All AQA Unit 1 Questions Higher

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1 All AQA Unit 1 Questions Higher 467 minutes 391 marks Page 1 of 46

2 Q1. A book has a front and back cover and 100 pages. The front and back cover are each 0.8 millimetres thick when measured to one decimal place. Each page is 0.15 millimetres thick when measured to two decimal places. Calculate the minimum thickness of the book. You must show your working. Answer... mm (Total 5 marks) Q2. (a) What is a census? (1) The table shows the number of each type of staff at three hospitals. Staff Hospital A Hospital B Hospital C Doctors Nurses Others Page 2 of 46

3 (b) Simon wants to take a stratified sample of size 10 from the staff at hospital A. Calculate the number of each type of staff that Simon should choose. Answer Doctors... Nurses... Others... (3) (c) Tracy wants a stratified sample of size 30 from the doctors in the three hospitals. Calculate how many doctors Tracy should choose from hospital B. Answer... (2) (Total 6 marks) Page 3 of 46

Grey kangaroos Lower quartile Median Upper quartile 85 cm 105 cm 120 cm Explain why the heights

4 Q3. The cumulative frequency diagram of the heights of 80 red kangaroos is shown below. The table below summarises the heights of 80 grey kangaroos. Grey kangaroos Lower quartile Median Upper quartile 85 cm 105 cm 120 cm Explain why the heights of the grey kangaroos are more consistent than the heights of the red kangaroos. You must show your working. (Total 4 marks) Page 4 of 46

5 Q4. The table summarises the travelling time to work of 80 people. Travelling time, t (minutes) Number of people 0 < t < t < t < t < t Calculate an estimate of the mean travelling time. Answer... minutes (Total 4 marks) Page 5 of 46

6 Q5. The histogram represents the birth weights of 150 babies. Thirty babies weighed over 4.5 kg Babies weighing under 2 kg are taken to the Special Care Baby Unit. Calculate the number of babies taken to the Special Care Baby Unit. Answer... (Total 3 marks) Page 6 of 46

Amy does this 60 times and calculates the relative frequency of red after every 10 goes. Her results are shown on the graph.

7 Q6. Amy has a bag containing red, green and blue balls. She wants to know the probability of picking a red ball from the bag. She picks a ball at random from the bag, records the colour and replaces the ball in the bag. Amy does this 60 times and calculates the relative frequency of red after every 10 goes. Her results are shown on the graph. (a) Use the graph to calculate the number of times Amy picked a red ball in the first 10 goes. Answer... (2) (b) What is the best estimate for the probability of picking a red ball? Explain your answer. (2) (Total 4 marks) Page 7 of 46

8 Q7. A bag contains 7 mint sweets, 3 fruit sweets and 5 toffee sweets. Sam chooses two sweets from the bag at random. Calculate the probability that she chooses one mint sweet and one fruit sweet. Answer... (Total 3 marks) Q8. A children s athletics club has 300 members. The table shows the number of members in each age group. Under 11 yrs yrs yrs 15 yrs and over Ciaran wants a stratified sample of 25 members. Calculate the number of members that he should choose from each age group. Answer Under 11 yrs yrs yrs yrs and over... (Total 3 marks) Page 8 of 46

9 Q9. On a day in November 45% of the pupils at a school have flu. Of the pupils who have flu, 80% are absent from school. 6% of the pupils who do not have flu are absent from school for other reasons. Work out the percentage of the pupils at the school who are absent on this day. You must show your working Answer... % (Total 4 marks) Q10. The number of visitors to a garden centre is recorded for 20 days. The results are shown in the ordered stem-and-leaf diagram. Key 5 2 represents 52 visitors (a) What was the greatest number of visitors to the garden centre on one day? Answer... (1) Page 9 of 46

