Use of symbols: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 2.1 Use of symbols, 2019–2025, with its mark scheme and examiner’s report.

All 111 questions on Use of symbols, as a list

June 2025 (R), Paper 1 Higher, Q8 (5 marks): (a) Simplify a × a 6 10 (b) Simplify c 30 ÷ c 12 (c) (i) Factorise y y 2 10 21 (ii) Hence, solve y y 2 10 21 0
June 2025 (R), Paper 1 Higher, Q15 (6 marks): (a) Solve 5 a 8 2 a 5 23 3 4 Show clear algebraic working. a = 1 y (b) Express in the form cyn where c and n are numbers to be found. 3
June 2025 (R), Paper 2 Foundation, Q22 (5 marks): (a) Write down the value of 50 5 9 5 3 5 k 5 2 (b) Find the value of k k = 4 5 3 (c) Simplify fully 2 d e
June 2025 (R), Paper 2 Higher, Q6 (5 marks): (a) Write down the value of 50 5 9 5 3 k 5 5 2 (b) Find the value of k k = 4 5 3 (c) Simplify fully 2 d e
June 2025, Paper 1 Foundation, Q21 (4 marks): x5 × x7 = xm (a) Find the value of m m = y8 ÷ y3 = yn (b) Find the value of n n = (c) Simplify fully (5a4r2)3
June 2025, Paper 1 Higher, Q4 (4 marks): x 5 × x 7 = x m (a) Find the value of m m = 8 ÷ y 3 = y n y (b) Find the value of n n = (c) Simplify fully (5a 2)3 4r
June 2025, Paper 1 Higher, Q15 (4 marks): where k is an integer. 3 3 (a) Find the value of k k = 21 (b) Show that can be written in the form c + d 3 − 2 where c and d are integers. Show each stage of yo
June 2025, Paper 2 Higher, Q15 (3 marks): Simplify fully a c 7 2 10
November 2024, Paper 1 Foundation, Q20 (6 marks): (a) Simplify p3 5 (b) Expand and simplify 2 n n n n 4 3 4 (c) Solve 2 x 5 x 4 3 Show clear algebraic working. x =
November 2024, Paper 1 Higher, Q3 (6 marks): (a) Simplify p3 5 (b) Expand and simplify 2 n 4 n 3 n n 4 (c) Solve 2 x 5 x 4 3 Show clear algebraic working. x =
November 2024, Paper 2 Higher, Q14 (3 marks): Given that 3 2 n 3 n 3 3 3 1 2 3 4 find the value of n Show your working clearly. n =
June 2024 (R), Paper 1 Foundation, Q22 (9 marks): (a) Simplify g ÷ g 9 2 (b) Expand 5 k k 2 ( 3 + 4 ) (c) (i) Factorise x − x − 2 2 63 (ii) Hence, solve x − x − = 0 2 2 63 (d) Solve the inequality 7 2 y
June 2024 (R), Paper 1 Higher, Q7 (9 marks): (a) Simplify g ÷ g 9 2 (b) Expand 5 k k 2 ( 3 + 4 ) (c) (i) Factorise x − x − 2 2 63 (ii) Hence, solve x − x − = 0 2 2 63 (d) Solve the inequality 7 2 y
June 2024 (R), Paper 1 Higher, Q14 (6 marks): (a) Expand and simplify 1 3 a b 2 (b) Simplify fully 9 5 a b
June 2024 (R), Paper 1 Higher, Q17 (4 marks): (a) 4 k12 Find the value of n n = 7 (b) Express in the form where c and d are integers. c + d − 2 3 Show your working clearly.
