NNC Year 6 Ratio and Proportion
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1 NNC Year 6 Ratio and Proportion 94 minutes 93 marks Page 1 of 46
2 Q1. A recipe for fruit squash is oranges (chopped) 300 g lemonade 1500 ml orange jiuce 750 ml makes enough for 6 people Trina wants to make enough squash for 10 people. How many millilitres of lemonade will she need? Brian is using 2 litres of orange juice and follows the same recipe. How many people is this enough for? Page 2 of 46
3 Q2. A and B are two chain wheels on a bike. For every 2 complete turns that wheel A makes, wheel B makes 5 complete turns. If wheel A makes 150 turns, how many turns will wheel B make? 1 mark If wheel B makes 90 turns, how many turns will wheel A make? 1 mark Page 3 of 46
4 Q3. This map has a scale of 1 centimetre to 6 kilometres. The road from Ridlington to Carborough measured on the map is 6.6cm long. What is the length of the road in kilometres? Page 4 of 46
5 Q4. Some children work out how much money two shopkeepers get from selling fruit. They use pie charts to show this. Mrs Binns gets 350 selling bananas. Estimate how much she gets selling oranges. 1 mark Mrs Binns gets a total of 1000 and Mr Adams gets a total of 800. Estimate how much more Mrs Binns gets than Mr Adams for selling peaches. 1 mark Page 5 of 46
6 Q5. Mr Green sells apples at 40p per kilogram. Mrs Ball sells apples at 24p per pound. Work out who sells the cheaper apples. Show how you worked it out mark Page 6 of 46
7 Q6. In a country dance there are 3 boys and 2 girls in every line. 42 boys take part in the dance. How many girls take part? Page 7 of 46
8 Q7. Children were asked to choose between a safari park and a zoo for the school trip. They had a vote. The result was a ratio of 10:3 in favour of going to a safari park. 130 children voted in favour of going to a safari park. How many children voted in favour of going to the zoo? Q8. Here are the ingredients for fish pie for two people. Omar makes fish pie for 3 people. Page 8 of 46
9 How many grams of fish should he use? Q9. Purple paint is made by mixing blue and red paint. Use the picture to work out the missing numbers. For 25 tins of purple paint you need... tins of blue paint and... tins of red paint. 1 mark Q10. Two of the ingredients of chocolate are cocoa and sugar. In milk chocolate, 20% of the mass is cocoa, 55% is sugar. Page 9 of 46
10 A bar of milk chocolate contains 50 grams of cocoa. How many grams of sugar does it contain? Q11. In a class the ratio of boys to girls is 7:4 There are 9 more boys than girls. How many children are in the class? Page 10 of 46
11 Q12. Shortcrust pastry is made using flour, margarine and lard. The flour, margarine and lard are mixed in the ratio 8 : 3 : 2 by weight. How many grams of margarine and lard are needed to mix with 200 grams of flour? Page 11 of 46
12 Q13. Peanuts cost 60p for 100 grams. What is the cost of 350 grams of peanuts? Raisins cost 80p for 100 grams. Jack pays 2 for a bag of raisins. How many grams of raisins does he get? Page 12 of 46
13 Q14. Here is a recipe for raspberry ice cream. This recipe is for 8 people. Josie makes enough raspberry ice cream for 12 people. How much cream does she use? litre 1 mark Fred makes raspberry ice cream in the same way. He uses 2½ kg of raspberries. How much sugar does he use? Page 13 of 46
14 Q15. A is the point (10, 60) B is the point (20, 20) M is the midpoint of line AB. Write the coordinates of M. (, ) 1 mark C is on the x-axis, directly below B. Write the coordinates of C. (, ) 1 mark Page 14 of 46
15 Q16. Paulo makes a sequence of numbers. He chooses a starting number and then subtracts equal amounts each time. The third number in his sequence is 45 The tenth number is 32 What is the first number in the sequence? Page 15 of 46
16 Q17. Cheddar cheese costs 7.50 for 1kg. Marie buys 200 grams of cheddar cheese. How much does she pay? 1 mark Cream cheese costs 3.60 for 1kg. Robbie buys a pot of cream cheese for 90p. How many grams of cream cheese does he buy? Page 16 of 46
17 Q18. k, m and n each stand for a whole number. They add together to make 1500 k + m + n = 1500 m is three times as big as n. k is twice as big as n. Calculate the numbers k, m and n. Q children are going on a trip. It costs 5 including lunch. Some children take their own packed lunch. They pay only 3 The 30 children pay a total of 110 Page 17 of 46