10 (b) Calculate the median number of visitors to the garden centre. Answer... (2) (Total 3 marks) Q11. Emily drives her car a distance of 310 miles which is correct to 2 significant figures. Her car uses 50 litres of petrol which is correct to the nearest litre. Find, in miles per litre, the maximum value for the petrol consumption of her car. You must show your working. Answer... miles per litre (Total 4 marks) Q12. In 2002 the number of visitors to four tourist attractions is shown in the table. Blackpool Pleasure Beach 6.2 million Edinburgh Castle Giant s Causeway Tate Modern 4.6 million (a) Write the number of visitors to Edinburgh Castle in standard form. Answer... (1) Page 10 of 46

11 (b) Blackpool Pleasure Beach claimed that it had more visitors than the other three added together. Is this claim true? You must show your working. (2) (Total 3 marks) Q13. A packet of crisps weighs 34 grams to the nearest gram. A multipack of crisps contains 10 packets. Work out the least and greatest weights of the multipack. (You can ignore the weight of the multipack wrapper.).... Answer Least... grams Greatest... grams (Total 2 marks) Page 11 of 46

12 Q14. A bag contains twelve numbered counters. The counters are either red or yellow. The table shows how the counters are coloured and numbered. Number on counter Colour Red Yellow For example there are 3 red counters numbered 40. A counter is taken at random from the bag and is not replaced. A second counter is then taken at random from the bag. Calculate the probability that the two counters taken from the bag have different colours and the total of the two numbers is Answer... (Total 5 marks) Page 12 of 46

13 Q15. The time, in minutes, spent queuing in a post office by each of 100 customers is summarised by the cumulative frequency diagram below. Use the cumulative frequency diagram to estimate (a) how many customers queued for more than 25 minutes. Answer... (2) (b) the median queuing time Answer... minutes (1) (c) the interquartile range of the queuing times... Answer... minutes (2) (Total 5 marks) Page 13 of 46

14 Q16. Bob has just retired. He often goes into town and sometimes uses the Internet café in the town. The probability that Bob goes to town on a Wednesday is The probability that Bob goes to town on a Wednesday and uses the Internet café is (a) One Wednesday Bob goes to town. Calculate the probability that he uses the Internet café Answer... (2) (b) Calculate the probability that Bob does not use the Internet café next Wednesday..... Answer... (2) (Total 4 marks) Page 14 of 46

15 Q17. (a) Explain how you could obtain a random sample of 50 residents from a village. (1) (b) The population of a town is The table below shows the population of the town by age group. Age group Under to to 65 Over 65 Population Calculate the number from each age group that would be needed for a stratified sample of size Answer Under to to 65 Over 65 (3) (Total 4 marks) Page 15 of 46

16 Q18. (a) The numbers in this calculation are given to 3 significant figures. Find the least possible value of You must show all your working. Answer... (3) (b) The maximum safe load of a lift is 1500 kg, to the nearest 50 kg. The lift is loaded with boxes weighing 141 kg and 150 kg, both weights given to the nearest kilogram. Can the lift safely carry 3 boxes weighing 141 kg each and 7 boxes weighing 150 kg each? You must show all your working. (3) (Total 6 marks) Page 16 of 46

17 Q19. The population of France is people. The area of France is square kilometres. Mean number of people = Calculate the mean number of people per square kilometre in France. Give your answer to a suitable degree of accuracy. Answer... (Total 3 marks) Q20. In Portugal, Brian spends 2.80 on ice cream. This price includes VAT which is 12% in Portugal. Find the amount of VAT which Brian paid. Answer... (Total 3 marks) Page 17 of 46

18 Q21. Philip and Abdul run in different races. The probability that Philip wins his race is 0.7 The probability that Abdul wins his race is 0.6 (a) Fill in the missing probabilities on the tree diagram. (1) (b) Calculate the probability that only one of the boys wins his race Answer... (3) (Total 4 marks) Page 18 of 46

19 Q22. A group of 80 trainee secretaries have their typing speeds tested. The table shows their results in words per minute (wpm). Speed, s (wpm) Number of typists Speed, s (wpm) Cumulative frequency 20 s < 30 8 < s < < s < < s < < s < 70 5 < 70 (a) (i) Complete the cumulative frequency column in the table. (1) (ii) Draw a cumulative frequency diagram on the grid below. (3) Page 19 of 46

