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

19 Rearrange this formula to make m the subject. k + m P = m m = … [4]

4 marks

Mark scheme: 19 k − k 4 M1 for squaring correctly or P 2 − 1 1 − P 2 M1 for multiplying by m or dividing by m final answer correctly M1 for correctly rearranging to isolate m M1 for correct division by 2-term factor To a maximum of M3 for an incorrect answer

This question in 0980/22 May/June 2019

22 A = B = (3 - 4 ) 0 1 (a) Find A-1, the inverse of A. … [2] (b) Calculate BA. … [2]

4 marks

Mark scheme: 22(a) 1  1 −4  2  1 − 4    oe isw B1 for k   soi or det = 3 soi 3  0 3   0 3  22(b) ( 9 8 ) 2 M1 for a 1 by 2 matrix 9 If 0 scored, SC1 for  or 9 8 or (9, 8) 8

This question in 0980/22 May/June 2019

2 Factorise 5p + pt. … [1]

1 marks

Mark scheme: 2 p(5 + t) final answer 1

This question in 0980/21 Oct/Nov 2019

11 y = w2 Rearrange the formula to write x in terms of w and y. x = … [2]

2 marks

Mark scheme: 11 4 2 2 2 2 M1 for correct multiplication [x = ] w y or w y final answer ( ) M1 for squaring correctly

This question in 0980/21 Oct/Nov 2019

19 Make y the subject of the formula. h 2 = x 2 + 2y 2 y = … [3]

3 marks

Mark scheme: 19 2 2 3 M1 for correct rearrangement for y or y2 term h − x [±] M1 for correct square root 2 M1 for correct division by 2 or 2

This question in 0980/22 May/June 2020

1 Simplify. 3a + 7b - 4a + b … [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 –a + 8b final answer 2 B1 for –a or [+]8b in final answer or for –a + 8b spoilt

This question in 0980/21 Oct/Nov 2020

7 Make x the subject of this formula. 2y = 5x - 7 x = … [2]

2 marks

Mark scheme: 7 2 y + 7 2 y 7 2 2 y 7 [ x = ] oe or [ x = ] + oe M1 for 2 y + 7 = 5 x oe or = x – oe 5 5 5 5 5 final answer

This question in 0980/21 Oct/Nov 2020

16 Factorise 6x 2 + 7x - 20 . … [2]

2 marks

Mark scheme: 16 (3x – 4)(2x + 5) final answer 2 B1 for (ax + b)(cx + d) where ac = 6 and ad + bc = 7 or bd = – 20

This question in 0980/21 Oct/Nov 2020

20 Expand and simplify. ( x - 2)( 2x + 5)( x + 3) … [3]

3 marks

Mark scheme: 20 2 x 3 + 7 x 2 − 7 x − 30 final answer 3 B2 for unsimplified expansion with at most one error or for simplified four-term expression of correct form with three terms correct or B1 for correct expansion of two brackets with at least three terms out of four correct

This question in 0980/22 May/June 2021

17 y = 1 - x Make x the subject of the formula. x = … [4]

4 marks

Mark scheme: 17 y + 2 4 M1 y (1 – x) = 3x – 2 or better [x = ] oe final answer y + 3 M1 for correctly isolating x terms on one side FT their first step/bracket expansion M1dep for correctly removing factor of x FT their previous step M1dep for correct division to isolate x Max 3 marks for an incorrect answer

This question in 0980/21 Oct/Nov 2021

15 Find the highest common factor (HCF) of 12a 3 b and 20a 2 b 2 . … [2]

2 marks

Mark scheme: 15 4a 2 b final answer 2 M1 for two correct parts out of three from 4, a2 and b in final answer