18 How many children are taking their own packed lunch? Q20. Three-quarters of a number is 48 What is the number? 1 mark Page 18 of 46
19 Q21. Here is a rectangle with six identical shaded squares inside it. The width of the rectangle is 7.2 centimetres. Calculate the length of the rectangle. Page 19 of 46
20 Q22. Mari is the presenter of a weekly radio show. She plays five new songs for every two old songs. Last week she played 15 new songs. How many songs did she play altogether? Q23. A and B are two numbers on the number line below. Page 20 of 46
21 The difference between A and B is 140 Write the values of A and B. Q24. Four large circles and five small circles fit exactly inside this rectangle. The diameter of a large circle is 17.5 centimetres. Calculate the diameter of a small circle. Not actual size Page 21 of 46
22 Q25. David and his friends prepare a picnic. Each person at the picnic will get: 3 sandwiches 2 bananas 1 packet of crisps The children pack 45 sandwiches. How many bananas do they pack? Page 22 of 46
23 Q26. Class 6 did a survey of the number of trees in a country park. This pie chart shows their results. Estimate the fraction of trees in the survey that are oak trees. 1 mark Page 23 of 46
24 The children counted 60 ash trees. Use the pie chart to estimate the number of beech trees they counted. 1 mark Q27. This shape is made from 4 shaded squares. Calculate the perimeter of the shape. Page 24 of 46
25 Q28. Two matchsticks have the same length as three bottle tops. How many bottle tops will have the same length as 50 matchsticks? Q29. Here is a recipe for fruit smoothies. Stefan uses the recipe to make smoothies. He uses 1 litre of yogurt. How many strawberries does he use? 1 mark Page 25 of 46
26 Amir uses the same recipe. He wants to make 5 smoothies. He has 1 litre of orange juice. How many more millilitres of orange juice does he need? Q30. A shop sells books, CDs and DVDs. This pie chart shows the sales of each in one week. Estimate the fraction of the total sales that were DVDs. 1 mark Page 26 of 46
27 In this week, 200 CDs were sold. Estimate how many books were sold. 1 mark Q31. These patterns are drawn on square grids. Pattern A Pattern B In pattern A, the ratio of black squares to grey squares is 1 : 2 What is the ratio of black squares to grey squares in pattern B? 1 : 1 mark Now look at this new pattern. What percentage of the new pattern is black? % 1 mark Page 27 of 46
28 Q32. There are 25 children in the lunch queue, including Nik. Nik says, There are twice as many children in front of me as there are behind me. How many children are in front of Nik? Page 28 of 46
29 Q33. A 5p coin has a diameter of 1.8 centimetres. Holly makes a straight line of 5p coins worth How long is Holly s line? Give your answer in metres. Page 29 of 46
30 Q34. Joe has some triangular tiles and some quarter-circle tiles. He uses 2 triangles and 7 quarter-circles to make this flying bird design. Joe makes some more of these flying bird designs. He uses 56 quarter-circles. How many triangles does he use? Page 30 of 46
31 Q35. Joe has some triangular tiles and some quarter-circle tiles. He uses 2 triangles and 7 quarter-circles to make this flying bird design. Joe makes some more of these flying bird designs. He uses 56 quarter-circles. How many triangles does he use? Page 31 of 46
32 M1. (a) Award TWO marks for the correct answer of 2500 ml, even if the working is incorrect. If answer is incorrect, award ONE mark for evidence of attempt to calculate the answer to by any appropriate method, eg: 6 people need 1500, so 12 people need 3000, 2 people need 300 (incorrect answer given), so 10 people need = 2800 (incorrect answer given) OR = 250, = (incorrect answer given). The writing of an expression such as alone is insufficient for the award of the mark. Up to 2 (b) Award TWO marks for the correct answer of 16, even if the working is incorrect. If answer is incorrect, award ONE mark for evidence of attempt to calculate the answer to by any appropriate method, eg: 750 is for 6 people, so 1500 is for 12 people, 2250 is for 18 people; 250 would be for 3 people (incorrect answer given), so 2000 is for 18 3 = 15 people (incorrect answer given) OR = 120 (incorrect answer given), = (incorrect answer given). The writing of an expression such as alone is insufficient for the award of the mark. Up to 2 [4] M2. (a) 375 Award the mark for correct answer, even if the working is incorrect. 1 (b) 36 Award the mark for correct answer, even if the working is incorrect. 1 Page 32 of 46