June 2024 (R), Paper 2 Foundation, Q22 (8 marks): (a) Solve 2 f f 4 17 3 Show clear algebraic working. f = (b) Simplify (e + 12)0 where e > 0 (c) Simplify fully 12 a h 4 6 ah 4 2 (d) Factorise fully 20x5y
June 2024 (R), Paper 2 Foundation, Q23 (2 marks): 3 3 n 3 10 3 Find the value of n n =
June 2024 (R), Paper 2 Higher, Q6 (8 marks): (a) Solve 2 f f 4 17 3 Show clear algebraic working. f = (b) Simplify (e + 12)0 where e > 0 (c) Simplify fully 12 a h 4 6 ah 4 2 (d) Factorise fully 20x5y
June 2024 (R), Paper 2 Higher, Q7 (2 marks): n 3 10 3 Find the value of n n =
June 2024, Paper 1 Foundation, Q25 (4 marks): (a) Simplify (2p) 0 where p > 0 9×y –3 = y n y (b) Find the value of n n = 4c 2 ) 3 (c) Simplify fully (5a
June 2024, Paper 1 Higher, Q10 (4 marks): (a) Simplify (2p) 0 where p > 0 9×y –3 = y n y (b) Find the value of n n = 4c 2 ) 3 (c) Simplify fully (5a
November 2023, Paper 2 Foundation, Q20 (8 marks): (a) Solve 2 x 5 x 2 5 6 Show clear algebraic working. x = (b) Simplify h 15 ÷ h 3 4 (c) Simplify fully 2 g k 3 5 n (d) Given that y 5 y y 12 7 y work out the va
November 2023, Paper 2 Higher, Q4 (8 marks): (a) Solve 2 x 5 x 2 5 6 Show clear algebraic working. x = (b) Simplify h 15 ÷ h 3 4 (c) Simplify fully 2 g k 3 5 (d) Given that y 5 y n y 12 y 7 work out the va
November 2023, Paper 2 Higher, Q12 (4 marks): 2 7 5 x 4 4 (a) Calculate the value of x x = 2 (b) Simplify fully 125 p y 6 24 3
June 2023 (R), Paper 1 Foundation, Q22 (4 marks): (a) Simplify m10 ÷ m3 kn × k4 = k12 (b) Write down the value of n n = (c) Simplify (3x6y8)2
June 2023 (R), Paper 1 Higher, Q6 (4 marks): (a) Simplify m10 ÷ m3 kn × k4 = k12 (b) Write down the value of n n = (c) Simplify (3x6y8)2
June 2023 (R), Paper 1 Higher, Q24 (5 marks): Given that 2n = 2x2 × 16x × 8 and x > 0 find an expression for x in terms of n State any restrictions on n
June 2023 (R), Paper 2 Foundation, Q22 (2 marks): (a) Simplify (4–2) 0 3–14 × 38 = 3m (b) Find the value of m m =
June 2023 (R), Paper 2 Higher, Q7 (2 marks): (a) Simplify (4–2)0 3–14 × 38 = 3m (b) Find the value of m m =
June 2023 (R), Paper 2 Higher, Q11 (2 marks): Express m k a b 6 10 2 where a, b and c are integers to be found. c 25
June 2023, Paper 1 Foundation, Q21 (8 marks): (a) Simplify (2c 4d 7) 3 (b) Find the value of 5y 0 where y > 0 2b 3 + 20a 3b (c) Factorise fully 16a 2 + 9x – 22 (d) (i) Factorise x 2 + 9x – 22 = 0 (ii) Hence
June 2023, Paper 1 Higher, Q6 (8 marks): (a) Simplify (2c 4d 7) 3 (b) Find the value of 5y 0 where y > 0 2b 3 + 20a 3b (c) Factorise fully 16a 2 + 9x – 22 (d) (i) Factorise x 2 + 9x – 22 = 0 (ii) Hence
June 2023, Paper 2 Higher, Q15 (7 marks): (a) Simplify fully 32 a 15 5 3 1 (b) Express in the form pxn where p and n are integers. 10 x (c) Solve 1 2 y 4 2 y 1 3 5 2 Show clear algebraic working. y
January 2023 (R), Paper 1 Foundation, Q18 (3 marks): (a) Simplify w12 ÷ w3 (b) Simplify 5m4p2× 2m3p
January 2023 (R), Paper 1 Higher, Q12 (2 marks): Solve 2–4x = 32 x =
January 2023 (R), Paper 2 Higher, Q12 (6 marks): (a) Simplify 2 y 0 3 ( ) (b) Simplify fully 16 a 4 4 (c) Expand and simplify 5x(3x + 4)(2x – 1)
January 2023, Paper 1 Higher, Q12 (2 marks): 3 (a) Work out the value of m m = 5–10 ÷ 5– 4 = 5n (b) Work out the value of n n =
January 2023, Paper 2 Foundation, Q24 (7 marks): (a) Write down the value of (m + 2)0 where m is a positive integer. (b) Simplify (3a2b4)3 (c) Factorise fully 14x2y4 + 21x3y2 The diagram shows a straight line
January 2023, Paper 2 Higher, Q9 (7 marks): (a) Write down the value of (m + 2)0 where m is a positive integer. (b) Simplify (3a2b4)3 (c) Factorise fully 14x2y4 + 21x3y2 The diagram shows a straight line
January 2023, Paper 2 Higher, Q26 (5 marks): Find the values of n such that 2 5 × × 10 n 2 n n 5 n 4 3 ( − ) 2 1 2 ( − ) = 1 20 2 Show clear algebraic working.
