Algebraic manipulation: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 2.2 Algebraic manipulation, 2019–2025, with its mark scheme and examiner’s report.

All 200 questions on Algebraic manipulation, as a list

June 2025 (R), Paper 1 Foundation, Q5 (7 marks): (a) Simplify 4e × 7f (b) Simplify d × d × d × d × d (c) Simplify 3a + 2k + a – 7k (d) Solve x + 6 = 15 x = (e) Solve 2r – 9 = 14 r =
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 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, Q17 (3 marks): Prove that, for any three numbers which are consecutive multiples of 4, the difference between the square of the largest number and the square of the smallest n
June 2025 (R), Paper 2 Foundation, Q5 (3 marks): (a) Simplify a + a + a + a + a (b) Simplify b × c × 7 (c) Solve 5 d = 40 d =
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 Foundation, Q17 (5 marks): (a) Factorise fully 18 c − 45 cd (b) Solve 5 2 x x 3 4 6 Show clear algebraic working. x =
June 2025 (R), Paper 2 Higher, Q1 (5 marks): (a) Factorise fully 18 c cd − 45 (b) Solve 5 2 x 3 x 4 6 Show clear algebraic working. x =
June 2025 (R), Paper 2 Higher, Q13 (5 marks): (a) Factorise 4 x − y 2 25 2 (b) Show that 4 x x ( 3 2 )( x 5 ) can be written in the form ax 3 + bx 2 + cx where a, b and c are integers to be found.
June 2025, Paper 1 Foundation, Q4 (2 marks): (a) Simplify 4 5 × e (b) Solve f 14 29 f =
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 1 Foundation, Q23 (6 marks): (a) Solve x – 4 = 3 + 2 x 6 Show clear algebraic working. x = (b) (i) Factorise y2 – 11y + 30 (ii) Hence solve y2 – 11y + 30 = 0
June 2025, Paper 1 Higher, Q6 (6 marks): (a) Solve x – 4 = 3 + 2 x 6 Show clear algebraic working. x = 2 – 11y + 30 (b) (i) Factorise y 2 – 11y + 30 = 0 (ii) Hence solve y
June 2025, Paper 1 Higher, Q12 (3 marks): Express 5 x 3 x as a single fraction in its simplest form. 4 6
June 2025, Paper 2 Foundation, Q3 (5 marks): (a) Simplify d + d + d + d (b) Simplify w × w × w × w × w (c) Solve 6x = 42 x = (d) Simplify 7r + 9y + 3r – 4y
June 2025, Paper 2 Higher, Q12 (3 marks): Expand and simplify 3 x x x 2 5 7 4
June 2025, Paper 2 Higher, Q21 (3 marks): The diagram shows a cuboid. Diagram NOT accurately drawn 2x cm y cm 3x cm The cuboid measures 3x cm by 2x cm by y cm The volume of the cuboid is 1014cm³ The tot
June 2025, Paper 2 Higher, Q23 (4 marks): 4 x 4 x 120 x 5 x p where p is an integer. x 2 x 2 x 5 180 10 60 Find the value of p Show clear algebraic working. p =
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, 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 Foundation, Q25 (6 marks): (a) (i) Factorise x x 2 5 24 (ii) Hence, solve x 5 x 24 0 2 (b) Solve the inequality 3 y y 5 7 10 Show clear algebraic working.
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 1 Higher, Q8 (6 marks): (a) (i) Factorise x x 2 5 24 (ii) Hence, solve x 2 5 x 24 0 (b) Solve the inequality 3 y y 5 7 10 Show clear algebraic working.
November 2024, Paper 1 Higher, Q15 (3 marks): Write 3 x 2 x 1 5 x 4 3 + bx 2 + cx where a, b and c are integers.
November 2024, Paper 2 Foundation, Q8 (10 marks): (a) Simplify 7 g 3 h 4 g 5 h (b) Simplify 7 a × m 4 (c) Solve 5 x 7 12 x = (d) Expand 5 7 k 3 y + (e) Factorise 9 12 Max has c counters. Bulan has 3 times as ma
November 2024, Paper 2 Higher, Q23 (4 marks): Show that 16 x 2 36 2 x 2 7 x 6 x n ( 7 8 ) x x x 7 2 5 14 where n is an integer to be found. Show clear algebraic working.
