Expressions and formulae: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 2.3 Expressions and formulae, 2019–2025, with its mark scheme and examiner’s report.

All 98 questions on Expressions and formulae, as a list

June 2025 (R), Paper 1 Foundation, Q23 (8 marks): (a) Expand x x ( − 3 ) t 4 (b) Make t the subject of m 5 (c) Simplify a × a 6 10 (d) Simplify c 30 ÷ c 12 (e) (i) Factorise y y 2 10 21 (ii) Hence, solve y y 2
June 2025 (R), Paper 2 Foundation, Q6 (2 marks): Here is a number machine. input output × 4 − 15 (a) Find the output when the input is 10 (b) Find the output when the input is −2
June 2025 (R), Paper 2 Foundation, Q13 (7 marks): (a) Factorise 15 − x 5 d = 5p + 7r (b) Work out the value of p when d = 35 and r = 2 p = Sweets are sold in small packets and large packets. There are 12 sweets
June 2025 (R), Paper 2 Higher, Q17 (4 marks): Make k the subject of p k 7 3 2
June 2025, Paper 1 Foundation, Q14 (5 marks): (a) Expand x x 7 (b) Factorise 8 y − 10 m 5 a 7 b (c) Work out the value of a when m = 48 and b = 3 a =
June 2025, Paper 2 Foundation, Q10 (3 marks): Lui is asked to work out the value of 30 – 4x when x = –5 Here is his working and his answer. 30 – 4x = 30 – 4 × –5 = 30 – 20 = 10 Lui’s answer is wrong. (a) Ex
June 2025, Paper 2 Foundation, Q12 (5 marks): (a) Make y the subject of w = 3y – 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 packe
June 2025, Paper 2 Higher, Q16 (4 marks): Make t the subject of the formula c t 2 7 8
November 2024, Paper 1 Foundation, Q5 (7 marks): (a) Simplify 8 d d d 4 7 (b) Simplify m × 10 p (c) Solve x 5 19 x = (d) Solve y = 6 8 y = (e) Simplify a a a a × × × k = 8 and n = 12 (f) Work out the value of
November 2024, Paper 1 Foundation, Q11 (2 marks): Make d the subject of the formula c 8 d 5
November 2024, Paper 2 Higher, Q12 (7 marks): (a) Solve 3 x 2 2 x 1 x 5 3 Show clear algebraic working. x = a bc (b) Make c the subject of the formula f c d
June 2024 (R), Paper 1 Foundation, Q10 (4 marks): Charlene is comparing cooking temperatures in degrees Celsius (°C) with cooking temperatures in degrees Fahrenheit (°F) She finds this rule to change from °C to
June 2024 (R), Paper 1 Foundation, Q13 (3 marks): Kye has some toy cars. He has n red cars. He has twice as many blue cars as red cars. He has 7 more green cars than red cars. (a) Write an expression, in terms
June 2024 (R), Paper 2 Foundation, Q9 (8 marks): (a) Simplify c × c × c (b) Simplify 12d × 3e (c) Solve k = 7 4 k = (d) Solve 2 g 3 6 g = (e) Expand x(x – 4) P y w 4 2 (f) Work out the value of P whe
June 2024 (R), Paper 2 Higher, Q13 (3 marks): OAB is a sector of a circle with centre O and radius r cm. A Diagram NOT accurately drawn 60° r cm O B Angle AOB = 60° The perimeter of the sector is P cm. Find
June 2024, Paper 1 Foundation, Q8 (6 marks): (a) Simplify 10x – 7y – 6x + 4y T = 4d – 6e (b) Work out the value of T when d = 13 and e = 7 T = (c) Solve 5p + 11 = 28 p =
June 2024, Paper 2 Foundation, Q11 (8 marks): (a) Simplify e × e × e × e × e (b) Simplify m + m + m 2 + 7g 2 – 4g 2 (c) Simplify 3g (d) Expand a (a + 8) (e) Factorise 15x + 20 Sophia sells d packs of toy ca
June 2024, Paper 2 Higher, Q15 (7 marks): (a) Make g the subject of e = g 11 + 2 (b) Solve the inequality 3y 2 + 4y – 32 > 0 Show your working clearly.
