Oxford Cambridge and RSA Level 3 Certificate Quantitative ...mei.org.uk/files/papers/H867_01_IQR_2017_June.pdf · Oxford Cambridge and RSA Level 3 Certificate Quantitative Problem

INSTRUCTIONS• Use black ink. You may use an HB pencil for graphs and diagrams.• Complete the boxes above with your name, centre number and candidate number.• Answer all the questions.• Write your answer to each question in the space provided.• Additional paper may be used if required but you must clearly show your candidate

number, centre number and question number(s).• Do not write in the barcodes.• You are advised that an answer may receive no marks unless you show sufficient detail

of the working to indicate that a correct method is being used.

INFORMATION• The total mark for this paper is 72.• The marks for each question are shown in brackets [ ].• This document consists of 20 pages.• Final answers should be given to a degree of accuracy appropriate to the context.

Turn over© OCR 2017 [601/4783/0]DC (CE/JG) 149920

Last name

First name

Candidatenumber

Centrenumber

Oxford Cambridge and RSA

Level 3 CertificateQuantitative Problem Solving (MEI)H867/01 Introduction to Quantitative Reasoning

Wednesday 17 May 2017 – MorningTime allowed: 2 hours

You must have:• the Insert (inserted)

You may use:• a scientific or graphical calculator

*6834940926*

OCR is an exempt Charity

* H 8 6 7 0 1 *

2

© OCR 2017

1 This question refers to the article “Lotteries and raffles”. This was given out as pre-release material and is available as an insert.

A couple have won the EuroMillions draw – for the second time.

The extraordinarily lucky pair, from Scunthorpe, Lincs, have scooped their second £1 million prize in less than two years.

That means they have beaten the incredible odds of over 1 in 253 billion in winning it twice.

The article above describes a couple who won twice on the Euromillions raffle.

(i) The median UK salary is £22 000 per year. How many years would it take one person at this salary to earn the total amount of £2 million won by the couple in the article? [2]

1 (i)

(ii) Suppose the couple invest the entire £2 million won in a savings bond paying 3.2% per year tax free. The interest is paid in equal weekly instalments.

How many complete weeks would it take for the couple to earn the median UK salary from interest alone? [4]

1 (ii)

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(iii) Assume that the newspaper is correct and the probability of winning this raffle twice with just two entries is 1 in 253 billion. Show that the probability of winning it once with one ticket is about 1 in 500 000, assuming that the outcomes are independent and the probability of winning each time is constant. [3]

1 (iii)

4

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2 The boxplots below show the results of a survey of many doctors’ estimates of smoking prevalence (i.e. the proportion of people they treat who smoke) along with the level of deprivation of the people they treat. People with low deprivation scores generally have higher incomes and better access to services.

Dots show outliers. “Least” refers to a group with a deprivation score below that which would get into the group with a deprivation score of 10. “Most” refers to a group with a deprivation score above that which would get into the group with a deprivation score of 50.

0 10 20 30 40 50 60 70 80

Most

Estimated smoking prevalence % 2013/14

50

40

30

20

10

LeastDeprivation score

Source: publichealthmatters.blog.gov.uk/2014/12/11/datablog-good-news-on-smoking/

(i) Summarise the main point this chart is showing. [1]

2 (i)

5


(ii) What is the median estimated smoking prevalence of those with a deprivation score of 50? [1]

2 (ii)

(iii) What is the interquartile range (IQR) in the estimated smoking prevalence of those with a deprivation score of 50? [2]

2 (iii)

(iv) The formula Upper Quartile + 1.5 × IQR is used to find a cut off point for high value outliers. Use this formula to find the cut off for outliers of those with a deprivation score of 50. [3]

2 (iv)

(v) Jemima says that groups with higher deprivation scores tend to have greater variation in the estimated smoking prevalence than groups with lower deprivation scores. Identify the feature of the chart which supports Jemima’s idea. [1]

2 (v)

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© OCR 2017

3 This question refers to the article “Car rental”. This was given out as pre-release material and is available as an insert.

