plumiAlgebraic manipulation: CAIE IGCSE Maths questions
Every CAIE IGCSE Maths exam question on 2.2 Algebraic manipulation, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 1, question 15: Factorise completely. 2 + 36 x 40 x [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058011-jun24-15-qp.webp)
![June 2024 Paper 2, question 19: Factorise completely. (a) 12 m 2 75 t 2 - [3] (b) xy 15 3 y 5 x + + + [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058021-jun24-19-qp.webp)
![June 2024 Paper 4, question 3: 3 (a) C xy 2 = 4 (i) Find C when x 5 and y 8 . = = C = [2] (ii) Find the positive value of y when C 15 and x 2 4 . . = = y = [2] (b) Write as a single fraction](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058041-jun24-03-qp.webp)
![June 2024 (0980) Paper 1, question 14: Factorise completely. 20 x 90 2 x - [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/098012-jun24v2-14-qp.webp)
![June 2024 (0980) Paper 1, question 20: Expand and simplify. ( x 4 )( x 7 ) - - [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/098012-jun24v2-20-qp.webp)
![June 2024 (0980) Paper 3, question 2: (a) Simplify. (i) 5 a 6 a 3 a - + [1] (ii) 6 x 2 6 x 4 x 2 x - - - [2] (b) Find the value of c 2 d 2 when c 7 and d =- . 5 + = [2] (c) The time, T minutes, to c](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/098032-jun24v2-02-qp.webp)
![June 2024 (0980) Paper 4, question 5: ` j . 3 5 (a) Simplify 25 6 2 x [2] (b) These are the first five terms of a sequence. 1 1 6 36 216 6 Find the nth term of the sequence. [2] (c) Expand and simpl](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/098042-jun24v2-05-qp.webp)
![June 2024 (0980) Paper 4, question 7: (a) Solve x 3 8 6 4 x . - = - x = [2] 2 + (b) Factorise fully 10 a 5 a . [2] (c) Factorise fully ( 2 x 3 ) 2 - . 9 - [2] 1 1 (d) f ( )x - , x g ( )x 3 x = ! = 4](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/098042-jun24v2-07-qp.webp)
![Specimen Paper 1, question 12: (a) Factorise. 9x + 12 [1] (b) Solve. 6x – 5 = 2x + 13 x = [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058001-spec-12-qp.webp)
![Specimen Paper 2, question 24: (a) Write x2 – 4x + 7 in the form (x – a)2 + b . [2] (b) Write down the coordinates of the turning point of the graph of y = x2 – 4x + 7 . ( , ) [1]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058002-spec-24-qp.webp)
![Specimen Paper 3, question 14: (a) 6cm 4cm NOT TO SCALE 5cm The diagram shows the net of a cuboid. (i) Find the volume of the cuboid. cm3 [2] (ii) Show that the total surface area of the cubo](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058003-spec-14-qp.webp)
![Specimen Paper 4, question 10: Factorise. 2x + 6 – 3xy – 9y [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058004-spec-10-qp.webp)
All 14 questions on Algebraic manipulation, as a list
- June 2024, Paper 1, Q15 (2 marks): Factorise completely. 2 + 36 x 40 x [2]
- June 2024, Paper 1, Q16 (3 marks): NOT TO SCALE x 7 + 3 x 12 - The diagram shows a rectangle with length x 3 12 and width x + . 7 - Find an expression for the perimeter of the rectangle. Give you
- June 2024, Paper 2, Q19 (5 marks): Factorise completely. (a) 12 m 2 75 t 2 - [3] (b) xy 15 3 y 5 x + + + [2]
- June 2024, Paper 4, Q3 (13 marks): 3 (a) C xy 2 = 4 (i) Find C when x 5 and y 8 . = = C = [2] (ii) Find the positive value of y when C 15 and x 2 4 . . = = y = [2] (b) Write as a single fraction
- June 2024 (0980), Paper 1, Q14 (2 marks): Factorise completely. 20 x 90 2 x - [2]
- June 2024 (0980), Paper 1, Q20 (2 marks): Expand and simplify. ( x 4 )( x 7 ) - - [2]
- June 2024 (0980), Paper 3, Q2 (12 marks): (a) Simplify. (i) 5 a 6 a 3 a - + [1] (ii) 6 x 2 6 x 4 x 2 x - - - [2] (b) Find the value of c 2 d 2 when c 7 and d =- . 5 + = [2] (c) The time, T minutes, to c
- June 2024 (0980), Paper 4, Q5 (18 marks): ` j . 3 5 (a) Simplify 25 6 2 x [2] (b) These are the first five terms of a sequence. 1 1 6 36 216 6 Find the nth term of the sequence. [2] (c) Expand and simpl
- June 2024 (0980), Paper 4, Q7 (11 marks): (a) Solve x 3 8 6 4 x . - = - x = [2] 2 + (b) Factorise fully 10 a 5 a . [2] (c) Factorise fully ( 2 x 3 ) 2 - . 9 - [2] 1 1 (d) f ( )x - , x g ( )x 3 x = ! = 4
- Specimen, Paper 1, Q12 (3 marks): (a) Factorise. 9x + 12 [1] (b) Solve. 6x – 5 = 2x + 13 x = [2]
- Specimen, Paper 2, Q24 (3 marks): (a) Write x2 – 4x + 7 in the form (x – a)2 + b . [2] (b) Write down the coordinates of the turning point of the graph of y = x2 – 4x + 7 . ( , ) [1]
- Specimen, Paper 2, Q26 (11 marks): y 24 x – 3 0 4 – 18 f(x) = x(x + 2)(x – 3) (a) On the diagram, sketch the graph of y = f(x) for –3 ⩽ x ⩽ 4 . Show the values of the intersections with the axes.
- Specimen, Paper 3, Q14 (9 marks): (a) 6cm 4cm NOT TO SCALE 5cm The diagram shows the net of a cuboid. (i) Find the volume of the cuboid. cm3 [2] (ii) Show that the total surface area of the cubo
- Specimen, Paper 4, Q10 (2 marks): Factorise. 2x + 6 – 3xy – 9y [2]
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