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Edexcel IGCSE Maths

Topic questions Pure mathematics Algebraic notation & vocabulary

Algebraic notation & vocabulary

46 questions · 287 marks · about 5.5 hours

Algebraic notation and vocabulary questions

Edexcel 4MA1 Algebraic notation and vocabulary 46 questions

Paper 1F June 2025 (R) Foundation tier, Question 5 7 marks

(a)

Simplify 4e ร— 7f

[1]
(b)

Simplify d ร— d ร— d ร— d ร— d

[1]
(c)

Simplify 3a + 2k + a โ€“ 7k

[2]
(d)

Solve x + 6 = 15

[1]
(e)

Solve 2r โ€“ 9 = 14

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

Paper 1F June 2025 Foundation tier, Question 21 4 marks

x5 ร— x7 = xm

(a)

Find the value of m

y8 รท 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 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 (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 June 2024 (R) Foundation tier, Question 22, also on the Higher paper 9 marks

(a)

Simplify g9 maths symbol g2

[1]
(b)

Expand 5k2(k3 + 4)

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

Factorise x2 maths symbol 2x maths symbol 63

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

Hence, solve x2 maths symbol 2x maths symbol 63 = 0

[1]
(d)

Solve the inequality 7 maths symbol 2y maths symbol 3y maths symbol 12

[3]
Reveal mark scheme Mark scheme for question 22(d)

Paper 1F June 2024 Foundation tier, Question 25 4 marks

(a)

Simplify (2p)0 where p maths symbol 0

y9maths symbolyโ€“3 = yn

[1]
(b)

Find the value of n

[1]
(c)

Simplify fully (5a4c2)3

[2]
Reveal mark scheme Mark scheme for question 25(c)

Paper 1H June 2024 (R) Higher tier, Question 7, also on the Foundation paper 9 marks

(a)

Simplify g9 maths symbol g2

[1]
(b)

Expand 5k2(k3 + 4)

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

Factorise x2 maths symbol 2x maths symbol 63

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

Hence, solve x2 maths symbol 2x maths symbol 63 = 0

[1]
(d)

Solve the inequality 7 maths symbol 2y maths symbol 3y maths symbol 12

[3]
Reveal mark scheme Mark scheme for question 7(d)

Paper 2F June 2024 (R) Foundation tier, Question 9 8 marks

(a)

Simplify c ร— c ร— c

[1]
(b)

Simplify 12d ร— 3e

[1]
(c)
Question 9, shown as an image
[1]
(d)

Solve 2g maths symbol 3 maths symbol 6

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

Expand x(x โ€“ 4)

P maths symbol 4y2 maths symbol w

[1]
(f)

Work out the value of P when y = โˆ’3 and w = 2

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

Paper 2F June 2024 (R) Foundation tier, Question 22 8 marks

(a)
Question 22, shown as an image

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 22(a)
(b)

Simplify (e + 12)0 where e > 0

[1]
(c)
Question 22, shown as an image
[2]
Reveal mark scheme Mark scheme for question 22(c)
(d)

Factorise fully 20x5y + 12x3y4

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

Paper 2F November 2023 Foundation tier, Question 20 8 marks

(a)
Question 20, shown as an image

Show clear algebraic working.

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

Simplify h15 maths symbol h3

[1]
(c)

Simplify fully maths symbol2g3k5 maths symbol4

[2]
Question 20, shown as an image

work out the value of n

[2]
Reveal mark scheme Mark scheme for question 20(d)

Paper 1F June 2023 Foundation tier, Question 21, also on the Higher paper 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 โ€“ 22

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

Hence solve x2 + 9x โ€“ 22 = 0

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

Paper 1H June 2023 Higher tier, Question 6, also on the Foundation paper 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 6(c)
(d)(i)

Factorise x2 + 9x โ€“ 22

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

Hence solve x2 + 9x โ€“ 22 = 0

[1]
Reveal mark scheme Mark scheme for question 6(d)(ii)

Paper 1H June 2023 (R) Higher tier, Question 6 4 marks

(a)

Simplify m10 รท 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 6(c)