Danielle wants to hire a car to take her from London to Edinburgh. The table below gives the distances in miles between some places in Britain.

Birm

ingh

am

Car

diff

Car

lisle

Dov

er

Hul

l

Lond

on

Man

ches

ter

New

cast

le

Nor

wic

h

Plym

outh

Aberdeen 425 532 232 587 375 545 355 234 487 628Dundee 348 449 153 542 287 461 273 169 411 543

Edinburgh 298 399 98 463 246 411 222 106 359 495Fort William 409 510 209 591 379 522 333 239 491 606

Glasgow 296 397 97 478 266 409 220 154 379 493Inverness 458 558 258 639 486 571 381 266 540 654

Oban 387 488 193 581 350 450 312 231 473 582Perth 346 446 146 504 292 459 267 151 405 542

Stirling 307 408 113 502 270 420 232 148 393 502Stranraer 306 406 106 487 276 419 227 164 388 503Ullapool 501 602 307 695 464 614 426 321 587 696

Wick 560 661 360 742 530 673 481 369 642 757

(i) Use the table above to find the distance from London to Edinburgh. [1]

3 (i)

Danielle needs a car for at least 5 people. She also wants to find the car with the best motorway fuel efficiency. She looks at the advert shown in the insert of the pre-release material.

(ii) Which car should she choose, assuming they are all available? [1]

3 (ii)

7


(iii) A car has a fuel efficiency of 30 miles per gallon for motorway driving. On the graph below plot a line showing the fuel required for distances between zero and 450 miles. Assume that the fuel consumption is proportional to distance travelled. [2]

3 (iii)

00

2

4

6

8

10

12

14

16

18

20

100 200 300 400

Fuel used(gallons)

Distance travelled (miles)

(iv) 1 gallon of petrol costs £4.96. Show how you can estimate, without a calculator, the amount of money which should be allowed to pay for petrol costs for a one-way trip from London to Edinburgh using a car with a motorway fuel efficiency of 30 mpg, assuming that nearly all of the journey is on the motorway. Write your answer to an appropriate level of accuracy. [5]

3 (iv) Do not use a calculator for this part of the question.

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© OCR 2017

4 The vertical line chart below shows the percentage change in average house prices in the UK over each of the 20 months from January 2008 to August 2009.

3.0

2.0

1.0

0.0

–1.0

–2.0

–3.0

–4.0

Jan-

08

Feb-

08

Mar

-08

Apr

-08

May

-08

Jun-

08

Jul-0

8

Aug

-08

Sep-

08

Oct

-08

Nov

-08

Dec

-08

Jan-

09

Feb-

09

Mar

-09

Apr

-09

May

-09

Jun-

09

Jul-0

9

Aug

-09

Percentagechangeover themonth

(i) Describe what is happening to average house prices during this period. [2]

4 (i)

(ii) In what percentage of months were average house prices rising according to the vertical line chart? [2]

4 (ii)

9


(iii) The vertical line chart shows that the average house price decreased by 1.7% during January 2009 and by 1.8% during February 2009. Hanna bought her house for £245 000 at the beginning of January 2009. A bank used the information from the graph to estimate the value of her house at the end of February 2009. What value did they find? Give your answer to the nearest pound. [4]

4 (iii)

(iv) Give two reasons why the value found in part (iii) might not give the true value of Hanna’s house. [2]

4 (iv)

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5 Manjit wants to open a sandwich shop on the high street to serve people of all ages in a town. He conducts a survey to find out how much people would pay for a sandwich.

(i) State one statistical issue which might occur if Manjit conducted the survey in a local sixth form college. [1]

5 (i)

Manjit conducts a survey on a representative sample of potential customers. He asks the question “What is the maximum you would be prepared to pay for a sandwich?”

The results of Manjit’s survey are summarised in the chart below.

