plumiSimplifying, expanding and factorising: OCR GCSE Maths questions
Every OCR GCSE Maths exam question on A4 Simplifying, expanding and factorising, 2017–2025, with its mark scheme and examiner’s report.
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All 48 questions on Simplifying, expanding and factorising, as a list
- June 2025, Paper 4, Q23 (7 marks): (a) Write this expression in its simplest factorised form. 2 2 ( x 4 )( x 4 ) x ( x 5 ) + - - - You must show your working. (a) (b) Use your answer to part (a)
- June 2025, Paper 5, Q10 (4 marks): Heidi is x years old. Finley is 5 years younger than Heidi. Zayn is 4 times Finley’s age. Find an expression in terms of x for the total age of Heidi, Finley an
- June 2025, Paper 5, Q20 (4 marks): Simplify. 2 x 36 - 2 x x 42 - -
- November 2024, Paper 4, Q1 (4 marks): Factorise fully. 2 + (a) 6 x 9 x (a) 2 + (b) x 8 x 15 + (b)
- November 2024, Paper 5, Q8 (2 marks): Here is a question and an incorrect answer. Question: Expand the brackets and simplify fully. 3( + 2 ) + a b a Answer: a 4 + 6 × b Explain why the answer is not
- November 2024, Paper 5, Q18 (6 marks): Solve. 2 x 5 - 4 x = x 4 - You must show your working. x = or x =
- November 2024, Paper 6, Q9 (6 marks): The next term in a Fibonacci sequence is found by adding together the previous two terms. In a particular Fibonacci sequence: • the first term is 3 • the second
- November 2024, Paper 6, Q20 (6 marks): ( 4 x a )( 4 x a x )( 2 ) 16 x bx 50 + - + = + - Find the two possible pairs of values for a and b. You must show your working. Pair 1: a = and b = Pair 2: a =
- June 2024, Paper 5, Q15 (3 marks): Expand and simplify. ( x 3 4 )( x 1 )( x 2 ) + + -
- June 2024, Paper 6, Q16 (4 marks): Write in the form kx 4 3 x
- June 2024, Paper 6, Q20 (5 marks): Write as a single fraction in its simplest form. 2 x 49 - 4 + ( x 7 )( x 3 ) + -
- November 2023, Paper 4, Q9 (4 marks): Here are two pieces of work. Each shows a question and an incorrect solution. For each part, describe the error made and write out a correct solution. (a) Quest
- November 2023, Paper 5, Q3 (4 marks): (a) Simplify. 2 5 3 a 4 a # (a) (b) Factorise fully. 2 - 4 x 12 x (b)
- November 2023, Paper 5, Q24 (3 marks): The x-coordinates of the intersections of the graphs of y x ax 7 and y 3 x b are the = + + = + 2 + solutions to the equation x 8 x 13 0 . + = Find the value of
- November 2023, Paper 6, Q6 (5 marks): The area of this rectangle can be written as ax bx 10 . - Not to scale 3x + 2 x + c Find the values of a, b and c. You must show your working. a = , b = and c =
- November 2023, Paper 6, Q21 (5 marks): Simplify fully. 3 2 x 8 x 15 x + + 3 x 9 x -
- June 2023, Paper 4, Q13 (2 marks): Here are two pieces of work. Each shows a question and the first line of an incorrect solution. For each part, describe the error made in the first line of the
- June 2023, Paper 5, Q15 (9 marks): (a) Factorise. 2 - 9 x 4 (a) (b) Solve by factorisation. 2 - 3 x 2 x 8 0 - = (b) x = or x = (c) Solve. 2 ( x 5 ) - 2 = 1 3 x - (c) x =
- June 2023, Paper 5, Q18 (3 marks): p m m , where p 2 0 , m 2 0 and p m . = ! 5 . Show that the value of x is 3
- June 2023, Paper 6, Q20 (7 marks): (a) Write ( 2 5 )( 4 ) in the form ( 2 ) . x x x a b - + + - You must show your working. (a) (b) Charlie, Dev and Eve all attempt to sketch the graph of y ( 2 x
- November 2022, Paper 6, Q11 (3 marks): Factorise fully 30 x 2 x 4 . -
- November 2022, Paper 6, Q20 (4 marks): Write as a single fraction in its simplest form. 6 x 45 + 10 - 3 5 x +