20 (b) Use your diagram to estimate the interquartile range... Answer... wpm (2) (Total 6 marks) Q23. A manager recorded the number of customers that entered his supermarket each hour over five days in June. The table shows a summary of his results. Number of Customers Minimum 8 Lower quartile 23 Median 25 Upper quartile 33 Maximum 42 Draw a box plot to show these results. (Total 3 marks) Page 20 of 46

21 Q24. The table shows the age, in years, of workers in a factory. Age, x (years) Number of workers 15 x < x < x < x < x < 60 8 Calculate an estimate of the mean age of these workers. Answer... years (Total 4 marks) Page 21 of 46

Q25. Arnie saw a camera priced at 250 in London. He saw the same camera priced at $297.50 in New York.

22 Q25. Arnie saw a camera priced at 250 in London. He saw the same camera priced at $ in New York. This is a 30% saving on the London price. How many dollars are there to the pound? Answer 1 = $... (Total 3 marks) Q26. (a) What is 12% of ? Answer... (2) Page 22 of 46

(b) What is the normal price of the garden seat? Answer... (3) (Total 5 marks) Q27. The table shows the consumption of water per person on average each day during various years.

23 (b) What is the normal price of the garden seat? Answer... (3) (Total 5 marks) Q27. The table shows the consumption of water per person on average each day during various years. Year Consumption (litres) (a) A 26% increase in consumption is predicted from 2004 to Calculate the predicted consumption in Answer... litres (3) (b) Calculate the percentage increase in consumption from 1976 to Answer... (3) Page 23 of 46

(c) The consumption in 1976 was 20% more than the consumption in 1960.

The pie charts show the age distribution in two villages A and B.

24 (c) The consumption in 1976 was 20% more than the consumption in Calculate the consumption in Answer... litres (3) (Total 9 marks) Q28. The pie charts show the age distribution in two villages A and B. The population of the villages is proportional to the area of the pie charts. There are 660 people over 65 in village A. Village A Village B Drawn to scale Page 24 of 46

25 How many people are over 65 in village B? Show clearly any measurements or assumptions that you make. Show your method clearly. Answer... (Total 5 marks) Q29. John has 2000 to invest. He sees this advert. Page 25 of 46

26 Will John double his money in ten years with SureFire Investments? You must show your working. (Total 4 marks) Q30. John has 2000 to invest. He sees this advert. Page 26 of 46

27 Will John double his money in ten years with SureFire Investments? You must show your working. (Total 4 marks) Page 27 of 46

28 their min cover 2 or their min page or 14.5 if correct Must have attempted one minimum their min cover 2 + their min page 100 Must have attempted two minimums 16 dep [5] M2. (a) A census surveys the whole population Survey by everyone (b) Any one correct method seen 1, 3, 6 Correct decimals or fractions only get A2 (c) 10 [6] Page 28 of 46

29 M3. Locating quartiles from graph (Red kangaroos IQR =) 50 cm (Grey kangaroos IQR =) 35 cm IQR red > IQR grey oe eg Lines on graph including to h axis OR 110 and 160 seen [4] M4. 4 or 5 correct midpoints seen or implied at least two products with intention to sum Accept incorrect midpoints but must be within classes including boundaries Note: Not class widths throughout Note: 1840 or or 5 correct products summed with intention to divide by 80 dep on 2nd or M2 dep 28 [4] Page 29 of 46

30 M5. 1 sq cm = 5 babies 150 little squares = 30 or [3] M6. (a) oe 5 no working M0A0 (b) 0.45 Larger sample, 60 goes/the last one [4] Page 30 of 46

31 M7. or or or Adding the two correct products dep or oe 0.2 SC1 [3] M8. One correct method seen 4, 6, 8, 7 or 3, 7, 8, 7 or 4, 7, 8, 6 for 3.75, 6.5, 8, 6.75 or 4, 7, 8, 7 A2 [3] M (0) (= 0.36) or (= 36) or 0.8(0) 45 (= 36) Chooses number of pupils eg, (100) = (45) 0.8(0) (45) = (36) (= 0.033) or (= 3.3) or (= 3.3) 0.55 (100) = (55) 0.06 (55) = (3.3) Page 31 of 46