Frequency

Less than £1 £1 to £1.99 £2 to £2.99 £3 to £4.99 £5 to £10 Over £50Price

40353025201510

50

(ii) Which group should be discarded as outliers? Explain why people may have given these responses. [2]

5 (ii)

11


(iii) Use this sample to estimate the mean maximum price potential customers are prepared to pay for a sandwich, excluding the outliers. [4]

5 (iii)

(iv) State two reasons why your answer to part (iii) is only an estimate of the true mean maximum price potential customers are prepared to pay. [2]

5 (iv)

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After further market research Manjit constructs this demand curve for sandwiches.

Price (£)

Number sold

00

1

2

3

4

5

6

100 200 300 400 500 600 700 800

13


Manjit uses this model and a spreadsheet to work out how to make the maximum profit. Manjit wants to sell each sandwich for a multiple of 50p. Each sandwich costs 80p to make. Manjit can make up to 700 sandwiches each day.

(v) Fill in the rest of the numbers in columns B, C and D. [5]

5 (v)A B C D

1 Customerprice (£)

Number soldper day

Production cost for Manjit (£)

Total profit(£)

2 1.00 700 560 140

3 1.50 625

4 2.00 550

5 2.50 475

6 3.00

7 3.50

8 4.00

9 4.50

10 5.00 100 80 420

(vi) What formula should Manjit type in cell C2 so that he can copy it down the column to give the number sold per day? [2]

5 (vi)

(vii) What formula should Manjit type in the cell D2 so that he can copy it down the column to give the profit? [2]

5 (vii)

(viii) State the price he should sell the sandwiches for to make the maximum profit. [1]

5 (viii)

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(ix) Manjit intends to sell sandwiches on 20 days each month. He estimates that his total costs (excluding making the sandwiches) will be £8 000 pounds each month.

Would you recommend that Manjit goes ahead with his plan to start this business? Give a reason for your answer and show relevant calculations. [2]

5 (ix)

15


6 This question refers to the article “Glaciers”. This was given out as pre-release material and is available as an insert.

(i) The water from a glacier feeds into a lake. A climate scientist estimates that 2 billion litres melts from the glacier each year. (Note: 1 billion =109)

Use the fact that 1 litre is 1000 cm3 to write 2 billion litres in cubic metres (m3). Give your answer in standard form. [3]

6 (i)

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(ii) The lake is modelled as a cylinder with radius 2 km as shown below. The axis of symmetry is vertical.

2 km

Show that the annual change in height of the lake due to the water melting from the glacier is 16 cm to the nearest centimetre. [4]

6 (ii)

17


The table below shows the percentage volume decrease in a glacier in three consecutive years.

Year Percentage reduction

1 4

2 10

3 8

(iii) Find the overall percentage reduction in volume in these three years. [3]

6 (iii)

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The long term average annual percentage volume decrease is 7%.

(iv) Assume that this average percentage reduction will continue. Which one of these graphs best represents the percentage of the 2016 glacier remaining in future years? Tick the appropriate box. [1]

A100

0Time since 2016 reading

% Remaining

C100


% Remaining

D100


% Remaining

B100


% Remaining

6 (iv) A B C D

Tick one box

19

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(v) How many complete years would it take for the glacier to reduce by 50% from its current volume? [3]

6 (v)

(vi) To make the comparisons between different years valid the measurements of the volume of the glacier are all conducted by the same team of scientists. State one other factor which must stay the same in all measurements to allow a valid comparison. [1]

6 (vi)

END OF QUESTION PAPER

20

© OCR 2017

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NOTES FOR GUIDANCE (CANDIDATES)• This insert contains a copy of the pre-release material for use with the question paper.• This document consists of 4 pages. Any blank pages are indicated.

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Level 3 CertificateQuantitative Problem Solving (MEI)H867/01 Introduction to Quantitative Reasoning

Insert

Wednesday 17 May 2017 – Morning*6834998544*

2

H867/01 Jun17© OCR 2017

Lotteries and raffles

In the UK National Lottery players enter by selecting 6 numbers from 1 to 59. Twice each week numbers are selected at random on a television show. To win the jackpot players must match all 6 numbers. If they match fewer numbers they may win a smaller amount. Players may enter multiple times for each draw, choosing a different set of numbers each time. Many players enter every draw. The outcome of each draw is independent.

