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

17 Write as a single fraction in its simplest form. 2 x x + 3 1 - + x + 3 x - 5 … [3]

3 marks

Mark scheme: 17 14 x − 6 3 B1 for common denominator ( x + 3 )( x − 5 ) final answer ( x + 3 )( x − 5 ) oe isw M1 for two of the products ( x + 3 )( x − 5 ) or − 2 x ( x − 5 ) or ( x + 3 )( x + 3 ) oe or better

This question in 0980/22 May/June 2019

18 Write - as a single fraction, in its simplest form. 2 x + 1 … [3]

3 marks

Mark scheme: 18 x 2 − 3 x − 8 x 2 − 3 x − 8 3 B1 for common denominator 2( x + )1 or 2x + 2 or 2 ( x + )1 2 x + 2 M1 for x ( x + )1 − 2 ( 2 x + 4 ) or better final answer

This question in 0980/21 Oct/Nov 2019

10 Simplify. p 4pq 2q # t … [2]

2 marks

Mark scheme: 10 2 p 2 2 B1 for correct unsimplified answer t

This question in 0980/22 May/June 2020

25 Simplify. 2x 2 + x - 15 ax + 3a - 2bx - 6b … [5]

5 marks

Mark scheme: 25 2 x − 5 5 B2 for (2x – 5)(x + 3) final answer or B1 for (2x + p)(x + q) where pq = –15 or a − 2b p + 2q = 1 B2 for (x + 3)(a – 2b) or B1 for x(a – 2b) + 3(a – 2b) or a(x + 3) – 2b(x + 3)

This question in 0980/22 May/June 2020

22 Simplify. x 2 - 5x 2x 2 - 50 … [4] Question 23 is printed on the next page.

4 marks

Mark scheme: 22 x x 4 B1 for x(x – 5) or final answer B2 for 2(x – 5)(x + 5) or (x – 5)(2x + 10) 2 ( x + 5 ) 2 x + 10 or (2x – 10)(x + 5) or B1 for 2(x2 – 25) or (x – 5)(x + 5)

This question in 0980/21 Oct/Nov 2020

22 Simplify. 2x 2 - 5x - 12 3x 2 - 12x … [4]

4 marks

Mark scheme: 22 2 x + 3 4 B2 for ( x − 4 )( 2 x + 3 ) final answer 3 x or B1 for (x + a) (2x + b) where ab = –12 or 2a + b = – 5 or x ( 2 x + 3 ) − 4 ( 2 x + 3 ) or 2 x ( x − 4 ) + 3 ( x − 4 ) B1 for 3 x ( x − 4 )

This question in 0980/22 May/June 2021

24 Solve. 1 9 + = 1 x + 1 x + 9 x = … or x = … [5]

5 marks

Mark scheme: 24 x = 3, x = –3 5 M2 for x + 9 + 9(x + 1) = (x + 1)(x + 9) oe nfww or better or M1 for x + 9 + 9(x + 1) or (x + 1)(x + 9) oe or better B1 for x 2 + x + 9 x + 9 seen M1 dep for [ 0 = ] x 2 − 9 oe simplified or better

This question in 0980/22 May/June 2021

19 Write as a single fraction in its simplest form. 2 x + 2 - x + 3 7 … [3]

3 marks

Mark scheme: 19 8 − 5 x − x 2 8 − 5 x − x 2 3 B1 for 7 × 2 – (x + 2)(x + 3) or better seen or 7( x + 3) 7 x + 21 B1 for common denominator 7(x + 3) oe isw final answer

This question in 0980/21 Oct/Nov 2021

22 Write as a single fraction in its simplest form. 5 4 + 3x + 2 2x - 1 … [3]

3 marks

Mark scheme: 22 22 x  3 3 B1 for a common denominator (3x + 2)(2x – 1) oe final answer  3 x  2  2 x  1 isw B1 for 5(2x – 1) + 4(3x + 2) oe isw

This question in 0980/22 May/June 2023

20 Write as a single fraction in its simplest form. 10x 2 - 60x (a) 2 x - x - 30 … [3] 7 5 (b) + x + 3 8x - 1 … [3]

6 marks

Mark scheme: 20(a) 10 x 3 B1 for 10x(x – 6) final answer B1 for (x – 6)(x + 5) x + 5 20(b) 61x + 8 3 B1 for common denominator of (x + 3)(8x – 1) final answer ( x + 3 )( 8 x − 1) isw B1 for 7(8x – 1) + 5(x + 3) or better isw

This question in 0980/21 Oct/Nov 2023

7 Simplify. p 2 (a) ' t t … [2] 3x x - 1 (b) - 4 2 … [2]

4 marks

Mark scheme: 7(a) p 2 p t final answer M1 for  or for cross cancelling of t 2 t 2 7(b) x + 2 x 1 2 3 x − 2 ( x − 1) or + final answer M1 for oe 4 4 2 4 x − 2 If 0 scored, SC1 for final answer 4 oe

This question in 0980/21 Oct/Nov 2025

22 Solve. 2 x = x - 1 x + 2 x = … or x = … [5]

5 marks

Mark scheme: 22 –1 and 4 5 B2 for x2 – 3x – 4 [= 0] or M1 for 2(x + 2) = x(x – 1) or better M2 for a correct method to solve their three-term quadratic in the numerator or M1 for (x + a)(x + b) where ab = –4 or a + b = –3 or x ( x − 4) + [1]( x − 4) or x ( x + 1) − 4( x + 1) or M1 for ( −3)2 −4 [1] −4 or better p + q p − q or if in the form or then r r M1 for p = −(−3) and r = 2(1) or better

This question in 0980/21 Oct/Nov 2025

25 Simplify. 10 ax + 6bx - 25a - 15 b 4 x 2 - 25 … [4]

4 marks

Mark scheme: 25 5a + 3b 4 B2 for (5a + 3b )(2 x − 5) final answer 2 x + 5 or B1 for 5a (2 x − 5) + 3b(2 x − 5) or for 2 x (5a + 3b ) − 5(5a + 3b ) B1 for (2 x + 5)(2 x − 5)

This question in 0980/21 Oct/Nov 2025