Inequalities — Paper 2 · IGCSE Mathematics - International 0607

7 3x + 2 H 5x - 6 (a) Solve the inequality. … [2] (b) Show your solution to part (a) on this number line. x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 [1]

3 marks

Mark scheme: 7(a) x ⩽ 4 or 4 ⩾ x 2 M1 for 2 + 6 ⩾ 5x – 3x oe If 0 scored, SC1 for x = 4, x < 4, x > 4, x ⩾ 4 7(b) Correct FT from(a) on number line 1 FT dep on inequality as answer to (a)

This question in 0607/22 May/June 2017

11 (a) Factorise x 2 - 3x - 10 . … [2] (b) Using your answer to part (a), solve x 2 - 3x - 10 2 0 . … [2] Questions 12 and 13 are printed on the next page.

4 marks

Mark scheme: 11(a) (x – 5)(x + 2) 2 B1 for (x + a)(x + b) where ab = –10 or a + b = –3 or for x(x – 5) + 2(x – 5) or x(x + 2) – 5(x + 2) 11(b) x < –2, x > 5 2 B1FT for correct 'inequalities' from (a)

This question in 0607/21 Oct/Nov 2017

10 Solve 3 - x H 2x + 15 . … [2]

2 marks

Mark scheme: 10 x ⩽ –4 oe 2 M1 for correctly moving one term

This question in 0607/23 May/June 2018

10 List the integer values of x for which - 4 G 2x 1 6 . … [2]

2 marks

Mark scheme: 10 −2, − 1, 0, 1, 2 2 M1 for 1 omission or 1 extra

This question in 0607/21 Oct/Nov 2018

6 The line with equation 2x + 3y = 6 is drawn on the grid. y 6 5 4 3 2 1 x 0 –4 –3 –2 –1 1 2 3 4 5 6 7 8 –1 –2 –3 –4 On the grid, show clearly the single region defined by these three inequalities. 2x + 3y G 6 x H- 3 y G- 1 [3]

3 marks

Mark scheme: 6 x = –3 ruled 3 B1 for each y = –1 ruled Correct region clearly shown

This question in 0607/22 Oct/Nov 2018

10 Solve. 4x + 9 G 3 (2x - 1) … [3]

3 marks

Mark scheme: 10 x ⩾ 6 3 B2 for ⩽ , <, >, = or M2 for 9 + 3 ⩽ 6x – 4x or M1 for 4x + 9 ⩽ 6x – 3 4 x or + 3 = 6x – 3 3

This question in 0607/22 Oct/Nov 2018

3 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 Write down the inequality shown above. … [1]

1 marks

Mark scheme: 3 −<3 x - 2 1

This question in 0607/23 Oct/Nov 2018

6 (a) Write down the integer solutions to this inequality. - 2 G 2x 1 8 … [2] (b) Solve 2 + 2x 2 5x + 14 . … [2]

4 marks

Mark scheme: 6(a) –1, 0, 1, 2, 3 2 B1 for 5 correct and 1 extra or 3 or 4 correct with no errors or M1 for −1 - x < 4 6(b) x < –4 final answer 2 M1 for 2 – 14 > 5x – 2x oe If 0 scored, SC1 for x = – 4 or x > –4 or x ⩽ – 4 or x ⩾ –4

This question in 0607/21 May/June 2019

9 (a) Solve 3x - 2 2 7x + 6 . … [2] (b) Show your solution to part (a) on this number line. x –5 –4 –3 –2 –1 0 1 2 3 4 5 [1]

3 marks

Mark scheme: 9(a) x < –2 2 B1 for x = or ⩽ or ⩾ –2 or M1 for –2 – 6 > 7x – 3x oe 9(b) Line/arrow from –2 to left with 1 FT from their inequality in (a) empty circle at –2

This question in 0607/23 Oct/Nov 2019

13 Solve. ( x - 4)( x + 3) 2 0 … [2]

2 marks

Mark scheme: 13 x > 4, x < −3 2 B1 for each

This question in 0607/22 May/June 2020

5 Solve. 9 - 2x G 5 (x + 6) … [3]

3 marks

Mark scheme: 5 x ⩾ –3 3 B2 for x * –3 where * is = or < or > or ⩽ or M1 for 9 – 2x ⩽ 5x + 30 M1FT for correctly isolating terms

This question in 0607/23 May/June 2020

7 Solve 2x + 3 1 5x - 12 . … [2]

2 marks

Mark scheme: 7 x > 5 2 M1 for 3 + 12 < 5x – 2x oe If 0 scored, SC1 for x * 5.

This question in 0607/22 May/June 2021

15 y 11 10 9 8 7 6 5 4 3 2 1 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 11 x – 1 – 2 – 3 The diagram shows the line x + y = 8 . On the diagram, show clearly the region defined by these inequalities. x + y G 8 x H 2 y G 3 [2] 2

2 marks

Mark scheme: 15 Correct diagram 2 B1 for x = 2 and y = 3 drawn 12 11 10 9 8 7 6 5 4 3 2 1 -3 -2 -1 O 1 2 3 4 5 6 7 8 9 10 11 12 -1 -2 -3

This question in 0607/22 May/June 2021

12 y A NOT TO B SCALE C D E F O x G 1 The diagram shows the lines y = x + 1, y = 3x and 3x + 4y = 12 . 2 These lines divide the space into 7 regions, A, B, C, D, E, F, and G. Write down the letter of the region which is defined by 1 (a) y G x + 1, y G 3x and 3x + 4y G 12 , 2 Region … [1] 1 (b) y H x + 1, y H 3x and 3x + 4y G 12 . 2 Region … [1]