People who enter the lottery are also entered into a raffle. In this type of game a fixed number of entries is selected at random to win a prize.

Many other countries have similar lottery and raffle systems. There is also a Europe-wide game called “Euromillions” which has a similar lottery and raffle structure to the UK National Lottery.

Although some prizes are very large the probability of winning the jackpot is very, very small; for example the probability of winning the jackpot in the UK National Lottery is about 1 in 45 million. Both lotteries and raffles are designed so that if they are played many times the amount a player would expect to win is less than the amount he or she would spend.

Glaciers

A glacier is a large body of ice found in very cold environments. Some of the largest glaciers are huge; they can be around 10 000 km3 or 1 × 1016 litres; that is 10 million billion litres!

Many glaciers are currently melting, with the water flowing into glacial lakes. Climate scientists often measure the amount of melted water coming out of a glacier to see if there is evidence of global warming. One possible consequence of global warming is that sea levels will rise.

3

H867/01 Jun17© OCR 2017

Car Rental

When renting a car, various factors are taken into account for the cost, including:

• the number of passengers the car can take,• the storage capacity,• the fuel efficiency.

Fuel efficiency can be measured in miles per gallon (MPG). Normally two figures are given. Fuel efficiency for “urban driving” and fuel efficiency for “motorway driving”.

For example, the advertisement below shows that the Chevrolet Aveo can carry four passengers, has a storage capacity of 12 cubic feet, an “urban driving” fuel efficiency of 25 miles per gallon and a “motorway driving” fuel efficiency of 34 miles per gallon.

4

H867/01 Jun17© OCR 2017


Copyright Information

OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.

If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity.

For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.

OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

Oxford Cambridge and RSA Examinations

Level 3 Certificate

Quantitative reasoning (MEI)

Unit H867/01 Introduction to quantitative reasoning

OCR Level 3 Certificate Quantitative Reasoning

Mark Schemes for June 2017

OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a wide range of qualifications to meet the needs of candidates of all ages and abilities. OCR qualifications include AS/A Levels, Diplomas, GCSEs, Cambridge Nationals, Cambridge Technicals, Functional Skills, Key Skills, Entry Level qualifications, NVQs and vocational qualifications in areas such as IT, business, languages, teaching/training, administration and secretarial skills. It is also responsible for developing new specifications to meet national requirements and the needs of students and teachers. OCR is a not-for-profit organisation; any surplus made is invested back into the establishment to help towards the development of qualifications and support, which keep pace with the changing needs of today’s society. This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which marks were awarded by examiners. It does not indicate the details of the discussions which took place at an examiners’ meeting before marking commenced. All examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes should be read in conjunction with the published question papers and the report on the examination. OCR will not enter into any discussion or correspondence in connection with this mark scheme. © OCR 2017

H867/01 Mark Scheme June 2017

3

Annotations and abbreviations

Annotation in scoris Meaning

and

BOD Benefit of doubt

FT Follow through

ISW Ignore subsequent working

M0, M1 Method mark awarded 0, 1

A0, A1 Accuracy mark awarded 0, 1

B0, B1 Independent mark awarded 0, 1

SC Special case

^ Omission sign

MR Misread

Highlighting

Other abbreviations in mark scheme

Meaning

E1 Mark for explaining

U1 Mark for correct units

G1 Mark for a correct feature on a graph

M1 dep* Method mark dependent on a previous mark, indicated by *

cao Correct answer only

oe Or equivalent

rot Rounded or truncated

soi Seen or implied

www Without wrong working


4

Subject-specific Marking Instructions

Annotations should be used whenever appropriate during your marking. The A, M and B annotations must be used on your standardisation scripts for responses that are not awarded either 0 or full marks. It is vital that you annotate standardisation scripts fully to show how the marks have been awarded. For subsequent marking you must make it clear how you have arrived at the mark you have awarded.