June 2024 (R), Paper 1 Foundation, Q11 (8 marks): (a) Simplify c + c + c + c + c (b) Simplify 7w + 10y ‒ 9w + 2y The nth term of a sequence is given by 7n – 4 (c) Find the 1st term and the 5th term of the s
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 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 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 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 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, Q26 (4 marks): Write 4 x as a single fraction in its simplest form. 3 5 x 4 1
June 2024, Paper 1 Foundation, Q2 (3 marks): (a) Simplify 10p – 4p + 9p (b) Simplify 9 × 4q (c) Solve 4r = 15 r =
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 1 Foundation, Q21 (5 marks): (a) Expand and simplify (m + 5) (m – 8) (b) Solve 3n – 4 = 5 n + 6 3 Show clear algebraic working. n =
June 2024, Paper 1 Higher, Q6 (5 marks): (a) Expand and simplify (m + 5) (m – 8) (b) Solve 3n – 4 = 5 n + 6 3 Show clear algebraic working. n =
June 2024, Paper 1 Higher, Q12 (5 marks): (a) Factorise fully 6y 2 – 5y – 4 (b) Express 2 x 1 7 5 x as a single fraction in its simplest form. 4 x 3 x
June 2024, Paper 1 Higher, Q25 (4 marks): f (x) = 17 − 3x 2 + 12x Write f (x) in the form a – b(x − c) 2 where a, b and c are constants. f (x) =
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 Foundation, Q27 (3 marks): (i) Factorise x (ii) Hence, solve x 2 + 9x – 22 = 0
June 2024, Paper 2 Higher, Q11 (3 marks): (i) Factorise x 2 + 9x – 22 2 + 9x – 22 = 0 (ii) Hence, solve x
June 2024, Paper 2 Higher, Q14 (7 marks): (a) Show that 3y (2y + 5) (y + 7) can be written in the form ay 3 + by 2 + cy where a, b and c are integers. x + x − (b) Solve 2 3 + 6 5 = 163 5 4 100 Show clea
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
June 2024, Paper 2 Higher, Q23 (3 marks): Simplify 4 x 9 180 5 Give your answer in the form 5 w where w is an expression in terms of x Show each stage of your working clearly. for Question 24
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 Foundation, Q16 (6 marks): (a) Factorise fully 12 pq − p 18 There are 56 metal bars in a box. Each metal bar is gold or silver or zinc. y metal bars are gold. (3y + 7) metal bars are silv
November 2023, Paper 1 Higher, Q2 (6 marks): (a) Factorise fully 12 pq − p 18 There are 56 metal bars in a box. Each metal bar is gold or silver or zinc. y metal bars are gold. (3y + 7) metal bars are silv
November 2023, Paper 1 Higher, Q11 (3 marks): Express 3 5 x as a single fraction in its simplest terms. x 4 6
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
November 2023, Paper 2 Higher, Q16 (3 marks): Expand and simplify (2x + 3)(x – 5)(x + 4)
November 2023, Paper 2 Higher, Q24 (5 marks): Solve x x x x x 2 3 4 3 4 5 8 Show clear algebraic working. x =
June 2023 (R), Paper 1 Foundation, Q7 (5 marks): (a) Simplify 6a × 2c (b) Simplify 4d + 3e + d – 5e (c) Solve 4x – 7 = 23 x =
June 2023 (R), Paper 1 Foundation, Q23 (3 marks): (a) Expand 4x(x – 5) (b) Factorise y2 – 9y + 20
June 2023 (R), Paper 1 Higher, Q7 (3 marks): (a) Expand 4x(x – 5) (b) Factorise y2 – 9y + 20
June 2023 (R), Paper 1 Higher, Q23 (4 marks): Simplify x 4 2 x 2 x ax 2 Give your answer in the form where a, b and c are integers. bx + 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, Paper 1 Foundation, Q5 (6 marks): (a) Simplify p + p + p + p (b) Simplify 5e + 6f + 7e – 2f (c) Solve 13 – x = 7 x = (d) Solve 4y + 7 = 43 y =
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 1 Higher, Q14 (3 marks): Factorise fully 50g 2 – 18
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 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, Q4 (6 marks): (a) Simplify 10y – y (b) Simplify 3p× 4p (c) Solve 7x = 42 x = (d) Solve n + 6 = 5 n = (e) Simplify 8c + 5d – 2c – 3d