June 2024, Paper 2 Higher, Q20 (3 marks): Given that k = x – y and x = 1 4y in the form a by 2 5 k express where a, b, c and d are integers. c dy x + 2
November 2023, Paper 1 Foundation, Q7 (7 marks): (a) Simplify 9d × 5c (b) Simplify 7p + 5n – 9p + 3n T = 8e − 6f (c) Work out the value of T when e = 9 and f = 5 T = (d) Solve 5m − 6 = 17 m =
November 2023, Paper 1 Higher, Q15 (3 marks): Make n the subject of the formula x n 3 4
November 2023, Paper 2 Foundation, Q10 (4 marks): Here is a number machine. input × y output − 17 When the input is 7 the output is 60 (a) Work out the value of y y = Here is a different number machine. input +
November 2023, Paper 2 Foundation, Q12 (6 marks): (a) Expand x(x + 3) (b) Factorise 8p + 10 (c) Make e the subject of y = eh ‒ f Janya thinks of a whole number. She calls her whole number w Janya writes down th
June 2023 (R), Paper 1 Foundation, Q14 (3 marks): A small bag of grain contains 2 kg of grain. A large sack of grain contains 7 kg of grain. Makenna buys r small bags of grain and h large sacks of grain. The to
June 2023 (R), Paper 2 Foundation, Q8 (5 marks): Georgia is a plumber. She uses this rule to work out the total cost, in euros, of her customers’ bills. number of hours work × 25 euros plus 30 euros plus the c
June 2023 (R), Paper 2 Foundation, Q16 (9 marks): (a) Factorise 6y – 27 (b) Expand p( p – 2) T = 5g + 4r (c) Work out the value of r when T = 46 and g = 17 r = P = m2 – 4c (d) Work out the value of P when m = –
June 2023 (R), Paper 2 Higher, Q1 (4 marks): P = m2 – 4c (a) Work out the value of P when m = –5 and c = 3 P = (b) Expand and simplify (x + 5)(x – 7)
June 2023 (R), Paper 2 Higher, Q17 (4 marks): Make x the subject of y = 3 x + 4
June 2023, Paper 1 Foundation, Q9 (3 marks): Here is a number machine. input × 10 + 6 output (a) Work out the output when the input is 14 Here is a different number machine. input × + 9 output When the inp
June 2023, Paper 2 Foundation, Q13 (6 marks): (a) Expand x(3 – x) (b) Factorise fully 12a – 18b There are 8 slices of cheese in each small pack of cheese. There are 20 slices of cheese in each large pack of
June 2023, Paper 2 Foundation, Q15 (4 marks): Finn is asked to find the value of 5 + 32 + 12 Here is his working and his answer. 5 + 32 + 12 = 82 + 12 = 64 + 12 = 76 Finn’s answer is wrong. (a) Explain what
June 2023, Paper 2 Higher, Q17 (7 marks): (a) Expand and simplify (x + 6)(3x – 2)(x + 6) e g (b) Make e the subject of w ef d
January 2023 (R), Paper 1 Foundation, Q12 (5 marks): Aarav uses this rule to estimate the time, in minutes, that a bus journey takes. Time = + 2.5 × length of journey in kilometres 1.5 × number of bus stops Aarav’
January 2023 (R), Paper 2 Foundation, Q14 (7 marks): (a) Expand x(10 – x) (b) Factorise 6y + 27 (c) Make m the subject of the formula h = m 2 + 4 (d) Solve 7g + 3 = 2g – 5 Show clear algebraic working. g =
January 2023, Paper 1 Foundation, Q13 (4 marks): p = t – ac t = 18 a = –3 c = 5 (a) Work out the value of p p = (b) Make x the subject of the formula d = 3x + 10
January 2023, Paper 1 Higher, Q19 (5 marks): The acceleration, a, of an object is given by a = v u − t where v = 45.23 correct to 2 decimal places u = 5.12 correct to 2 decimal places t = 8.5 correct to 2
January 2023, Paper 2 Foundation, Q8 (5 marks): Here is a number machine. × 5 – 7 input output (a) Work out the output when the input is 9 Here is a different number machine. ÷ 5 input output When the input i
June 2022 (R), Paper 1 Foundation, Q9 (4 marks): (a) Simplify 6p + 2t + p – 3t A = 8x – 3y (b) Work out the value of A when x = 5 and y = 4 A =
June 2022 (R), Paper 1 Foundation, Q14 (5 marks): Jakub has bought a chicken. He is going to use this rule to work out the number of minutes it will take to cook his chicken. Cooking time (minutes) Multiply the
June 2022 (R), Paper 1 Foundation, Q18 (4 marks): In a warehouse there are two types of shelves, type R and type S. These two types of shelves are arranged into shelving units that form a sequence of patterns.
