plumiEquations: CAIE IGCSE Maths questions
Every CAIE IGCSE Maths exam question on 2.5 Equations, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 1, question 10: NOT TO hcm SCALE 6cm 15cm The total surface area of this cuboid is 369 cm2. Work out the value of h. h = [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058011-jun24-10-qp.webp)
![June 2024 Paper 1, question 22: Solve the simultaneous equations. You must show all your working. 6 x 2 y 29 + = 3 x 4 y 17 - = x = y = [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058011-jun24-22-qp.webp)
![June 2024 Paper 2, question 12: Solve the simultaneous equations. You must show all your working. 3 x 5 y 5 + = 2 4 x 3 y 46 - = x = y = [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058021-jun24-12-qp.webp)
![June 2024 Paper 3, question 1: (a) The cost of a cinema ticket is $6.30 . (i) Work out the total cost of 4 tickets. $ [1] (ii) The cinema sells 10 tickets for the price of 9 tickets. A group](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058031-jun24-01-qp.webp)
![June 2024 Paper 4, question 8: (a) On the axes, sketch the graph of y x 2 7 x 18 . = + - On your sketch, write the values where the graph meets the x-axis and the y-axis. y O x [4] (b) (i) Fi](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058041-jun24-08-qp.webp)
![June 2024 (0980) Paper 2, question 21: Solve the simultaneous equations. You must show all your working. 4 y 3 x 13 + = y x 2 18 = - x = y = or x = y = [5]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/098022-jun24v2-21-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 1, question 19: Rearrange the formula to make t the subject. w = 7t – 5 t = [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058001-spec-19-qp.webp)
![Specimen Paper 1, question 23: Solve the simultaneous equations. 3x – 5y = 22 7x + 10y = 8 x = y = [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058001-spec-23-qp.webp)
![Specimen Paper 4, question 15: y = u x 2 (a) Find the value of y when u = 7 and x = 25. y = [2] (b) Rearrange the formula to write x in terms of u and y. x = [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058004-spec-15-qp.webp)
![Specimen Paper 4, question 18: Solve. y 3 3 y − = 2 1 4 y = [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/058004-spec-18-qp.webp)
All 17 questions on Equations, as a list
- June 2024, Paper 1, Q10 (4 marks): NOT TO hcm SCALE 6cm 15cm The total surface area of this cuboid is 369 cm2. Work out the value of h. h = [4]
- June 2024, Paper 1, Q22 (3 marks): Solve the simultaneous equations. You must show all your working. 6 x 2 y 29 + = 3 x 4 y 17 - = x = y = [3]
- June 2024, Paper 2, Q12 (4 marks): Solve the simultaneous equations. You must show all your working. 3 x 5 y 5 + = 2 4 x 3 y 46 - = x = y = [4]
- June 2024, Paper 3, Q1 (15 marks): (a) The cost of a cinema ticket is $6.30 . (i) Work out the total cost of 4 tickets. $ [1] (ii) The cinema sells 10 tickets for the price of 9 tickets. A group
- June 2024, Paper 3, Q5 (13 marks): (a) H F I NOT TO f° 105° SCALE e° 52° E G The diagram shows a triangle EFG and a straight line HFI. HFI is parallel to EG. (i) Angle EFG 105 ° . = Write down th
- June 2024, Paper 4, Q8 (15 marks): (a) On the axes, sketch the graph of y x 2 7 x 18 . = + - On your sketch, write the values where the graph meets the x-axis and the y-axis. y O x [4] (b) (i) Fi
- June 2024 (0980), Paper 2, Q21 (5 marks): Solve the simultaneous equations. You must show all your working. 4 y 3 x 13 + = y x 2 18 = - x = y = or x = y = [5]
- 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 1, Q19 (2 marks): Rearrange the formula to make t the subject. w = 7t – 5 t = [2]
- Specimen, Paper 1, Q23 (3 marks): Solve the simultaneous equations. 3x – 5y = 22 7x + 10y = 8 x = y = [3]
- Specimen, Paper 2, Q21 (9 marks): In this question, all measurements are in centimetres. NOT TO SCALE h ( h + 2 ) x ( x 1 ) + The height of the triangle is h and the height of the rectangle is (
- Specimen, Paper 4, Q15 (4 marks): y = u x 2 (a) Find the value of y when u = 7 and x = 25. y = [2] (b) Rearrange the formula to write x in terms of u and y. x = [2]
- Specimen, Paper 4, Q18 (3 marks): Solve. y 3 3 y − = 2 1 4 y = [3]
- Specimen, Paper 4, Q24 (6 marks): The straight line y = 2x + 1 intersects the curve y = x2 + 3x – 4 at the points A and B. Find the coordinates of A and B. Give your answers correct to 2 decimal
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