PLC Papers. Created For:

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1 PLC Papers Created For:

2 Compare Fractions, Decimals and Percentages 2 Grade 4 Objective: Compare quantities by calculating equivalent fractions, decimals and percentages. Question 1 Write down three-quarters as a percentage....(1) Question 2 Complete the blanks to make the statements correct. (a) 50% = 2...(1) (b) 0.7 = 10...(1) (c) 1 3 =...%...(1) Question 3 (a) Write ¼ as a percentage...(1) (b) Write 30% as a decimal...(1) (c) Write ¼, 30% and 0.2 in order with the smallest first...(1)

3 Question 4 Work out the difference between 10% of 350 and ½ of 76...(3) Total /10

4 Compare lengths, area, volume 2 Grade 4 Objective: Compare lengths, areas and volumes using ratio notation. Question 1 (a) Share 45 kg in the ratio 2 : 3... (1) (b) Share 5 minutes in the ratio 9 : 6 Give your answer in seconds....metres (2) Question 2 The parallelogram below has area of 42 cm 2 It is to be enlarged with a scale factor of 5. What will the area of the enlarged parallelogram be?

5 Question 3 A tank has a volume of 32m³. It is enlarged with scale factor 3. (a) What is the height of the enlarged tank?..(1) (b) What is the volume of the enlarged tank?.. (3) (Total 4 marks) Total /10

6 Compare quantities using ratio 2 Grade 4 Express a multiplicative relationship between two quantities Question 1 Here is a list of ingredients for making a peach dessert for 6 people. Bob is going to make a peach dessert for 15 people. Work out the amount of each ingredient he needs....g jelly...sponge fingers...ml custard...g peaches

7 Question 2 A barrel of squash contains orange juice and water in the ratio 2:5. If there are 18 litres more water than orange juice, how much liquid is in the barrel? Question 3 The side lengths of a rectangle are in the ratio 3:8. If the longer side is 12cm more than the shorter side, what is the perimeter of the rectangle? (Total 4 marks) Total /10

8 Convert standard units 2 Grade 3 Objective: Convert standard units (eg time, length, volume, mass) in numerical contexts. Question 1 (a) Convert 3.5 hours into minutes?...mins (1) (b) Convert 380 minutes into hours and minutes. hours mins (1) (c) Convert 1.5 litres to millilitres.ml (1) (d) Convert 2.25 kg to grams..g (1) (Total 4 marks)

9 Question 2 You should know that 1 gallon = 4.5 litres (a) Convert 10 gallons to litres.litres (2) (b) Convert 18 litres to gallons gallons (2) (Total 4 marks) Question 3 (a) Convert 345 cm to metres....m (1) (b) Convert 3470 metres into km.km(1) Total /10

10 Division of a quantity as a ratio 2 Grade 4 Objective: Express the division of a quantity into two parts as a ratio Question 1 In Year 11 at the school, the ratio of the number of pupils who study P.E to the number of pupils who study Dance is 2 : pupils in Year 11 study Dance. Work out the number of pupils in Year 11 who study P.E. Question 2... Matt, Camilla and Steve share some money in the ratios 5 : 9 : 6 In total, Matt and Camilla receive 56 Work out the amount of money Steve receives....

11 Question 3 James and Sanjana share some sweets in the ratio 3 : 8 Sanjana gets 32 sweets. How many sweets does James get? Question 4... Pritam, Sarah and Emily share some money in the ratios 3 : 6 : 4 Sarah gets $15 more than Emily. Work out the amount of money that Pritam gets. $... Total /10

12 Express one quantity as a fraction of another 2 Grade 3 Objective: Express one quantity as a fraction of another where the fraction is less than one or greater than 1. Question 1 What fraction of a circle is: (a) 60 degrees?..(1) (b) 72 degrees?..(1) (c) 18 degrees?..(1) (d) 450 degrees?..(1) (Total 4 marks) Question 2 What fraction of 250, is 100?..

