Fractions, decimals and percentages — Paper 1 · IGCSE Mathematics 0580

3 Write 5 as a decimal, correct to two decimal places. 9 Answer [2]

2 marks

Mark scheme: 3 0.56 2 B1 for 5 ÷ 9 or digits 55 (….) or digits 56 Common answer for B1 is 0.55

This question in 0580/11 Oct/Nov 2004

15 (a) Write down a common multiple of 6 and 8. Answer (a) [1] (b) Work out 5 3 − . 6 8 Give your answer as a fraction in its lowest terms. You must show all your working. Answer (b) [2]

3 marks

Mark scheme: 15 (a) multiple of 24 1 ignore extras if lowest correct 11 2 M1 for a correct attempt at two equivalent fractions (b) 24 5×8 3×6 (e.g.. 48 and 48 seen or better) ww. and decimals alone zero

This question in 0580/11 May/June 2005

9 0.072 72% 0.702 7 7 7.2% 10 100 From the values listed above, write down (a) the smallest, Answer(a) [1] (b) the largest, Answer(b) [1] (c) the two which are equal. Answer(c) and [1]

3 marks

Mark scheme: 9 (a) 7 1 Allow 0.07 or 7% 100 (b) 72% 1 72 Allow 0.72 or 100 (c) 0.072 and 7.2% 1 In this form. [15]

This question in 0580/11 Oct/Nov 2005

9 9 2 0.09 90% 9% 0.9 900% 1000 100 Write down the three numbers from the list above which have the same value. Answer [1]

1 marks

Mark scheme: 2 9 1 0.09 9% 100 4

This question in 0580/11 May/June 2006

19 Joseph, Maria and Rebecca each win a prize. For Their total prize money is $30. Examiner's Use 7 Joseph wins of the $30. 12 Maria wins 30% of the $30. Rebecca wins the rest of the $30. Calculate the amount each receives. Answer Joseph $ [2] Maria $ [2] Rebecca $ [1]

5 marks

Mark scheme: 19 (Joseph $) 17.5(0) 2 M1 for 30 ÷ 12 x 7. (Maria $) 9 2 M1 for 30 ÷ 100 x 30. (Rebecca $) 3.50 1ft 30 – c’s Joseph – c’s Maria. 6

This question in 0580/11 May/June 2006

10 Write these fractions in order with the smallest first. 33 2 6 50 3 10 Answer < < [2]

2 marks

Mark scheme: 10 6 33 2 2 SC1 for reverse order. M1- at least 2 fractions correctly compared in 10 50 3 the same form. (decimal, percentage or common denominator) 15

This question in 0580/11 Oct/Nov 2006

5 ... 9 (a) Write in the missing number. = 6 18 [1] (b) Without using your calculator and writing down all your working, show that 2 5 7 1 − = . 9 6 18 Answer(b) [2]

3 marks

Mark scheme: 9 (a) 15 1 (b) 119 oe B1 Eg 5466 Allow 99 + 29 or better 18 22 − 1518 = 187 oe E1 Must be finally reduced to 187

This question in 0580/11 Oct/Nov 2007

7 > = < Choose one of the symbols above to complete each of the following statements. 5 (a) 74% 7 [1] _3  1  (b)   8  2  [1]

2 marks

Mark scheme: 7 (a) > 1 (b) = 1

This question in 0580/11 Oct/Nov 2008

5 3 For14 Without using your calculator, work out ÷ 3 . 8 4 Examiner's Use Give your answer as a fraction in its lowest terms. You must show all your working. Answer [3]

3 marks

Mark scheme: 14 15 W1 seen 4 5 4 × their M1 Must be inversion of an improper fraction 8 15 5 ' 15 ' ' 20 ' Can be implied by ÷ = . 8 4 120 1 A1 ww no marks 6 IGCSE – October/November 2008 0580 and 0581 11

This question in 0580/11 Oct/Nov 2008

1 [ < > = Y For Examiner's Choose one of the above symbols to make a correct statement in the answer space. Use 4 Answer 0.4 [1] 9

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 < 1 ( accept ≤ or both symbols)

This question in 0580/11 May/June 2009

11 (a) Find the lowest common multiple of 7 and 9. Answer(a) [1] 8 _ 5 (b) Without using a calculator, work out , leaving your answer as a fraction. 9 7 You must show all your working. Answer(b) [2]

3 marks

Mark scheme: 11 (a) 63 1 ×8 − 5 (b) ( 7 ×9 ) oe M1 their 63 11 63 final answer A1ft ft their (a)

This question in 0580/11 May/June 2009

6 Work out the value of 3 3 ×1 1 . 4 7 Show all your working and leave your answer as a fraction. Answer [2]

2 marks

Mark scheme: 6 15 8 M1 and seen 4 7 120 8 120 oe fraction or 4 oe A1 isw incorrect cancelling after oe 28 28 28 Final answer is a decimal, maximum M1.

This question in 0580/11 Oct/Nov 2009

2 Write the following numbers in order starting with the smallest. 2 0.283 28 % 7 Answer < < [1]

1 marks

Mark scheme: 2 28% < 0.283 < 2 1 7

This question in 0580/12 Oct/Nov 2009

6 Work out the value of 2 2 ×1 1 . 3 11 Show all your working and leave your answer as a fraction. Answer [2]

2 marks

Mark scheme: 6 8 12 M1 and seen 3 11 96 30 96 oe fraction or 2 oe A1 isw incorrect cancelling after oe 33 33 33 Final answer is a decimal, maximum M1.

This question in 0580/12 Oct/Nov 2009

4 1 litre of apple juice is poured into 3 glasses. Examiner's Use 2 The first glass contains litre. 5 1 The second glass contains litre. 4 What fraction of a litre does the third glass contain? Show all your working clearly. Answer [2]

2 marks

Mark scheme: 7 2 × 4 5 × 1 8 5 4 or equivalent fraction isw www 2 M1 for + or + or 0.4 + 0.25 20 4 × 5 4 × 5 20 20 8 5 or 1− − or 1 − 0.4 − 0.25 or 40 + 25 20 20 or 400 + 250 or 1000 − 400 − 250 seen 7 If M0 then SC1 for with no, incomplete or 20 wrong working. Condone if followed by 0.35 or 35%

This question in 0580/12 May/June 2010

4 I = K= Examiner's Use For each part, choose a symbol from those above to make a correct statement. 5 (a) 0.55 [1] 9 2 (b) 66% [1] 3

2 marks

Mark scheme: 4 (a) > 1 (b) < 1 their ( 21000 − 16800) 4200

This question in 0580/13 May/June 2010

7 Mrs Duval makes one litre of ice cream. Examiner's 1 3 Use She eats litre and her children eat litre. 8 5 Without using your calculator, find what fraction of a litre of ice cream is left. Show all your working clearly. Answer [2]

2 marks

Mark scheme: 11 3 × 8 5 × 1 5 24 7 or equivalent fraction isw www 2 M1 for + or + or 0.6 + 0.125 40 5 × 8 8 × 5 40 40 cao Condone if followed by 0.275 or 27.5% 5 24 or 1 − − or 1 − 0.6 − 0.125 or 600 + 125 40 40 or 60 + 12.5 or 1000 − 600 − 125 seen 11 If M0, then SC1 for with no, incomplete or 40 wrong working.