- June 2022, Paper 4, Q14 (2 marks): ( 2 3 )( )( 3 ) 6 11 17 30 x x a bx x x x + + + = + - - Find the value of a and the value of b. a = b =
- June 2022, Paper 4, Q19 (9 marks): (a) Write as a single fraction in its simplest form. 4 2 n - 2 2 3 1 n n + + (a) (b) Simplify. 2 x x 12 - - 2 2 3 20 x x - - (b) FOR QUESTION 20
- June 2022, Paper 6, Q4 (4 marks): You are given that k 8 7 10 2 a a a # = 5 5 ma where k and m are integers. Find the value of k and the value of m. k = and m =
- June 2022, Paper 6, Q7 (3 marks): (a) Multiply out and simplify. _ _i i x 4 x 5 - + (a) (b) Factorise. 2 - x 25 (b)
- November 2021, Paper 5, Q17 (5 marks): Simplify fully. 2 2 x 50 - 2 7 10 x x + +
- November 2021, Paper 6, Q3 (2 marks): Multiply out and simplify. 3 ( x 2 ) ( x 1 ) + - -
- November 2020, Paper 4, Q17 (3 marks): Expand and simplify. ( 1 )( 1 )( 2 ) x x x + - +
- November 2020, Paper 5, Q2 (5 marks): (a) Solve. 4 x 3 13 + = (a) x = (b) Multiply out and simplify. 5 2 ( x 3 ) 2 ( x 4 ) + + - (b)
- November 2020, Paper 6, Q21 (6 marks): Write as a single fraction in its simplest form. x x 1 6 x + + - 2 2 2 4 x x x + - -
- November 2019, Paper 4, Q5 (3 marks): Multiply out and simplify. ( 4 x y x )( 3 y ) + -
- November 2019, Paper 4, Q16 (4 marks): Show that can be written in the form x , where a is an integer. + 2 - 1 - 1 1 x x +
- November 2019, Paper 5, Q3 (6 marks): Martina has answered some questions on algebra. In each question, she has made an error. Describe her error and give the correct answer to each problem. Simplif
- November 2019, Paper 5, Q17 (3 marks): Show that can be expressed as a3 . a # a
- November 2018, Paper 4, Q13 (1 mark): Tenzin is given this question. Factorise fully. 2x2 + 6x x x Here is his answer. 2x2 + 6x = x(2x + 6) x x x x Explain why Tenzin’s answer is not correct.
- November 2018, Paper 5, Q20 (7 marks): (a) Prove that 2 x 1 3 x 2 x 3 x 5 2 is a perfect square. + + + + + (b) Gemma says The equation (2x + 1)(3x + 2) + x (3x + 5) + 2 = -12 has no solutions. Explai
- November 2018, Paper 6, Q21 (6 marks): Show that simplifies to an integer. + - x 5 x 7 ( 5 )( 7 ) x x + - + -
- June 2018, Paper 4, Q20 (6 marks): Solve this equation, giving your answers correct to 1 decimal place. 5 3 2 + = x 2 x 3 + - x = or x =
- June 2018, Paper 5, Q17 (4 marks): ( )( 3 2 )( 1 ) = bx 12 x a x x cx dx + + + + + - Find the value of a, b, c and d. a = b = c = d =
- June 2018, Paper 6, Q19 (4 marks): Show that x x x a + + + simplifies to x where a and b are integers. 2 b - 2 x x 10 + -
- November 2017, Paper 4, Q2 (3 marks): (a) Simplify. 6 2 (i) a a ' (a)(i) b5 3 (ii) ( ) (ii) (b) Factorise. 2 6 x x - (b)
- November 2017, Paper 4, Q13 (8 marks): (a) Solve. x2 - 6x + 15 = 3x - 5 (a) x = or x = (b) Expand and simplify. (2x - 1)(x + 5)(3x - 2) (b)
- November 2017, Paper 5, Q4 (3 marks): (a) Factorise. x2 – 432 (a) (b) Calculate. 572 – 432 (b)
- June 2017, Paper 4, Q16 (3 marks): Write x 10 x 16 in the form x a b . + + +
- June 2017, Paper 5, Q5 (5 marks): (a) Rearrange the equation to make x the subject. y 7 x 3 = - (a) x = (b) Factorise. 2 - (i) x xy (b)(i) 2 + (ii) x 8 x 12 + (ii)
- June 2017, Paper 5, Q17 (6 marks): (a) Simplify. 2 x 16 - 2 3 4 x x - - (a) _ i _ i _ i is identical to x 3 2 (b) x 3 x 4 x 5 ax 17 x b . + - + + - + Find the value of a and the value of b. (b) a
- June 2017, Paper 6, Q16 (4 marks): (a) Simplify. 3 3 y 4 y - (a) (b) Write as a single fraction in its simplest form. 3 4 + 1 2 x x - + (b)
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