Algebraic manipulation — Paper 3 · IGCSE Mathematics (9-1) 0980

5 (a) T = 3a 2 b Find the value of T when a = 4 and b = 5. T = … [2] (b) (i) Multiply out the brackets. x ( 3 - 5 x) … [2] (ii) Factorise fully. 5x - 20x 2 … [2] (c) NOT TO SCALE 3a + b 4a - 5b a + 2b Find an expression for the perimeter of this triangle. Give your answer in its simplest form. … [3]

9 marks

Mark scheme: 5(a) 240 2 M1 for 3 × 42 × 5 oe 5(b)(i) 3x – 5x2 final answer 2 B1 for 3x or – 5x2 5(b)(ii) 5x(1 – 4x) final answer 2 B1 for 5(x – 4x2) or x(5 – 20x) 5(c) 8a – 2b 3 M1 for 3a + b + 4a – 5b + a + 2b B1 for 8a or – 2b

This question in 0980/32 May/June 2020

4 (a) Simplify. 6a - 3b + 2a - 4b … [2] (b) Expand. 5 ( x - 3) … [1] (c) Solve these equations. x (i) = 18 3 x = … [1] (ii) 5x + 18 = 8 x = … [2] (iii) 12x - 3 = 4x + 21 x = … [2] (d) 6 10 # 6 x = 6 2 Find the value of x. x = … [1] (e) The Fraser family and the Singh family go to the cinema. The Fraser family buys 6 adult tickets and 2 child tickets for $124. The Singh family buys 3 adult tickets and 5 child tickets for $100. Find the price of an adult ticket and the price of a child ticket. Adult ticket $ … Child ticket $ … [5]

14 marks

Mark scheme: 4(a) 8a – 7b 2 B1 for 8a or –7b in final answer or for 8a – 7b seen then spoilt 4(b) 5x – 15 1 4(c)(i) 54 1 4(c)(ii) −2 2 M1 for 18 8 5x = 8 – 18 or x + = or better oe 5 5 4(c)(iii) 3 2 M1 for 12x – 4x = 21 + 3 or better oe 4(d) −8 cao 1 4(e) 17.5[0] 5 B1 for 6a + 2c = 124 B1 for 3a + 5c = 100 9.5[0] oe M1FT for a correct method to eliminate one variable A1 for 17.5[0] A1 for 9.5[0] If 0 scored after B0, B1 or B2, SC1 for two values that satisfy one of the/their original equations or family

This question in 0980/31 Oct/Nov 2020

7 (a) Simplify. 5g - 3h - 7g + 6h … [2] (b) j = 4k + 7m Find the value of j when k =- 5 and m = 6 . j = … [2] (c) Factorise completely. 14x 3 + 49x … [2] (d) Solve. 8 ( 3t - 9) = 108 t = … [3] (e) (i) 9 24 ' 9 w = 9 5 Find the value of w. w = … [1] (ii) 4x 2 = 256 Find the value of x. x = … [1] (f) Ranjit’s age is x years. Suzi’s age is 3 times Ranjit’s age. Juan’s age is 4 years more than Suzi’s age. The total of their ages is 46 years. Use this information to write down an equation and solve it to find the value of x. x = … [4]

15 marks

Mark scheme: 7(a) –2g +3h final answer 2 B1 for –2g or 3h in final answer or –2g+ 3h seen then spoilt 7(b) 22 2 M1 for 4  –5 + 7  6 or B1 for –20 or [+]42 7(c) 7x(2x2 + 7) final answer 2 B1 for 7(2x3 +7x) or x(14x2 + 49) or correct answer seen then spoilt 7(d) 7.5 3 M1 for a first correct step 24t – 72 = 108 or 3t –9 =13.5 M1FT for a second correct step e.g. 24t =180 or 3t =22.5 7(e)(i) 19 1 7(e)(ii) 8 1 7(f) x + 3x + 3x + 4 = 46 4 M2 for a correct equation which would or 7x + 4 = 46 lead to 7x + 4 = 46 leading to x = 6 or B1 for 3x or 3x + 4 seen M1 for 7x = 42 or for rearranging their equation to ax = b B1 for [x =] 6

This question in 0980/31 Oct/Nov 2022

8 (a) T = 5P + 3Q Find the value of T when P = 6 and Q = 8 . T = … [2] (b) Simplify. 3a - 7b + 2a + 4b … [2] (c) Multiply out. 5 ( 2x - 3y) … [1] (d) Solve. 5x - 1 = 3x + 19 x = … [2] (e) Make t the subject of the formula p = t5 - 3 . t = … [2] (f) Entry to a castle costs $x for an adult and $y for a child. Entry for 2 adults and 3 children costs $15.00 . Entry for 3 adults and 5 children costs $23.50 . Write down a pair of simultaneous equations to show this information and solve them to find the value of x and the value of y. You must show all your working. x = … y = … [6]

15 marks

Mark scheme: 8(a) 54 2 M1 for 5×6 + 3×8 or 30 or 24 8(b) 5a – 3b final answer 2 B1 for 5a or – 3b in final answer or for correct answer seen and spoilt 8(c) 10x – 15y final answer 1 8(d) 10 2 M1 for 5x – 3x = 19 + 1 or better 8(e) p  3 2 M1 for p + 3 = 5t or 5p t 53 oe [t=] oe final answer 5 8(f) 2x + 3y = 15 and 3x + 5y = 23.5 B2 B1 for each correctly equating one set of M1 FT coefficients correct method to eliminate one M1 FT variable Dependent on the coefficients being the same for one of the variables Correct consistent use of addition or subtraction using their equations [x =] 4.5 A1 [y =] 2 A1 If M0 scored, SC1 for 2 values satisfying one of correct equations or their equations