This question in 0580/13 May/June 2010

19 In this question, you must show all the steps in your working. For Examiner's Without using a calculator, find the value of Use 1 4 (a) 1 ÷ 2 , 3 5 Answer(a) [3] 13 3 (b) + . 15 5 Give your answer as a mixed number. Answer(b) [3]

6 marks

Mark scheme: 19 (a) 4 × 5 M2 M1 for 4 ÷ 14 3 14 3 5 and M1 for ‘correct’ expression with their inverted 2nd fraction 10 20 A1 Allow isw for attempt to cancel only 21 42 13 3× 3 13 9 (b) + or better or equivalent B2 If B0, then B1 for + their or equivalent 15 15 15 15 pair of fractions 7 1 B1ft Independent 15 ft their improper fraction given as a mixed number

This question in 0580/11 Oct/Nov 2010

13 Dominic, Esther, Flora and Galena shared a pizza. For Examiner's 1 2 Use (a) Dominic ate of the pizza and Esther ate of the pizza. 5 7 18 Show that of the pizza remained. 35 Do not use your calculator and show all your working. Answer (a) [2] 2 (b) Flora ate of the pizza that remained. 3 Find the fraction of the pizza that was left for Galena. Answer(b) [2]

4 marks

Mark scheme: 1 × 7 + 2 × 5 1 × 7 2 × 5 13 (a) Two stage proof 2 M1 for or + 5 × 7 5 × 7 5 × 7 4 2 5 1 or alt − or − 5 7 7 5 17 18 17 35 M1dep for 1− their or + = 35 35 35 35 28− 10 25− 7 or alt oe or oe 35 35 6 1 18 (b) final answer 2 M1 for × oe 35 3 35 12 If zero SC1 for answer of 35 10 × 8 0 5 × 90

This question in 0580/12 Oct/Nov 2010

10 Change 18.75% into a fraction. For Examiner's Write your answer in its lowest terms. Use Answer [2]

2 marks

Mark scheme: 3 1875 10 2 B1 for or any equivalent fraction. 16 10000

This question in 0580/13 Oct/Nov 2010

 1  12 Simplify  1 2  . Give your answer as a fraction. Answer [2]

2 marks

Mark scheme: 8 1 12 2 M1 for 1 ÷ (1 )3 oe 27 2 27 or SC1 for 8

This question in 0580/13 Oct/Nov 2010

11 Without using your calculator, and leaving your answer as a fraction, work out 1 7 2 – . 6 12 You must show all your working. Answer [3]

3 marks

Mark scheme: 26 7 5 13 7 2 7 1 7 11 – or 2 – oe M2 M1 for − or − or − oe 12 12 12 6 12 212 12 6 12 7 19 112 or 12 oe A1

This question in 0580/11 May/June 2011

5 7 7 For 5 Show that 1 ÷ 1 = . Examiner's 9 9 8 Use Write down all the steps in your working. Answer [2]

2 marks

Mark scheme: 14 16 14 7 5 Working must be shown. 2 M1 and M1 = oe 9 9 16 8 or visible cancelling 2 16

This question in 0580/12 May/June 2011

3 2 6 I p I 5 3 Which of the following could be a value of p? 16 4 0.67 60% (0.8)2 27 9 Answer [2]

2 marks

Mark scheme: 16 6 0.82 2 M1 conversion of (= 0.5(9..)) and 27 0.82 (= 0.64) to decimals seen 3 3

This question in 0580/12 May/June 2011

18 27 For 13 (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: 13 (a) 36 1 (b) Correct working 2 M1 for 7 oe improper fraction 6 12 4 M1 for = oe or visible cancelling 21 7

This question in 0580/13 May/June 2011

7 (a) Calculate 60% of 200. Answer(a) [1] (b) Write 0.36 as a fraction. Give your answer in its lowest terms. Answer(b) [2]

3 marks

Mark scheme: 7 (a) 120 1 9 36 18 (b) cao 2 B1 or 25 for100 50 2

This question in 0580/11 Oct/Nov 2011

1  2 1  For 11 Without using your calculator, work out  +  . Examiner's 2  3 4  Use Show all your working clearly and give your answer as a fraction. Answer [3]

3 marks

Mark scheme: 11k 11 final answer www Method 1 (Addition first) 24 k 8 3 8 + 3 B1 or oe 12 +12 12 1 × their 11 M1 2 × their 12 A1 Method 2 (Multiplication first) 2 1 1 1 B1 + or + oe 6 8 3 8 ad + bc a c M1 for their + bd b d A1 11 11 If M0, SC1 if is only followed by 12 24 or if zero, SC1 if work is entirely in decimals & with answer of .0 458 3 to .0 45835

This question in 0580/11 Oct/Nov 2011

1 1 1 3 For 12 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 12 212 cao with correct working 3 M1 (1+) 12 + 12 + 12 oe A1 (1)12 or 12 oe

This question in 0580/12 Oct/Nov 2011

5 9 14 Without using your calculator, work out 1 + . 6 10 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 14 + 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

This question in 0580/11 May/June 2012

2 For 1 Write as a percentage. Examiner's 5 Use Answer %[1]

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 40 1

This question in 0580/13 May/June 2012

2 Write three hundredths as a decimal. Answer [1]

1 marks

Mark scheme: 2 [0].03 1

This question in 0580/11 Oct/Nov 2012

11 Write down all your working to show that the following statement is correct. 8 1 + 9 34 = 1 45 2 + 2 Answer [2]

2 marks

Mark scheme: 9 17 5 18 34 45 11 or ÷ M1 or ÷ 5 9 2 45 18 18 2 18 17 2 34 34 18 34 × = M1 × = 9 5 45 18 45 45 2 2

This question in 0580/11 Oct/Nov 2012

3 5 For 1 Work out × . Examiner's 7 8 Use Give your answer as a fraction. Answer [1]