Paper 1H June 2023 (R) Higher tier, Question 24 5 marks

Also involves The discriminant

Given that

2n = 2x2 maths symbol 16x ร— 8

and

x maths symbol 0

find an expression for x in terms of n State any restrictions on n

[5]
Reveal mark scheme Mark scheme for question 24

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

Also involves Straight line graphs ยท 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 1F June 2022 Foundation tier, Question 24 4 marks

(a)

Simplify 8 maths symbol (4t)0

x6 รท xโˆ’5 = xp

[1]
(b)

Find the value of p

[1]
(c)

Simplify fully (2k2m4)3

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

Paper 2F June 2022 (R) Foundation tier, Question 9 5 marks

(a)

Simplify amaths symbolaร—amaths symbolaร—a

[1]
(b)

Simplify 8bร—3c

[1]
(c)

Expand 3(x + 4)

Q = 5v2 โ€“ w

[1]
(d)

Work out the value of Q when v = fraction and w = fraction

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

Paper 2F June 2022 (R) Foundation tier, Question 23 8 marks

(a)
Question 23, shown as an image

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 23(a)
(b)

Simplify a0where a maths symbol 0

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

Factorise fully 10c3d2 + 15cd4

[2]
Reveal mark scheme Mark scheme for question 23(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 1F January 2022 (R) Foundation tier, Question 23 5 marks

(a)

Simplify x4 maths symbol x5

[1]
(b)

Simplify (4y2)3

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

Factorise n2 โ€“ 7n + 12

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

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 1F November 2021 Foundation tier, Question 13, also on the Higher paper 3 marks

(a)

Simplify e8 maths symbol e2

[1]
(b)

Expand and simplify (x โ€“ 3)(x + 1)

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

Paper 1H November 2021 Higher tier, Question 1, also on the Foundation paper 3 marks

(a)

Simplify e8 maths symbol e2

[1]
(b)

Expand and simplify (x โ€“ 3)(x + 1)

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

Paper 1F January 2021 Foundation tier, Question 25, also on the Higher paper 5 marks

(a)

Simplify (2x3y5)4

[2]
Reveal mark scheme Mark scheme for question 25(a)
(b)(i)

Factorise x2 + 5x โ€“ 36

[2]
Reveal mark scheme Mark scheme for question 25(b)(i)
(b)(ii)

Hence, solve x2 + 5x โ€“ 36 = 0

[1]
Reveal mark scheme Mark scheme for question 25(b)(ii)

Paper 1H January 2021 Higher tier, Question 9, also on the Foundation paper 5 marks

(a)

Simplify (2x3y5)4

[2]
Reveal mark scheme Mark scheme for question 9(a)
(b)(i)

Factorise x2 + 5x โ€“ 36

[2]
Reveal mark scheme Mark scheme for question 9(b)(i)
(b)(ii)

Hence, solve x2 + 5x โ€“ 36 = 0

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

Paper 2F January 2021 Foundation tier, Question 7 8 marks

(a)

Simplify p + p + p + p + p + p

[1]
(b)

Simplify 5y2 + 6y2 โ€“ 3y2

[1]
(c)

Simplify emaths symbolemaths symbolemaths symbolemaths symbole

[1]
(d)

Simplify 5cmaths symbol4d

[1]
(e)

Solve x โ€“ 7 = 19

182 + 152 โ€“ 53 = 4n

[1]
(f)

Work out the value of n.

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

Factorise 9t โ€“ 6

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

Paper 2F January 2021 Foundation tier, Question 19 7 marks

(a)

Expand and simplify 4 x (2 x + 5) โ€“ 3 x (2 x โ€“ 3)

Question 19, shown as an image
[2]
Reveal mark scheme Mark scheme for question 19(a)
(b)

work out the value of n.