13 Question 3. What fraction of 400 is: (a) 68.(1) (b) 600..(1) Question 4. What fraction of 30 is: (a) 6 miles.(1) (b) 3miles (1) Total /10

14 Expressing one quantity as a percentage of another 2 Grade 4 Objective: Understand that a percentage means "parts per hundred", and express one quantity as a percentage of another, including percentages greater than 100% Question 1 Susie brings 500 flapjacks to a local fair. Susie sells 450 of the flapjacks. What percentage of the flapjacks did Susie not sell?...% Question 2 Samuel gains 13 out of 20 in a Maths test. Work out his Maths test mark as a percentage....% Question 3 Bryan buys a car costing He pays a deposit Express the amount that he has left to pay as a percentage of the original cost of the car....%

15 Question 4 The population of a country is 3.54 x The number of people that own a dog is 1.24 x Calculate the percentage of the population that own a dog. Give your answer correct to 2 significant figures....% Total /10

16 Percentage Change 2 Grade 5 Objective: Solve problems involving percentage change, including original value problems. Question 1. During August 2015 the number of people visiting Woodlands Adventure Park fell from 76,800 to 65,280. What was the percentage decrease? % Question 2. In January 2012 the average price of a 3-bed semi-detached house in Hitchin was 362,500. In January 2016 the average price had increased to 482,000. What was the percentage increase, to the nearest one per cent? %

17 Question 3. Toby got 18 questions wrong on a test. He got 70% of the questions correct. Work out the total number of questions in the test. Question 4. Markus takes his family out for a meal. He pays 184 including a 15% tip. How much tip did he leave? Question 5. In New York City a sales tax of 4.5% is added onto all merchandise at the till. Emily spends $ in one shop. How much did her goods come to before the sales tax? $ Total /10

18 Problems involving ratios 2 Grade 4 Objective: Solve problems involving ratios, e.g. conversion, comparison, scaling, mixing, concentrations Question 1 On a farm the number of cows and the number of sheep are in the ratio 6 : 5 the number of sheep and the number of pigs are in the ratio 2 : 1 The total number of cows, sheep and pigs on the farm is 189 How many sheep are there on the farm? Question 2 Build-a-mix makes concrete. 1 cubic metre of concrete has a weight of 2400 kg. 15% of the concrete is water.... The rest of the ingredients of concrete are cement, sand and stone. The weights of these ingredients are in the ratio 1 : 2 : 5 Work out the weight of cement, of sand and of stone in 1 cubic metre of concrete. cement = kg sand = kg stone = kg (Total 4 marks)

19 Question 3 Rob is learning about the planets. Rob makes a model of the Sun. He also makes a model of the planet Jupiter. Rob is going to hang the two models in the school hall. Rob wants a distance of 16 m between the two models. The real distance between the planet Jupiter and the Sun is km. Work out the scale Rob should use. Give your answer in the form 1 : n... Total /10

20 Proportion and ratio 2 Grade 4 Objective: Understand and use proportion as equality of ratios Question 1 Lewis has a copper pipe with a length of 150 cm and a mass of 800 grams. He cuts a piece of the copper pipe with a length of 90 cm. Work out the mass of this piece of copper pipe. Question 2... grams * 225 grams of flour are needed to make 9 cakes. Marian wants to make 20 of these cakes. She has 475 grams of flour. Does Marian have enough flour to make 20 cakes? You must show all your working.

21 Question 3 5 schools sent some students to a conference. One of the schools sent both boys and girls. This school sent 16 boys. The ratio of the number of boys it sent to the number of girls it sent was 1 : 2 The other 4 schools sent only girls. Each of the 5 schools sent the same number of students. Work out the total number of students sent to the conference by these 5 schools. (Total 4 marks) Total /10

22 Ratio Sharing 2 Grade 4 Objective: Divide a quantity in a given ratio. Question 1. Ken and Susan share 20 in the ratio 1 : 3 Work out how much money each person gets. Ken... Susan... Question 2. Amy, Beth and Colin share 36 sweets in the ratio 2 : 3 : 4 Work out the number of sweets that each of them receives.