32 (0.36) + (0.033) or (36) + (3.3) (36) + (3.3) Dependent on M2 in all methods dep 39.3 SC2 Answer 3930 [4] 0. (a) 83 (b) = 10.5th value Locating 65 and 67 or locating 5 and 7 or 5/7 on diagram 66 [3] (Allow ) Ignore 305 if seen as well Ignore 50.5 if seen as well if correct Page 32 of 46

33 Allow 6.3, 6.4, 6.363, 6.36, etc provided there is evidence to support these answers (B2 awarded) Always check the working eg = 6.36 (2 dp) scoring B0A0 [4] 2. (a) Allow (b) Attempt to add , and 4.6 million Numbers all in same form with at least two correct (oe) and Yes Must have both [3] 3. Sight of 33.5 or g and 345 g Allow for gets Allow for 345 Need both answers SC1 One correct answer [2] Page 33 of 46

34 4.... or... or... Any first probability multiplied by some other probability seen or or 2 Any correct product of two probabilities All correct products doubled (may come later) + + = Adding exactly 3 (or 6) correct products oe 0.16, 0.17, 16% or 17% from correct method SC3 for question with replacement fully correct [5] 5. (a) 100 their attempt at reading at 25 Allow misread of scale , , , 84, OK 12 (b) 14 Allow a value of 13.5 to 14.5 inclusive Page 34 of 46

35 (c) Locating and subtracting the quartiles (allow ± square on each reading) 8 to 10 Depends on correct M mark if seen [5] 6. (a) p = p = Correct equation seen in any form oe 0.58, 58% not 0.6 or 60% (b) 1 or + [ (1 their (a))] = oe, 0.65, 65% Page 35 of 46

36 For (b) Note incorrect method leading to correct answer cafe not cafe T NT café not cafe + = + = = [4] 7. (a) Any suitable random method Number all population and draw numbers (names) from hat/random number tables/raffle, use random numbers Page 36 of 46

37 (b) Correct method seen eg 1000 Can be implied by any correct value Any two correct answers Accept decimals here also dp rounded or truncated All four correct answers 197, 411, 270, 122 Must be integers Use of 100 misread only if seen or follows scheme with 2 correct decimals or integers [4] 8. (a) Any 1 correct limit if correct Their min 12.3 must be > 12.2 Their max 15.6 must be < 15.7 Their min 7.20 must be > etc Page 37 of 46

38 (b) 3 their max their max = 1478 if correct Their max 141 must be < 142 Their max 150 must be < 151 Lower bound lift load = 1475 So this load cannot be safely carried Only award if fully correct: both 1475 and 1478 seen [6] ( ) Condone invisible brackets Allow if not in standard form and at least one correct or both 2 zeros out (5.83 7) (5.47 5) M M0 110 or 107 ft to 2 sf or 3 sf Allow but no ft to 4 sf ft [3] M = 1.12 of pre-vat price or 112% or (= 2.5) VAT = 2.80 VAT = 2.80 (their 2.50) = 0.30 = 0.30 or 0.3 [3] Page 38 of 46

39 M21. (a) All 3 missing probabilities correctly filled in (b) or ft from unambiguous tree diagram except if 0.5 used Either seen in (b) or 0.28 or Adding the 2 correct products If no working in (b) answer can follow tree diagram if fully correct to answer in (b) => * Working in (b) can be ft from incorrect tree diagram as long as it is not ambiguous (=> A0) = 0.46 [4] M22. (a) (i) 8, 38, 62, 75, 80 Rest of question must be from an increasing cumulative frequency diagram (not linear) (ii) Upper class boundaries used ± square Their correct heights ± square Ignore (20, 0) Ignore curve before (30, 8) ft Straight lines or smooth curve connecting points ± square Ignore curve before (30, 8) Page 39 of 46

