PLC Papers Created For: Year 10 Topic Practice Papers: Error Intervals
Checking Calculations 1 Grade 4 Objective: Check calculations using approximation and estimation (including using technology) Question 1. For each calculation write down the solution you consider to be the best estimate. (a) 4.56 x 21.76 (i) 10 (ii) 100 (iii) 1000.. (1) (b) 2.76 x 99 (i) 27 (ii) 270 (iii) 2700.... (1) (c) 32.1 2.431 (i) 1.6 (ii) 16 (iii) 160... (1) (d) 3.12 2 (i) 8 (ii) 6 (iii) 9.... (1) (Total 4 marks)
Question 2 Use an estimate to show if these answers are correct and explain your answer (a) 12% of 39.98 = 14.78.... (b) 96% of 124.87 = 119.88. (c) 23% of 103.87 = 2.39. (Total 6 marks)
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Checking Calculations 2 Grade 4 Objective: Check calculations using approximation and estimation (including using technology) Question 1. For each calculation write down the solution you consider to be the best estimate. (a) 56.987 7.876 (i) 6 (ii) 7 (iii) 9.. (1) (b) 1.11 x 27.8 (i) 20 (ii) 30 (iii) 40.... (1) (c) 82.1 0.99 (i) 8 (ii) 80 (iii) 800... (1) (d) 9.99 2 (i) 20 (ii) 100 (iii) 1000.... (1) (Total 4 marks)
Question 2 Use an estimate to show if these answers are correct and explain your answer (a) 48% of 3244.45 = 1557.34.... (b) 11% of 49.76 = 9.87. (c) 23% of 103.87 = 50.67. (Total 6 marks)
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Checking Calculations 3 Grade 4 Objective: Check calculations using approximation and estimation (including using technology) Question 1. (a) Cakes cost 47p each. Estimate the cost of 18 cakes (b) Cakes cost 47p each. Estimate the cost of 94 cakes..(1)..(1) (c) Cakes cost 47p each. Gertrude buys 32 cakes and pays with a 20 note. Estimate the amount of change that she will receive... (Total 5 marks) Question 2 (a) A supermarket sells boxes of crisps in different sizes. Box A contains 21 packets of crisps cost 1.93 Box B contains 38 bags of crisps and costs 3.49 Use estimates to explain which box is better value. Show your working and explain your answer. (3)
(b) James buys 4 boxes of box A and pays with a 20 note. Estimate the amount of change that he should receive... (Total 5 marks) Total /10
Checking Calculations 4 Grade 4 Objective: Check calculations using approximation and estimation (including using technology) Question 1. Four friends share the cost of a meal equally between them. The meal costs 27.71. (a) Estimate how much each friend should pay (b) They each pay with a 10 note. Estimate the amount of change they should receive..... (c) One of the friends has forgotten their money. Estimate how much should the remaining friends each pay now... (Total 6 marks) Question 2 A taxi company charges 93p per mile (a) James travels to an airport 18 miles away and is charged a fare of 32. She thinks that this is wrong. Use estimates to show that she is correct.....
(b) Thomas wants to use the same taxi company to travel to work every day. He works four miles from home. Estimate how much this will cost him per 5-day working week..... (Total 4 marks) Total /10
Decimals1 Grade 3 Objective: Understand adding subtracting multiplying and dividing decimals. Question 1 Three parcels weigh 7.2 kg, 15.02 kg and 3.1 kg. Find their total mass. Question 2 Work out 0.8965 0.5 Question 3 (a) Tom gets paid 3.15 an hour. One week he worked for 26 hours. How much is his weekly pay?
(b) Tom is saving for a gift. He wants to give his friend a gift that costs 100.27. How much more money does Tom need after he has worked 26 hours in one week. Question 4 1 bottle of milk = 1.39 Lacey bought five bottles of milk. How much will it cost altogether? Total /10
Decimals 2 Grade 3 Objective: Understand adding, subtracting multiplying and dividing decimals. Question 1 Work out a) 0.3 0.2 b) 0.03 0.12 Question 2 Work out 0.8965 0.05 Question 3 Electricity is 41p per unit. Helen s household uses 250 units. Work out the total cost of the electricity.