An element of professional judgement is required in the marking of any written paper. Remember that the mark scheme is designed to assist in marking incorrect solutions. Correct solutions leading to correct answers are awarded full marks but work must not be judged on the answer alone, and answers that are given in the question, especially, must be validly obtained; key steps in the working must always be looked at and anything unfamiliar must be investigated thoroughly. Correct but unfamiliar or unexpected methods are often signalled by a correct result following an apparently incorrect method. Such work must be carefully assessed. When a candidate adopts a method which does not correspond to the mark scheme, award marks according to the spirit of the basic scheme; if you are in any doubt whatsoever (especially if several marks or candidates are involved) you should contact your Team Leader.

The following types of marks are available. M A suitable method has been selected and applied in a manner which shows that the method is essentially understood. Method marks are not usually lost for numerical errors, algebraic slips or errors in units. However, it is not usually sufficient for a candidate just to indicate an intention of using some method or just to quote a formula; the formula or idea must be applied to the specific problem in hand, eg by substituting the relevant quantities into the formula. In some cases the nature of the errors allowed for the award of an M mark may be specified. A Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. Accuracy marks cannot be given unless the associated Method mark is earned (or implied). Therefore M0 A1 cannot ever be awarded. B Mark for a correct result or statement independent of Method marks.


5

E A given result is to be established or a result has to be explained. This usually requires more working or explanation than the establishment of an unknown result. Unless otherwise indicated, marks once gained cannot subsequently be lost, eg wrong working following a correct form of answer is ignored. Sometimes this is reinforced in the mark scheme by the abbreviation isw. However, this would not apply to a case where a candidate passes through the correct answer as part of a wrong argument.

When a part of a question has two or more ‘method’ steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. (The notation ‘dep *’ is used to indicate that a particular mark is dependent on an earlier, asterisked, mark in the scheme.) Of course, in practice it may happen that when a candidate has once gone wrong in a part of a question, the work from there on is worthless so that no more marks can sensibly be given. On the other hand, when two or more steps are successfully run together by the candidate, the earlier marks are implied and full credit must be given.

The abbreviation ft implies that the A or B mark indicated is allowed for work correctly following on from previously incorrect results. Otherwise, A and B marks are given for correct work only — differences in notation are of course permitted. A (accuracy) marks are not given for answers obtained from incorrect working. When A or B marks are awarded for work at an intermediate stage of a solution, there may be various alternatives that are equally acceptable. In such cases, exactly what is acceptable will be detailed in the mark scheme rationale. If this is not the case please consult your Team Leader. Sometimes the answer to one part of a question is used in a later part of the same question. In this case, A marks will often be ‘follow through’. In such cases you must ensure that you refer back to the answer of the previous part question even if this is not shown within the image zone. You may find it easier to mark follow through questions candidate-by-candidate rather than question-by-question.

Wrong or missing units in an answer should not lead to the loss of a mark unless the scheme specifically indicates otherwise. Candidates are expected to give numerical answers to an appropriate degree of accuracy, with 3 significant figures often being the norm. Small variations in the degree of accuracy to which an answer is given (e.g. 2 or 4 significant figures where 3 is expected) should not normally be penalised, while answers which are grossly over- or under-specified should normally result in the loss of a mark. The situation regarding any particular cases where the accuracy of the answer may be a marking issue should be detailed in the mark scheme rationale. If in doubt, contact your Team Leader.

Rules for replaced work If a candidate attempts a question more than once, and indicates which attempt he/she wishes to be marked, then examiners should do as the candidate requests.


6

If there are two or more attempts at a question which have not been crossed out, examiners should mark what appears to be the last (complete) attempt and ignore the others. NB Follow these maths-specific instructions rather than those in the assessor handbook.

For a genuine misreading (of numbers or symbols) which is such that the object and the difficulty of the question remain unaltered, mark according to the scheme but following through from the candidate’s data. A penalty is then applied; 1 mark is generally appropriate, though this may differ for some units. This is achieved by withholding one A mark in the question. Note that a miscopy of the candidate’s own working is not a misread but an accuracy error.

Anything in the mark scheme which is in square brackets […] is not required for the mark to be earned, but if present it must be correct.