1 marks

Mark scheme: 1 15 1 56

This question in 0580/12 Oct/Nov 2012

1 Write 45% as a fraction in its simplest form. For Examiner's Use Answer … [1] _____________________________________________________________________________________

1 marks

Mark scheme: Qu Answers Mark Part Answers 1 9 1 20 cao

This question in 0580/11 May/June 2013

1 3 7 Show that 1 ÷ = 8. 2 16 Do not use a calculator and show all the steps of your working. Answer [2] _____________________________________________________________________________________

2 marks

Mark scheme: 3 k 7 correct working; 2 M1 for 2 k 3 16 3k 16 n e.g. × = 8 and A1 for × = 8 2 3 2 k 3n

This question in 0580/11 May/June 2013

17 For Examiner's = < > Use Write one of the three symbols between each pair of numbers. Each symbol can be used more than once. 1 (a) 30% … [1] 3 (b) –2 … –3 [1] (c) π … 10 [1] _____________________________________________________________________________________

3 marks

Mark scheme: 17 (a) < 1 (b) > 1 (c) < 1

This question in 0580/12 May/June 2013

6 2 Examiner′s19 Without using a calculator, work out ÷ 1 . 7 3 Use Write down all the steps in your working. Answer … [3] _____________________________________________________________________________________

3 marks

Mark scheme: 5 k 19 with 2 correct steps seen 3 B1 for 3k 18k 6 3 35k and M1 for × their 7 5

This question in 0580/12 May/June 2013

8 Without using a calculator, show that 3 5 3 ÷ 2 14 = 1 53 . You must show each step of your working. Answer [2] _____________________________________________________________________________________

2 marks

Mark scheme: 8 18 9 M1 and seen 5 4 18 9 72 24 8 3 × or or and oe seen A1 Not essential to see 1 5 5 4 45 15 5

This question in 0580/13 May/June 2013

21 Do not use a calculator in this question and show all the steps of your working. For Examiner′s Use Give each answer as a fraction in its lowest terms. Work out. 3 1 (a) – 4 12 Answer(a) … [2] 1 4 (b) 2 2 × 25 Answer(b) … [2] _____________________________________________________________________________________

4 marks

Mark scheme: 21 (a) – oe M1 Must be shown. 12 12 8 2 [=] oe [=] M1 Both fractions must be shown 12 3 5 4 (b) × oe M1 Must be shown 2 25 Cancelling shown M1 Dependent and cancelling shown 20 2 2 or oe [=] or a fraction and then must be shown 50 5 5

This question in 0580/11 Oct/Nov 2013

1 15 Without using a calculator, work out 3 7 - 1 25 . Give your answer as a fraction in its lowest terms. You must show each step of your working. Answer … [3] _____________________________________________________________________________________

3 marks

Mark scheme: − B115 7 5 5 × their 22 7 × their 7 oe − oe or M1 35 35 5 × their 22 − 7 × their 7 oe 35 61 26 or 1 cao A1 35 35 [ ]

This question in 0580/13 Oct/Nov 2013

2 x 2 9 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 9 18 2 M1 for + or better 18 36 2 3 1

This question in 0580/11 May/June 2014

18 In this question, do not use your calculator and show all the steps in your working. 1 5 23 (a) Show that 3 – 2 = . 5 8 40 Answer(a) [2] 7 23 (b) Work out ÷ . 8 40 Give your answer as a mixed number in its simplest form. Answer(b) … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 16 21 8 25 18 (a) and oe and oe M1 5 8 40 40 40 8 25 128 105 + − − oe 40 40 40 M1 40 40 oe or 8 × their 16 5 × their 21 − 40 40 oe with numerators evaluated 7 40 (b) × oe M1 8 23 12 1 cao A1 23

This question in 0580/11 May/June 2014

5 1 1 16 Without using your calculator, work out – # 1 6 2 2 ` j. Write down all the steps of your working. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 1 1 3 =  × 1 oe B1 16  2  4  2 5 × 2 3 × 3 and oe or better M1FT 6 × 2 4 × 3 1 oe A1 12 working must be shown

This question in 0580/12 May/June 2014

1 2 16 Find the fraction that is half-way between and . 2 3 Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 7 7 3 4 16 oe 2 B1 for or ( and ) 12 6 6 6 6 8 or etc., 12 and12 5.3 or 6

This question in 0580/13 May/June 2014

1 723 Without using a calculator, work out 1 – . 4 9 Write down all the steps in your working. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 5 23 oe B1 Do not allow decimals for the B1, 4 M1 or A1 5 × 9 7 × 4 45 28 and oe or better M1 e.g. 36 and 36 4 × 9 9 × 4 17 5 oe working must be shown A1 Follow through their for the M1 36 4 mark. Alt method 1: B1 for 1 + 2 4 9 M1 for 1 × 9 and 2 × 4 oe e.g. 4 × 9 4 × 9 9 8 and 36 36 Alt method 2: B1 for 1 − 7 + 1 4 9 M1 for oe e.g. 9 and 8 36 36 ISW converting fraction answer to decimal.

This question in 0580/13 May/June 2014

7 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: 3 and7 2 M1 Equivalent denominators can be used, working must 12 12 be shown. 5 cao A1 12

This question in 0580/11 Oct/Nov 2014

1 7 .14 Without using a calculator, work out 1 ÷ 6 8 Show all your working and give your answer as a fraction in its lowest terms. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 7 14 oe B1 6 7 8 56 42 M1 Or M1 for ÷ or equivalent division with their × oe 6 7 48 48 4 1 fractions with common denominators cancelled or 1 cao 3 3 A1 must see working

This question in 0580/12 Oct/Nov 2014

44 Work out of 153. 9 Answer … [1] __________________________________________________________________________________________

1 marks

Mark scheme: 4 68 1

This question in 0580/12 Feb/March 2015

45006 (a) Write as a fraction in its simplest form. 5500 Answer(a) … [1] (b) Write 0.73 as a fraction. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 96 (a) 1 11 (b) 1 73 100

This question in 0580/12 Feb/March 2015

16 Without using your calculator, work out 2 97 ÷ 56 . Give your answer as a fraction in its lowest terms. You must show each step of your working. Answer … [4] __________________________________________________________________________________________

4 marks

Mark scheme: 25 25 16 B1 (Alt) 9 9 a 6 their 25 × 2 5 × 3 × where a > b M1 ÷ oe b 5 9 × 2 6 × 3 150 their 25 × 2 Their oe or M1FT oe or 45 dep 5 × 3 their correct full cancelling 50 15 ÷ oe with 18’s cancelled 18 18 10 1 A1 or 3 nfww 3 3