June 2022 (R), Paper 1 Higher, Q16 (6 marks): (a) Expand and simplify (3x – 1)(x + 2)(3x + 1) − 2  x  2 5 (b) Simplify fully   xy 8 2
June 2022 (R), Paper 2 Foundation, Q23 (8 marks): (a) Solve p = 3 p − 5 10 Show clear algebraic working. p = 0 where a > 0 (b) Simplify a xy 3 (c) Simplify fully 3 6 x y 2 (d) Factorise fully 10c 3d 2 + 15cd 4
June 2022 (R), Paper 2 Foundation, Q24 (2 marks): 2 = 2 x 4 n Find an expression for x in terms of k and n x =
June 2022 (R), Paper 2 Higher, Q6 (8 marks): (a) Solve p = 3 p − 5 10 Show clear algebraic working. p = 0 where a > 0 (b) Simplify a xy 3 (c) Simplify fully 3 6 x y 2 (d) Factorise fully 10c 3d 2 + 15cd 4
June 2022 (R), Paper 2 Higher, Q7 (2 marks): = 2 x n 4 Find an expression for x in terms of k and n x =
June 2022, Paper 1 Foundation, Q24 (4 marks): (a) Simplify 8 × (4t)0 x6 ÷ x−5 = xp (b) Find the value of p p = (c) Simplify fully (2k2m4) 3
June 2022, Paper 1 Higher, Q9 (4 marks): (a) Simplify 8 × (4t)0 x6 ÷ x−5 = xp (b) Find the value of p p = (c) Simplify fully (2k2m4) 3
June 2022, Paper 2 Higher, Q24 (3 marks): = 3 x × 6 9 n 2 + 8 Express x in terms of n Show your working clearly and simplify your expression. x =
January 2022 (R), Paper 1 Foundation, Q23 (5 marks): (a) Simplify x4 × x5 (b) Simplify (4y2)3 (c) Factorise n2 – 7n + 12
January 2022 (R), Paper 1 Higher, Q9 (5 marks): (a) Simplify x4 × x5 (b) Simplify (4y2)3 (c) Factorise n2 – 7n + 12
January 2022 (R), Paper 1 Higher, Q19 (3 marks): Given that xm 3 x (a) find the value of m m = Given that a, b and c are integers, (b) express 3x2 + 12x + 19 in the form a(x + b)2 + c
January 2022 (R), Paper 2 Foundation, Q23 (4 marks): (a) Write down the value of x0 n Given that 2–3 × 29 = 2 (b) find the value of n n = 206 m Given that 7 7 7 3 214 7 (c) find the value of m m =
January 2022 (R), Paper 2 Higher, Q6 (4 marks): (a) Write down the value of x0 n Given that 2–3 × 29 = 2 (b) find the value of n n = 206 m Given that 7 7 7 3 214 7 (c) find the value of m m =
January 2022, Paper 1 Foundation, Q16 (6 marks): (a) Simplify a7 × a4 (b) Simplify w15 ÷ w3 (c) Simplify (8x5y3)2 (d) Make t the subject of c = t3 – 8v
January 2022, Paper 1 Higher, Q1 (6 marks): (a) Simplify a7 × a4 (b) Simplify w15 ÷ w3 (c) Simplify (8x5y3)2 c = t3 – 8v (d) Make t the subject of
January 2022, Paper 1 Higher, Q13 (6 marks): (a) Expand and simplify 5x(x + 2)(3x – 4) 3 −  16 w 8  4 (b) Simplify completely   y 20
November 2021, Paper 1 Foundation, Q13 (3 marks): (a) Simplify e 8 e 2 ÷ (b) Expand and simplify (x – 3)(x + 1)
November 2021, Paper 1 Higher, Q1 (3 marks): (a) Simplify e 8 e 2 ÷ (b) Expand and simplify (x – 3)(x + 1)
November 2021, Paper 2 Foundation, Q17 (4 marks): (a) Write down the value of m, given that 34 ´ 35 = 3m m = (b) Write down the value of n, given that 7 = 5n n = (c) Find the value of p, given that 7 8 7 2 6 7
November 2021, Paper 2 Foundation, Q24 (4 marks): (a) Simplify (3x2y)0 (b) (i) Factorise x2 – 5x – 36 (ii) Hence solve x2 – 5x – 36 = 0
