Mark scheme for question 12(a)
(b)
Question 12, shown as an image
[2]
Reveal mark scheme Mark scheme for question 12(b)

Paper 1F June 2023 (R) Foundation tier, Question 7 5 marks

(a)

Simplify 6a × 2c

[1]
(b)

Simplify 4d + 3e + d – 5e

[2]
(c)

Solve 4x – 7 = 23

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

Paper 1F June 2023 (R) Foundation tier, Question 8 4 marks

(a)

Write down the prime number that lies between 90 and 100

[1]
(b)

Find the cube root of 79 507

[1]
(c)

Work out the value of 42 × 53

[2]
Reveal mark scheme Mark scheme for question 8(c)

Paper 1F June 2023 (R) Foundation tier, Question 17 3 marks

Write 2250 as a product of powers of its prime factors. Show your working clearly.

[3]
Reveal mark scheme Mark scheme for question 17

Paper 1F June 2023 Foundation tier, Question 21 8 marks

(a)

Simplify (2c4d7)3

[2]
(b)

Find the value of 5y0 where y maths symbol 0

[1]
(c)

Factorise fully 16a2b3 + 20a3b

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

Factorise x2 + 9x – 22

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

Hence solve x2 + 9x – 22 = 0

[1]
Reveal mark scheme Mark scheme for question 21(d)(ii)

Paper 1F June 2023 (R) Foundation tier, Question 22 4 marks

(a)

Simplify m10 ÷ m3

kn maths symbol k4 = k12

[1]
(b)

Write down the value of n

[1]
(c)

Simplify (3x6y8)2

[2]
Reveal mark scheme Mark scheme for question 22(c)

Paper 1H June 2023 Higher tier, Question 15 6 marks

Question 15, shown as an image

Work out the value of n Show your working clearly.

[3]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Find 4% of 4.5 maths symbol 10157 Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 15(b)

Paper 2F January 2023 Foundation tier, Question 7 5 marks

(a)

Simplify c × c × c maths symbol c maths symbol c

[1]
(b)

Solve 5 + x = 12

[1]
Question 7, shown as an image
[1]
(d)

Expand 5(2 + 3h)

[1]
(e)

Factorise g2 + 7g

[1]
Reveal mark scheme Mark scheme for question 7(e)

Paper 2F January 2023 Foundation tier, Question 11 4 marks

Also involves Powers and roots

(a)

Work out the value of (4 + 3 + 6)2

64 = 4n

[1]
(b)

Write down the value of n

[1]
Question 11, shown as an image

Write down all the figures on your calculator display.

[2]
Reveal mark scheme Mark scheme for question 11(c)

Paper 2F January 2023 Foundation tier, Question 24, also on the Higher paper 7 marks

Also involves Straight line graphs · Factors, multiples and primes

(a)

Write down the value of (m + 2)0 where m is a positive integer.

[1]
Reveal mark scheme Mark scheme for question 24(a)
(b)

Simplify (3a2b4)3

[2]
(c)

Factorise fully 14x2y4 + 21x3y2

The diagram shows a straight line drawn on a grid.

Figure for question 24
[2]
Reveal mark scheme Mark scheme for question 24(c)
(d)

Write down an equation of the line.

[2]
Reveal mark scheme Mark scheme for question 24(d)

Paper 2H January 2023 Higher tier, Question 9, also on the Foundation paper 7 marks

(a)

Write down the value of (m + 2)0 where m is a positive integer.

[1]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Simplify (3a2b4)3

[2]
(c)

Factorise fully 14x2y4 + 21x3y2

The diagram shows a straight line drawn on a grid.

Figure for question 9
[2]
Reveal mark scheme Mark scheme for question 9(c)
(d)

Write down an equation of the line.

[2]
Reveal mark scheme Mark scheme for question 9(d)

Paper 2H January 2023 (R) Higher tier, Question 12 6 marks

(a)
Question 12, shown as an image
[1]
(b)
Question 12, shown as an image
[2]
Reveal mark scheme Mark scheme for question 12(b)
(c)

Expand and simplify 5x(3x + 4)(2x – 1)

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

Paper 1H June 2022 Higher tier, Question 9 4 marks

(a)

Simplify 8 maths symbol (4t)0

x6 ÷ x−5 = xp

[1]
(b)

Find the value of p

[1]
(c)

Simplify fully (2k2m4)3

[2]
Reveal mark scheme Mark scheme for question 9(c)

Paper 1H June 2022 (R) Higher tier, Question 12 3 marks

P = 33maths symbol52maths symbol7 Q = 32maths symbol5maths symbol72

(a)

Write down the highest common factor (HCF) of P and Q

P = 33maths symbol52maths symbol7 Q = 32maths symbol5maths symbol72

[1]
(b)

Work out the value of P3maths symbolQ Give your answer in the form 3xmaths symbol5ymaths symbol7z where x, y and z are positive integers.