(b) Gas is 31p per unit. Helen s household uses 225 units. Work out the total cost of the gas. Question 4 Evaluate: Total /10
Decimals 3 Grade 3 Objective: Understand adding subtracting multiplying and dividing decimals. Question 1 7 cans of a drink cost 5.11. How much does one drink cost? Question 2 Work out 10.7865 0.5 Question 3 (a) Sunny, Pat and Tom went out one evening and it cost them altogether 87.60. How much does each one of them have to pay?
(b) 6 people each weigh 75.9 kg. Find their total weight? Question 4 1 bottle of milk = 1.29 Kurt bought five bottles of milk how much will it cost altogether? Total /10
Decimals 4 Grade 3 Objective: Understand adding, subtracting multiplying and dividing decimals. Question 1 a) How much change from a 20 note do I get if I buy 3 meals each costing 5.55? b) Which answer will be bigger: 6-3.28 or 21-18.67 Question 2 Laura, Kristina and Khalid to see a movie. It cost them 28.50. How much will each one of them have to pay? w ill
Question 3 Gas is 31p per unit. Ivy s household uses 150 units. (a) Work out the total cost of the gas. (b) Electricity is 51p per unit. Ivy s household uses 212 units. Work out the total cost of the electricity. Total /10
Error intervals 1 Grade 5 Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) Find the range of numbers that would round to 300 (to one significant figure).. (b) Find the range of numbers that would round to 3000 (to 1 significant figure).. Question 2 (Total 4 marks) Use inequality signs to show the range of possible values for (a) =8.5 to (2 s.f)...
(b) =4.0 (to 1 d.p).. (Total 4 marks) 3. Question 3. Complete the inequality to show the range of values that would round to 0.2 (to 1 decimal place). 0.2< (Total 2 marks) Total /10
Error intervals 2 Grade 5 Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) Find the range of numbers that would round to 500 (to one significant figure).. (b) Find the range of numbers that would round to 5000 (to 1 significant figure).. Question 2 (Total 4 marks) Use inequality signs to show the range of possible values for (a) =0.5 (1.d.p)..
(b) =50 (1 s.f0.. (Total 4 marks) 3. Question 3. Complete the inequality to show the range of values that would round to 0.4 (to 1 decimal place). 0.4< (Total 2 marks) Total /10
Error intervals 3 Grade 5 Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) A book contains 310 pages to the nearest 10 pages. Find the range of values for which the number of pages could lie?.. (b) A different book contains 500 pages when rounded to one significant figure. Find the range of values for which the actual number of pages could lie... Question 2 (Total 4 marks) (a) Use inequality signs to show the range of possible values for a car costing 3000 when rounded to the nearest thousand pounds..
(b) The same car has travelled 46000miles when rounded to two significant figures. Once again using inequality notation show the range of values within which the number of miles could lie... (Total 4 marks) Question 3. A field has a perimeter of 310 metres when rounded to the nearest 10 metres. Complete the inequality to show the range of values that would round to 310 metres correct to the nearest 10 metres.. 310< (Total 2 marks)
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Error intervals 4 Grade 5 Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) A box of oranges contains 40 oranges correct to one significant figure. Show the range of values representing the number of oranges the box could contain... (b) Each orange contains 5 grams of sugar correct to the nearest gram. Show the range of values which represent the amount of sugar that each orange could contain... Question 2 (Total 4 marks) (a) Use inequality signs to show the range of possible values for a salary given as 35000 when rounded to the nearest thousand pounds..
