Equations — Paper 2 · IGCSE Mathematics (9-1) 0980

14 Solve the simultaneous equations. You must show all your working. 5x + 8y = 4 1 2 x + 3y = 7 x = … y = … [3]

3 marks

Mark scheme: 14 Correctly eliminating one variable M1 [x =] − 4 A2 A1 for one correct [y =] 3 If M0 scored, SC1 for 2 values satisfying one of the original equations

This question in 0980/22 May/June 2019

20 Solve the equation 3x 2 - 2x - 10 = 0 . Show all your working and give your answers correct to 2 decimal places. x = … or x = … [4]

4 marks

Mark scheme: 20 2 B2 2 −−( 2 ) ± ( −2 ) − 4 ( 3 )( −10 ) B1 for ( −2 ) − 4 ( 3 )( −10 ) or better 2 × 3 p + q p − q and if in form or then r r B1 for p = −(− 2) and r = 2(3) −1.52 and 2.19 final ans cao B1B1 If B0B0, SC1 for −1.5 and 2.2 or −1.523 to −1.522... and 2.189 … or 1.52 and −2.19 or −1.52 and 2.19 seen in working

This question in 0980/22 May/June 2019

6 Solve. x - 2 = 3 3 x = … [2]

2 marks

Mark scheme: 6 11 2 x 2 M1 for x − 2 = 3 × 3 oe or = 3 + oe or better 3 3

This question in 0980/21 Oct/Nov 2019

14 Solve the equation. 1 - x = 5 3 x = … [2]

2 marks

Mark scheme: 14 –14 2 M1 for 1 – x = 3 × 5 or better x 1 or = 5 − or better 3 3

This question in 0980/22 May/June 2020

8 a = 5c Find b when a = 5.625 and c = 2 . b = … [2]

2 marks

Mark scheme: 8 [±] 7.5 oe 2 b 2 M1 for 5.625 = or better 2 × 5

This question in 0980/22 May/June 2021

8 Solve the simultaneous equations. You must show all your working. 4x - 2y =- 13 - 3x + 4y = 11 x = … y = … [3]

3 marks

Mark scheme: 8 Correctly eliminates one M1 variable [x =] – 3 , [y =] 0.5 oe A2 A1 for either correct If M0 scored, SC1 for 2 values satisfying one of the original equations If 0 scored, SC1 for correct answers from no working

This question in 0980/21 Oct/Nov 2021

11 Solve the simultaneous equations. x - 3y = 7 2x - 3y = 11 x = … y = … [2]

2 marks

Mark scheme: 11 [x =] 4 2 B1 for each [y =] –1

This question in 0980/21 Oct/Nov 2022

12 One solution of the equation ax 2 + b = 181 is x = 8 . a and b are both positive integers greater than 1. (a) Find the value of b. b = … [2] (b) Write down the other solution of the equation ax 2 + b = 181. x = … [1]

3 marks

Mark scheme: 12(a) 53 2 M1 for a × 82 + b = 181 oe seen 12(b) –8 1

This question in 0980/22 May/June 2023

21 Solve the simultaneous equations. You must show all your working. 4y + 3x = 13 y = x 2 - 18 x = … y = … or x = … y = … [5]

5 marks

Mark scheme: 21 4 x 2  3 x  85   0  M2 2 2 2 13  3 x x  18  3 x  13 or x  18  or 16 y  113 y  7   0  M1 for 4   4 oe simplified 2  13  4 y  or y     18 oe or better  3  correct method to solve their M1 2 3 3 4 4 85 quadratic equation e.g. factors, oe, (4x – 17)(x + 5) 2  4 quadratic formula, completing the square  113    113  2 4 16  7 oe, 2 16 (16y – 1)(y – 7) x = −5 y = 7 B2 B1 for one correct pair or two correct x values or 17 1 two correct y values x = oe y = oe If B0 scored and at least 2 method marks scored, 4 16 SC1 for correct substitution of both of their x values or their y values into 4y + 3x = 13 or y = x2 – 18

This question in 0980/22 May/June 2024

12 Solve the simultaneous equations. You must show all your working. 5x + 6y = 9 3x - 2y = - 17 x = … y = … [3]

3 marks

Mark scheme: 12 Correctly eliminating one variable M1 x = –3 A1 If A0 scored SC1 for 2 values satisfying one of the original equations. y = 4 A1

This question in 0980/21 Oct/Nov 2024

17 Solve. 3x 2 - 7x - 16 = 0 You must show all your working and give your answers correct to 2 decimal places. x = … or x = … [4]

4 marks

Mark scheme: 17  −−  7  ( − 7 ) 2 − 4 ( 3 )( −16 ) B2 B1 for ( − 7 ) 2 − 4 ( 3) ( −16 ) ) or better oe 2  3 p + q p − q and if in the form or then r r B1 for p = – (–7) and r = 2(3) 3.75 and –1.42 B2 B1 for each or SC1 for answers 3.8 or 3.754… and –1.4 or –1.42… or –1.421 or 3.75 and –1.42 seen in working or –3.75 and 1.42 as final answers

This question in 0980/21 Oct/Nov 2024

8 The cost of one orange is t cents. The cost of one apple is w cents. The total cost of 3 oranges and 1 apple is 51 cents. The total cost of 6 oranges and 5 apples is 129 cents. Use simultaneous equations to find the value of t and the value of w. You must show all your working. t = … w = … [5]

5 marks

Mark scheme: 8 3t + w = 51 2 B1 for each 6t + 5w = 129 Correctly eliminating one variable from M1 e.g. 6t + 2w = 102 and 6t + 5w = 129 their equations leading to 3w = 27 or w = 51 − 3t and 6t + 5(51 − 3t ) = 129 [t =] 14 A2 A1 for [t =] 14 [w =] 9 A1 for [w =] 9 If M1A0A0 scored, M1 SC1 for two values satisfying one of their original equations or if M0 scored, SC1 for 2 correct answers

This question in 0980/21 Oct/Nov 2025

17 I = M ( k2 + c 2 ) (a) Find the value of I when M = 7, k = 3 and c = 2. I = … [2] (b) Rearrange the formula to write k in terms of I, M and c. k = … [3]

5 marks

Mark scheme: 17(a) 91 2 M1 for 7(32 + 22) oe 17(b) 2 3 M1 for correctly dividing by M I 2 I − Mc  − c or  M1 for correctly isolating term in k2 M M M1 for correctly taking square root final answer Maximum M2 if answer is incorrect

This question in 0980/21 Oct/Nov 2025