33 M3. Award TWO marks for 39.6 km, even if there are errors in the working. If the answer is incorrect, award ONE mark for evidence of correct partial result by any appropriate method (not repeated addition only), eg: = (incorrect answer given) = 396 The writing of an expression such as: alone, without attempt at calculation, is insufficient for the mark. Up to 2 M4. (a) Award ONE mark for an answer in the range 85 to 125, inclusive. (b) Award ONE mark for the correct answer of 50. Accept any estimate in the range 45 to 55, inclusive. 1 1 M5. Evidence of conversion from lbs to kg OR kg to lbs, such as multiplication or division by 2 or 2.2, eg: There s more than 2 pounds in a kilogram so it will be about 50p for a kg of apples. So, Mr Green. 40p per kg is about 20p a pound. No mark is awarded or forfeited for the name, Mr Green or Mrs Ball. [1] Page 33 of 46
34 M6. Award TWO marks for the correct answer of 28. If answer is incorrect, award ONE mark for evidence of appropriate strategy, eg: b and 2g 6b and 4g... 42b and An actual calculation is not required for the award of one mark. Appropriate strategy must include use of 3 : 2 (boys : girls) ratio. Up to 2 M7. Award TWO marks for the correct answer of 39. If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg: = 13 AND 3 13 Calculation need not be performed for the award of ONE mark, but the method shown must be capable of producing the correct answer. Up to 2 M8. Award TWO marks for the correct answer of 375. If the answer is incorrect, award ONE mark for an appropriate method, such as: Calculation need not be performed for the award of ONE mark, but the method shown must be capable of producing the correct answer. Up to 2 Page 34 of 46
35 M9. 15 and 10 Both numbers to be correct. [1] M10. Award TWO marks for the correct answer of If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg OR OR 5 50 Calculation need not be completed for the award of the mark. Up to 2 M11. Award TWO marks for the correct answer of 33. If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg = 11; 7 4 = 3; 9 3 = OR an extension of ratio sequence, eg 7:4 14:8 21:12 Calculation need not be completed for the award of the mark. Up to 2 Page 35 of 46
36 M12. Award TWO marks for the correct answer of margarine lard 75g 50g If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg = 25 margarine = 3 25 lard = 2 25 OR the use of ratio, eg 8 : 3 : 2 80 : 30 : : 15 : : wrong answer : : 75 : wrong answer Up to 2 M13. (a) Award TWO marks for the correct answer of 2.10 OR 210p If the answer is incorrect, award ONE mark for evidence of appropriate working, eg = = wrong answer Accept for TWO marks 2.10p OR 210 OR 2.10 Accept for ONE mark 2.1 OR 210 OR 2.10p as evidence of appropriate working. Calculation must be performed for the award of ONE mark. Up to 2 (b) Award TWO marks for the correct answer of 250 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg = = wrong answer. Calculation must be performed for the award of ONE mark. Up to 2 [4] Page 36 of 46
37 M14. (a) OR 0.75 Accept equivalent fractions. 1 (b) Award TWO marks for the correct answer of 625 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg OR Accept for ONE mark OR 6.25 OR 62.5 OR 6250 as evidence of appropriate method. Calculation need not be performed for the award of the mark. Up to 2 [3] M15. (a) (15, 40) 1 (b) (20, 0) Accept answers written on the diagram with or without brackets and commas. Coordinates must be written in the correct order. 1 M16. Award TWO marks for the correct answer of 67 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 7 gaps = 77 1 gap = 11 Answer need not be obtained for the award of the mark. Up to 2 Page 37 of 46
38 M17. (a) (b) Award TWO marks for the correct answer of 250 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg = Answer need not be obtained for the award of ONE mark. Up to 2 [3] M18. Award TWO marks for all three answers correct, as shown: k = m = n = If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 2n + 3n + n OR a trial and improvement method, eg = = = 1200 Accept for ONE mark any permutation of the correct answers, eg k = 750, m = 250, n = 500 Answer need not be obtained for the award of ONE mark. A trial and improvement method must show evidence of improvement. Up to 2 (U1) M19. Award TWO marks for the correct answer of 20 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 30 5 = = = = 3 each, with 20 left over 20 2 = = 20 Page 38 of 46