[2]
Reveal mark scheme Mark scheme for question 19(b)
(c)(i)

Solve the inequality 7t โ€“ 8 < 2t + 7

[2]
Reveal mark scheme Mark scheme for question 19(c)(i)
(c)(ii)

On the number line below, represent the solution set of the inequality solved in part (c)(i)

Question 19, shown as an image

โ€“5 โ€“4 โ€“3 โ€“2 โ€“1 0 1 2 3 4 5

[1]
Reveal mark scheme Mark scheme for question 19(c)(ii)

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 1F November 2020 (R) Foundation tier, Question 19, also on the Higher paper 6 marks

(a)

Simplify h7maths symbolh2

G = c2 โ€“ 4c

[1]
(b)

Find the value of G when c = โ€“5

[2]
Question 19, shown as an image

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 19(c)

Paper 1H November 2020 (R) Higher tier, Question 3, also on the Foundation paper 6 marks

(a)

Simplify h7maths symbolh2

G = c2 โ€“ 4c

[1]
(b)

Find the value of G when c = โ€“5

[2]
Question 3, shown as an image

Show clear algebraic working.

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

Paper 2F November 2020 Foundation tier, Question 21 6 marks

(a)

Simplify g6 maths symbol g4

[1]
(b)

Simplify (3cd4)2

[2]
(c)

Solve the simultaneous equations

4 x + 3 y = 17 x + 2 y = 5

Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 21(c)

Paper 2H November 2020 Higher tier, Question 1 6 marks

(a)

Simplify g6 maths symbol g4

[1]
(b)

Simplify k10 รท k3

[1]
(c)

Simplify (3cd4)2

[2]
(d)

Solve the inequality 4x + 7 > 2

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

Paper 1H January 2020 (R) Higher tier, Question 3 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)
Question 3, shown as an image
[2]
Reveal mark scheme Mark scheme for question 3(d)

Paper 1H January 2020 Higher tier, Question 7 9 marks

(a)

Expand and simplify (mโˆ’ 8)(m+ 5)

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

Factorise fully 5y+ 20y2

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

Simplify (p2+ 3)0

[1]
Question 7, shown as an image

Show clear algebraic working.

[4]
Reveal mark scheme Mark scheme for question 7(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 2F January 2020 (R) Foundation tier, Question 18 4 marks

(a)

Expand e (3 e โ€“ 5)

[1]
(b)

Factorise 35 + 5f

[1]
(c)

Simplify (4pq2)3

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

Paper 1F June 2019 Foundation tier, Question 6 5 marks

(a)

Simplify 6e maths symbol 2f

[1]
(b)

Simplify 5m + 7kmaths symbolm + k

[2]
(c)

Solve 5 y + 3 = 14

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

Paper 1F June 2019 Foundation tier, Question 16 8 marks

Also involves Indices

P = 2 g + 3 h

(a)

Work out the value of P when g = 7 and hmaths symbol

[2]
(b)

Simplify e9 รท e5

[1]
(c)

=Simplify (เฏ˜y2)8

[1]
(d)

Expand and simplify (x + 9)(x โ€“ 2)

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

Factorise fully 16c4p2 + 20cp3

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

Paper 1H June 2019 Higher tier, Question 3 6 marks

Also involves Indices

(a)

Simplify e9 รท e5

[1]
(b)

Simplify (เฏ˜y2)8

[1]
(c)

Expand and simplify (x + 9)(x โ€“ 2)

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

Factorise fully 16c4p2 + 20cp3

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

Paper 1F June 2018 Foundation tier, Question 16 9 marks

(a)

Simplify y5 ร— y9

[1]
(b)

Simplify (2m3)4

[2]
(c)

Solve 5(x + 3) = 3xmaths symbol Show clear algebraic working.

[3]
Reveal mark scheme Mark scheme for question 16(c)
(d)(i)

Factorise x2 + 2xmaths symbol

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

Hence, solve x2 + 2xmaths symbol

[1]

Paper 1H June 2018 Higher tier, Question 3 9 marks

(a)

Simplify y5maths symboly9

[1]
(b)

Simplify (2m3)4

[2]
(c)

Solve 5(x + 3) = 3 x โ€“ 4 Show clear algebraic working.

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

Factorise x2 + 2x โ€“ 24

[2]
Reveal mark scheme Mark scheme for question 3(d)(i)
(d)(ii)

Hence, solve x2 + 2x โ€“ 24 = 0

[1]

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)

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