This question in 0980/32 May/June 2023

7 (a) Simplify. 5a + 3b + 2a - 4b … [2] (b) P = 8x + 3y Find the value of x when P = 21 and y =-5 . x = … [2] (c) Make v the subject of the formula S = kv2 . v = … [2] (d) Multiply out and simplify. ( x - 3)( x + 5) … [2] (e) Nasser has x marbles. Selina has 15 more marbles than Nasser. Hanif has 3 times as many marbles as Selina. In total they have 150 marbles. Find the value of x. x = … [5]

13 marks

Mark scheme: 7(a) 7a – b final answer 2 B1 for 7a or –b in final answer or 7a – b seen then spoilt 7(b) 4.5 2 M1 for 21 = 8x + 3  −5 oe or better 7(c) S 2 2 S final answer M1 for v = or S = k  v k k 7(d) x2 + 2x – 15 final answer 2 B1 for three correct terms from x2 – 3x + 5x – 15 7(e) 18 5 B1 for x + 15 or 3  their (x + 15) oe M1 for x + their (x + 15) + their (3( x + 15)) = 150 or better M1 for 5x + 60 = 150 or better or their linear equation simplified to ax + b = 150 M1 for their [ax + b = c] 150 − b solved to x = a

This question in 0980/31 Oct/Nov 2023

2 (a) Simplify. (i) 5a - 6a + 3a … [1] (ii) 6x 2 - 6x - 4x 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 cook a chicken with a mass of m kg is T = 35m + 20 . (i) Make m the subject of the formula. m = … [2] (ii) Find the mass of a chicken that takes 83 minutes to cook. … kg [2] (d) Solve these simultaneous equations. You must show all your working. 5x - 6y = 24 15x + 8y = 33 x = … y = … [3]

12 marks

Mark scheme: 2(a)(i) 2a final answer 1 2(a)(ii) 2x2 – 7x final answer 2 B1 for 2x2 or −7x in final answer or for 2x2 – 7x seen then spoilt. 2(b) 74 2 B1 for 49 or 25 2(c)(i) T  20 2 T 20 [m =] final answer M1 for T – 20 = 35m or  m  35 35 35 2(c)(ii) 1.8 2 FT their (c)(i) for 2 marks or 1 mark M1 for (83 – 20) ÷ 35 2(d) Correctly eliminates one variable M1 Making the coefficients the same for one of the variables and correct consistent use of addition or subtraction using their equations alternative substitution method. M1 for correct rearrangement of one equation to make either x or y the subject and correct substitution of their rearrangement into 2nd equation. [x =] 3 A1 If A0 scored SC1 for 2 values satisfying one of the original equations. [y =] −1.5 A1

This question in 0980/32 May/June 2024

10 (a) Solve. 4x - 7 = 3 x = … [2] (b) Simplify. 2 (i) `x6j … [1] (ii) `5x 3 y 4j # `2 x 2 y 2j … [2] (c) Expand and simplify. (i) 4a + 5 - 2 ( a - 1) … [2] (ii) ( d + 7)( d - 3) … [2]

9 marks

Mark scheme: 10(a) 2.5 oe 2 7 3 M1 for 4x = 3 + 7 or for x − = oe 4 4 10(b)(i) x12 final answer 1 10(b)(ii) 10x5y6 final answer 2 B1 for two of 10, x5, y6 correct in final answer or for 10x5y6 seen then spoilt 10(c)(i) 2a + 7 final answer 2 B1 for 2a or + 7 seen in final answer or for 2a + 7 seen then spoilt 10(c)(ii) d 2 + 4d – 21 final answer 2 B1 for d 2 + 7d – 3d – 21 with at least 3 terms correct

This question in 0980/31 Oct/Nov 2024

14 (a) P = 6 a + 5b Find the value of b when P = 25 and a = 3 . b = … [2] (b) Make T the subject of the formula W = kT + y . T = … [2]

4 marks

Mark scheme: 14(a) 1.4 2 M1 for 25 = 6 +3 5b or better 14(b) W − y W y 2 W y T =  or T =  − M1 for W − y = kT or = T + k k k k k final answer

This question in 0980/32 May/June 2025

22 In this question, all lengths are in centimetres. NOT TO 4x - 9 SCALE 2x - 5 2x + 2 The diagram shows a right-angled triangle. (a) Write down an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest form. … [2] (b) The perimeter of the triangle is 40 cm. Work out the value of x. x = … [2] (c) Work out the area of the triangle. … cm2 [3]

7 marks

Mark scheme: 22(a) 8x − 12 final answer 2 M1 for 2 x −+5 2 x + 2 + 4 x − 9 soi or better or B1 for 8x or −12 , in final expression or correct expression seen then spoilt 22(b) 6.5 2 12 40 M1 for 8x = 40 + 12 or x − = 8 8 or a correct first step in rearranging their kx + j = 40 k ≠ 0, j ≠ 0 22(c) 60 3 FT their (b) for 3 marks if their (b) > 2.5 M2 for 1  ( 2  their (b) − 5 )  ( 2  their (b) + 2 ) oe or 2 better or M1 for substituting their (b) into 2 x − 5 and 2 x + 2 1 or M1 for  (2 x − 5)  (2 x + 2) 2

This question in 0980/32 May/June 2025

17 Factorise. 21x - 7xy … [2]

2 marks

Mark scheme: 17 7x(3 – y) 2 B1 for 7(3x – xy) or x(21 – 7y) or for 7x(3 – y) seen then spoilt

This question in 0980/31 Oct/Nov 2025