November 2021, Paper 2 Higher, Q1 (4 marks): (a) Write down the value of m, given that 34 ´ 35 = 3m m = (b) Write down the value of n, given that 7 = 5n n = 8 2 (c) Find the value of p, given that 7 7 7 6
November 2021, Paper 2 Higher, Q8 (4 marks): (a) Simplify (3x2y)0 (b) (i) Factorise x2 – 5x – 36 (ii) Hence solve x2 – 5x – 36 = 0
November 2021, Paper 2 Higher, Q12 (7 marks): (a) Simplify (64p9q12) 3 (b) Write as a single fraction 2 4 9 + - 3 x 5 x 10 x Give your answer in its simplest form. (c) Expand and simplify 4x(x – 5)(2x + 3)
June 2021, Paper 1 Foundation, Q20 (6 marks): (a) Expand and simplify 3x(2x + 3) – x(3x + 5) (b) Make t the subject of the formula p = at – d Given that w 5 × w n = w 10 w 3 (c) work out the value of n. n =
June 2021, Paper 1 Higher, Q5 (6 marks): (a) Expand and simplify 3x(2x + 3) – x(3x + 5) (b) Make t the subject of the formula p = at – d Given that w 5 × w n = w 10 w 3 (c) work out the value of n. n =
June 2021, Paper 1 Higher, Q11 (4 marks): 2 × 16 = 2 x (a) Find the value of x. Show your working clearly. x = ( 11 − 6 5 ) n = 11 11 4 (b) Find the value of n. Show your working clearly. n =
June 2021, Paper 2 Higher, Q14 (3 marks): Simplify fully   y 10 16
January 2021 (R), Paper 1 Foundation, Q8 (4 marks): (a) Simplify a×a× a×a (b) Simplify 4b×5c (c) Simplify 6d + 2e + d – 5e
January 2021 (R), Paper 1 Foundation, Q21 (5 marks): (a) Make c the subject of A = c y – 5z (b) Write down the value of g 0 (c) Factorise x 2 – 11x + 24
January 2021 (R), Paper 1 Higher, Q6 (5 marks): (a) Make c the subject of A = c y – 5z (b) Write down the value of g 0 (c) Factorise x 2 – 11x + 24
January 2021 (R), Paper 1 Higher, Q12 (9 marks): (a) Simplify (16e (b) Write 2 x + 1 x − 2 as a single fraction in its simplest form. + 4 3 k + 3 = 16 × 2 k Given that 4 (c) find the value of k. Show your work
January 2021 (R), Paper 2 Foundation, Q15 (4 marks): (a) Simplify (3k 2) 4 4n) ÷ (3n –5) (b) Simplify (21m
January 2021 (R), Paper 2 Higher, Q4 (4 marks): (a) Simplify (3k 2) 4 4n) ÷ (3n –5) (b) Simplify (21m
January 2021 (R), Paper 2 Higher, Q19 (7 marks): (a) Simplify 8 × 4 Give your answer in the form 2 a where a is an integer. Show each stage of your working clearly. 4   4 −  =   1  Given that n 5 where
January 2021, Paper 1 Foundation, Q25 (5 marks): (a) Simplify (2x 3y 5) 4 (b) (i) Factorise x 2 + 5x – 36 (ii) Hence, solve x 2 + 5x – 36 = 0
January 2021, Paper 1 Higher, Q9 (5 marks): (a) Simplify (2x 3y 5) 4 (b) (i) Factorise x 2 + 5x – 36 (ii) Hence, solve x 2 + 5x – 36 = 0
January 2021, Paper 2 Foundation, Q19 (7 marks): (a) Expand and simplify 4x(2x + 5) – 3x(2x – 3) 5 n Given that y × y = y 13 6 y (b) work out the value of n. n = (c) (i) Solve the inequality 7t – 8 < 2t + 7 (i
January 2021, Paper 2 Foundation, Q20 (4 marks): (a) Write down the value of y 0 141 140 (b) Work out 9 6 . × 10 + 6 4 . × 10 × 16 3 2 . 10 Give your answer in standard form.