23 Question 3. Peter won 75 as a prize. He gave 4/5 of the prize money as a present to Roger and Bethan. Roger and Bethan shared the present in the ratio 2:3 Work out how much they each got. Roger... Bethan... Total /10 (Total 4 marks)

24 Ratio and fractions 2 Grade 4 Objective: Relate ratios to fractions and linear functions Question 1 The ratio of girls to boys in a school is 5 : 7. What fraction of these students are girls? (Total 1 mark) Question 2 Ann and Bob shared 240 in the ratio 3 : 5 Ann gave a half of her share to Colin. Bob gave a tenth of his share to Colin. What fraction of the 240 did Colin receive? (Total 5 marks)

25 Question 3 Peter won 75 as a prize. He gave 4 of the prize money as a present to Roger and Bethan. 5 Roger and Bethan shared the present in the ratio 2:3 Work out how much they each got.... (Total 4 marks) Total /10

26 Use ratio notation 2 Grade 3 Objective: Use ratio notation, including reduction to simplest form. Question 1. Simplify the following ratios: (a) 3:12 (1) (b) 28:7 (1) (c) 12:60 (1) (d) 1 5 : 3 10 (1) (Total 4 marks) Question 2 Share the following into the given ratios. (a) 50 kg into 2:5:3... (2) (b) 45 minutes into 9:6... (2) (Total 4 marks)

27 Question 3 Reduce each of the following ratios to the form n:1 (a) 20:5.(1) (b) 40:8.(1) Total /10

28 Use scale factors, diagrams and maps 2 Grade 3 Objective: Use scale factors, diagrams and maps (including geometrical problems) Question 1 A 2 cm B C 6 cm D Line CD is bigger than line AB. What is the scale factor of the enlargement?.. (Total 1 mark) Question 2 Using scale of 1:25 5 cm on a map is actually how many metres in real life?. Question 3 Using scale of 1:30 7 metres will be drawn as how many cms on a map?

29 Question 4 25m 15m A rectangular field is really 25 metres by 15 metres. On a scale drawing 1: 50 (a) What length will I draw for the field on the map?..(1) (b) What width will I draw for the field on the map? (1) (c) What angle will each corner be? (1)

30 Question 5 These triangles are mathematically similar. (not drawn accurately) The height of the smaller triangle is 3 cms. The height of the bigger triangle is 9 cms What is the scale factor of this enlargement? The angle at the top of the smaller triangle is 25 degrees. What is the angle at the top of the bigger triangle? (1).(1) Total /10

31 PLC Papers Created For:

32 Compare Fractions, Decimals and Percentages 2 Grade 4 SOLUTIONS Objective: Compare quantities by calculating equivalent fractions, decimals and percentages. Question 1 Write down three-quarters as a percentage. 75% (A1)...(1) Question 2 Complete the blanks to make the statements correct. (a) 50% = 1 2 (A1)...(1) (b) 0.7 = 7 10 (A1)...(1) (c) 1 3 = % (A1)...(1) Question 3 (a) Write ¼ as a percentage 25% (A1)...(1) (b) Write 30% as a decimal 0.3 (A1)...(1) (c) Write ¼, 30% and 0.2 in order with the smallest first 0.2, ¼, 30% (A1)...(1)

33 Question 4 Work out the difference between 10% of 350 and ½ of 76 10% of 350 = 35 (M1) ½ of 76 = 38 (M1) = a difference of 3 (A1)...(3) Total /10

34 Compare lengths, area, volume 2 Grade 4 SOLUTIONS Objective: Compare lengths, areas and volumes using ratio notation. Question 1 (a) Share 45 kg in the ratio 2 : 3 45 / 5 = 9 per share 18 : 27 (A1)... (1) (b) Share 5 minutes in the ratio 9 : 6 Give your answer in seconds. 5 minutes = 300 seconds 300/15 = 20 secs per share (M1) 180 : 120 (A1)...metres (2) Question 2 The parallelogram below has area of 42 cm 2 It is to be enlarged with a scale factor of 5. What will the area of the enlarged parallelogram be? Area factor is 5 x 5 = 25 (M1) 42 x 25 (M1) = 1050 cm 2 (A1)

35 Question 3 A tank is 4 m tall, and has a volume of 32m³. It is enlarged with scale factor 3. (a) What is the height of the enlarged tank? 4m x 3 = 12 m (A1) (b) What is the volume of the enlarged tank? Volume factor is 3 x 3 x 3 = 27 (M1) 32 x 27 (M1) 864 m³ (A1).. (Total 4 marks) Total /10