This question in 0580/12 Feb/March 2015

4 3 .16 Without using a calculator, work out 1 5 ÷ 7 Show all your working and give your answer as a fraction in its lowest terms. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 9 63 16 B1 or 5 35 63 15 9 7 9 × 7 M1 or their ÷ or equivalent division with their × or 35 35 5 3 5 × 3 fractions with common denominators 21 1 A1 or 4 cao 5 5

This question in 0580/11 May/June 2015

3 Write 0.88 as a fraction in its simplest form. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 22 88 3 cao 2 M1 for oe seen 25 100

This question in 0580/13 May/June 2015

5 7 . ÷14 Without using a calculator, work out 1 8 9 Show all your working and give your answer as a fraction in its lowest terms. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 15 135 14 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 0580/13 May/June 2015

5 4 (a) Work out of 168. 12 Answer(a) … [1] 3 (b) Write as a decimal. 8 Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 4 (a) 70 1 (b) [0].375 cao final answer 1

This question in 0580/11 Oct/Nov 2015

2 3 .11 Without using a calculator, work out ÷ 5 4 Give your answer as a fraction. You must show each step of your working. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 2 4 2 × 411 M1 × 5 3 5 × 3 8 = or equivalent fraction A1 15

This question in 0580/11 Oct/Nov 2015

1 4 Show that .03 ! 3 . Answer [1]

1 marks

Mark scheme: 3 1 3 4 [0.3=]10 and [ 3 = ] 9 1 1 or = .0 33[ 3K] 3

This question in 0580/12 Oct/Nov 2015

5 14 (a) Write down the number in the list below that has the same value as 8 . 3 25 55 5 0.58 64 80 62.5% Answer(a) … [1] 5 (b) Find 8 of $208.56 . Answer(b) $ … .[1]

2 marks

Mark scheme: 14 (a) 62.5[%] 1 (b) 130.35 cao 1

This question in 0580/12 Oct/Nov 2015

1 11 20 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 20 2 or 1 or or M1 Accept any correct conversion with common denominator 12k 12 12 12 4 × 3 27 11 16 their ( − = ) oe M1 Correct resolving of their subtraction with denominator 12k 12 12 12 showing full working 1 4 1 or cao A1 Working and then simplified answer must both be seen 3 3

This question in 0580/12 Oct/Nov 2015

2 1 116 Work out + – , giving your answer as a fraction in its lowest terms. 3 6 4 Do not use a calculator and show all the steps of your working. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 8 2 3 16 Any two of , or oe M1 M1 for any 2 correct over a common denominator, 12 12 12 4 1 eg and 6 6 8 2 3 + − oe M1 12 12 12 13 1 or SC2 for final answer or 1 with full working 12 12 7 A1 12

This question in 0580/13 Oct/Nov 2015

18 Without using your calculator, work out 1 127 + 1320 . 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 35 k ( or 95 k ) 39 k 18 + M1 accept + 60 60 60 k 60 k 7 67 134 k 74 k 14 k 2 A2 or A1 for or or or 2 30 30 60 k 160 k 60 k

This question in 0580/12 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 0580/11 May/June 2016

12 Complete the table. Fraction Decimal 1 = 0.5 2 = 0.25 3 = 10 2 = 25 [3]

3 marks

Mark scheme: 112 1 4 [0].3 1 1 0.08

This question in 0580/12 May/June 2016

5 3 # 7 .18 Without using a calculator, work out 2 8 Show all your working and give your answer as a mixed number in its lowest terms. … [3]

3 marks

Mark scheme: 21 3 18 × oe M1 Must be shown 8 7 1 9 63 for oe e.g. 18 cao final answer A2 A1 8 56

This question in 0580/12 May/June 2016

1 1 # 1 5 .11 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 11 × oe M1 Must be shown 12 5 1 A1 final answer cao 10 AC

This question in 0580/13 May/June 2016

2 18 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 8 and oe M1 Correct fractions with common denominator 12 12 5 cao A1 12

This question in 0580/11 Oct/Nov 2016

14 Calculate. 4 (a) of 90 5 … [1] 7.1 # 4 .8 (b) 15.3 - 9.62 … [1] (c) 3 4913 … [1]

3 marks

Mark scheme: 14 (a) 72 1 (b) 6 1 (c) 17 1

This question in 0580/11 Oct/Nov 2016

2 (a) Write 9% as a fraction. … [1] 3 (b) Write 10 as a decimal. … [1]

2 marks

Mark scheme: 9 2 (a) 1 100 (b) [0].3 1

This question in 0580/12 Oct/Nov 2016

3 2 1 20 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] Question 21 is printed on the next page.

4 marks

Mark scheme: 20 Common denominator 24 B1 accept k × 24 18 16 3 18 k 16 k 3k Two correct from , and oe M1 accept , and 24 24 24 24 k 24 k 24 k 31 31k 7 k 7 A2 A1 for or or cao 24 24 k 124 k 124

This question in 0580/12 Oct/Nov 2016

3 1 10 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 10 and oe must be shown M1 and 30 30 30 k 30 k 23 cao A1 30 x 30 x 16

This question in 0580/13 Oct/Nov 2016

3 14 (a) Write 5 as a decimal. … [1] (b) Write 48% as a fraction in its simplest form. … [2]

3 marks

Mark scheme: 14 (a) 0.6 1 12 48 (b) 2 B1 for or equivalent fraction 25 100

This question in 0580/13 Oct/Nov 2016

3 Find the value of (a) 196 , … [1] 24 (b) 3 . .02 … [1]

2 marks

Mark scheme: 3 (a) 14 1 (b) 3000 1

This question in 0580/12 Feb/March 2017

1 117 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 17 or B1 oe improper fraction 3 2 10 2 20 15 their × their M1 accept ÷ 3 5 6 6 1 13 cao A1

This question in 0580/12 Feb/March 2017

2 519 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: 19 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 0580/11 May/June 2017

8 Write these numbers in order of size, smallest first. 7 1 0.3 33% 22 3 … 1 … 1 … 1 … [2] smallest

2 marks

Mark scheme: 8 7 1 2 B1 for 0.32 or 0.31[8…], 0.33 and 0.333 0.3 33% or percentages 22 3

This question in 0580/12 May/June 2017

10 (a) Write 0.03 as a percentage. … % [1] (b) Write 37% as a fraction. … [1]

2 marks

Mark scheme: 10(a) 3 1 10(b) 37 1 100

This question in 0580/12 May/June 2017

5 121 (a) 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] (b) Show that 4 1 4 1 6 # 1 5 = 7 2 . Do not use a calculator and show all the steps of your working. [2]