January 2021, Paper 2 Higher, Q5 (7 marks): (a) Expand and simplify 4x(2x + 5) – 3x(2x – 3) 5 n Given that y × y = y13 6 y (b) work out the value of n. n = (c) (i) Solve the inequality 7t – 8 < 2t + 7 (ii
January 2021, Paper 2 Higher, Q6 (4 marks): (a) Write down the value of y0 141 140 (b) Work out 9 6 . × 10 + 6 4 . × 10 × 16 3 2 . 10 Give your answer in standard form.
January 2021, Paper 2 Higher, Q11 (3 marks): Simplify fully   6 10 18 t w
November 2020 (R), Paper 1 Foundation, Q19 (6 marks): (a) Simplify h7×h2 G = c2 – 4c (b) Find the value of G when c = –5 G = x − (c) Solve 5 3 = 2x + 3 4 Show clear algebraic working. x =
November 2020 (R), Paper 1 Higher, Q3 (6 marks): (a) Simplify h7×h2 G = c2 – 4c (b) Find the value of G when c = –5 G = x − (c) Solve 5 3 = 2x + 3 4 Show clear algebraic working. x =
November 2020 (R), Paper 1 Higher, Q21 (5 marks): Given that M = 18 4 n × 2 3 ( n − 6 n ) × 3 2 1 4 ( − n ) 12 2 find the values of n for which M = 2
November 2020 (R), Paper 2 Foundation, Q23 (2 marks): Given that 150x = 1 (a) write down the value of x. x = Given that 3–8 ÷ 3–6 = 3n (b) find the value of n. n =
November 2020 (R), Paper 2 Higher, Q10 (2 marks): Given that 150x = 1 (a) write down the value of x. x = Given that 3–8 ÷ 3–6 = 3n (b) find the value of n. n =
November 2020, Paper 1 Foundation, Q9 (7 marks): c = 4 d = 7 (a) Work out the value of 3c + 2d p = −6 m = −2 (b) Work out the value of 2p2 + 3m There are 6 eggs in a small box of eggs. There are 12 eggs in a l
November 2020, Paper 2 Foundation, Q21 (6 marks): (a) Simplify g6 × g4 (b) Simplify (3cd4)2 (c) Solve the simultaneous equations 4x + 3y = 17 x + 2y = 5 Show clear algebraic working. x = y =
November 2020, Paper 2 Higher, Q1 (6 marks): (a) Simplify g6 × g4 (b) Simplify k10 ÷ k3 (c) Simplify (3cd4)2 (d) Solve the inequality 4x + 7 > 2
November 2020, Paper 2 Higher, Q11 (8 marks): (a) Simplify fully (8e15) 3 − 4 y   (b) Express in the form ayn where a and n are integers.   2 x x (c) Solve 4 − 2 5 − 3 − = 6 3 4 Show clear algebraic w
November 2020, Paper 2 Higher, Q12 (3 marks): Given that 3 x = 81 3 9 find the value of x. Show clear algebraic working. x =
January 2020 (R), Paper 2 Foundation, Q12 (6 marks): (a) Simplify k + k + k + k f = 9 × 9 × 9 × 9 (b) (i) Write f as a single power of 9 (ii) Write f as a single power of 3 (c) Write 517 × 52 as a single power of
January 2020 (R), Paper 2 Foundation, Q18 (4 marks): (a) Expand e(3e – 5) (b) Factorise 35 + 5f (c) Simplify (4pq2)3
January 2020 (R), Paper 2 Higher, Q1 (3 marks): (a) Write 517 × 52 as a single power of 5 (b) Write 800 as a product of its prime factors. Show your working clearly.