2 marks

Mark scheme: 12(a) F 1 12(b) C 1

This question in 0607/21 Oct/Nov 2021

6 x 1 2 Write down all the integer values of x. … [1]

1 marks

Mark scheme: 6 –1, 0, 1 1

This question in 0607/22 Oct/Nov 2021

1 On the number line, show the inequality - 2 G x 1 3 . x – 4 – 3 – 2 – 1 0 1 2 3 4 [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 2 B1 for either correct line or correct ends –2 3 Two lines scores max of 1 mark

This question in 0607/21 May/June 2022

15 (a) Factorise fully. 6x 2 - 7x - 3 … [2] (b) Solve. 6x 2 - 7x - 3 1 0 … [3]

5 marks

Mark scheme: 15(a) (2 x  3)(3 x  1) final answer 2 M1 for ( ax  b )( cx  d ) where ac= 6 AND bd = –3 or ad  bc 7 or for 2 x (3 x  1)  3(3 x  1) or for 3 x (2 x  3)  (2 x  3) 15(b) 1 3 3 FT their factors from (a)   x  final answer 3 2 or 1 3 ‘ x  AND x  ’ final answer 1 3 3 2 B2 for ‘ x  [or] x  ’ 3 2 (must include the word AND) 1 3 or B1 for x  or B1 for x  3 2 1 or B1 for  x  AND  x  3 soi 3 2

This question in 0607/21 May/June 2022

3 Show this inequality on the number line. - 3 1 x G 4 x –6 –5 – 4 –3 –2 –1 0 1 2 3 4 5 6 [2]

2 marks

Mark scheme: 3 2 –3 4 Correct line B1 for correct line or correct ends Correctly marked ends

This question in 0607/23 May/June 2022

6 Solve 2x + 6 2 5x - 10 . … [2]

2 marks

Mark scheme: 6 16 1 2 16 x < or x < final answer B1 for x * where * is =, >, ⩽ or ⩾ 3 53 3 OR M1 for 6 + 10 > 5x – 2x oe

This question in 0607/22 Oct/Nov 2022

7 Solve. 4x - 3 H 9 … [2]

2 marks

Mark scheme: 7 x 3 final answer 2 M1 for 4 x 9 + 3

This question in 0607/22 Feb/March 2023

3 (a) Solve x + 9 2 6 . … [1] (b) Show your answer to part (a) on this number line. x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 [1]

2 marks

Mark scheme: 3(a) x > –3 or –3 < x 1 3(b) 1 FT their inequality from (a) –3 Correct line with correct end oe

This question in 0607/22 May/June 2023

4 (a) Write 1.8796 correct to 4 significant figures. … [1] 4 (b) Work out 5 . ` j … [1] (c) x is an integer and x G 1. Write down the values of x. … [1] (d) Find the highest common factor (HCF) of 24 and 42. … [1]

4 marks

Mark scheme: 4(a) 1.880 cao 1 4(b) 25 1 4(c) –1, 0, 1 1 4(d) 6 1

This question in 0607/21 Oct/Nov 2023

4 (a) Solve 11 + 2x 2 5 . … [2] (b) Show your solution to part (a) on this number line. x – 5 – 4 –3 –2 –1 0 1 2 3 4 [1]

3 marks

Mark scheme: 4(a) x > –3 2 M1 for 2x > 5 – 11 or B1 for x * –3 where * is =, <, ⩽, ⩾ 4(b) 1 FT their (a) dep on (a) being an inequality –3

This question in 0607/23 Oct/Nov 2023

2 Show the inequality –2 1 x G 3 on the number line. x −4 −3 −2 −1 0 1 2 3 4 [2]

2 marks

Mark scheme: 2 2 B1 for line going from –2 to 3 or B1 for both ‘circles’ correct and no complete –2 3 line drawn

This question in 0607/22 Feb/March 2025

13 y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 Find the 3 inequalities that define the shaded region. … [4]

4 marks

Mark scheme: 13 x  5 4 B2 for x [=] 5, x + y 4= oe, y 1= x + 2 oe x + y 4 oe 2 1 y x + 2 oe or B1 for y 1= x + 2 oe or x + y 4= oe 2 2 B1 for one correct inequality

This question in 0607/22 Feb/March 2025

11 Solve. 7 - 3x 2 2 x - 8 … [2]

2 marks

Mark scheme: 11 x < 3 final answer 2 M1 for isolating x terms e.g. 7 + 8 > 2x + 3x or better

This question in 0607/21 May/June 2025

18 Solve. 3 ( 2x + 1 ) 2 5 - 4 x … [3]

3 marks

Mark scheme: 18 1 3 B1 for 6x + 3 x > oe final answer M1 for collecting terms 5 e.g. 6x + 4x > 5 – 3

This question in 0607/23 May/June 2025

14 y A B E D C G F O x 1 The lines with equations x = 2 , y = x and x + y = 5 are shown on the diagram. 2 These lines divide the space into 7 different regions A, B, C, D, E, F and G. Write down the inequalities which define (a) region A … [1] (b) region C … [1] (c) region E. … [2]

4 marks

Mark scheme: 14(a) x ⩽ 2 and x + y ⩾ 5 oe 1 14(b) 1 1 y < x and x + y ⩾ 5 oe 2 14(c) 1 2 B1 for 2 correct x ⩽ 2 and y > x and x + y ⩽ 5 oe 2

This question in 0607/21 Oct/Nov 2025