Fractions, decimals and percentages — Paper 2 · IGCSE Mathematics 0580

1 1 c _ d 10 Write + – as a single fraction in its simplest form. c d cd Answer [3]

3 marks

Mark scheme: 10 2 3 M1 d + c – c + d or better M1 common denominator cd used c

This question in 0580/21 May/June 2009

3a 4 Examiner's 4 Write as a single fraction + . Use 8 5 Answer [2]

2 marks

Mark scheme: 15a + 32 4 oe 2 B1 15a + 32 seen 40 15 a 32 or SC1 + on answer line 40 40

This question in 0580/22 May/June 2010

19 The braking distance, d metres, for Alex’s car travelling at v km/h is given by the formula Examiner's Use 200d = v(v + 40). (a) Calculate the missing values in the table. v 0 20 40 60 80 100 120 (km/h) d 0 16 48 96 (metres) [2] (b) On the grid below, draw the graph of 200d = v(v + 40) for 0 Y v Y 120. d 100 90 80 70 60 Distance 50 (metres) 40 30 20 10 v 0 10 20 30 40 50 60 70 80 90 100 110 120 Speed (km / h) [3] (c) Find the braking distance when the car is travelling at 110 km/h. Answer(c) m [1] (d) Find the speed of the car when the braking distance is 80 m. Answer(d) km/h [1]

7 marks

Mark scheme: 19 (a) 6, 30, 70 2 B1 for 2 correct (b) graph 3 P2 7 plots correct from table P1 5 or 6 plots correct from table C1 smooth curve through the points in the given range within one small square of the plots or the correct position (c) 82.5 or ft ±1 1ft (d) 108 or ft ±1 1ft

This question in 0580/22 May/June 2010

8 Write as a single fraction in its simplest form x x − 1 + . 3 2 Answer [2]

2 marks

Mark scheme: 5x 3 8 2 B1 for 5x – 3 seen 6 5 3 SC1 x − on answer line 6 6 5 k

This question in 0580/23 May/June 2010

7 7 1 8 Show that + 1 = 2 . 27 9 27 Write down all the steps in your working. Answer [2]

2 marks

Mark scheme: 8 Answer given so only working scores 2 M1 7/27 + 48/27 or 7/27 + (1)21/27 marks M1 completely correct finish

This question in 0580/22 Oct/Nov 2010

3 1 1 For 5 Show that 3 + 1 = 5 . Examiner's 4 3 12 Use Write down all the steps in your working. Answer [2]

2 marks

Mark scheme: 15 4 45 16 5 Correct working 2 M1 + = + 4 3 12 12 61 1 M1 = 5 12 12 20 80

This question in 0580/23 Oct/Nov 2010

18 27 For 7 (a) Find the value of x when = . Examiner's 24 x Use Answer(a) x = [1] 2 1 4 (b) Show that ÷ 1 = . 3 6 7 Write down all the steps in your working. Answer(b) [2]

3 marks

Mark scheme: 7 (a) 36 1 7 (b) correct working 2 M1 for 6 oe improper fraction M1 for 1221 = 74 oe or visible cancelling

This question in 0580/23 May/June 2011

1 1 1 3 For 5 Jiwan incorrectly wrote 1 + + + = 1 . Examiner's 2 3 4 9 Use Show the correct working and write down the answer as a mixed number. Answer [3]

3 marks

Mark scheme: 1 6 4 3 13 25 5 212 cao with correct working 3 M1 (1+) 12 + 12 + 12 oe A1 (1)12 or 12 oe 2

This question in 0580/22 Oct/Nov 2011

5 9 For 12 Without using your calculator, work out 1 + . Examiner's 6 10 Use You must show your working and give your answer as a mixed number in its simplest form. Answer [3]

3 marks

Mark scheme: 55 27 25 27 12 + oe or )1( + oe M1 for denominator of 30k 30 30 30 30 82 52 oe or )1( oe M1 for denominator of 30k dependent on previous M1 30 30 11 2 M2 must be scored A1 If M0 scored then SC1 for common denominator of 15 30k seen k

This question in 0580/21 May/June 2012

1 1 1 p 4 1 + + = 2 3 4 12 Work out the value of p. Show all your working. Answer p = [2]

2 marks

Mark scheme: 4 25 (correct working essential) 2 M1 for 18 + 4 + 3 with denominator 12 must be soi (oe is possible) 4 4 k

This question in 0580/22 May/June 2012

12 Without using your calculator, work out the following. For Show all the steps of your working and give each answer as a fraction in its simplest form. Examiner's Use 11 1 (a) − 12 3 Answer(a) [2] 1 11 (b) ÷ 4 13 Answer(b) [2]

4 marks

Mark scheme: 12 (a) M1 correct use of a common denominator 11 4 − oe 2 12 12 7 cao ww 0 A1 12 13 (b) 1 2 M1 inversion and operation change × oe 4 11 13 cao ww 0 A1 44

This question in 0580/23 May/June 2012

2 Show that + = 0.17. 10 5 Write down all the steps in your working. Answer [2]

2 marks

Mark scheme: 1 4 2 + or 0.12 + 0.42 oe M1 100 25 1 16 + = 0.17 or 0.01 + 0.16 = 0.17 M1 Independent 100 100 300× 12