4 marks

Mark scheme: 21(a) 5 3 M1 5 k 3k − oe oe for − 6 6 6 k 6 k 1 A1 cao final answer 3 21(b) 25 9 225 B2 25 9 × = oe B1 for or 6 5 30 6 5

This question in 0580/12 May/June 2017

3 Write 16% as (a) a decimal, … [1] (b) a fraction. … [1]

2 marks

Mark scheme: 3(a) [0].16 1 3(b) 16 1 oe 100

This question in 0580/13 May/June 2017

11 Complete these calculations to make them correct. 24 + 8 (a) = … 4 [1] (b) -18 ÷ … = 2 [1] 7 … 21 (c) # = 8 40 … [1]

3 marks

Mark scheme: 11(a) 8 1 11(b) −9 1 11(c) 3 1 or equivalent fraction 5

This question in 0580/13 May/June 2017

11 3 218 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: 18 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 5 A2 10 k cao A1 for or10 6 12 12 k

This question in 0580/13 May/June 2017

3011 (a) Write the fraction in its lowest terms. 54 … [1] (b) Complete this table. Fraction Decimal Percentage 9 = … = … 100 [2]

3 marks

Mark scheme: 11(a) 5 9 cao 1 11(b) [0].09 then 9 [%] 2 B1 for each

This question in 0580/11 Oct/Nov 2017

2 1112 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: 12 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 0580/11 Oct/Nov 2017

5 Write the following in order of size, starting with the smallest. 31 5 64% 0.63 50 8 … 1 … 1 … 1 … [2] smallest

2 marks

Mark scheme: 5 31 5 2 B1 for 3 in correct order , , 0.63, 64% or M1 for 0.62 or 62% and 0.625 or 50 8 62.5% or 4 fractions with a common denominator

This question in 0580/12 Oct/Nov 2017

1120 (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: 20(a) 2 1 3 cao 3 20(b) 3 5 M1 For correct method to find common [and ] oe denominator 12 12 12 20 e.g. and 48 48 2 A1 cao 3

This question in 0580/12 Oct/Nov 2017

7 Complete the table. Fraction Decimal Percentage 1 = = 25% 4 = 0.8 = [2]

2 marks

Mark scheme: 7 0.25 2 B1 for two correct 8 oe 10 80

This question in 0580/13 Oct/Nov 2017

16 Work out 3 17 1 - 1 4 , giving your answer as a mixed number in its lowest terms. Do not use a calculator and show all the steps of your working. … [3]

3 marks

Mark scheme: 16 22 5 1 1 B1 22 k 5k or 2 – Allow or 7 4 7 4 7 k 4 k Correct step for dealing with mixed numbers 88 35 4 7 M1 Correct method to find common or 2 or 28 28 28 28 4 7 denominator e.g. 3 or 28 128 25 25 A1 128 128

This question in 0580/13 Oct/Nov 2017

2 Write 0.007 as a fraction. … [1]

1 marks

Mark scheme: 2 7 1 1000

This question in 0580/11 May/June 2018

3 623 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: 23 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 0580/11 May/June 2018

24 Without using your calculator, work out the following. You must show all your working and give each answer as a fraction in its simplest form. 2 1 (a) - 3 12 … [2] 3 5 (b) 3 ' 4 7 14 … [3]

5 marks

Mark scheme: 24(a) 8 1 M1 For correct fractions with a common and oe denominator 12k 12 12 7 A1 cao 12 24(b) 24 61 B1 or equivalent improper fractions or 7 14 their 24 14 M1 their 48 their 61 × oe or ÷ 7 their 61 14 14 oe common denominator 48 A1 cao 61

This question in 0580/12 May/June 2018

1 Write 75% as a fraction in its simplest form. … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 3 1 4

This question in 0580/13 May/June 2018

2 118 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: 18 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 0580/13 May/June 2018

4 Write these in order of size, starting with the smallest. 3 7 0.38 30 % 8 20 … 1 … 1 … 1 … [2] smallest

2 marks

Mark scheme: 4 7 3 2 B1 for three in correct order 30%, , , 0.38 or M1 for 0.35 and 0.375 20 8

This question in 0580/11 Oct/Nov 2018

3 116 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: 16 3 4 3 18 M2 9 × oe or ÷ oe with common B1 for oe seen 8 9 8 8 4 denominator 3 4 or M1 for ×their 8 9 1 A1 cao 6

This question in 0580/11 Oct/Nov 2018

9 Complete the table. Fraction Percentage 1 = 4 = 47% 3 = 5 [3]

3 marks

Mark scheme: 9 25% 3 B1 for each 47 100 60%

This question in 0580/12 Oct/Nov 2018

16 Calculate. (a) .413 … [1] (b) - 4 - 5 2 - 2 # 4 # - 3 ^ h … [1] 4.88 - 2.36 (c) 5.3 + 1.9 … [1] (d) 56.25 - 3 15.625 … [1]

4 marks

Mark scheme: 16(a) 68.921 1 16(b) –53 1 16(c) [0].35 1 16(d) 5 1

This question in 0580/12 Oct/Nov 2018

1 212 Without using a calculator, work out ' . 4 3 You must show all your working and give your answer as a fraction. … [2]

2 marks

Mark scheme: 12 1 3 3 8 M1 × or ÷ oe 4 2 12 12 3 A1 Accept equivalent fractions oe 8

This question in 0580/13 Oct/Nov 2018

1 525 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: 25 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 0580/12 Feb/March 2019

31 Write as a decimal. 4 … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 [0].75 1

This question in 0580/11 May/June 2019

1.6 + 9.6213 p = 5.9 - 4.3 (a) By writing each number correct to 1 significant figure, work out an estimate for p. You must show all your working. … [2] (b) Calculate the exact value of p. … [1]

3 marks

Mark scheme: 13(a) 2 + 10 2 M1 6 − 4 51 A1 13(b) 58.6 1

This question in 0580/11 May/June 2019

5 215 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: 15 5 4 M1 2 correct fractions with a suitable common + oe denominator 6k 6 6 1 A2 9 1 cao A1 for oe 2 6

This question in 0580/11 May/June 2019

7 (a) Shade five-eighths of this rectangle. [1] (b) Shade two more squares so that this grid has rotational symmetry of order 4. [1]

2 marks

Mark scheme: 7(a) Any 15 blocks shaded 1 7(b) 2 correct squares shaded 1

This question in 0580/12 May/June 2019

' 7 .20 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: 20 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 0580/12 May/June 2019