7

Question Answer Marks Guidance AO Level

1 (i)

M1

A1

o.e. Also allow for 2×10k

÷ 22000 for any value of

k.

accept awrt 91 isw

90 gets M1A0 www

1

1

E

E

[2]

1 (ii)

So 18 Complete weeks

M1

M1

M1

A1

Finding interest paid by

any method

Finding interest for a

shorter timespan

Dividing by their weekly

amount

Cao. Must be rounded

up.

1

2

2

3

E

E

E

C

[4]


8


1 (iii) EITHER

If probability of winning once is , probability of winning twice is

M1

M1

A1

2

2

1

A

A

A

[3]

OR using given answer

Values close so 1 in 500,000 is correct

M1

M1

A1

[3]

OR Using integers

So 1 in 500,000 is correct

M1

M1

A1

Also allow for 253billion

÷ 500000

Use of rounding

Must use 1 in… or

probability notation

[3]


9


OR

So 1 in 500,000 is correct

M1

M1

A1

Use of “approximately”

Must use 1 in… or

probability notation

[3]

OR

Tree diagram with or 0.000002 on suitable branches but not multiplied

SC1

2 (i) People with a higher deprivation score tend to smoke more. E1 Must make a link with

deprivation. 3 E

[1]

2 (ii) 30 B1 Allow 28 to 32 3 E

[1]

2 (iii) IQR = 35 – 23

=12

M1

A1

Award for UQ-LQ clear

Allow (32 to 36) – (21.5

to 24) if not labelled

Allow 10 – 14 www

2

1

E

E

[2]


10

2 (iv) Upper quartile is 35

35 + 1.5 ”12”

= 53

B1

M1

A1ft

Must be (34 to 36)

Allow their UQ and IQR

from (iii)

Ft their UQ and IQR

from (iii)

1

1

1

E

E

E

[3]

2 (v) Boxes tend to get wider (or whiskers tend to get wider) as deprivation scores increase. E1 Accept that the range or

IQR increases

Accept more spread out

or more variation

3 C

[1]


11

3 (i) 411 (miles) B1 3 E

[1]

3 (ii) Ford Focus B1 2 E

[1]

3 (iii)

G1

G1

Straight line starting

from 0.

Correct gradient

(for example, ends at

(450, 15) or through

(300, 10)).

Allow a small

division

SC1 At least four

correct points not

joined – ignore errors

2

3

E

E

[2]


12

3 (iv) Amount of fuel from graph or from distance ÷ 30

Rounded answer 14

Using cost £5 per gallon

14 × 5

= (£) 70

M1

A1

B1

M1

A1

Allow 13 or 14

Soi

FT their 14

Must be to 1 or 2

significant figures

2

2

2

2

3

E

E

E

E

E

[5]

4 (i) Two distinct comments about prices not changes for example:

Prices went down and then they went up (with no dates given)

Prices going down until February 2009

Until February 2009, the prices fall by different amounts in each month.

(Do not allow for prices fluctuate)

E1

E1

Allow “initially” and

“first 13 months” or

similar

Allow for last six

months – allow without

time reference if

implied by another

comment.

Ignore incorrect

comments

3

3

C

C

[2]

4 (ii)

M1

A1

Allow for fraction oe 2

2

C

C

[2]


13

4 (iii) EITHER

245000 × 0.983 × 0.982 oe

(£)236 499.97

≈(£)236500

M1

M1

A1

A1

Attempt at one factor

Both correct factors or

× 0.965306 seen

May be implied by

correct rounded answer

Ft their answer dep on

at least 1 method mark.

2

1

1

1

E

E

C

E

[4]

OR

245000× 0.983 oe

240835 × 0.982 oe

(£)236 499.97

≈(£)236500

M1

M1

A1

A1

Allow for 2 stage

calculation

Ft their answer dep on

at least 1 method mark.

Allow for changes in

reverse order

(240590 seen)

[4]


14

4 (iv) Two distinct comments for example:

The area where the house is might not have had the same growth as the national trend.

She might have paid too much for the house initially.

Hanna might have improved her home.