This question in 0980/22 May/June 2022

20 Factorise completely. (a) 2m + 3p - 8km - 12kp … [2] (b) 5x 2 - 20y 2 … [3]

5 marks

Mark scheme: 20(a)  2 m  3 p 1  4 k  final 2 B1 for 2 m  3 p  4 k  2 m  3 p  or better answer or 2 m 1  4 k   3 p 1  4 k  or correct answer seen and spoilt 20(b) 5  x  2 y  x  2 y  final 3 B2 for (5x – 10y)(x + 2y) or (x – 2y)(5x + 10y) or correct answer seen then spoilt answer or B1 for 5 x 2  4 y 2   or for  x  2 y  x  2 y 

This question in 0980/22 May/June 2022

19 Expand and simplify. ( 2x + 3)( x - 2) 2 … [3]

3 marks

Mark scheme: 19 2 x 3 − 5 x 2 − 4 x + 12 final answer 3 B2 for correct expansion of the three brackets unsimplified or for simplified four- term expression of correct form with three terms correct or B1 for correct expansion of two of the three given brackets with at least three terms out of four correct

This question in 0980/21 Oct/Nov 2022

20 Factorise completely. (a) 1+ x - y - xy … [2] (b) 2x 3 - 18xy 2 … [3]

5 marks

Mark scheme: 20(a) (1 + x )(1 − y ) final answer 2 B1 for 1 + x − y (1 + x ) or 1 – y + x(1 – y) or correctly x 2 − 9 y 220(b) 2 x ( x + 3 y )( x − 3 y ) final answer 3 B2 for 2 x ( ) factorising into two brackets e.g. 2 x 2 + 6 xy x 2 − 3 xy 2 x + 6 y ) ( )( x − 3 y ) , ( )( or B1 for 2 x 3 − 9 xy 2 or x 2 x 2 − 18 y 2 ( ) ( ) or for ( x + 3 y )( x − 3 y )

This question in 0980/21 Oct/Nov 2022

18 Make x the subject of the formula. 3x c = 2x - 5 x = … [4]

4 marks

Mark scheme: 18 5c 4 M1 for correctly clearing the denominator and oe final answer expanding bracket 2c  3 or correctly clearing the denominator and dividing by c M1 for correctly collecting terms in x on one side and terms not in x on the other M1 for correct factorising M1 for correct division dependent on x appearing only once in a factorised expression Maximum 3 marks for an incorrect answer

This question in 0980/22 May/June 2023

5 Factorise completely. (a) 42mk - 35m … [2] (b) h 2 - 144 … [1]

3 marks

Mark scheme: 5(a) 7m(6k – 5) final answer 2 B1 for 7(6mk – 5m) or m(42k – 35) as final answer or 7m(6k – 5) seen and then spoiled 5(b) (h + 12)(h – 12) final answer 1

This question in 0980/21 Oct/Nov 2023

7 Factorise. 28x - 35 … [1]

1 marks

Mark scheme: 7 7(4x – 5) final answer 1

This question in 0980/21 Oct/Nov 2024

22 The graph of y = ( x + 2)( x - 1) 2 is shown on the grid. y 4 3 2 1 x -2 -1 0 1 2 -1 (a) Show that y = ( x + 2 )( x - 1 ) 2 can be written as y = x 3 - 3x + 2 . [2] (b) By drawing a suitable straight line, solve the equation 2x 3 - 5x = 0 . x = … or x = … or x = … [4] Question 23 is printed on the next page.

6 marks

Mark scheme: 22(a) x2 – x – x + 1 M1 or x2 + 2x– x – 2 A correct unsimplified expansion A1 e.g. x3 + 2x2 –x2 –2x – x2 –2x + x + 2 oe leading to [y = ] x3 – 3x + 2 22(b) y = 2 – 0.5x ruled B2 B1 for [y =] 2 – 0.5x soi or for y = 2 – kx drawn or for y = k – 0.5x drawn –1.5 to –1.6 B2 B1 for two correct values 0 1.5 to 1.6

This question in 0980/21 Oct/Nov 2024

23 ( x - 5) 2 + k = x 2 - px - 21 Find the value of p and the value of k. p = … k = … [2]

2 marks

Mark scheme: 23 [p = ] 10 2 B1 for each [k = ] –46

This question in 0980/21 Oct/Nov 2024

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