2 Write 0.45 as a fraction in its simplest form. … [1]

1 marks

Mark scheme: 2 9 1 20

This question in 0580/13 May/June 2019

12 717 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: 17 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 0580/13 May/June 2019

5 116 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: 16 5 8 M1 × 16 7 5 A1 cao 14

This question in 0580/11 Oct/Nov 2019

18 Complete the table. Fraction Decimal Percentage 3 = 0.75 = 4 = 0.2 = 20% 2 = = 8% 25 [3]

3 marks

Mark scheme: 18 75% 3 B1 for each 1 oe fraction 5 [0].08

This question in 0580/11 Oct/Nov 2019

7 Write these in order of size, starting with the smallest. 7 5 0.8 78% 8 7 … 1 … 1 … 1 … [2] smallest

2 marks

Mark scheme: 7 5 7 2 B1 for three in correct order 78% 0.8 or M1 for two of 0.875, 0.71[4…] and 7 8 0.78

This question in 0580/12 Oct/Nov 2019

5 217 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: 17 29 5 5 2 M1 29 k 5k or − Allow or 8 3 28 3 8k 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. 3 and 24 124 23 A1 1 cao 24

This question in 0580/12 Oct/Nov 2019

15 413 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: 13 15 7 15 16 M1 × or ÷ oe 28 4 28 28 15 A2 105 cao A1 for oe 16 112

This question in 0580/12 Feb/March 2020

1 7 620 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: 20 M2 M2 for correct method for common denominator 56 21 − 7 24 24 or B1 for 3 35 6 M1 their × 24 25 7 A1 20

This question in 0580/11 May/June 2020

17 Write 2 - 4 as a decimal. … [1]

1 marks

Mark scheme: 17 0.0625 1

This question in 0580/12 May/June 2020

3 1118 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: 18 7 9 B1 4 12 21 2 M1 1 − 12 12 5 5 A1 6 6

This question in 0580/12 May/June 2020

1 216 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: 16 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 0580/13 May/June 2020

603 Write in its simplest form. 105 … [1]

1 marks

Mark scheme: 3 4 1 cao 7

This question in 0580/11 Oct/Nov 2020

2 314 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: 14 8 11 M1 and oe improper fractions 3 4 88 A1 oe improper fraction 12 1 A1 Dep on first A1 7 cao final answer If M0 scored, 3 8 11 SC1 for or oe improper fraction 3 4

This question in 0580/11 Oct/Nov 2020

5 117 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: 17 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 cao 8

This question in 0580/12 Oct/Nov 2020

1 120 Without using a calculator, work out 1 # 2 . 7 10 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 20 8 21 M1 and oe improper fractions 7 10 168 A1 oe improper fractions 70 2 A1 Dep on first A1 2 cao final answer 8 21 5 If M0 scored, SC1 for or oe 7 10 improper fractions

This question in 0580/13 Oct/Nov 2020

1 219 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: 19 9 11 M1 and oe improper fractions 4 3 99 A1 oe improper fraction 12 1 A1 dep on 1st A1 84cao final answer 9 11 If M0 scored, SC1 for or oe improper 4 3 fraction

This question in 0580/12 Feb/March 2021

2 (a) Find the value of 225. … [1] 2 (b) Write down the reciprocal of . 3 … [1] (c) Work out three‑quarters of one‑third. … [1] (d) Work out - 7 - ( 6 - 8) . … [1]

4 marks

Mark scheme: 2(a) 15 1 2(b) 1 1 12 oe 2(c) 1 1 oe 4 2(d) –5 1

This question in 0580/11 May/June 2021

3 516 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: 16 11  5  3 1 B1 Correct step for dealing with mixed  −  + number 8  6  8 6 11k Allow 8 k 33 20 9 4 M1 Correct method to find common and and denominator 24 24 24 24 9 20 e.g. 124 and 24 13 A1 cao 24

This question in 0580/11 May/June 2021

2 318 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: 18 2 7 M2 10 × or B1 for oe 3 10 7 14 30 2 7 ÷ oe with common or M1 for × their 21 21 3 10 denominator 7 A1 cao 15

This question in 0580/12 May/June 2021

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

2 marks

Mark scheme: 4(a) 18 1 cao 25 4(b) 1 1 cao 250

This question in 0580/13 May/June 2021

2 116 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: 16 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 6 6 denominator 2 A1 cao 9

This question in 0580/13 May/June 2021

1 Fraction Decimal Percentage 1 = 0.5 = 50 2 = 0.25 = … … 1 = = 20 5 … Complete the table. [3]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1 1 3 B1 for each in correct place oe fraction 25 4 0.2

This question in 0580/11 Oct/Nov 2021

4 (a) Write 9% as a decimal. … [1] (b) Write 0.6 as a fraction in its simplest form. … [1]

2 marks

Mark scheme: 4(a) [0].09 cao 1 4(b) 3 1 5

This question in 0580/12 Oct/Nov 2021

1 7 120 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: 20 1 6 2 7 M1 × 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 0580/12 Oct/Nov 2021

1 Write 1 (a) as a percentage, 2 … % [1] (b) 0.7 as a fraction, … [1] 11 (c) as a decimal. 20 … [1]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 50 1 1(b) 7 1 or equivalent fraction 10 1(c) 0.55 cao 1

This question in 0580/13 Oct/Nov 2021

12 (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: 12(a) ≠ and > indicated 1 12(b) 7– (3 – 1) + 2 = 7 cao 1

This question in 0580/13 Oct/Nov 2021

1 1122 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: 22 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 0580/12 Feb/March 2022

3 214 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: 14 9 2 M1 Allow any correct denominator 21k and oe 21 21 1 A1 cao and correct working 3

This question in 0580/11 May/June 2022

15 This is Arania’s method to divide 213 by 12 without using a calculator. 2 1 213 ' 12 = 426 ' 25 2 = 852 ' 50 = 1704 ' 100 = 17.04 1 Show how to use Arania’s method to work out 135 ' 12 without using a calculator. 2 [2]

2 marks

Mark scheme: 5 270 ÷ 25 M1 [=] 540 ÷ 50 A1 [=] 1080 ÷ 100 [=] 10.8[0]

This question in 0580/12 May/June 2022

1 523 Without using a calculator, work out 4 - 2 . 8 6 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 23 33 17 1 5 B1 Correct step for dealing with mixed numbers or  8 6 28 6 33k 17 k Allow or 8 k 6 k 99 68 20 M1 Correct method to find common denominator and 32  24 24 24 24 3 20 e.g. 4 and 2 24 24 7 A1 124 cao and correct working