40 (b) Locating and subtracting quartiles ie If no working check graph From 60, 20 or their quartiles eg 17.5, 52.5 or methods = 14 ft [5] M23. Median at 25 X or small mark in a box ± Quartiles at 23 and 33 and box ± sq Whiskers to 8 and 42 sq ± sq [3] M24. Any one correct mid-point seen and used ie 17.5, 22.5, 27.5, 35 or 50 Used in fx (not just added) ie 70, 225, 165,... * Look out for 17, 23, 27 used (35, 50) leading to correct answer => M3 A0 fx fx for their x in class or on boundary, at least 2 products summed Dep on 2nd Their fx divided by their 50 dep = 32.6 Accept 32 or 33 from fully correct method [4] Page 40 of 46

41 M (1.7) oe (= 425) 1.7 (0) [3] M26. (a) or or or (.00) or after 30 seen is non-contradictory fw 1 for incorrect money notation (b) Sight of % = (1%) = (= 1.25) 125(.00) 1 for incorrect money notation Penalise for further contradictory working eg, = 140 [5] Page 41 of 46

42 M27. (a) Their 39 M2 for dep is A0 (b) is M0 unless 1 or 100% subtracted, then it is M2 36.4, if awarded 36 from T & I is M0 (c) 120% = is M2 1% = T & I must get 91.6 to 91.7 Beware = 92 M0 [9] Page 42 of 46

43 M28. Radius A = 1.5cm Radius B = 2.5 cm These must be clearly stated or implied (eg 2.25π, 6.25π) at some stage in solution (population A) NB Scale factor such as 0.6, 1.66, NB Check pie charts for these. 6.25(π) 2.25(π) for attempt to compare areas. eg 25:9, population in B Allow implies Alt. Radius A = 1.5cm Radius B = 2.5cm These must be clearly stated or implied (eg 2.25π, 6.25π) at some stage in solution. NB Scale factor such as 0.6, 1.66, NB Check pie charts for these. implies Compares a population to an area for village A eg 660 (=) π 1980:2.25π Finds a value for person per area or area per person people per cm cm 2 per person Calculates area of quadrant in B and either multiplies or divides by appropriate value 1375 [5] Page 43 of 46

44 M29. Sight of % of 2000 = 144 (2000) their Their must be 1.72 or Calculating at least 5 intermediate values correctly 2144, (368), (0496), ( ), ( ) All 10 correct ( ), ( ), (.09479), ( ) ( ) No penalty for rounding or truncating to nearest pound or 1 decimal place. Truncated values 2144, 2298, 2463, 2640, 2830, 3033, 3251, 3485, 3735, 4004 ( ) Rounded values 2144, 2298, 2463, 2640, 2830, 3034, 3252, 3486, 3737, 4006 ( ) No penalty for incorrect money notation eg > Yes 4008.(46) or 2.004(2..) ft if only one error made and relevant conclusion drawn. Accept > 2 for 3/4 marks NB student who takes 2000 as year 1 gets to 3739 for year 10 and says no 2/4 SC /4 marks (, ) ft [4] Page 44 of 46

45 M30. Sight of % of 2000 = 144 (2000) their Their must be 1.72 or Calculating at least 5 intermediate values correctly 2144, (368), (0496), ( ), ( ) All 10 correct ( ), ( ), (.09479), ( ) ( ) No penalty for rounding or truncating to nearest pound or 1 decimal place. Truncated values 2144, 2298, 2463, 2640, 2830, 3033, 3251, 3485, 3735, 4004 ( ) Rounded values 2144, 2298, 2463, 2640, 2830, 3034, 3252, 3486, 3737, 4006 ( ) No penalty for incorrect money notation eg > Yes 4008.(46) or 2.004(2..) ft if only one error made and relevant conclusion drawn. Accept > 2 for 3/4 marks NB student who takes 2000 as year 1 gets to 3739 for year 10 and says no 2/4 SC /4 marks (, ) ft [4] Page 45 of 46

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Mark Scheme (Results) Summer 2009

Mark Scheme (Results) Summer 2009 GCSE GCSE Mathematics (Linear) - 1380 Paper: 1380_2F 2 NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional