Algebraic fractions — Paper 2 · IGCSE Mathematics - International 0607

14 Simplify. x 2 - x x 2 - 1 … [3] Questions 15 and 16 are printed on the next page.

3 marks

Mark scheme: 14 x 3 B1 for x ( x − 1) final answer x + 1 B1 for ( x − 1)( x + 1)

This question in 0607/22 Oct/Nov 2017

13 Simplify fully. 3t - t 2 9 - t 2 … [3]

3 marks

Mark scheme: 13 t 3 B1 for t(3 – t) final answer B1 for (3 – t)(3 + t) 3 + t

This question in 0607/21 May/June 2018

18 Write as a single fraction in its simplest form. n + 1 n - 1 - n - 1 n + 1 … [4]

4 marks

Mark scheme: 18 4 n 4 n 4 M1 for common denominator ( n − 1)( n + 1) or or final n 2 − 1 ( n − 1)( n + 1) n 2 − 1 answer M2 for ( n 2 + 2 n + 1) − ( n 2 − 2 n + 1) or better or M1 for ( n + 1) 2 or ( n − 1) 2 oe

This question in 0607/22 May/June 2018

15 Write as a single fraction in its simplest form. 7 5 - x - 1 2x + 3 … [3]

3 marks

Mark scheme: 15 9 x + 26 3 M1 for denominator ( x − 1)( 2 x + 3 ) final answer ( x − 1)( 2 x + 3 ) B1 for 7 ( 2 x + 3 ) − 5 ( x − 1) oe seen or SC2 for final answer 9 x + 16 ( x − 1)( 2 x + 3 ) If expanded denominator must be 2 x 2 + x − 3

This question in 0607/23 Oct/Nov 2018

18 Simplify. y 2 - 9 xy + 3x … [3] Question 19 is printed on the next page.

3 marks

Mark scheme: 18 y − 3 3 B1 for ( y − 3)( y + 3) final answer x B1 for x ( y + 3)

This question in 0607/22 May/June 2019

17 Simplify 2 . a - 4 … [4]

4 marks

Mark scheme: 17 b − c 4 B2 for (b − c )( a + 2) oe final answer a − 2 or B1 for b ( a + 2) − c ( a + 2) or a (b − c ) + 2(b − c ) B1 for ( a − 2)( a + 2)

This question in 0607/21 Oct/Nov 2019

15 Simplify. 3 - a 3p - 6t - ap + 2at … [3] Question 16 is printed on the next page.

3 marks

Mark scheme: 15 1 3 B2 for ( p − 2t )(3 − a ) final answer p − 2t or B1 for 3( p − 2t ) − a ( p − 2t ) or for p (3 − a ) − 2t (3 − a )

This question in 0607/21 May/June 2020

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

3 marks

Mark scheme: 16 6 − x 3 B1 for x – 2 (x – 3) or better oe final answer M1 for common denominator x(x – 3) x ( x − 3) oe

This question in 0607/21 May/June 2020

3 Simplify fully. 5x 4 12 # 15x … [2]

2 marks

Mark scheme: 3 1 2 M1 for an equivalent fraction 9

This question in 0607/21 Oct/Nov 2020

17 Simplify. 3x - 6y - ax + 2ay x 3 - 2x 2 y … [4]

4 marks

Mark scheme: 17 3 − a 4 B2 for ( x − 2 y )(3 − a ) x 2 or B1 for x (3 − a ) − 2 y (3 − a ) or 3( x − 2 y ) − a ( x − 2 y ) B1 for x 2( x − 2 y )

This question in 0607/23 Oct/Nov 2020

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

3 marks

Mark scheme: 14 5 a 2 − 3a + 4 5 a 2 − 3a + 4 3 M1 for denominator 2 a ( a + 4 ) or 2 a ( a + 4) 2 a 2 + 8 a B1 for 3a × 2 a − ( a − 1)( a + 4 ) or better final answer

This question in 0607/22 Feb/March 2021

16 Simplify 2 . x - 2 x - 3 … [3]

3 marks

Mark scheme: 16 xy 3 B1 for xy(x – 3) final answer B1 for (x – 3)(x + 1) x + 1

This question in 0607/22 May/June 2021

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

2 marks

Mark scheme: 19 7 − 2 x 2 B1 for 3 – 2( x − 2) final answer x − 2

This question in 0607/23 May/June 2021

18 Simplify. w 2 - 9 2w 2 + 5w - 3 … [4]

4 marks

Mark scheme: 18 w − 3 4 B1 for ( w − 3)( w + 3) final answer 2 w − 1 B2 for ( w + 3 )( 2 w − 1) or B1 for ( w + a )( 2 w + b ) where ab = –3 or 2a + b = 5 or 2 w( w + 3) − ( w + 3) or w(2 w − 1) + 3(2 w − 1)

This question in 0607/22 Oct/Nov 2021

- =12 2x + 3 2x - 3 bx 2 - c Find the values of a, b and c. a = … b = … c = … [4]

4 marks

Mark scheme: 12 [ a = ] − 24 4 B1 for (2 x + 3)(2 x − 3) or better as denominator [ b = ] 4 2 2 M1 for (2 x − 3) − (2 x + 3) seen [ c = ] 9 2 2 B1 for 4 x − 12 x + 9 or 4 x + 12 x + 9 or 4 x 2 − 9 or 4 x × − 6

This question in 0607/23 Oct/Nov 2021

11 Simplify. ax 2 + 5ax + bx + 5b x 2 - 25 … [3]

3 marks

Mark scheme: 11 ax + b 3 B1 for (ax + b)(x + 5) final answer B1 for (x + 5)(x – 5) x − 5

This question in 0607/22 Oct/Nov 2022

17 Simplify. 4 - 3x 2 - x - 2 Write your answer as a single fraction in its simplest form. … [3]

3 marks

Mark scheme: 17 5 x − 8 3 B1for common denominator x – 2 final answer M1 for 2(x – 2) – (4 – 3x) or better x − 2 seen

This question in 0607/23 Oct/Nov 2022

14 Solve - = 0. x - 1 3 x = … [3]

3 marks

Mark scheme: 14 −2 3 M1 for removal of fractions 3( x + 1) − ( x − 1)[ = 0] oe or 3( x + 1) − ( x − 1)[ = 0] oe 3( x − 1) M1 for isolating x from their equation

This question in 0607/22 Oct/Nov 2023

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

3 marks

Mark scheme: 15 4 x + 17 3 B1 for common denominator oe final answer (x – 1)(2x + 5) ( x − 1)(2 x + 5) B1 for 3(2x + 5) – 2(x – 1)

This question in 0607/23 Oct/Nov 2023

14 Write as a single fraction in its simplest form. 8 3 - 4x - 1 2 x + 1 … [3]

3 marks

Mark scheme: 14 4 x + 11 3 B1 for (4 x − 1)(2 x + 1) as denominator final answer (4 x − 1)(2 x + 1) (could be expanded) M1 for 8(2 x + 1) − 3(4 x − 1)

This question in 0607/21 Oct/Nov 2024

22 Write as a single fraction in its simplest form. 3 2 - x - 2 … [2] Question 23 is printed on the next page.

2 marks

Mark scheme: 22 2 x − 7 7 − 2 x 2 B1 for 2(x – 2) – 3 or better seen or final answer x − 2 2 − x

This question in 0607/23 May/June 2025

19 Simplify. 4 a 2 + 4 ab - 15b 2 2a 2 + 2ac - 3ab - 3bc … [5]

5 marks

Mark scheme: 19 2 a + 5b 5 B2 for (2a – 3b)(2a + 5b) oe final answer or M1 for a pair of brackets which give 2 a + c terms correct. B2 for (2a – 3b)(a + c) or M1 for 2a(a + c) – 3b(a + c) or a(2a – 3b) + c(2a – 3b)

This question in 0607/21 Oct/Nov 2025