This question in 0580/23 Oct/Nov 2012

For 1 3 5 Show that 1 ÷ = 8. Examiner′s 2 16 Use Do not use a calculator and show all the steps of your working. Answer [2] _____________________________________________________________________________________

2 marks

Mark scheme: 3 k 5 correct working; 2 M1 for 2 k 3k 16n e.g. × = 8 3 k 16n 2 k 3n and A1 for × = 8 2 k 3n 2

This question in 0580/21 May/June 2013

2 x 2 2 y = 2 + x 2 Find the value of y when x = 6. Give your answer as a mixed number in its simplest form. Answer y = … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 1 2 36 2 18 2 M1 for + or better 18 36 2 n f

This question in 0580/21 May/June 2014

5 Without using a calculator, work out 1 + 1 . 4 6 Write down all the steps in your working and give your answer as a fraction in its simplest form. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 5 3 and 2 M1 Equivalent denominators can be used, 12 12 working must be shown. 5 cao A1 12

This question in 0580/21 Oct/Nov 2014

4 2 .12 Without using a calculator, work out 5 ÷ 2 3 Write down all the steps of your working and give your answer as a fraction in its simplest form. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 12 8 40 3 15 B1 or accept or 3 15 8 40 4 3 12 40 × their oe M1 or ÷ their or equivalent division with 5 8 15 15 fractions with common denominators 3 cao A1 10

This question in 0580/22 May/June 2015

8 Without using a calculator, work out 1 78 ÷ 59 . Show all your working and give your answer as a fraction in its lowest terms. Answer … [3]

3 marks

Mark scheme: 15 135 8 B1 or 8 72 15 9 135 40 their × oe M1 or ÷ or equivalent division with 8 5 72 72 fractions with common denominators 27 3 or 3 cao A1 8 8

This question in 0580/23 May/June 2015

10 Write the recurring decimal .015o as a fraction. [ .015o means 0.1555...] Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 14 10 oe must be fraction 2 M1 for 155. − 5.1 oe 90 or k B1 for 90  2 

This question in 0580/21 Oct/Nov 2015

1 11 12 Without using your calculator, work out 2 4 - 12 . You must show all your working and give your answer as a fraction in its lowest terms. Answer … [3]

3 marks

Mark scheme: 3 15 27 9 × 3 12 2 or 1 or or M1 Accept any correct conversion with common 12 12 12 4 × 3 denominator 12k 27 11 16 their ( − = ) oe M1 Correct resolving of their subtraction with 12 12 12 denominator 12k showing full working 1 4 1 or cao 3 3 A1 Working and then simplified answer must both be seen 12 4

This question in 0580/22 Oct/Nov 2015

11 Write the following as single fractions. x (a) x + 2 Answer(a) … [1] 2 (b) x + x Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 3x 11 (a) oe final answer 1 2 x 2 + 2 (b) 1 oe final answer x

This question in 0580/23 Oct/Nov 2015

2 1 1 – +15 Work out 4 , giving your answer as a fraction in its lowest terms. 3 6 Do not use a calculator and show all the steps of your working. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 8 2 3 15 Any two of , oe M1 M1 for any 2 correct over a common denominator 12 12 or12 4 1 e.g. and 6 6 8 2 3 13 1 + − oe M1 or SC2 for final answer or 1 with full working 12 12 12 12 12 7 A1 12 2 ( s ut )

This question in 0580/23 Oct/Nov 2015

6 Write the recurring decimal .04o as a fraction. [ .04o means 0.444…] … [2]

2 marks

Mark scheme: 4 6 oe, must be fraction 2 M1 for 10 × 0.4 − 0.4 oe 9

This question in 0580/22 Feb/March 2016

9 Without using your calculator, work out 1 7 + 13 . 12 20 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 35( or 95) 39 35k ( or 95k ) 39 k 9 + M1 accept + 60 60 60 k 60 k 7 67 134 k 74 k 14 k 230 A2 or A1 for 30 or 60 k or 160 k or 2 60 k 1 6 × 20000 2

This question in 0580/22 Feb/March 2016

6 2 16 Without using a calculator, work out 7 ' 1 3 . Show all your working and give your answer as a fraction in its lowest terms. … [3]

3 marks

Mark scheme: 6 3 18 35 5 16 × or ÷ oe M2 B1 for oe 7 5 21 21 3 6 3 or M1 for × their 7 5 18 cao A1 35

This question in 0580/21 May/June 2016

1 1 # 1 5 .5 Without using a calculator, work out 12 Show all your working and give your answer as a fraction in its lowest terms. … [2]

2 marks

Mark scheme: 1 6 5 × oe M1 Must be shown 12 5 1 final answer cao A1 10

This question in 0580/23 May/June 2016

8 Write the recurring decimal 0.32˙ as a fraction. [0.32˙ means 0.3222…] … [2]

2 marks

Mark scheme: 29 8 oe, must be a fraction 2 M1 for 32.2 − 3.2 90 k or B1 for 90 1 1 1 1

This question in 0580/23 May/June 2016

2 14 Work out - , giving your answer as a fraction in its lowest terms. 3 4 Do not use a calculator and show all the steps of your working. … [2]