(b) The same company claims to provide work for 120 people correct to two significant figures. Use inequality notation to show the number of people that could be employed by the company... (Total 4 marks) Question 3. A football stadium records it s attendance correct to two significant figures, complete the inequality to show the range of values within which the attendance could lie.. 55000< (Total 2 marks)
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PLC Papers Created For: Year 10 Topic Practice Papers: Error Intervals
Checking Calculations 1 Grade 4 Solutions Objective: Check calculations using approximation and estimation (including using technology) Question 1. For each calculation write down the solution you consider to be the best estimate. (a) 4.56 x 21.76 (i) 10 (ii) 100 (iii) 1000 (b) 2.76 x 99 (i) 27 (ii) 270 (iii) 2700 (c) 32.1 2.431 (i) 1.6 (ii) 16 (iii) 160 (B1) 100.. (1).. (B1) 270.. (1). (B1) 16.. (1) (d) 3.12 2 (i) 8 (ii) 6 (iii) 9.. (B1) 9.. (1) (Total 4 marks)
Question 2 Use an estimate to show if these answers are correct and explain your answer (a) 12% of 39.98 = 14.78 (M1) 10% of 40 = 4 so incorrect (A1).... (b) 96% of 124.87 = 119.88 (M1) 100 % of 125 is 125 so correct (A1) (c) 23% of 103.87 = 2.39. (M1) 25% of 100 = 25 so incorrect
(A1). (Total 6 marks) Total /10
Checking Calculations 2 SOLUTIONS Grade 4 Objective: Check calculations using approximation and estimation (including using technology) Question 1. For each calculation write down the solution you consider to be the best estimate. (a) 56.987 7.876 (i) 6 (ii) 7 (iii) 9 (b) 1.11 x 27.8 (i) 20 (ii) 30 (iii) 40 (c) 82.1 0.99 (i) 8 (ii) 80 (iii) 800 7 (B1).. (1) 30 (B1.... (1) 80 (B1 (1) (d) 9.99 2 (i) 20 (ii) 100 (iii) 1000 100 (B1.. (1) (Total 4 marks)
Question 2 Use an estimate to show if these answers are correct and explain your answer (a) 48% of 3244.45 = 1557.34 50% of 3200=1600 so correct (M1) (A1).... (b) 11% of 49.76 = 9.87 10% of 50= 5 so incorrect (M1) (A1) (c) 23% of 103.87 = 50.67. 25% of 100 = 25 so incorrect (M1) (A1)
. (Total 6 marks) Total /10
Check Calculations 3 Grade 4 Solutions Objective: Check calculations using approximation and estimation (including using technology) Question 1. (a) Cakes cost 47p each. Estimate the cost of 18 cakes 50p x 20 = 10.00 (b) Cakes cost 47p each. Estimate the cost of 94 cakes = 10.00..(1) (B1) 50p x 100 = 50.00 = 50.00..(1) (B1) (c) Cakes cost 47p each. Gertrude buys 32 cakes and pays with a 20 note. Estimate the amount of change that she will receive. 50p x 30 = 15.00 20.00-15.00 = 5.00 = 5.00.. (M1) (A1) (Total 5 marks)
Question 2 (a) A supermarket sells boxes of crisps in different sizes. Box A contains 21 packets of crisps cost 1.93 Box B contains 38 bags of crisps and costs 3.49 Use estimates to explain which box is better value. Show your working and explain your answer. 2.00 20= 10p each (box A) Box B is better value as you get almost twice as many crisp but it doesn t cost twice as much 3) (M2) (A1) (b) James buys 4 boxes of box A and pays with a 20 note. Estimate the amount of change that he should receive. 4x 2.00 = 8.00 20.00-8.00= 12.00 = 12.00.. (Total 5 marks) (M1) (A1) Total /10
Checking Calculations 4 Grade 4 Solutions Objective: Check calculations using approximation and estimation (including using technology) Question 1. Four friends share the cost of a meal equally between them. The meal costs 27.71. (a) Estimate how much each friend should pay 28.00 4 = 7.00 = 7.00.. (M1) (A1) (b) They each pay with a 10 note. Estimate the amount of change they should receive. 28.00 4 = 7.00 Each friend receives 10-7 = 3 3 x 4 =12 12 total 3 each.. (M1) (A1) (c) One of the friends has forgotten their money. Estimate how much should the remaining friends each pay now. 27.00 3 = 9.00 9.00.. (M1) (A1) (Total 6 marks)
Question 2 A taxi company charges 93p per mile (a) James travels to an airport 18 miles away and is charged a fare of 32. She thinks that this is wrong. Use estimates to show that she is correct. 20 x 1.00 = 20.00 = 20.00. (M1) (A1) (b) Thomas wants to use the same taxi company to travel to work every day. He works four miles from home. Estimate how much this will cost him per 5-day working week. 5( 1.00 x 4)= 20.00 = 20.00.. (M1) (A1) (Total 4 marks) Total /10
Decimals1 Grade 3 Solutions Objective: Understand adding subtracting multiplying and dividing decimals. Question 1 Three parcels weigh 7.2 kg, 15.02 kg and 3.1 kg. Find their total mass. = 7.2kg + 15.02kg + 3.1kg (M1) = 25.32 kg (A1) Question 2 Work out 0.8965 0.5 = 0.8965 (x 10) = 8.965 5 0.5 ( x 10) (M1) = 1.793 (A1) Question 3 (a) Tom gets paid 3.15 an hour. One week he worked for 26 hours. How much is his weekly pay? 1 hour = 3.15 x 26 x 26 26 hours = ( 3.15 x 26) (M1) = 81.90 (A1)
(b) Tom is saving for a gift. He wants to give his friend a gift that costs 100.27. How much more money does Tom need after he has worked 26 hours in one week. = 100.27-81.90 (M1) = 18.37 (A1) Question 4 1 bottle of milk = 1.39 Lacey bought five bottles of milk. How much will it cost altogether? 1 bottle of milk = 1.39 x 5 x 5 5 bottles of milk = ( 1.39 x 5) (M1) = 6.95 (A1) Total /10
Decimals 2 Grade 3 Solutions Objective: Understand adding, subtracting multiplying and dividing decimals. Question 1 Work out a) 0.3 0.2 = 0.06 (A1) b) 0.03 0.12 =0.0036 (A1) Question 2 Work out 0.8965 0.05 =89.65/5 (M1) =17.93 (A1) Question 3 Electricity is 41p per unit. Helen s household uses 250 units. Work out the total cost of the electricity. 41p x 250 (M1) = 10250p or 102.50 (A1)
(b) Gas is 31p per unit. Helen s household uses 225 units. Work out the total cost of the gas. 31p x 225 = 6975p (M1) 69.75 (A1) Question 4 Evaluate: = 1.35/ 0.5 (M1) =2.7 (A1) Total /10
Decimals 3 Grade 3 Solutions Objective: Understand adding subtracting multiplying and dividing decimals. Question 1 7 cans of a drink cost 5.11. How much does one drink cost? 5.12 / 7 (M1) 0.73 (A1) Question 2 Work out 10.7865 0.5 107.865/5 (M1) =21.573 (A1) Question 3 (a) Sunny, Pat and Tom went out one evening and it cost them altogether 87.60. How much does each one of them have to pay? 87.60 / 3 (M1) 29.20 (A1)
(b) 6 people each weigh 75.9 kg. Find their total weight? 6 x 75.9 (M1) =455.4 kg (A1) Question 4 1 bottle of milk = 1.29 Kurt bought five bottles of milk how much will it cost altogether? 5 x 1.29 (M1) = 6.45 (A1) Total /10
Decimals 4 Grade 3 Solutions Objective: Understand adding, subtracting multiplying and dividing decimals. Question 1 a) How much change from a 20 note do I get if I buy 3 meals each costing 5.55? 3 x 5.55 = 16.65 (M1) 20.00-16.65 = 3.35 (A1) b) Which answer will be bigger: 6-3.28 or 21-18.67 = 2.72 = 2.33 (M1) = 6-3.28 is bigger (A1) Question 2 Laura, Kristina and Khalid to see a movie. It cost them 28.50. How much each will one of them have to pay? 28.50/3 (M1) = 9.50 (A1)
Question 3 Gas is 31p per unit. Ivy s household uses 150 units. (a) Work out the total cost of the gas. 31 x 150 (M1) =4650 p or 46.50 (A1) (b) Electricity is 51p per unit. Ivy s household uses 212 units. Work out the total cost of the electricity. 51 x 212 (M1) = 10812 p or 108.12 (A1) Total /10
Error intervals 1 SOLUTIONS Grade 5 Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) Find the range of numbers that would round to 300 (to one significant figure) (b) 250. 300<350 (A2).. (c) Find the range of numbers that would round to 3000 (to 1 significant figure) (d) 2500. 3000<3500 (A2).. Question 2 (Total 4 marks) Use inequality signs to show the range of possible values for (a) =8.5 to (2 s.f). (e) 8.45. 8.5<8.55 (A2)..
(b) =4.0 (to 1 d.p) (f) 3.95 4.0<4.05 (A2).. (Total 4 marks) 3. Question 3. Complete the inequality to show the range of values that would round to 0.2 (to 1 decimal place) 0.15. 0.2<0.25 (A2) (Total 2 marks)
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Error intervals 2 SOLUTIONS Grade 5 Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) Find the range of numbers that would round to 500 (to one significant figure) 450. 500<550 (A2).. (b) Find the range of numbers that would round to 5000 (to 1 significant figure) (c) 4500. 5000<5500 (A2).. Question 2 (Total 4 marks) Use inequality signs to show the range of possible values for (a) =0.5 (1.d.p) (d) 0.45. 0.5<0.55 (A2)..
(b) =50 (1 s.f0 (e) 45. 50<55 (A2).. (Total 4 marks) 3. Question 3. Complete the inequality to show the range of values that would round to 0.4 (to 1 decimal place). 0.4< (a) 0.35. 0.4<0.45 (A2) (Total 2 marks)
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Error intervals 3 Grade 5 Solutions Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) A book contains 310 pages to the nearest 10 pages. Find the range of values for which the number of pages could lie?. <. (B2) (b) A different book contains 500 pages when rounded to one significant figure. Find the range of values for which the actual number of pages could lie. <. (B2) Question 2 (Total 4 marks) (a) Use inequality signs to show the range of possible values for a car costing 3000 when rounded to the nearest thousand pounds
. <.. (B2) (b) The same car has travelled 46000miles when rounded to two significant figures. Once again using inequality notation show the range of values within which the number of miles could lie.. <... (B2) (Total 4 marks) Question 3. A field has a perimeter of 310 metres when rounded to the nearest 10 metres. Complete the inequality to show the range of values that would round to 310 metres correct to the nearest 10 metres. <
(B2) (Total 2 marks) Total /10
Error intervals 4 Grade 5 Solutions Objective: Use inequality notation to specify simple error intervals due to truncation or rounding. Question 1. (a) A box of oranges contains 40 oranges correct to one significant figure. Show the range of values representing the number of oranges the box could contain.. <.. (B2) (b) Each orange contains 5 grams of sugar correct to the nearest gram. Show the range of values which represent the amount of sugar that each orange could contain.. <5.5.. (B2) Question 2 (Total 4 marks) (a) Use inequality signs to show the range of possible values for a salary given as 35000 when rounded to the nearest thousand pounds. <.. (B2)
(b) The same company claims to provide work for 120 people correct to two significant figures. Use inequality notation to show the number of people that could be employed by the company.. <.. (B2) (Total 4 marks) Question 3. A football stadium records its attendance correct to two significant figures, complete the inequality to show the range of values within which the attendance could lie.. < (B2)
(Total 2 marks) Total /10