36 Compare quantities using ratio 2 Grade 4 Solutions Express a multiplicative relationship between two quantities Question 1 Here is a list of ingredients for making a peach dessert for 6 people. Bob is going to make a peach dessert for 15 people. Work out the amount of each ingredient he needs = 2.5 M = = = = 500 A2 for all four correct answers g jelly sponge fingers ml custard g peaches

37 Question 2 A barrel of squash contains orange juice and water in the ratio 2:5. If there are 18 litres more water than orange juice, how much liquid is in the barrel? 5-2 = = 6 M1 2 6 = = 30 M = 42 A1 Question 3 The side lengths of a rectangle are in the ratio 3:8. If the longer side is 12cm more than the shorter side, what is the perimeter of the rectangle? 8-3 = = 2.4 M = = 19.2 M1 2( ) = 52.8 M cm A1 (Total 4 marks) Total /10

38 Convert standard units 2 Grade 3 SOLUTIONS Objective: Convert standard units (eg time, length, volume, mass) in numerical contexts. Question 1 (a) Convert 3.5 hours into minutes? 3 hours is 180 mins + 30 mins = 210 mins (A1)...mins (1) (b) Convert 380 minutes into hours and minutes. 6 hours 20 mins (A1) hours mins (1) (c) Convert 1.5 litres to millilitres 1.5 x 1000 = 1500 ml (A1).ml (1) (d) Convert 2.25 kg to grams 2.25 x 2250 g (A1)..g (1) (Total 4 marks) Question 2 You should know that 1 gallon = 4.5 litres (a) Convert 10 gallons to litres 4.5 x 10 (M1) 45 litres (A1).litres (2) (b) Convert 18 litres to gallons 18 / 4.5 (M1) 4 gallons (A1) gallons (2) (Total 4 marks)

39 Question 3 (a) Convert 345 cm to metres 3.45 m (A1)....m (1) (b) Convert 3470 metres into km km (A1).km(1) Total /10

40 Division of a quantity as a ratio 2 Grade 4 Solutions Objective: Express the division of a quantity into two parts as a ratio Question 1 In Year 11 at the school, the ratio of the number of pupils who study P.E to the number of pupils who study Dance is 2 : pupils in Year 11 study Dance. Work out the number of pupils in Year 11 who study P.E = 35 M = 70 A1 Question 2... Matt, Camilla and Steve share some money in the ratios 5 : 9 : 6 In total, Matt and Camilla receive 56 Work out the amount of money Steve receives = = 4 M1 4 6 M1 24 A1...

41 Question 3 James and Sanjana share some sweets in the ratio 3 : 8 Sanjana gets 32 sweets. How many sweets does James get? 32 8 = 4 M1 4 3 = 12 A1 Question 4... Pritam, Sarah and Emily share some money in the ratios 3 : 6 : 4 Sarah gets $15 more than Emily. Work out the amount of money that Pritam gets. 6 4 = = 7.5 M M1 $22.50 A1 $... Total /10

42 (d) 450 degrees? (A1)..(1) Express one quantity as a fraction of another 2 Grade 3 SOLUTIONS Objective: Express one quantity as a fraction of another where the fraction is less than one or greater than 1. Question 1 What fraction of a circle is: (a) 60 degrees? (b) 72 degrees? (c) 18 degrees? 1 6 (A1)..(1) 1 5 (A1)..(1) 1 12 (A1)..(1) (Total 4 marks) Question 2 What fraction of 250, is 100? 100/250 (M1) = 2 5 (A1) (Total 2 mark) Question 3. What fraction of 400 is: (a) (A1).(1) (b) (A1)..(1)

43 Question 4. What fraction of 30 is: (a) 6 miles 1 5 (A1).(1) (b) 3miles 1 10 (A1) (1) Total /10

44 Expressing one quantity as a percentage of another 2 Grade 4 Solutions Objective: Understand that a percentage means "parts per hundred", and express one quantity as a percentage of another, including percentages greater than 100% Question 1 Susie brings 500 flapjacks to a local fair. Susie sells 450 of the flapjacks. What percentage of the flapjacks did Susie not sell? = M A1...% Question 2 Samuel gains 13 out of 20 in a Maths test. Work out his Maths test mark as a percentage M1 65% A1 Question 3...% Bryan buys a car costing He pays a deposit Express the amount that he has left to pay as a percentage of the original cost of the car = 9000 M M % A1...%