[2]

Paper 1H June 2022 (R) Higher tier, Question 16 6 marks

(a)

Expand and simplify (3 x – 1)(x + 2)(3 x + 1)

[3]
Reveal mark scheme Mark scheme for question 16(a)
(b)
Question 16, shown as an image
[3]
Reveal mark scheme Mark scheme for question 16(b)

Paper 2F June 2022 (R) Foundation tier, Question 19 3 marks

Write 1200 as a product of powers of its prime factors. Show your working clearly.

[3]
Reveal mark scheme Mark scheme for question 19

Paper 2F June 2022 (R) Foundation tier, Question 24, also on the Higher paper 2 marks

Find an expression for x in terms of k and n

[2]
Reveal mark scheme Mark scheme for question 24

Paper 2H June 2022 (R) Higher tier, Question 6 8 marks

(a)
6 Question 6, shown as an image

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 6(a)
(b)

Simplify a0where a maths symbol 0

[1]
(c)
Question 6, shown as an image
[2]
Reveal mark scheme Mark scheme for question 6(c)
(d)

Factorise fully 10c3d2 + 15cd4

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

Paper 2H June 2022 (R) Higher tier, Question 7, also on the Foundation paper 2 marks

Find an expression for x in terms of k and n

[2]
Reveal mark scheme Mark scheme for question 7

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 ÷ w3

[1]
(c)

Simplify (8x5y3)2

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

Make t the subject of c = t3 – 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 ÷ w3

[1]
(c)

Simplify (8x5y3)2

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

Make t the subject of c = t3 – 8v

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

Paper 1H January 2022 Higher tier, Question 13 6 marks

(a)

Expand and simplify 5 x (x + 2)(3 x – 4)

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

(b) Simplify completely

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

Paper 2F January 2022 (R) Foundation tier, Question 23, also on the Higher paper 4 marks

(a)

Write down the value of x0

Given that 2–3 maths symbol 29 = 2n

[1]
(b)

find the value of n

Question 23, shown as an image
[1]
(c)

find the value of m

[2]
Reveal mark scheme Mark scheme for question 23(c)

Paper 2H January 2022 (R) Higher tier, Question 6, also on the Foundation paper 4 marks

(a)

Write down the value of x0

Given that 2–3 maths symbol 29 = 2n

[1]
(b)

find the value of n

Question 6, shown as an image
[1]
(c)

find the value of m

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

Paper 2H January 2022 Higher tier, Question 12 3 marks

a = 6 maths symbol 1040

Work out the value of a3 Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 12

Paper 1H November 2021 Higher tier, Question 7 3 marks

Write 3.6 maths symbol 103 as a product of powers of its prime factors. Show your working clearly.

[3]
Reveal mark scheme Mark scheme for question 7

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

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 – 11x + 24

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

Paper 1F January 2021 (R) Foundation tier, Question 24 4 marks

A = 28maths symbol35maths symbol114 B = 26maths symbol3maths symbol118

(a)

Find the highest common factor (HCF) of A and B.

[2]
Reveal mark scheme Mark scheme for question 24(a)
(b)

Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM as a product of powers of its prime factors.

[2]
Reveal mark scheme Mark scheme for question 24(b)

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 – 11x + 24

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

Paper 1H January 2021 (R) Higher tier, Question 12 9 marks

Also involves Solving exponential equations

(a)
Question 12, shown as an image
[2]
(b)

Write fraction maths symbol fraction as a single fraction in its simplest form.

Given that 4k+ 3 = 16maths symbol2k

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

find the value of k. Show your working clearly.

[4]
Reveal mark scheme Mark scheme for question 12(c)

Paper 2F January 2021 Foundation tier, Question 20 4 marks

(a)

Write down the value of y0

[1]
(b)
Question 20, shown as an image

Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 20(b)

Paper 1F November 2020 Foundation tier, Question 23, also on the Higher paper 3 marks

A = 2 maths symbol 343 B = 16 maths symbol 337

(a)

Find the highest common factor (HCF) of A and B.

[1]
(b)

Express the number A maths symbol B as a product of powers of its prime factors. Give your answer in its simplest form.