2 marks

Mark scheme: 8 3 4 and oe M1 Correct fractions with common denominator 12 12 5 cao 12 A1 1

This question in 0580/21 Oct/Nov 2016

8 Write as a single fraction. 2 3 1 - - p t … [2]

2 marks

Mark scheme: pt − 2t − 3 p 2t + 3 p 8 final answer 2 B1 for pt − 2t − 3 p or 1 − pt pt

This question in 0580/21 Oct/Nov 2016

12 (a) Write $0.70 as a fraction of $5.60, giving your answer in its lowest terms. … [1] (b) Write the recurring decimal .018o o as a fraction in its lowest terms. [ .018o o means 0.181818… ] … [2]

3 marks

Mark scheme: 1 12 (a) cao 1 8 2 . . . . (b) 2 M1 for 18.18 − 0.18 oe 11 2 k or B1 for (k not 0 or 1) 11k

This question in 0580/21 Oct/Nov 2016

15 Work out. 3 1 (a) 2 - c m c m 5 2 … [1] 2 (b) (1 2 ) c 3 m … [2]

3 marks

Mark scheme: 5 15 (a)  1 8 (b) (8) final answer 2 B1 for final answer 8 without brackets Page 4 Mark Sccheme Syllabuss Paper Cambridge IGCSE – Occtober/November 2016 0580 21

This question in 0580/21 Oct/Nov 2016

3 2 114 Without using your calculator, work out + - . 4 3 8 You must show all your working and give your answer as a mixed number in its simplest form. … [4]

4 marks

Mark scheme: 14 Common denominator 24 B1 accept k × 24 18 16 3 18k 16 k 3k Two correct from , and oe M1 accept , and 24 24 24 24 k 24 k 24 k 7 31 31k 7 k 124 cao A2 A1 for 24 or 24 k or 124 k

This question in 0580/22 Oct/Nov 2016

3 1 5 Without using a calculator, work out 5 + 6 . Write down all the steps of your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 18 5 18 k 5 k 5 and oe must be shown M1 and 30 30 30 k 30 k 23 cao A1 30

This question in 0580/23 Oct/Nov 2016

13 Write the recurring decimal .02o as a fraction. [ .02o means 0.222…] … [2]

2 marks

Mark scheme: 2 13 oe, must be a fraction 2 M1 for 2.2 – 0.2 oe 9 k or B1 for 9

This question in 0580/23 Oct/Nov 2016

6 Write the recurring decimal .017o as a fraction. Show all your working. … [2]

2 marks

Mark scheme: 6 10 k × 0.17 − [10] × 0.17 k ⩾1 oe M1 16 8 or oe nfww A1 90 45

This question in 0580/22 Feb/March 2017

1 18 Without using your calculator, work out 3 ' 2 . 3 2 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 10 5 8 or B1 oe improper fractions 3 2 10 2 20 15 their × their M1 accept ÷ 3 5 6 6 1 13 cao A1 2  1  2

This question in 0580/22 Feb/March 2017

2 57 Without using a calculator, work out 1 + . 3 7 Write down all the steps of your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 7 14 ( or 35 ) 15 M1 14 k ( or 35k ) 15k + accept + 21 21 21k 21k 8 A2 50 8 29 29 2 cao or A1 for or 1 or or 1 21 21 21 21 21

This question in 0580/21 May/June 2017

5 19 Without using a calculator, work out - . 6 2 Show all the steps of your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 9 5 3 M1 5 k 3k – oe oe for − 6 6 6 k 6 k 1 A1 cao final answer 3

This question in 0580/22 May/June 2017

14 Write the recurring decimal .063o o as a fraction in its lowest terms. You must show all your working. … [3]

3 marks

Mark scheme: 14 10k+2 × [0].63& & − 10k × [0].63& & oe M1 where k > 1 63 A1 6300 7 or equivalent fraction e.g. but not 99 9900 11 7 B1 11

This question in 0580/23 May/June 2017

11 3 219 Without using your calculator, work out - - 12 c 4 3 m. You must show all your working and give your answer as a fraction in its simplest form. … [4]

4 marks

Mark scheme: 19 common denominator 12 B1 accept k × 12 throughout 9 8 M1 9 k 8 k one correct from or oe accept or 12 12 12 k 12 k A2 10 10 k 5 A1 for or cao 12 12 k 6

This question in 0580/23 May/June 2017

2 1110 Without using a calculator, work out 1 - . 3 15 Write down all the steps of your working and give your answer as a fraction in its lowest terms. … [3]

3 marks

Mark scheme: 10 5 2 4 B1 5 k + Allow 3 3 15 3k 25 11 10 4 M1 Correct method to find common denominator [and ] [and ] 15 15 15 15 75 33 e.g. and 45 45 5 Follow through their for the M1 mark 3 14 14 A1 cao cao 15 15

This question in 0580/21 Oct/Nov 2017

11 Write the recurring decimal .048o o as a fraction. Show all your working. … [2]

2 marks

Mark scheme: 11 48.48 – 0.48 oe M1 48 16 SC1 for or or equivalent fraction with 99 33 no/insufficient working 48 16 A1 or or equivalent fraction 99 33

This question in 0580/22 Oct/Nov 2017

1113 (a) Write as a mixed number. 3 … [1] 1 5 (b) Without using a calculator, work out + . 4 12 Show all the steps of your working and give your answer as a fraction in its lowest terms. … [2]

3 marks

Mark scheme: 13(a) 2 1 3 cao 3 13(b) 3 5 M1 For correct method to find common denominator [and ] oe 12 12 12 20 e.g. and 48 48 2 A1 cao 3

This question in 0580/22 Oct/Nov 2017

3 Write the recurring decimal .063o o as a fraction. … [1]

1 marks

Mark scheme: 3 7 1 oe 11

This question in 0580/21 May/June 2018

3 613 Without using your calculator, work out 1 # . 4 35 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 13 7 M1 k 6 or × where k > 4 4 4 35 3 A2 42 21 6 cao A1 for or or 10 140 70 20

This question in 0580/21 May/June 2018

2 16 Without using your calculator, work out - . 3 12 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 6 8 1 M1 For correct fractions with a common and oe denominator 12k 12 12 7 A1 cao 12

This question in 0580/22 May/June 2018

2 115 Without using a calculator, work out ' 1 . 3 5 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 15 6 B1 18 accept equivalent fractions e.g. 5 15 2 5 M1 10 18 ×their or ÷ oe 3 6 15 15 5 A1 cao 9

This question in 0580/23 May/June 2018

3 114 Without using your calculator, work out ' 2 . 8 4 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 14 3 4 3 18 M2 9 × oe or ÷ oe with B1 for oe seen 8 9 8 8 4 common denominator 3 4 or M1 for × their 8 9 1 A1 cao 6

This question in 0580/21 Oct/Nov 2018

71 Work out of 198 kg. 11 … kg [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 126 1

This question in 0580/23 Oct/Nov 2018

13 Change the recurring decimal .018o to a fraction. You must show all your working. … [2]

2 marks

Mark scheme: 13 1.88… – 0.188.. oe M1 e.g. 18.88… – 1.88… or 18.88… – 0.188… 17 B1 or equivalent fraction 90

This question in 0580/23 Oct/Nov 2018

3 Write the recurring decimal .023o o as a fraction. … [1]

1 marks

Mark scheme: 3 23 1 99

This question in 0580/22 Feb/March 2019

1 521 Without using a calculator, work out 3 ' . 8 12 You must show all your working and give your answer as a mixed number in its simplest form. … [4]

4 marks

Mark scheme: 21 25 B1 75 or 8 24 25 12 75 10 M1 75 24 their × or their ÷ oe × 8 5 24 24 24 10 300 M1 75 60 30 their oe oe e.g.1800 , , , ,15 40 240 10 8 4 2 1 A1 7 cao 2

This question in 0580/22 Feb/March 2019

9 Write the recurring decimal .047o as a fraction. Show all your working. … [2]

2 marks

Mark scheme: 9 47.77…– 4.77… oe M1 43 A1 Allow equivalent fractions 90 43 If M0 then SC1 for or equivalent 90 fraction with no/insufficient working

This question in 0580/21 May/June 2019

5 214 Without using a calculator, work out + . 6 3 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 14 5 4 M1 2 correct fractions with a suitable common + oe denominator 6k 6 6 1 A2 9 12 cao A1 for 6 oe

This question in 0580/21 May/June 2019

3 Write the recurring decimal .07o as a fraction. … [1]

1 marks

Mark scheme: 3 7 1 9

This question in 0580/22 May/June 2019

' 7 .13 Without using a calculator, work out 2 14 3 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 13 9 7 63 12 M2 9 × or ÷ oe with common B1 for oe seen 4 3 28 28 4 denominator 9 7 or M1 for their × 4 3 1 A1 5 cao 4

This question in 0580/22 May/June 2019

3 Giulio’s reaction times are measured in two games. In the first game his reaction time is 13 of a second. In the second game his reaction time is 18 of a second. Find the difference between the two reaction times. … s [1]

1 marks

Mark scheme: 3 5 1 or 0.208 or 0.2083… 24

This question in 0580/23 May/June 2019

12 79 Without using a calculator, work out # . 35 9 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 9 84 4 7 12 1 4 1 M1 Accept any correct cancelling or × or × or × 315 35 3 5 9 5 3 4 A1 cao 15

This question in 0580/23 May/June 2019

5 18 Without using a calculator, work out # 1 . 16 7 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 8 5 8 M1 × 16 7 5 A1 cao 14

This question in 0580/21 Oct/Nov 2019

10 Write the recurring decimal .067o as a fraction. Show all your working and give your answer in its simplest form. … [2]

2 marks

Mark scheme: 10 67.7 – 6.7 oe M1 61 A1 k If 0 scored, SC1 for 90 90

This question in 0580/22 Oct/Nov 2019

5 211 Without using a calculator, work out 3 - 1 . 8 3 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 11 29 5 5 2 M1 29 k 5 k or 8 3 28 − 3 Allow 8k or 3k Correct step for dealing with mixed numbers 87 40 16 M1 Correct method to find common and [ 2 ]15 and 15 16 24 24 24 24 denominator e.g. 324 and 124 23 A1 124 cao

This question in 0580/22 Oct/Nov 2019

2 1 215 Without using a calculator, work out + # . 3 4 3 Write down all the steps of your working and give your answer as a fraction in its simplest form. … [4]

4 marks

Mark scheme: 15 2 1 1 2  1  M1 M1 for correct first step to deal with oe or × 1 +   multiplication 12 2 3 3  4  8 2 2 5 M1 M1 for correct working for common [ + ] oe × 12 12 3 4 2 denominator with their oe or correct 12 evaluation of bracket 5 A2 10 cao A1 for oe 6 12

This question in 0580/23 Oct/Nov 2019

1 3.56 5 196 8 7 12 From the list, write down a number that is (a) a multiple of 3, … [1] (b) a cube number, … [1] (c) a prime number, … [1] (d) an irrational number. … [1]

4 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 12 1 1(b) 8 1 1(c) 5 1 1(d) 7 1

This question in 0580/22 Feb/March 2020

15 45 Without using a calculator, work out ' . 28 7 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 5 15 7 15 16 M1 × or ÷ oe 28 4 28 28 15 A2 105 cao A1 for oe 16 112

This question in 0580/22 Feb/March 2020

13 Write the recurring decimal .026o as a fraction. You must show all your working. … [2]

2 marks

Mark scheme: 13 2.6 − 0.26 oe M1 4 A1 k oe fraction nfww If M0 scored SC1 for 15 90

This question in 0580/22 Feb/March 2020

1 7 68 Without using a calculator, work out 2 - # . e 3 8 o 25 You must show all your working and give your answer as a fraction in its simplest form. … [4]

4 marks

Mark scheme: 8 56 21 M2 M2 for correct method for common − 24 24 denominator 7 or B1 for 3 35 6 M1 their × 24 25 7 A1 20

This question in 0580/21 May/June 2020

8 Write 2 - 4 as a decimal. … [1]

1 marks

Mark scheme: 8 0.0625 1

This question in 0580/22 May/June 2020

3 1111 Without using a calculator, work out 1 - . 4 12 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 11 7 9 B1 4 12 21 2 M1 1 − 12 12 5 5 A1 6 6

This question in 0580/22 May/June 2020

1 27 Without using a calculator, work out 3 - 2 . 4 3 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 7 Correct common denominator M1 Correct method M1 3 − 8 12 + 3 − 8 e.g. 1 or or 12 12 ((3 × 4) + 1) × 3 − ( ( 2 × 3 ) + 2 ) × 4 39 − 32 or 12 12 7 A1 cao 12

This question in 0580/23 May/June 2020

2 36 Without using a calculator, work out 2 # 2 . 3 4 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 6 8 11 M1 and oe improper fractions 3 4 88 A1 oe improper fraction 12 1 A1 dep on 1st A1 7 cao final answer 8 11 3 If M0 scored SC1 for or oe 3 4 improper fraction

This question in 0580/21 Oct/Nov 2020

13 Write the recurring decimal .017o as a fraction in its simplest form. You must show all your working. … [3]

3 marks

Mark scheme: 13 17.77… – 1.77… oe M1 M1 for correct working shown 8 A2 16 cao B1 for oe seen 45 90

This question in 0580/21 Oct/Nov 2020

5 110 Without using a calculator, work out ' 1 . 6 3 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 10 5 3 5 8 M2 4 5 3 × or ÷ oe M1 for seen or for × their 6 4 6 6 3 6 4 5 their 8 or for ÷ 6 6 5 A1 dep on M2 cao 8

This question in 0580/22 Oct/Nov 2020

1 27 Without using a calculator, work out 2 # 3 . 4 3 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 7 9 11 M1 and oe improper fractions 4 3 99 A1 oe improper fraction 12 1 A1 dep on 1st A1 8 cao final answer 4 9 11 If M0 scored SC1 for or oe 4 3 improper fraction

This question in 0580/22 Feb/March 2021

8 Write .037o o as a fraction. … [1]

1 marks

Mark scheme: 8 37 1 oe fraction 99

This question in 0580/22 Feb/March 2021

3 58 Without using a calculator, work out 1 - . 8 6 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 8 11 5 3 1 B1 Correct step for dealing with mixed [– ] + number 8 6 8 6 11k Allow 8k 33 20 9 4 M1 Correct method to find common and and denominator 24 24 24 24 9 20 e.g. 1 and 24 24 13 A1 cao 24

This question in 0580/21 May/June 2021

2 39 Without using a calculator, work out ' 1 . 3 7 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 9 2 7 M2 10 × or B1 for oe 3 10 7 14 30 2 7 ÷ oe with common denominator or M1 for × their 21 21 3 10 7 A1 cao 15

This question in 0580/22 May/June 2021

11 Write .004o o as a fraction in its simplest form. … [1]

1 marks

Mark scheme: 11 4 1 cao 99

This question in 0580/22 May/June 2021

2 Write as a fraction in its simplest form. (a) 72% … [1] (b) 0.004 … [1]

2 marks

Mark scheme: 2(a) 18 1 cao 25 2(b) 1 1 cao 250

This question in 0580/23 May/June 2021

2 19 Without using a calculator, work out 1 ' 7 . 3 2 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 9 5 2 M2 5 15 × oe or B1 for oe or oe 3 15 3 2 5 2 or M1 for their × their 10 45 3 15 ÷ oe with common denominator 6 6 2 A1 cao 9