January 2020, Paper 1 Foundation, Q21 (9 marks): (a) Expand and simplify (m − 8)(m + 5) (b) Factorise fully 5y + 20y2 (c) Simplify ( p2 + 3)0 − x (d) Solve 3(2x − 5) = 9 2 Show clear algebraic working. x = for
January 2020, Paper 1 Higher, Q7 (9 marks): (a) Expand and simplify (m − 8)(m + 5) (b) Factorise fully 5y + 20y2 (c) Simplify ( p2 + 3)0 (d) Solve 3(2x − 5) = 9 − x 2 Show clear algebraic working. x =
January 2020, Paper 2 Foundation, Q17 (3 marks): (a) Simplify x 9 x 2 (b) Write 7 8 × 7 4 as a single power of 7 7 3
January 2020, Paper 2 Higher, Q1 (3 marks): (a) Simplify x 9 x 2 × (b) Write 7 8 7 4 as a single power of 7 7 3
June 2019 (R), Paper 1 Foundation, Q22 (4 marks): (a) Simplify t9 ÷ t3 (b) Simplify w5 q w7 (c) Simplify (5xy2)3
June 2019 (R), Paper 1 Higher, Q9 (4 marks): (a) Simplify t9 ÷ t3 (b) Simplify w5 q w7 (c) Simplify (5xy2)3
June 2019 (R), Paper 2 Higher, Q14 (4 marks): (a) Simplify fully ( x y 12 8 ) 4 3 x Given that 3 n = 9 y (b) find an expression for n in terms of x and y. n =
June 2019, Paper 1 Foundation, Q16 (8 marks): P = 2g + 3h (a) Work out the value of P when g = 7 and h í (b) Simplify e9 ÷ e5 F 6LPSOLI\ ௘y2)8 (d) Expand and simplify (x + 9)(x – 2) (e) Factorise f
June 2019, Paper 1 Higher, Q3 (6 marks): (a) Simplify e9 ÷ e5 E 6LPSOLI\ ௘y2)8 (c) Expand and simplify (x + 9)(x – 2) (d) Factorise fully 16c4p2 + 20cp3
June 2019, Paper 1 Higher, Q12 (8 marks): (a) Factorise 2x2íx + 6 (b) Solve 4 m + 9 ím 3 Show clear algebraic working. m = y 4 (c) Write in the form yb where b is a fraction. y
January 2019 (R), Paper 1 Higher, Q15 (8 marks): (a) Simplify (3x2y5)4 (b) Expand and simplify 4n(n – 3)(n + 5) (c) Factorise 4c2 – 9d2 (d) Simplify fully x 2 − 7 x + 12 4 x − x 2
January 2019 (R), Paper 2 Higher, Q8 (5 marks): (a) Simplify fully 15 k m 4 3 5 km 2 (b) Solve the inequality 7 < 4x − 1  17
January 2019 (R), Paper 2 Higher, Q10 (7 marks): (a) Simplify fully 16 x y 8 6 2 (b) Solve 8 − 2 x 2 x − 3 4 − = 3 2 Show clear algebraic working. x = 1 (c) Make f the subject of m ef = 3
January 2019 (R), Paper 2 Higher, Q14 (6 marks): (a) Given that a = 3x and b = 3y express in terms of a or b or a and b, (i) 32x (ii) 3x + 4y (iii) 3y − 1 a = 3x and b = 3y ab = 2187 a2b = 177 147 (b) Work out
January 2019, Paper 1 Higher, Q16 (4 marks): (a) Rationalise the denominator of a + b where a is an integer and b is a prime number. a 4 b − Simplify your answer. −5   y x m (b) Given that where x ≠ y =
January 2019, Paper 2 Foundation, Q11 (8 marks): (a) Solve 5m + 7 = 24 m = t − e (b) Make t the subject of k = 2 (c) Simplify p8 ÷ p3 (d) Simplify n0 (e) Simplify (3x2y5)3
January 2019, Paper 2 Higher, Q12 (9 marks): (a) Simplify n0 (b) Simplify (3x2y5)3 (c) Factorise fully 2e2 – 18 6 a + r (d) Make r the subject of m = 5 r

Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel International GCSE Maths paper.

Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.

2,567 questions