E1

E1

Any two distinct

sensible answers

Ignore incorrect

comments

3

3

C

A

[2]

5 (i) Biased sample

College students aren’t representative of all potential customers / tend to buy cheaper

sandwiches / don’t tend to use sandwich shops

E1 3 C

[1]

5 (ii) ‘Over £50’ B1 3 E

For example:

They didn’t take the survey seriously.

They misunderstood

They thought it was 50p

E1 3 C

[2]


15

5 (iii)

= 15 + 22.50 + 87.50 + 60 + 37.50

= 222.5 OR 223

Total frequency = 100

= (£) 2.225 OR 2.23 OR 223p

M1

A1

B1

B1

Attempt at midpoint ×

frequency including at

least two correct

midpoints or resulting

products.

Midpoints can be either

1.5 or 1.495 etc.

can be implied

SC1 for using

maximum (289.05 or

290) or minimum (155)

in each class

award if seen

Also allow £2.22 oe

FT their 222.5

1

1

1

1

C

C

C

C

[4]

5 (iv) Data was grouped / midpoints used instead of true values

He used a sample (which will not always give the true population value).

He included £5 - £10 which might also not be sensible values

He excluded the outliers

E1

E1

Allow sensible

comment. Must be a

different point Ignore

incorrect comments

3

3

C

A

[2]


16

5 (v) 700 560 140

625 500 437.5

550 440 660

475 380 807.5

400 320 880

325 260 877.5

250 200 800

175 140 647.5

100 80 420

M1

M1

M1

A1

A1

At least one correct

bold number in each

column

1st column entirely

correct.

2nd

and 3rd

column

entirely correct.

.

2

2

2

2

2

E

E

C

E

C

[5]

5 (vi) If C2 attempted

= 0.8 * B2 oe

B1

0.8 * B2 seen isw 1 E

B1 Fully correct – correct

brackets and use of $B

acceptable (B$2 not

acceptable)

1 E

[2]

If “number sold per day” attempted, providing a formula for B2

= 850 – 150 * A2

Or = 700 – 150 * (A2 – 1)

SC1 for (850 or 700)

minus function of A2

SC2 for = (850 or 700)

minus function of A2

[2]

If the candidate provides a formula that completes column B for the number sold per day by

providing formula for cell B3

= B2 - 75

B1

B1

B2- 75 oe

= B2- 75 oe

[2]


17

If candidate indicates that C2 is not the number sold oe

Allow two marks for indicating that C2 is not the number sold per day.

[2] Ignore any formula

given

If response contains confusion with cell references and number sold per day

Refer unexpected responses to the Principal Examiner

[2]

5 (vii) = A2 * B2 – C2 B1

B1

A2 * B2

Fully correct 2

1

E

E

[2]

5 (viii) £3 A1 FT from their table 3 C

[1]

5 (ix) Monthly profit: (880 x 20) – 8000 = (£)9600

OR annual profit £115200

OR 134 sandwiches at £3 needed to break even

Yes, as he would make a profit.

B1

E1

Allow for 9600 seen

FT their 880 from table

FT their profit. Must be

based on a relevant

calculation

2

3

C

C

[2]


18

6 (i) 2 × 109 × 1000 ml or cm

3 ( = 2 × 10

12)

Using 1,000,000 cm3 = 1m

3

2,000,000,000 × 1000 ÷ 1,000,000

2 × 106 (m

3)

B1

M1

A1

Soi

FT their 2 × 1012

Cao.

Must be in standard

form. www

1

2

1

C

C

A

[3]

6 (ii) EITHER

Area of lake = π × 20002 ( = 1.2566… × 10

11 m

2)

V = π ×20002 × h

= 0.159 m or 15.9 cm

= 16cm (to nearest cm)

B1

M1

M1

A1

Any units

Consistent units

Must rearrange.