45 Question 4 The population of a country is 3.54 x The number of people that own a dog is 1.24 x Calculate the percentage of the population that own a dog. Give your answer correct to 2 significant figures = M1 for either answer 3, = M1 3.5 % A1...% Total /10

46 Percentage Change 2 Grade 5 SOLUTIONS Objective: Solve problems involving percentage change, including original value problems. Question 1. During August 2015 the number of people visiting Woodlands Adventure Park fell from 76,800 to 65,280. What was the percentage decrease? (M1) 15 (A1) % Question 2. In January 2012 the average price of a 3-bed semi-detached house in Hitchin was 362,500. In January 2016 the average price had increased to 482,000. What was the percentage increase, to the nearest one per cent? (M1) 33 (A1) %

47 Question 3. Toby got 18 questions wrong on a test. He got 70% of the questions correct. Work out the total number of questions in the test. 18 = 30% (M1) 0.6 = 1% 60 = 100% 60 (A1) Question 4. Markus takes his family out for a meal. He pays 184 including a 15% tip. How much tip did he leave? 184 = 115% (M1) 1.6 = 1% 160 = 100% 160 (A1) Question 5. In New York City a sales tax of 4.5% is added onto all merchandise at the till. Emily spends $ in one shop. How much did her goods come to before the sales tax? $ = 104.5% (M1) $1.28 = 1% $128 = 100% $128 (A1) Total /10

48 Problems involving ratios 2 Grade 4 Solutions Objective: Solve problems involving ratios, e.g. conversion, comparison, scaling, mixing, concentrations Question 1 On a farm the number of cows and the number of sheep are in the ratio 6 : 5 the number of sheep and the number of pigs are in the ratio 2 : 1 The total number of cows, sheep and pigs on the farm is 189 How many sheep are there on the farm? 6 : 5 = 12: 10 2:1 = 10 : 5 M1 C : S : P 12 : 10 : 5 M1 189 = 70 A1 Question 2 Build-a-mix makes concrete. 1 cubic metre of concrete has a weight of 2400 kg. 15% of the concrete is water.... The rest of the ingredients of concrete are cement, sand and stone. The weights of these ingredients are in the ratio 1 : 2 : 5 Work out the weight of cement, of sand and of stone in 1 cubic metre of concrete = 360 M = = 255 M = 255 kg cement = 510 kg sand A2 for all three correct answers = 1275 kg stone cement = kg sand = kg stone = kg (Total 4 marks)

49 Question 3 Rob is learning about the planets. Rob makes a model of the Sun. He also makes a model of the planet Jupiter. Rob is going to hang the two models in the school hall. Rob wants a distance of 16 m between the two models. The real distance between the planet Jupiter and the Sun is km. Work out the scale Rob should use. Give your answer in the form 1 : n 16 metres : 8 x : M1 16 : : M1 1 : A1... Total /10

50 Proportion and ratio 2 Grade 4 Solutions Objective: Understand and use proportion as equality of ratios Question 1 Lewis has a copper pipe with a length of 150 cm and a mass of 800 grams. He cuts a piece of the copper pipe with a length of 90 cm. Work out the mass of this piece of copper pipe = M M1 480 A1... grams Question 2 * 225 grams of flour are needed to make 9 cakes. Marian wants to make 20 of these cakes. She has 475 grams of flour. Does Marian have enough flour to make 20 cakes? You must show all your working = 25 M = 500 M1 No, she is 25g short C1

51 Question 3 5 schools sent some students to a conference. One of the schools sent both boys and girls. This school sent 16 boys. The ratio of the number of boys it sent to the number of girls it sent was 1 : 2 The other 4 schools sent only girls. Each of the 5 schools sent the same number of students. Work out the total number of students sent to the conference by these 5 schools = 32 M = 48 M M1 240 A1 (Total 4 marks) Total /10

52 Ratio Sharing 2 Grade 4 Solutions Objective: Divide a quantity in a given ratio. Question 1. Ken and Susan share 20 in the ratio 1 : 3 Work out how much money each person gets = 4 or 20 4 = 5 (M1) 5 x 1 = 5 (A1) & 5 x 3 = 15 (A1) Ken 5 Susan 15 Question 2. Amy, Beth and Colin share 36 sweets in the ratio 2 : 3 : 4 Work out the number of sweets that each of them receives = 9 or 36 9 = 4 (M1) 4 x 2 = 8 (A1), 4 x 3 = 12 & 4 x 4 = 16 (A1) Amy 8 sweets Beth 12 sweets Colin 16 sweets Question 3.