This question in 0580/23 May/June 2021

5 27 Without using a calculator, work out 1 + . 6 5 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 7 25 or 55 12 M1 25k or 55k 12k and Accept and 30 30 30k 30k 7 A2 67 k 37k 230 cao A1 for 30k or 1 30k

This question in 0580/21 Oct/Nov 2021

1 7 16 Without using a calculator, work out ' + . 3 6 5 You must show all your working and give your answer as a fraction in its simplest form. … [4]

4 marks

Mark scheme: 6 1 6 2 7 M1 × oe or ÷ oe 3 7 6 6 2 A1 oe 7 2 1 M1 10 7 their + with a correct method to find e.g. + oe 7 5 35 35 fractions with a common denominator 17 A1 If order of operations not correct SC2 for cao 35 10 answer with correct working for 41 1  7 1  ÷  +  3  6 5  35 6 or SC1 for + oe 30 30

This question in 0580/22 Oct/Nov 2021

4 (a) = ! 2 1 Put a ring around each of the symbols that make this statement correct. 0.5 … 5% [1] (b) Insert one pair of brackets to make this statement correct. 7 - 3 - 1 + 2 = 7 [1]

2 marks

Mark scheme: 4(a) ≠and > indicated 1 4(b) 7 – (3 – 1) + 2 = 7 cao 1

This question in 0580/23 Oct/Nov 2021

9 Write the recurring decimal .027o o as a fraction. … [1]

1 marks

Mark scheme: 9 3 1 oe fraction 11

This question in 0580/23 Oct/Nov 2021

11 312 Without using a calculator, work out + . 12 4 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 12 11 9 M1 Allow any correct common denominator + oe 12k 12 12 2 A2 20 13 cao A1 for 12 or equivalent improper fraction or mixed number

This question in 0580/23 Oct/Nov 2021

13 (a) Simplify h 2 # h 5 . … [1] 7 -3 (b) Simplify . b x l … [1] (c) a 8 ' a p = a 2 Find the value of p. p = … [1]

3 marks

Mark scheme: 13(a) h 7 final answer 1 13(b) x 3 1 final answer 343 13(c) 6 1

This question in 0580/22 Feb/March 2022

1 1115 Without using a calculator, work out 2 # . 3 14 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 15 7 M1 k 11 oe improper fraction or × where k > 3 3 3 14 5 A2 77 11 35 16 cao A1 for 42 or 6 or 142

This question in 0580/22 Feb/March 2022

3 27 Without using a calculator, work out - . 7 21 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 7 9 and 212 oe M1 Allow any correct denominator 21k 21 1 A1 cao and correct working 3

This question in 0580/21 May/June 2022

1 28 s = at 2 (a) Work out the value of s when a = 0.9 and t = 4. s = … [1] (b) Rearrange the formula to find t in terms of s and a. t = … [2]

3 marks

Mark scheme: 8(a) 7.2 oe 1 8(b) 2s 2 s 1 2 [±] final answer M1 for  t or 2s = at2 or better a a 2 2 xy  y 2 or y 14 x  7 y  9 7 y  2 x  y  final answer 2 B1 for 7   or 7 y  2 x  y  seen then spoilt

This question in 0580/21 May/June 2022

2 58 Without using a calculator, work out ' . 9 6 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 8 2 6 4 15 M1  or  oe 9 5 18 18 4 A1 cao 15

This question in 0580/23 May/June 2022

1 59 Without using a calculator, work out + . 3 6 You must show all your working and give your answer as a mixed number in its simplest form. … [2]

2 marks

Mark scheme: 9 2 5 M1 i.e. correct fractions with common + oe denominator 6k 6 6 1 A1 16 cao

This question in 0580/21 Oct/Nov 2022

5 17 Without using a calculator, work out - . 9 6 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 7 10 3 M1 Allow any correct common denominator and 18k 18 18 7 A1 cao 18

This question in 0580/22 Oct/Nov 2022

10 Calculate. (a) 2000 # 1.23 … [1] 1 6 (b) 2 # 8 17 … [1] 4.5 ( cos 30°) (c) - 2 3 … [1]

3 marks

Mark scheme: 10(a) 3456 1 10(b) 3 1 0.75 or oe 4 10(c) 1 1 0.25 or 4

This question in 0580/22 Oct/Nov 2022

18 Write .0419o o as a fraction in its simplest form. You must show all your working. … [3]

3 marks

Mark scheme: 18 419.19 − 4.19 oe M1 83 A2 415 cao Al for oe 198 990 k If M0 scored SC1 for or correct 990 answer with insufficient working

This question in 0580/22 Oct/Nov 2022

5 25 Without using a calculator, work out - . 7 3 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 5 15 14 M1 Allow any correct common denominator and oe 21k 21 21 1 A1 cao 21

This question in 0580/23 Oct/Nov 2022

13 Convert .024o to a fraction. You must show all your working and give your answer in its simplest form. … [2]

2 marks

Mark scheme: 13 2.4 − 0.24 oe M1 11 B1 k cao If 0 scored SC1 for . 45 90

This question in 0580/23 Oct/Nov 2022

1 510 Without using a calculator, work out 2 ' . 7 9 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 10 15 9 M2 15  oe B1 for oe 7 5 7 135 35 their 15 9 or  oe with common or M1 for  oe 63 63 7 5 denominator

This question in 0580/21 May/June 2023

4 57 Without using a calculator, work out ' 1 . 7 21 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 7 4 21 M2 26 21 × oe B1 for or oe 7 26 21 26 or 4 21 or M1 for × oe 12 26 7 their 26  oe with common 21 21 denominator 6 A1 cao 13

This question in 0580/22 May/June 2023

16 Write .0621o o as a fraction in its simplest form. You must show all your working. … [3]

3 marks

Mark scheme: 16 621.21… – 6.21… oe M1 41 A2 615 cao A1 for oe 66 990 k 41 If M0 scored SC1 for or for answer with 990 66 insufficient working

This question in 0580/22 May/June 2023

14 Write .0581o o as a fraction. You must show all your working and give your answer in its simplest form. … [3]

3 marks

Mark scheme: 14 581.81...− 5.81...oe M1 32 A2 576 cao A1 for oe 55 990 k 32 If M0 scored SC1 for or for answer 990 55 with insufficient working.

This question in 0580/23 May/June 2023

12 Write .042o as a fraction in its simplest form. You must show all your working. … [3]

3 marks

Mark scheme: 12 42.22… – 4.22… oe M1 M1 for correct working shown 19 A2 38 cao A1 for oe seen 45 90 k 19 If M0 scored SC1 for or for answer 90 45 with insufficient working.

This question in 0580/21 Oct/Nov 2023

1 38 Without using a calculator, work out 3 - 1 . 8 4 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 8 B1 Correct step for dealing with mixed numbers 25 7 1 3 or − 25 k 7 k 8 4 28 4 Allow or 8 k 4 k M1 Correct method to find common denominator 25 14 1 6 and 2 and oe 1 6 100 − 56 8 8 8 8 e.g. 3 − 1 , 8 8 32

This question in 0580/22 Oct/Nov 2023

5 117 Without using a calculator, work out 1 ' . 6 15 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 7 11 15 M2 11  or B1 for oe 6 11 6 55k 22 k their 11 15  oe with common or M1 for their  30 k 30 k 6 11 denominator 1 A1 2 cao 2

This question in 0580/23 Oct/Nov 2023

1 511 Without using a calculator, work out 1 - . 4 6 You must show all your working and give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 11 5 1 1 B1 Correct method for dealing with mixed or + number 4 4 6 5k Allow 4 k 15 10 M1 Correct method to find common and denominator 12 12 10 e.g. 31 and 12 12 5 A1 cao 12

This question in 0580/22 Feb/March 2024

15 Write .0146oo as a fraction in its simplest form. You must show all your working. … [3]

3 marks

Mark scheme: 15 146.46  1.46 oe M1 29 A2 145 cao Al for oe 198 990 k If M0 scored SC1 for with insufficient 990 working.

This question in 0580/21 May/June 2024

1 713 Without using a calculator, work out 2 ' 1 . 4 8 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 13 9 8 M2  oe or 4 15 18 15  oe with common 8 8 9 15 denominator B1 for oe or oe 4 8 their 9 8 or M1 for  oe 4 their 15 1 A1 dep on M2 15 cao

This question in 0580/22 May/June 2024

3 1 8 Without using a calculator, work out - . 7 14 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 8 6 1 M1 Allow any correct denominator 14k and oe 14 14 5 A1 cao 14

This question in 0580/23 May/June 2024

21 Write the recurring decimal .04.1 as a fraction in its simplest form. You must show all your working. … [2]

2 marks

Mark scheme: 21 41.11...– 4.11... oe M1 37 A1 37 cao If M0 scored SC1 for answer with 90 90 insufficient working.

This question in 0580/23 May/June 2024

1 2 Find the reciprocal of 1 4. … [1]

1 marks

Mark scheme: 2 4 1 or 0.8 5

This question in 0580/21 Oct/Nov 2024

3 Use one of the symbols 1, 2 or = to make each statement true. 2 … 0.2861 7 99 … 11% 900 13 … 40 [2]

2 marks

Mark scheme: 3 < 2 B1 for two correct = =

This question in 0580/21 Oct/Nov 2024

2 6 7 Without using a calculator, work out ' . 7 11 You must show all your working and give your answer as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 7 2 11 M1  or 7 6 22 42  oe with common 77 77 denominator 11 A1 cao 21

This question in 0580/22 Oct/Nov 2024

18 (a) % = {8 # 10 -1 , .08o , 8%, .008} A = { a: 0.08 1 a G 0.8 } B = { b: b H 0.8 } % A B Complete the Venn diagram. [3] (b) Shade the region ( A , C ) + Bl in the Venn diagram. % A B C [1]

4 marks

Mark scheme: 18(a) 3 B2 for three correctly placed A B or B1 for two correctly placed or correct conversion of 8 × 10–1, 8% and 0.08 ξ0.08 8 × 10–1 0. 8ሶ to 0.8, 0.08, 0.2[8…] or 0.3 8% 18(b) 1 A B C

This question in 0580/22 Oct/Nov 2024

12 (a) Write as a single fraction in its simplest form. x 3 x x + 2 + - 4 8 12 … [3] (b) Factorise. 3 x ( a + 4y) - ay - 4y 2 … [1]

4 marks

Mark scheme: 12(a) 13 x − 4 3 13 x + 4 final answer SC2 for final answer 24 24 6 x + 9 x − 2 x − 4 or M2 for oe or 24 better 6 x + 3 ( 3 x ) − 2 ( x + 2 ) or M1 for oe 24 12(b) (3x – y)(a + 4y) final answer 1

This question in 0580/22 Feb/March 2025

17 Work out. 5 o + 0.28 9 Give your answer as a fraction in its simplest form. … [4]

4 marks

Mark scheme: 17 38 4 76 cao B3 for oe fraction 45 90 OR M3 for any complete correct method with common denominators 76 that would reach oe e.g. 90 28.8− 2.8 50 + oe 100 − 10 90 50 18 8 + + oe 90 90 90 84.4 − 8.4  oe 100 − 10 or M2 for any correct method to convert 0.28 to fractional form e.g. 28.8− 2.8 oe 100 − 10 2 8.8− 0.8 + oe 10 100 − 10 or M1 for correct method to add their fractions with a common denominator e.g. 50 26 + their oe 90 90 50 18 8 + + their oe 90 90 90 or for method to subtract to eliminate recurring parts 28.8… – 2.8… oe 8.88… – 0.08… oe or B1 for a correct conversion between a relevant recurring decimal and a fraction e.g. 5 8 = 0.5 , 0.08 = 9 90

This question in 0580/22 Feb/March 2025

4 Work out. 5 2 3 - # 6 3 8 … [3]

3 marks

Mark scheme: 4 7 3 6 oe M1 for oe 12 24 M1 for correct use of common denominator in 5 6 20 6 subtraction – their , e.g. and oe 6 24 24 24 1 If 0 scored, SC1 for answer oe 16

This question in 0580/21 May/June 2025

7 Write the recurring decimal .026o as a fraction. Give your answer in its simplest form. … [3]

3 marks

Mark scheme: 7 4 3 24 B2 for oe 15 90 or M1 for 26.66… – 2.66… oe or for 90x = 24 oe 2 6 or for + oe 10 90

This question in 0580/21 May/June 2025

14 Write .025o as a fraction. … [2]

2 marks

Mark scheme: 14 23 2 M1 for 25.55… – 2.55… oe oe fraction 90 or for 90x = 23 oe 2 5 or for + oe 10 90

This question in 0580/22 May/June 2025

7 Work out. 5 7 (a) - 6 12 Give your answer as a fraction in its simplest form. … [2] 1 8 (b) 1 ' 3 15 Give your answer as a mixed number in its simplest form. … [3]

5 marks

Mark scheme: 7(a) 1 2 M1 for correct method to find common cao 4 10 7 denominator e.g. and , 12 12 60 42 and 72 72 7(b) 1 3 4 15 2 cao M2 for  2 3 8 20 8 or  oe with common 15 15 denominator 4 their k 15 or M1 for or for  , where 3 3 8 k > 3

This question in 0580/23 May/June 2025

o o16 Write .0328 as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 16 65 3 65 cao B2 for a fraction equivalent to e.g. 198 198 325 990 3 28 or M1 for 328.28 − 3.28 oe or + 10 990 k oe or 990x = 325 or 990

This question in 0580/23 May/June 2025

o o11 Write .024 as a fraction in its simplest form. … [2]

2 marks

Mark scheme: 11 8 2 24 cao B1 for oe 33 99 or M1 for 24.24… – 0.24… oe

This question in 0580/21 Oct/Nov 2025

9 Rajid has a full bottle of juice. 1 He drinks of the full bottle on Monday. 3 3 He drinks of the full bottle on Tuesday. 7 Find the fraction of the bottle of juice remaining. … [3]

3 marks

Mark scheme: 9 5 3 16 B2 for oe 21 21 OR 1 3 M1 for 1 − − oe 3 7 a b M1 for converting and to two 3 7 fractions with a common denominator 1  1  3 e.g. (or their  1 −  ) and to 3  3  7 7 k 9 k and 21k 21k 14k 9 k or and where k is an integer 21k 21k

This question in 0580/22 Oct/Nov 2025

o o20 Work out 0.114 + 0 .2 . Give your answer as a fraction. … [3]

3 marks

Mark scheme: 20 311 3 M2 for 314.14− 3.14 oe oe fraction 990 113 198 or + 990 990 or M1 for 114.14− 1.14 oe 113 or 0.314 or 990

This question in 0580/23 Oct/Nov 2025

26 Write as a single fraction in its simplest form. mp 15 (a) # 25 y m … [2] 3 4 (b) + 2x - 5 x - 3 … [3]

5 marks

Mark scheme: 26(a) 3 p 2 15 p 3mp final answer cao B1 for or final answer 5 y 25 y 5my or for correct answer spoilt 26(b) 11 x − 29 3 B1 for 3( x − 3) + 4(2 x − 5) or better final answer (2 x − 5)( x − 3) seen B1 for common denominator of or (2 x − 5)( x − 3) oe isw 11x − 29 2 final answer 2 x − 11x + 15

This question in 0580/23 Oct/Nov 2025