June 2022 (R), Paper 1 Higher, Q2 (4 marks): In a warehouse there are two types of shelves, type R and type S. These two types of shelves are arranged into shelving units that form a sequence of patterns.
June 2022 (R), Paper 2 Foundation, Q9 (5 marks): (a) Simplify a×a×a×a×a (b) Simplify 8b× 3c (c) Expand 3(x + 4) Q = 5v 2 – w (d) Work out the value of Q when v = 1 2 and w = 1 4 Q =
June 2022 (R), Paper 2 Foundation, Q17 (3 marks): Molly uses this number machine to work out the amount of tax that she has to pay on the money she earns. Number of Amount of tax multiply by 12 add 50 multiply
June 2022, Paper 2 Foundation, Q11 (7 marks): (a) Simplify c × c × c × c × c × c (b) Simplify 2h3 + 5h3 − h3 (c) Expand x(x + 5) (d) Factorise 9y − 12 Rosanna sells m small bags of marbles and p large bags
June 2022, Paper 2 Higher, Q14 (7 marks): (a) Expand and simplify (5 − x)(2x + 3)(x + 4) Show your working clearly. (b) Make c the subject of g = c + 3 − 7 4 + c
June 2022, Paper 2 Higher, Q19 (3 marks): a = x = x − y − 3 7 4 3 Express a in the form py + q where p, q, r and s are integers. ry + s Give your answer in its simplest form. a =
January 2022 (R), Paper 1 Foundation, Q13 (4 marks): (a) Factorise 6x – 15 There are 200 bolts in each box of bolts. Samira buys c boxes of bolts. Samira uses the bolts she bought to fill packets of bolts. There a
January 2022 (R), Paper 2 Foundation, Q8 (3 marks): Danielle is going to print some business cards. She uses this rule to work out the total cost, in euros, of printing the business cards. Total cost = price per
January 2022 (R), Paper 2 Foundation, Q15 (6 marks): (a) Solve 5c = 15 c = (b) Expand x(8 – x) T = 5m – 6n (c) Work out the value of T when m = 4.2 and n = –2.5 T = (d) Make g the subject of k = 2g + t
January 2022 (R), Paper 2 Higher, Q15 (4 marks): Make t the subject of n 2 t 3
January 2022, Paper 1 Foundation, Q12 (3 marks): Alisa, Jena and Mikael each pick cucumbers. Alisa picks C cucumbers. Jena picks 5 fewer cucumbers than Alisa. Mikael picks twice as many cucumbers as Alisa. The
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
November 2021, Paper 1 Higher, Q17 (8 marks): (a) Factorise 6y2 – y – 5 2 f + 3 (b) Make f the subject of w = 8 - f (c) Express 4x2 – 8x + 7 in the form a(x + b)2 + c where a, b and c are integers.
November 2021, Paper 2 Foundation, Q12 (8 marks): T = 6p – 4d (a) Work out the value of T when p = 8 and d = 3 T = T = 6p – 4d (b) Work out the value of p when T = – 41 and d = 5 p = (c) Solve 4(x – 3) = 7x + 1
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, Q21 (4 marks): Given that x = and that = y y + a − 9 5 5 2 find an expression for x in terms of a. Give your expression as a single fraction in its simplest form.
June 2021, Paper 2 Foundation, Q12 (6 marks): This formula can be used to work out the cost, in riyals, of hiring a bicycle in Qatar for a number of days. Cost = 65 × number of days + 44 Ghalia hired a bicy
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 2 Foundation, Q7 (8 marks): Here are five times, in a single day, using the 24‑hour clock. A B C D E 11 53 15 20 08 20 18 12 16 45 (a) Write down the letter of the time nearest to 6 pm (b)
January 2021 (R), Paper 2 Foundation, Q11 (8 marks): w = 5y 2 – y 3 (a) Work out the value of w when y = –2 w = (b) Factorise fully 8p 2 – 2p (c) Expand 4t(3t – 2) (d) Expand and simplify (5x – 2)(x + 4)
January 2021 (R), Paper 2 Higher, Q1 (8 marks): w = 5y 2 – y 3 (a) Work out the value of w when y = –2 w = (b) Factorise fully 8p 2 – 2p (c) Expand 4t(3t – 2) (d) Expand and simplify (5x – 2)(x + 4)
January 2021, Paper 1 Foundation, Q12 (5 marks): (a) Expand x(4 – x) t = ab – c a = 1.5 b = 2.4 c = –5.6 (b) Work out the value of t. t = (c) Make d the subject of y = dx – e
January 2021, Paper 1 Higher, Q15 (3 marks): a = v − u t v = 9.6 correct to 1 decimal place u = 3.8 correct to 1 decimal place t = 1.84 correct to 2 decimal places Calculate the upper bound for the value o
January 2021, Paper 2 Foundation, Q5 (5 marks): Here is a number machine. input output + 5 ÷ 2 × 3 (a) Work out the output when the input is 7 (b) Work out the input when the output is 160 When the input is n
January 2021, Paper 2 Higher, Q14 (7 marks): (a) Solve 9 7 3 7 − = 4.55 5 4 Show clear algebraic working. a = ac + 8 (b) Make c the subject of the formula p = 3 + c
November 2020 (R), Paper 1 Foundation, Q5 (8 marks): (a) Simplify w + w + w + w – w (b) Simplify 4 ×a× 2 (c) Simplify f× f ×f×f×f (d) Simplify 4c + 4h + 5c – 6h (e) Factorise 10d + 15 (f) Make t the subject of e =
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 2 Foundation, Q8 (7 marks): The following rule is used to work out the total cost, in euros, of hiring a room. Total cost = 9 euros for each hour plus 20 euros Paolo hires the room for 5 h
November 2020 (R), Paper 2 Higher, Q17 (4 marks): Given that n > 0 make n the subject of the formula y = n 2 + d n 2
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, Q14 (5 marks): (a) Factorise 25f – 10 (b) Make y the subject of the formula c = 5y – h (c) Solve the inequality 4x + 7 > 2
November 2020, Paper 2 Higher, Q15 (4 marks): Make x the subject of y = x + 3
January 2020 (R), Paper 1 Foundation, Q6 (7 marks): (a) Simplify 3r × 5t (b) Solve 4x + 5 = 27 x = P = 7w – 5y (c) Find the value of P when w = 2 and y = 4 P = Q = 2u2 − 5 (d) Find the value of Q when u = −3 Q =
January 2020 (R), Paper 1 Foundation, Q16 (8 marks): (a) Make a the subject of d = g + 2ac (b) Factorise fully 9e f − 12 f (c) Expand and simplify (x + 2)(x − 5) (d) Simplify fully n × n 4 7 n 5