53 Peter won 75 as a prize. He gave 4/5 of the prize money as a present to Roger and Bethan. Roger and Bethan shared the present in the ratio 2:3 Work out how much they each got. ( 75 5) x 4 = 60 (M1) = 5 or 60 5 = 12 (M1) 12 x 2 = 24 (A1) 12 x 3 = 36 (A1) Roger 24 Bethan 36 (Total 4 marks) Total /10

54 Ratio and fractions 2 Grade 4 Solutions Objective: Relate ratios to fractions and linear functions Question 1 The ratio of girls to boys in a school is 5 : 7. What fraction of these students are girls? = 12 5 A (Total 1 mark) Question 2 Ann and Bob shared 240 in the ratio 3 : 5 Ann gave a half of her share to Colin. Bob gave a tenth of his share to Colin. What fraction of the 240 did Colin receive? = 30 M = = 45 (Colin) M = = 15 ( Colin) M1 Colin = 60 M = 1 4 A (Total 5 marks)

55 Question 3 Peter won 75 as a prize. He gave 4 of the prize money as a present to Roger and Bethan. 5 Roger and Bethan shared the present in the ratio 2:3 Work out how much they each got. # 60 5 = 12 M M1 or (Roger) A1 36 (Bethan) A1... (Total 4 marks) Total /10

56 Use ratio notation 2 Grade 3 SOLUTIONS Objective: Use ratio notation, including reduction to simplest form. Question 1. Simplify the following ratios: (a) 3:12 (b) 28:7 1:4 (A1) 4:1 (A1) (1) (1) (c) 12:60 1:5 (A1) (1) (d) 1 5 : 3 10 Question 2 = 2 10 : 3 10 = 2:3 (A1) (1) (Total 4 marks) Share the following into the given ratios. (a) 50 kg into 2:5:3 10 shares, 50 = 5 kg per share (M1) 10 10:25:15 (A1)... (2) (b) 45 minutes into 9:6 15 shares, 45 = 3 mins per share = 27:18 (M1) 15 = 9:6 = 3:2 (A1)... (2) (Total 4 marks)

57 Question 3 Reduce each of the following ratios to the form n:1 (a) 20:5 4:1 (A1).(1) (b) 40:8 5:1 (A1).(1) Total /10

58 Use scale factors, diagrams and maps 2 Grade 3 SOLUTIONS Objective: Use scale factors, diagrams and maps (including geometrical problems) Question 1 A 2 cm B C 6 cm D Line CD is bigger than line AB. What is the scale factor of the enlargement? Scale factor 3 (A1).. (Total 1 mark) Question 2 Using scale of 1:25 5 cm on a map is actually how many metres in real life? 5 x 25 = 125 cm (M1) 1.25 metres (A1). Question 3 Using scale of 1:25 7 metres will be drawn as how many cms on a map? 7 metres is 700 cms (M1) 700/25 = 28 cm on the map (A1)

59 Question 4 25m 15m A rectangular field is really 250 metres by 150 metres. On a scale drawing 1cm: 50m (a) What length will I draw for the field on the map? 250/50 = 5 cm on map (A1)..(1) (b) What width will I draw for the field on the map? 150/50 = 3 cms on map (A1) (1) (c) What angle will each corner be? 90 degrees (A1) (1)

60 Question 5 These triangles are mathematically similar. (not drawn accurately) The height of the smaller triangle is 3 cms. The height of the bigger triangle is 9 cms What is the scale factor of this enlargement? Scale factor 3 (A1) (1) The angle at the top of the smaller triangle is 25 degrees. What is the angle at the top of the bigger triangle? 25 degrees (A1).(1) Total /10