January 2023 (R), Paper 1 Foundation, Q23 (5 marks): (a) Factorise fully 18c3d2 – 21c2 (b) (i) Factorise y2 – 3y – 18 (ii) Hence, solve y2 – 3y – 18 = 0
January 2023 (R), Paper 1 Higher, Q8 (5 marks): (a) Factorise fully 18c3d2 – 21c2 (b) (i) Factorise y2 – 3y – 18 (ii) Hence, solve y2 – 3y – 18 = 0
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 (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 (R), Paper 2 Higher, Q19 (3 marks): Prove algebraically that, for any three consecutive even numbers, the sum of the squares of the smallest even number and the largest even number is 8 more than
January 2023 (R), Paper 2 Higher, Q24 (6 marks): The diagram shows a solid cone and a solid sphere. Diagram NOT accurately drawn r l h r The cone has base radius r, slant height l and perpendicular height h Th
January 2023 (R), Paper 2 Higher, Q26 (4 marks): Write x − x − x − x + 4 17 15 2 7 3 2 2 ( ) × + 29 − 4 x 2 x − 1 x − 25 2 as a single fraction in its simplest form.
January 2023, Paper 1 Foundation, Q7 (5 marks): (a) Simplify 5p × 9k (b) Simplify 3e + 2f + 8e – 7f (c) Solve 2d + 7 = 16 d =
January 2023, Paper 1 Foundation, Q25 (6 marks): (a) Factorise y2 – 2y – 48 (b) Write down the inequality shown on the number line x –2 –1 0 1 2 3 4 5 (c) Solve the inequality 7w + 6 > 12w + 14
January 2023, Paper 1 Higher, Q10 (6 marks): (a) Factorise y2 – 2y – 48 (b) Write down the inequality shown on the number line x –2 –1 0 1 2 3 4 5 (c) Solve the inequality 7w + 6 > 12w + 14
January 2023, Paper 1 Higher, Q13 (3 marks): Expand and simplify 3x(2x – 5)2 Show clear algebraic working.
January 2023, Paper 2 Foundation, Q7 (5 marks): (a) Simplify c × c × c × c × c (b) Solve 5 + x = 12 x = (c) Solve y 6 = 3 y = (d) Expand 5(2 + 3h) (e) Factorise g2 + 7g
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
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, Q21 (5 marks): (a) Expand 3c 3(c + 4) (b) (i) Factorise x 2 + 8x – 9 2 + 8x –9 = 0 (ii) Hence, solve x
June 2022 (R), Paper 1 Higher, Q5 (5 marks): (a) Expand 3c 3(c + 4) (b) (i) Factorise x 2 + 8x – 9 2 + 8x –9 = 0 (ii) Hence, solve x
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, 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, 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 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, Q23 (3 marks): Express − × as a single fraction in its simplest form.  x − x − − x 2 36 6 4
June 2022, Paper 1 Foundation, Q2 (3 marks): (a) Simplify 12a + 3a – 7a (b) Simplify 8 × 3b (c) Solve c 3 = 9 c =
June 2022, Paper 1 Foundation, Q8 (6 marks): (a) Simplify 12g − 8e − 5g + 6e A = 3b − 5c (b) Work out the value of A when b = 12 and c = 4 A = (c) Solve 4p + 9 = 24 p =
June 2022, Paper 1 Foundation, Q20 (5 marks): (a) Expand and simplify (n − 6)(n + 4) (b) Solve 2x − 3 = 3 x − 5 4 Show clear algebraic working. x =
June 2022, Paper 1 Higher, Q5 (5 marks): (a) Expand and simplify (n − 6)(n + 4) (b) Solve 2x − 3 = 3 x − 5 4 Show clear algebraic working. x =
June 2022, Paper 1 Higher, Q11 (5 marks): (a) Factorise 9x2 − 4y2 (b) Express 7 x + 3 − x as a single fraction in its simplest form. 8 4
June 2022, Paper 1 Higher, Q24 (4 marks): Express each of a, b and c in terms of q so that q + 12x − qx2 can be written as a − b (x − c) 2 a = b = c =
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 Foundation, Q27 (3 marks): (i) Factorise x2 + 5x − 24 (ii) Hence, solve x2 + 5x − 24 = 0
June 2022, Paper 2 Higher, Q11 (3 marks): (i) Factorise x2 + 5x − 24 (ii) Hence, solve x2 + 5x − 24 = 0
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, Q7 (5 marks): (a) Simplify 3c + 5d – c + 2d (b) Simplify 8e × 5f (c) Solve 5r – 3 = 8 r =
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 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, Q12 (5 marks): (a) Expand and simplify n(n – 4)(3n + 5) (b) Express 3 x + 2 1 + + x 2 x 4 as a single fraction in its simplest form.
January 2022 (R), Paper 1 Higher, Q15 (3 marks): Using algebra, prove that, given any 3 consecutive whole numbers, the sum of the square of the smallest number and the square of the largest number is always 2
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, Paper 1 Foundation, Q7 (5 marks): (a) Solve 5x = 30 x = (b) Solve y – 7 = 12 y = (c) Simplify h + h + h + h + h (d) Simplify 5a + 7f – 2a + 4f
January 2022, Paper 1 Foundation, Q21 (5 marks): (a) Solve the inequality 5x – 7  2 (b) (i) Factorise y2 – 2y – 35 (ii) Hence, solve y2 – 2y – 35 = 0
January 2022, Paper 1 Higher, Q6 (5 marks): (a) Solve the inequality 5x – 7  2 (b) (i) Factorise y2 – 2y – 35 (ii) Hence, solve y2 – 2y – 35 = 0
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
January 2022, Paper 2 Foundation, Q16 (7 marks): (a) Expand and simplify x(2x − 3) + 7(2x + 1) − 5 (b) Expand and simplify (y + 4)(2 − y) (c) Factorise fully 15b5c − 35b3c9
January 2022, Paper 2 Higher, Q1 (4 marks): (a) Expand and simplify (y + 4)(2 − y) (b) Factorise fully 15b5c − 35b3c9
January 2022, Paper 2 Higher, Q18 (3 marks): Prove that when the sum of the squares of any two consecutive odd numbers is divided by 8, the remainder is always 2 Show clear algebraic working.
November 2021, Paper 1 Foundation, Q7 (6 marks): (a) Solve 5x = 20 x = (b) Simplify 3a ´ 8b (c) Simplify 8w – 4y + w – 3y (d) Factorise fully 16 + 12t
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 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, Q3 (2 marks): (a) Simplify 4x + 5x – 2x (b) Simplify 4p × 7
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, Q4 (4 marks): (a) Simplify 3 × 10d (b) Simplify 8e + e − 5e (c) Solve 6g = 42 g = (d) Solve 24 = 10 + h h =
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 Foundation, Q24 (5 marks): (a) Factorise fully 25a4c7d + 45a9c3h (b) Solve (2x + 5)2 = (2x + 3)(2x – 1) x =
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, Q9 (5 marks): (a) Factorise fully 25a4c7d + 45a9c3h (b) Solve (2x + 5)2 = (2x + 3)(2x – 1) x =
June 2021, Paper 1 Higher, Q13 (3 marks): Expand and simplify 4x(3x + 1)(2x – 3) Show your working clearly.
June 2021, Paper 1 Higher, Q17 (3 marks): Using algebra, prove that, given any 3 consecutive even numbers, the difference between the square of the largest number and the square of the smallest number i
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, Q8 (7 marks): (a) Simplify w × w × w × w × w (b) Simplify 5a × 3c (c) Simplify 3e + 2 f − e + 5 f (d) Solve 5x – 7 = x + 12 Show clear algebraic working. x =
June 2021, Paper 2 Foundation, Q23 (3 marks): (i) Factorise x2 + 2x – 24 (ii) Hence solve x2 + 2x – 24 = 0
June 2021, Paper 2 Higher, Q9 (3 marks): (i) Factorise x2 + 2x – 24 (ii) Hence solve x2 + 2x – 24 = 0
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, Q15 (5 marks): (a) Expand 5(3a + 4) . (b) Factorise 4c – 14 . (c) Solve 5x – 11 = x + 6 Show clear algebraic working. x = .
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 1 Higher, Q16 (5 marks): (a) Expand and simplify (x + 4)(x – 2)(x + 1) (b) Express x 2 – 10x + 40 in the form (x + a) 2 + b, where a and b are integers.
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 (R), Paper 2 Higher, Q15 (4 marks): Prove algebraically that the product of any two odd numbers is always an odd number.
January 2021 (R), Paper 2 Higher, Q18 (5 marks): Solve the equation 5 3 + = 2 x 2 + 2 x + 2 x Show clear algebraic working.
January 2021, Paper 1 Foundation, Q7 (4 marks): (a) Simplify 10x + 4y + 3x – 6y (b) Solve 2n + 5 = 16 n =
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 Foundation, Q21 (5 marks): (a) Factorise fully 15y 4 + 20uy 3 (b) Solve 4 – 3x = 5 − 8 x 4 Show clear algebraic working. x =
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, Q5 (5 marks): (a) Factorise fully 15y 4 + 20uy 3 (b) Solve 4 – 3x = 5 − 8 x 4 Show clear algebraic working. x =
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 1 Higher, Q12 (6 marks): (a) Express − as a single fraction. x − x + 2 1 Give your answer in its simplest form. (b) Expand and simplify 2x(x – 5)(x – 3)
January 2021, Paper 1 Higher, Q18 (3 marks): Given that (8 – x )(5 + x ) = y x + 21 where x is a prime number and y is an integer, find the value of x and the value of y. Show each stage of your working cl
January 2021, Paper 2 Foundation, Q7 (8 marks): (a) Simplify p + p + p + p + p + p 2 + 6y 2 – 3y 2 (b) Simplify 5y (c) Simplify e×e×e×e×e (d) Simplify 5c× 4d (e) Solve x – 7 = 19 x = 2 + 15 2 – 5 3 = 4n 18 (f
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 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, Q11 (3 marks): Simplify fully   6 10 18 t w
January 2021, Paper 2 Higher, Q21 (4 marks): Write × − ( x − 7 ) 2 x + 5 x − 13 x − 6 5 8 as a single fraction in its simplest form. Show clear algebraic working. for Question 22
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 Higher, Q14 (3 marks): Expand and simplify (4x + 1)(x – 3)(5x + 6)
November 2020 (R), Paper 2 Foundation, Q12 (3 marks): (a) Expand 4(m + 2) (b) Solve 2x + 5 = –19 x =
November 2020 (R), Paper 2 Foundation, Q22 (5 marks): (a) Factorise x2 – x – 42 (b) Solve the inequality 3x + 15 < 8x + 3 Show clear algebraic working.
November 2020 (R), Paper 2 Higher, Q9 (5 marks): (a) Factorise x2 – x – 42 (b) Solve the inequality 3x + 15 < 8x + 3 Show clear algebraic working.
November 2020, Paper 1 Foundation, Q7 (6 marks): (a) Simplify 5c × d (b) Solve x + 5 = 12 x = (c) Solve 9y = 36 y = (d) Simplify 8k + 5m – 2k + 6m (e) Expand 4(3g + 1)
November 2020, Paper 1 Foundation, Q20 (8 marks): (a) Solve 5(4 – x) = 7 – 3x Show clear algebraic working. x = (b) Factorise fully 16m3g3 + 24m2g5 (c) (i) Factorise y2 – 2y – 48 (ii) Hence, solve y2 – 2y – 48
November 2020, Paper 1 Higher, Q7 (8 marks): (a) Solve 5(4 – x) = 7 – 3x Show clear algebraic working. x = (b) Factorise fully 16m3g3 + 24m2g5 (c) (i) Factorise y2 – 2y – 48 (ii) Hence, solve y2 – 2y – 48
November 2020, Paper 1 Higher, Q21 (5 marks): Express x 2 1 9 − 4 7 × − x x 2 x x 3 − 2 3 − 13 − 10 − 1 as a single fraction in its simplest form.
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
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, Q18 (4 marks): (a) Expand e(3e – 5) (b) Factorise 35 + 5f (c) Simplify (4pq2)3
January 2020 (R), Paper 2 Higher, Q21 (7 marks): (a) Simplify fully 10 x 2 + 23 x + 12 4 x 2 − 9 8 5 y y y + 2 2 × 2 3 2 = 4 n (b) Find an expression for n in terms of y. Show clear algebraic working and simpl
January 2020 (R), Paper 2 Higher, Q25 (3 marks): N is a multiple of 5 A = N + 1 B = N – 1 Prove, using algebra, that A2 – B2 is always a multiple of 20
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 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 1 Higher, Q15 (8 marks): Diagram NOT accurately drawn (x + 1) cm (3 − x) cm (2x + 5) cm The diagram shows a cuboid of volume V cm3 (a) Show that V = 15 + 16x − x2 − 2x3 There is a value
January 2020, Paper 2 Foundation, Q5 (2 marks): (a) Simplify 10a×b (b) Solve n + 3 = 7 n =
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, Q17 (3 marks): Prove that the difference between two consecutive square numbers is always an odd number. Show clear algebraic working.
January 2020, Paper 2 Higher, Q24 (4 marks): Express x x  4 3  9 − 4 3 − ÷  x − x − x − x + 2 5 2 3 6 2 17 5 as a single fraction in its simplest form.
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 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 (R), Paper 2 Foundation, Q13 (7 marks): (a) Solve 3f - 5 = 11 (b) Expand w(w + 3) y= 5e + 20 (c) Work out the value of y when e = -3 y=. (d) Factorise x2 - 5x - 36
June 2019 (R), Paper 2 Higher, Q5 (2 marks): Factorise x2íxí
June 2019 (R), Paper 2 Higher, Q17 (4 marks): The table gives information about the first six terms of a sequence of numbers. Term number 1 2 3 4 5 6 1 2 2 3 3 4 4 5 5 6 6 7 × × × × × × Term of sequence 2 2
June 2019, Paper 1 Foundation, Q6 (5 marks): (a) Simplify 6e × 2f (b) Simplify 5m + 7kím + k (c) Solve 5y + 3 = 14 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 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
June 2019, Paper 2 Higher, Q22 (3 marks): Simplify fully 6 + 13 − 5 x 2 4 − 25
January 2019 (R), Paper 1 Foundation, Q8 (4 marks): (a) Simplify 5x + 4y – x – y (b) Solve 2t + 3 = 12 t =
January 2019 (R), Paper 1 Higher, Q12 (5 marks): Here are the first four terms of a sequence of fractions. 1 2 3 4 1 3 5 7 The numerators of the fractions form the sequence of whole numbers 1 2 3 4 … The denom
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 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, Q25 (4 marks): (a) Factorise fully 12d2e + 16d2e2 (b) Simplify fully 15 k m 4 3 5 km 2
January 2019 (R), Paper 2 Higher, Q20 (4 marks): (a) Write 3x2 − 12x + 7 in the form a(x + b)2 + c The line L is the line of symmetry of the curve with equation y = 3x2 − 12x + 7 (b) Using your answer to part
January 2019, Paper 1 Foundation, Q8 (6 marks): (a) Simplify 2e – 3f + 4e – 7f (b) Expand and simplify 5(4x + 3) – (3x – 1) (c) Factorise fully 4p + 6pq
January 2019, Paper 1 Foundation, Q13 (8 marks): (a) Expand and simplify (e + 3)(e – 5) 2 y + 1 (b) Solve y = 5 Show clear algebraic working. y = (c) Solve x2 + 3x – 18 = 0 Show your working clearly.
January 2019, Paper 1 Higher, Q1 (7 marks): (a) Factorise fully 4p + 6pq (b) Expand and simplify (e + 3)(e – 5) 2 y 1 + (c) Solve y = 5 Show clear algebraic working. y =
January 2019, Paper 1 Higher, Q11 (3 marks): Express 5 2 x + as a single fraction in its simplest terms. − 3 2 x
January 2019, Paper 2 Foundation, Q4 (4 marks): (a) Simplify 4m + 2m – m (b) Simplify 5p × 7 (c) Solve 8g = 40 g = (d) Solve 19 – k = 4 k =
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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