This question in 0580/12 May/June 2022

1 722 Without using a calculator, work out 4 - 1 . 6 8 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 22 B1 Correct step for dealing with mixed 25 15 1 7 or  numbers 6 8 36 8 25k 15 k Allow or 6 k 8 k M1 Correct method to find common 100 45 4 21 and oe [3] and denominator 24 24 24 24 4 21 e.g. 4 and 1 24 24 7 A1 2 final answer 24

This question in 0580/13 May/June 2022

516 (a) Complete the table of values for y = . x x –5 –4 –2.5 –2 –1 1 2 2.5 4 5 y –1 –2 –2.5 –5 5 2.5 2 1 [2] 5 (b) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 5 4 3 2 1 x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 1 – 2 – 3 – 4 – 5 [4]

6 marks

Mark scheme: 16(a) –1.25, 1.25 oe 2 B1 for each 16(b) Correct curve 4 B3FT for 9 or 10 correctly plotted points B2FT for 7 or 8 correctly plotted points B1FT for 5 or 6 correctly plotted points

This question in 0580/11 Oct/Nov 2022

5 110 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: 10 10 3 M1 Allow any correct common denominator and 18k 18 18 7 A1 cao 18

This question in 0580/12 Oct/Nov 2022

14 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: 14(a) 3456 1 14(b) 3 1 0.75 or 4 14(c) 1 1 0.25 or 4

This question in 0580/12 Oct/Nov 2022

7 Jo counts the number of each type of nut in a bag. The pie chart shows the results. Peanuts Hazelnuts 108° 120° Almonds Brazil nuts (a) Measure the size of the angle for the peanuts. … [1] (b) What fraction of the nuts are almonds? Give your answer in its simplest form. … [1] (c) There are 45 hazelnuts in the bag. Calculate the total number of nuts in the bag. … [2]

4 marks

Mark scheme: 7(a) 48 1 7(b) 1 1 cao 3 7(c) 150 2 45 M1 for  360 oe 108

This question in 0580/13 Oct/Nov 2022

5 212 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: 12 15 14 M1 Allow any correct common denominator and oe 21k 21 21 1 A1 cao 21

This question in 0580/13 Oct/Nov 2022

2 (a) Write 0.7 as a fraction. … [1] 13 (b) Write as a percentage. 20 … % [1]

2 marks

Mark scheme: 2(a) 7 1 or equivalent fraction 10 2(b) 65 1

This question in 0580/12 Feb/March 2023

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

2 marks

Mark scheme: 16 4 1 4 56 M1  oe or  oe 7 8 7 7 1 A1 cao 14

This question in 0580/12 Feb/March 2023

248 Write the fraction in its simplest form. 84 … [1]

1 marks

Mark scheme: 8 2 1 cao 7

This question in 0580/11 May/June 2023

1 520 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: 20 15 9 M2 15  oe B1 for oe 7 5 7 135 35 their 1 5 9 or  oe or M1 for  oe 63 63 7 5 with common denominator 6 A1 37 cao

This question in 0580/11 May/June 2023

4 514 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: 14 4 21 M2 26 21  oe B1 for or oe 7 26 21 26 12 26 4 21 or  oe with common denominator or M1 for oe 21 21 7 their 26 6 A1 cao 13

This question in 0580/12 May/June 2023

2 Write down a fraction that is equivalent to 7. 9 … [1]

1 marks

Mark scheme: 2 7 k 1 where k is an integer >1 9 k

This question in 0580/13 May/June 2023

6 Write down the reciprocal of 16 as a decimal. … [1]

1 marks

Mark scheme: 6 0.0625 1

This question in 0580/13 May/June 2023

11 124 Without using a calculator, work out 5 + 2 . 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: 24 M1 Accept with other correct common k 27  denominators 12 12 11 3 71 f 27 f [5] + [2] e.g. 24, 36, 48 such as and or 12 12 12 f 12 f 71 c oe oe 12 12 1 A2 1 8 cao A1 for fraction equivalent to 8 6 6 49 k 1k 7 e.g. or 8 or 7 6 k 6 k 6

This question in 0580/13 May/June 2023

81 Write as a decimal. 10 … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 0.8 1

This question in 0580/12 Oct/Nov 2023

1 319 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: 19 25 7 1 3 B1 Correct step for dealing with mixed numbers. or or 2 − 8 4 8 4 25k 7 k Allow or 8k 4 k 25 14 1 6 M1 Correct method to find a common and or [2] and denominator 8 8 8 8 1 6 e.g. 3 and1 8 8 3 A1 1 8

This question in 0580/12 Oct/Nov 2023

5 1113 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: 13 11 15 55k 22 k M2 11  or  oe with B1 for oe 6 11 30 k 30 k 6 common denominator their 11 15 or M1 for  6 11 1 A1 2 cao 2

This question in 0580/13 Oct/Nov 2023

24 (a) Shade of this shape. 9 [1] 2 (b) Write as a percentage. 9 … % [1]

2 marks

Mark scheme: 4(a) 8 squares shaded 1 4(b) 22.2 or 22.22… 1

This question in 0580/12 Feb/March 2024

1 524 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: 24 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 3 10 e.g. [1] and 12 12 5 A1 cao 12

This question in 0580/12 Feb/March 2024

1 (a) Write 0.8 as a fraction. … [1] (b) Write 28% as a decimal. … [1] (c) Write 4876 correct to the nearest hundred. … [1]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 8 1 oe fraction 10 1(b) 0.28 1 1(c) 4900 cao 1

This question in 0580/11 May/June 2024

6 (a) Work out. 28 - 16 ' 2 … [1] (b) Find the reciprocal of 4. 5 … [1]

2 marks

Mark scheme: 6(a) 20 1 6(b) 1 1 1.25 or 1 oe 4

This question in 0580/11 May/June 2024

1 719 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: 19 9 8 M2  oe 4 15 18 15 or  oe with common denominator 8 8 9 15 B1 for or oe 4 8 their 9 8 or M1 for  oe 4 their 15 1 A1 Dep on M2 15 cao

This question in 0580/12 May/June 2024

3 1 15 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: 15 6 1 M1 Allow any correct denominator 14k and oe 14 14 5 A1 cao 14

This question in 0580/13 May/June 2024

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

2 marks

Mark scheme: 5 < 2 B1 for two correct = =

This question in 0580/11 Oct/Nov 2024

1 7 Find the reciprocal of 1 4. … [1]

1 marks

Mark scheme: 7 4 1 or 0.8 5

This question in 0580/11 Oct/Nov 2024

1 4 23 Without using a calculator, work out 5 - 3 . 3 7 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 23 B1 Correct step for dealing with mixed numbers 16 25 1 4 or − 16 k 25 k 3 7 23 7 Allow or 3k 7 k M1 Correct method to find common denominator 112 75 and 72 and 7 21 21 21 e.g. 5 and 312 12 21 21 21 16 A1 121 cao

This question in 0580/11 Oct/Nov 2024

21 Without using a calculator, work out 2 3 # 1 1 . 4 2 You must show all your working and give your answer as a mixed number in its simplest form. … [3] Question 22 is printed on the next page.