January 2020 (R), Paper 1 Higher, Q3 (8 marks): (a) Make a the subject of d = g + 2ac (b) Factorise fully 9e f − 12 f (c) Expand and simplify (x + 2)(x − 5) (d) Simplify fully n × n 4 7 n 5
January 2020 (R), Paper 2 Foundation, Q23 (3 marks): The diagram shows a box in the shape of a cuboid. Diagram NOT accurately drawn x cm 1.2 cm The box is put on a table. The face of the box in contact with the ta
January 2020 (R), Paper 2 Higher, Q9 (3 marks): The diagram shows a box in the shape of a cuboid. Diagram NOT accurately drawn x m 1.2 m The box is put on a table. The face of the box in contact with the tabl
January 2020, Paper 1 Foundation, Q8 (7 marks): (a) Simplify 6m − 2k + 5m − k P = 2a + 3b (b) Work out the value of P when a = 5 and b = 8 P = P = 2a + 3b (c) Work out the value of a when P = 16 and b = 20 a
January 2020, Paper 1 Higher, Q16 (3 marks): P = 2a − c d a = 58.4 correct to 3 significant figures. c = 20 correct to 2 significant figures. d = 3.6 correct to 2 significant figures. Work out the upper bo
January 2020, Paper 2 Foundation, Q13 (7 marks): (a) Expand x(5 – x) (b) Factorise 3y – 21 (c) Make p the subject of the formula f = 3p – d Sergio buys m boxes of seeds and n packets of seeds. Each box contain
January 2020, Paper 2 Higher, Q16 (4 marks): Make x the subject of y = x − 4
June 2019 (R), Paper 1 Foundation, Q8 (8 marks): (a) Simplify a + a + a + a (b) Simplify 3c × 5c (c) Simplify 3e + 7g + 5e – 4g (d) Solve x – 9 = 14 x = (e) Factorise 5y + 15 (f) Make y the subject of H = 3y –
June 2019 (R), Paper 1 Foundation, Q10 (5 marks): Here is a number machine. input q7 –9 output (a) Work out the output when the input is 8 (b) Work out the input when the output is 82 The input is y. (c) Find a
June 2019 (R), Paper 1 Foundation, Q13 (3 marks): Potatoes cost 2 dollars per kg. Carrots cost 3 dollars per kg. Alfred buys p kg of potatoes and c kg of carrots. The total cost is T dollars. Write down a formu
June 2019 (R), Paper 1 Higher, Q18 (6 marks): (a) Expand and simplify (x + 2)(2x + 3)(x – 7) Show your working clearly. x + m 2 (b) Make m the subject of p = 2 m − y
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 2 Foundation, Q9 (8 marks): Yuen has 2 more sweets than Simon. Giulia has 3 times as many sweets as Yuen. Simon, Yuen and Giulia have a total of T sweets. (a) Write down a formula for T in
June 2019, Paper 2 Higher, Q15 (4 marks): Make x the subject of the formula y = x + 1
January 2019 (R), Paper 2 Foundation, Q11 (6 marks): (a) Factorise 3x2 – x (b) Expand 4(2y + 3) C = 5a + 4d (c) Work out the value of C when a = –3 and d = 6 C = P = 3t2 + 7t (d) Work out the value of P when t = –
January 2019 (R), Paper 2 Foundation, Q13 (7 marks): (a) Solve 7x + 3 = x – 18 x = (b) Make w the subject of t = 7w + 3 Pencils cost 2 dollars each. Rulers cost 3 dollars each. Edith buys p pencils and r rulers. T
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, Paper 1 Foundation, Q9 (4 marks): h = 6q – 2u (a) Work out the value of h when q = 3 and u = –5 h = B = 3m + 2p (b) Work out the value of p when B = 2 and m = 5 p =
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

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