[2]
Reveal mark scheme Mark scheme for question 23(b)

Paper 1H November 2020 Higher tier, Question 10, also on the Foundation paper 3 marks

A = 2 maths symbol 343 B = 16 maths symbol 337

(a)

Find the highest common factor (HCF) of A and B.

[1]
(b)

Express the number A maths symbol B as a product of powers of its prime factors. Give your answer in its simplest form.

[2]
Reveal mark scheme Mark scheme for question 10(b)

Paper 2F November 2020 (R) Foundation tier, Question 3 3 marks

Here are the first five terms of a number sequence.

1 3 9 27 81

(a)

Find the next term of this sequence.

[1]
(b)

Explain how you found this term.

The 9th term of this number sequence is 6561

[1]
Reveal mark scheme Mark scheme for question 3(b)
(c)

Find the 10th term of this sequence.

[1]
Reveal mark scheme Mark scheme for question 3(c)

Paper 2F November 2020 (R) Foundation tier, Question 15 3 marks

Write 880 as a product of powers of its prime factors. Show your working clearly.

[3]
Reveal mark scheme Mark scheme for question 15

Paper 2F November 2020 (R) Foundation tier, Question 23 2 marks

23Given that 150x = 1

(a)

write down the value of x.

Given that 3–8 ÷ 3–6 = 3n

[1]
(b)

find the value of n.

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

Paper 1F January 2020 (R) Foundation tier, Question 16 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 f− 12f

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

Expand and simplify (x+ 2)(x− 5)

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

Paper 1F January 2020 Foundation tier, Question 21 9 marks

(a)

Expand and simplify (m − 8)(m + 5)

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

Factorise fully 5y+ 20y2

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

Simplify (p2+ 3)0

[1]
Question 21, shown as an image

Show clear algebraic working.

[4]
Reveal mark scheme Mark scheme for question 21(d)

Paper 2F January 2020 (R) Foundation tier, Question 12 6 marks

(a)

Simplify k + k + k + k

Question 12, shown as an image
[1]
(b)(i)

Write f as a single power of 9

[1]
(b)(ii)

Write f as a single power of 3

[1]
(c)

Write 517 maths symbol52 as a single power of 5

[1]
(d)

Write 800 as a product of its prime factors. Show your working clearly.

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

Paper 2H January 2020 (R) Higher tier, Question 1 3 marks

(a)

Write 517 maths symbol52 as a single power of 5

[1]
(b)

Write 800 as a product of its prime factors. Show your working clearly.

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

Paper 1F June 2019 Foundation tier, Question 14 4 marks

(a)

Find the highest common factor (HCF) of 40 and 64

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

A = 2n × 3 × 5m

Write 8 A as a product of powers of its prime factors.

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

Paper 1H June 2019 (R) Higher tier, Question 20 3 marks

a = 25 maths symbol 1014n where n is an integer. Find an expression, in terms of n, for fraction Give your answer in standard form.

[3]
Reveal mark scheme Mark scheme for question 20

Paper 1H June 2018 (R) Higher tier, Question 14 8 marks

(a)

Simplify (2e2 f3)3

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

Expand and simplify (3xmaths symboly)(x + 3y)

Question 14, shown as an image
[2]
Reveal mark scheme Mark scheme for question 14(b)
(c)

Find the value of k.

[2]
Reveal mark scheme Mark scheme for question 14(c)
(d)
Question 14, shown as an image
[2]
Reveal mark scheme Mark scheme for question 14(d)

Paper 2F June 2018 Foundation tier, Question 7 5 marks

(a)

Write 7 maths symbol 7 maths symbol 7 maths symbol 7 maths symbol 7 as a power of 7

[1]
Reveal mark scheme Mark scheme for question 7(a)
(b)

Show that 64 is both a square number and a cube number.

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

Find the value of 113

[1]
(d)
Question 7, shown as an image
[1]
Reveal mark scheme Mark scheme for question 7(d)

Paper 2F June 2018 Foundation tier, Question 24, also on the Higher paper 4 marks

(a)

Find the value of n.

[2]
Reveal mark scheme Mark scheme for question 24(a)
(b)

(13–6)4maths symbol 135 = 13k

Find the value of k.

[2]
Reveal mark scheme Mark scheme for question 24(b)

Paper 2H June 2018 Higher tier, Question 10, also on the Foundation paper 4 marks

(a)

Find the value of n.

[2]
Reveal mark scheme Mark scheme for question 10(a)
(b)

(13–6)4maths symbol 135 = 13k

Find the value of k.

[2]
Reveal mark scheme Mark scheme for question 10(b)

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