3 marks

Mark scheme: 21 11 3 M1 oe improper fractions and 4 2 33 A1 oe improper fractions 8 1 A1 A1 dep. on first A1 4 cao final answer 11 3 8 If M0 scored SC1 for or 4 2 2  4 + 3 1  2 + 1 NOT or for SC1 4 2

This question in 0580/12 Oct/Nov 2024

2 Write 0.75 as a fraction. … [1]

1 marks

Mark scheme: 2 75 1 or equivalent fraction 100

This question in 0580/13 Oct/Nov 2024

2 Write 0.07 (a) as a percentage … % [1] (b) as a fraction … [1] (c) in standard form. … [1]

3 marks

Mark scheme: 2(a) 7 1 2(b) 7 1 100 2(c) 7  10− 2 1

This question in 0580/12 Feb/March 2025

18 (a) Complete the table of values for y = . x x -6 -4 -3 -2 -1 1 2 3 4 6 y -3 -6 6 3 [3] 12 (b) On the grid, draw the graph of y = for - 6 G x G -1 and 1 G x G 6 . x y 12 10 8 6 4 2 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -2 -4 -6 -8 -10 -12 [4] (c) On the grid, draw the line y =- 9 . [1] 12 (d) Use your graph to solve =- 9 . x x = … [1]

9 marks

Mark scheme: 18(a) −2 − 4 − 12 12 4 2 3 B2 for 4 correct or B1 for 1 correct 18(b) Correct curve 4 B3FT for 9 points correctly plotted or B2FT for 7 points correctly plotted or B1FT for 5 points correctly plotted 18(c) y = −9 correctly drawn, ruled 1 18(d) −1.4 to − 1.2 1 FT their curve and y = −9

This question in 0580/12 Feb/March 2025

22 Work out 1 7 - 4 . 15 5 Give your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 22 2 3 10 cao B2 for final answer or equivalent fraction 3 15 OR 22 7 1 B1 for or + 15 15 5 3  4 3  1 M1 for oe or oe 3  5 3  5

This question in 0580/12 Feb/March 2025

2 Write three-quarters as (a) a decimal … [1] (b) a percentage. … % [1]

2 marks

Mark scheme: 2(a) 0.75 1 2(b) 75 1

This question in 0580/12 May/June 2025

L-----4------ 4 Lb ts [1] Shade < of the rectangle.

1 marks

Mark scheme: 6 14 squares shaded 1

This question in 0580/12 May/June 2025

7 1 21 Work out 2 # 1 . 9 5 Give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 21 1 3 10 3 cao nfww B2 for 3 3 OR 25 6 M1 for and 9 5 150 A1 for 45 25 6 If 0 scored SC1 for or seen. 9 5

This question in 0580/12 May/June 2025

1 (a) Write the number 70 000 000 in words. … [1] (b) (i) Write down the value of the 5 in the number 0.25 . Give your answer as a fraction. … [1] (ii) Find the value of the reciprocal of 0.25 . … [2]

4 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Seventy million(s) cao 1 1(b)(i) 5 1 1 or 100 20 1(b)(ii) 4 2 1 4 M1 for oe or 0.25 1

This question in 0580/13 May/June 2025

4 (a) Write down all the factors of 24. … [2] 3 (b) Write down the reciprocal of . 7 … [1]

3 marks

Mark scheme: 4(a) 1 2 3 4 6 8 12 24 2 B1 for 6 correct and no extras or 8 correct and one extra 4(b) 7 1 oe 3

This question in 0580/11 Oct/Nov 2025

9 (a) Shade 3of this grid. 4 [1] (b) Work out 15% of 80. … [2]

3 marks

Mark scheme: 9(a) 15 rectangles shaded 1 9(b) 12 2 15 M1 for full correct method e.g. 80  100 oe

This question in 0580/11 Oct/Nov 2025

9 16 (a) Complete the table of values for y = . x x – 4.5 –3 –2 –1.5 –1 1 1.5 2 3 4.5 y –2 –3 – 6 –9 9 6 4.5 2 [2] 9 (b) On the grid, draw the graph of y = for - 4.5 G x G - 1 and 1 G x G 4 .5 . x y 9 8 7 6 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 [4]

6 marks

Mark scheme: 16(a) –4.5 3 2 B1 for each 16(b) Correct graph drawn 4 B3FT for 9 points correctly plotted or B2FT for 7 points correctly plotted or B1FT for 5 correctly plotted

This question in 0580/11 Oct/Nov 2025

2 5 28 Work out 8 ' 1 . 3 8 Give your answer as a mixed number in its simplest form. … [3] Question 29 is printed on the next page.

3 marks

Mark scheme: 28 1 3 16 13 5 cao B2 for oe or 5 oe 3 3 39 26 8 or M2 for oe 3 their 13 their 26 8 or  oe 3 13 26 13 or B1 for oe or oe 3 8

This question in 0580/11 Oct/Nov 2025

3 6 (a) Write as a decimal. 4 … [1] 9 (b) Write as a percentage. 100 … % [1] (c) Write 143% as a decimal. … [1]

3 marks

Mark scheme: 6(a) 0.75 1 6(b) 9 1 6(c) 1.43 cao 1

This question in 0580/12 Oct/Nov 2025

18 Work out. 5 1 2 ' 4 6 4 Write your answer as a fraction in its simplest form. … [3]

3 marks

Mark scheme: 18 2 3 17 4 cao M2 for  3 6 17 their17 4 or M1 for  6 their17 17 4 or B1 for or17 or 6 4 17 Alternative : 34 51 M2 for  12 12 their 34 their 51 or M1 for  12 12

This question in 0580/12 Oct/Nov 2025

25 Work out. 3 2 # 1 4 3 Give your answer as a mixed number in its simplest form. … [3]

3 marks

Mark scheme: 25 1 3 3 15 5 1 cao B2 for or or oe 4 112 12 4 5 or B1 for 3

This question in 0580/13 Oct/Nov 2025