39 OR a trial and improvement method, eg 30 3 = = = 120 Calculation must be performed for the award of ONE mark. A trial and improvement method must show evidence of improvement, but a final answer need not be reached for the award of ONE mark. Up to 2 (U2) M [1] M21. Award TWO marks for the correct answer of 12 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg Answer need not be obtained for the award of ONE mark. Accept for ONE mark 1.2 OR 120 as evidence of appropriate method. Up to 2 (U1) Page 39 of 46
40 M22. Award TWO marks for the correct answer of 21 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg = OR 5 new 2 old 10 new 4 old 15 new 6 old Award ONE mark for an answer of 6 OR for 6 shown with no evidence of an incorrect method. Answer need not be given for the award of ONE mark. Up to 2 M23. Award TWO marks for the correct answer as shown: A = B = If the answer is incorrect, award ONE mark for evidence of appropriate working, eg = 20 Accept minus 80 Do not accept 80 Answer need not be obtained for the award of ONE mark. Accept for ONE mark: A = 80 AND B = wrong answer OR A = 80 AND B = blank OR A = 80 AND B = 60 OR A = 80 AND B = 60 OR A = 60 AND B = 80 Up to 2 (U1) Page 40 of 46
41 M24. Award TWO marks for the correct answer of 14 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg = Accept for ONE mark 140 OR 1.4 as evidence of appropriate method. Answer need not be obtained for the award of ONE mark. Up to 2 (U1) M25. Award TWO marks for the correct answer of 30 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 45 3 = Answer need not be obtained for the award of ONE mark. Up to 2 M26. (a) Answer in the range to inclusive. Range includes,, and Accept decimals (0.1 to 0.15 inclusive) or percentages (10% -15% inclusive). 1 (b) Answer in the range 40 to 50 inclusive. 1 Page 41 of 46
42 M27. Award TWO marks for the correct answer of 50 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 15 3 = = wrong answer Calculation must be performed for the award of ONE mark. Up to 2 (U1) M28. Award TWO marks for the correct answer of 75 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg = wrong answer Working must be carried through to reach an answer for the award of ONE mark. Up to 2 (U1) M29. (a) 40 1 Page 42 of 46
43 (b) Award TWO marks for the correct answer of 250 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg: = OR litre 2 smoothies 1 litre 4 smoothies 1 litres 5 smoothies 1 1 = 1000 Accept for ONE mark an answer of litre OR sight of litre with no evidence of an incorrect method. Accept for ONE mark an answer of 1250 OR sight of 1250 with no evidence of an incorrect method. Answer need not be obtained for the award of ONE mark. Up to 2 [3] M30. (a) Answer in the range to inclusive Range includes and Accept decimals or percentages. (0.13 to 0.2 inclusive) (13% to 20 % inclusive) 1 (b) Answer in the range 500 to 800 inclusive 1 M31. 1 : % Do not accept equivalent fractions or decimals 1 Page 43 of 46
44 M or 8 or Answer of 17 with or equivalent seen (the only error is to fail to subtract 1 at the start) or Shows understanding of a correct method even if there are computational errors eg 24 = 12 Do not accept answer of 17 without or equivalent seen 1 U1 M33. Award TWO marks for the correct answer of 3.6 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg: = = OR 20 5p coins make p coins make Answer must be in metres for the award of TWO marks. Accept for ONE mark 360 centimetres. If the answer is incorrect, accept for ONE mark an answer of 36 multiplied by any power of 10 with no evidence of an incorrect method. Answer need not be obtained for the award of ONE mark. Up to 2 Page 44 of 46
45 M34. Award TWO marks for the correct answer of 16 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg: 56 7 = OR 7 quarter-circles 2 triangles 14 quarter-circles 4 triangles 28 quarter-circles 8 triangles 56 quarter-circles Answer need not be obtained for the award of ONE mark. Up to 2 M35. Award TWO marks for the correct answer of 16 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg: 56 7 = OR 7 quarter-circles 2 triangles 14 quarter-circles 4 triangles 28 quarter-circles 8 triangles 56 quarter-circles Answer need not be obtained for the award of ONE mark. Up to 2 Page 45 of 46
46 Page 46 of 46
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