Their 2 × 106 must be

used

Must claim given

answer with correct

units

AG

2

2

2

3

A

A

A

A

[4]


19

OR using given answer

h = 15.5 cm, V = 1.945 × 106 – too small

h = 16.5 cm, V = 2.073 × 106 – too big

So h = 16 cm to the nearest cm

M1

A1

M1

A1

Substituting one value

15.5 ≤ h ≤ 16.5

One correct value for V

(h = 16 cm, V = 2.0106

× 106)

Using another value

that establishes range

for h that rounds to 16.

Correct conclusion

including a phrase “to

the nearest cm” or

“which is about 16cm”

oe

[4]

6 (iii) 0.96 × 0.90 × 0.92 M1 Alternative:

96 less 10% = 86.4,

86.4 less 8% = 79.5

Allow if seen as part of

a volume calculation

2 C

= 0.795 A1 or 79.5 2 C

So 20.5% reduction. A1 Allow 20 or 21without

“% reduction” 2 A

[3]

6 (iv) A B1 3 C

[1]


20

6 (v) 100 × 0.93n = 50 or 0.93

n = 0.5 M1 Can be implied. 2 A

Not all values need to be shown

n 100 × 0.93n (1dp)

1 93

2 86.5

3 80.4

4 74.8

5 69.6

6 64.7

7 60.2

8 56.0

9 52.0

10 48.4

M1 Value for 100 × 0.93n

or 0.93n for any n > 1

Also allow for attempt

to solve their indicial

equation using logs or

BC

2 A

10 years A1 Needs evidence either

by solving the equation

to 1dp and rounding, or

by establishing that n =

9 is not enough and

that n = 10 is needed

3 A

[3]

6 (vi) e.g. Measured at the same place / same time of year/day / used same equipment E1 3 E

[1]

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Published: 16 August 2017 Version 1.0 1

Unit level raw mark and UMS grade boundaries June 2017 series

For more information about results and grade calculations, see www.ocr.org.uk/ocr-for/learners-and-parents/getting-your-results

AS GCE / Advanced GCE / AS GCE Double Award / Advanced GCE Double Award

GCE Mathematics (MEI) Max Mark a b c d e u

4751 01 C1 – MEI Introduction to advanced mathematics (AS) Raw 72 63 58 53 49 45 0 UMS 100 80 70 60 50 40 0

4752 01 C2 – MEI Concepts for advanced mathematics (AS) Raw 72 55 49 44 39 34 0 UMS 100 80 70 60 50 40 0

4753 01 (C3) MEI Methods for Advanced Mathematics withCoursework: Written Paper Raw 72 54 49 45 41 36 0

4753 02 (C3) MEI Methods for Advanced Mathematics withCoursework: Coursework Raw 18 15 13 11 9 8 0

4753 82 (C3) MEI Methods for Advanced Mathematics withCoursework: Carried Forward Coursework Mark Raw 18 15 13 11 9 8 0

UMS 100 80 70 60 50 40 0 4754 01 C4 – MEI Applications of advanced mathematics (A2) Raw 90 67 61 55 49 43 0

UMS 100 80 70 60 50 40 0

4755 01 FP1 – MEI Further concepts for advanced mathematics(AS) Raw 72 57 52 47 42 38 0

UMS 100 80 70 60 50 40 0

4756 01 FP2 – MEI Further methods for advanced mathematics(A2) Raw 72 65 58 52 46 40 0

UMS 100 80 70 60 50 40 0

4757 01 FP3 – MEI Further applications of advanced mathematics(A2) Raw 72 64 56 48 41 34 0

UMS 100 80 70 60 50 40 0

4758 01 (DE) MEI Differential Equations with Coursework: WrittenPaper Raw 72 63 56 50 44 37 0

4758 02 (DE) MEI Differential Equations with Coursework:Coursework Raw 18 15 13 11 9 8 0

4758 82 (DE) MEI Differential Equations with Coursework: CarriedForward Coursework Mark Raw 18 15 13 11 9 8 0

UMS 100 80 70 60 50 40 0 4761 01 M1 – MEI Mechanics 1 (AS) Raw 72 57 49 41 34 27 0

UMS 100 80 70 60 50 40 0 4762 01 M2 – MEI Mechanics 2 (A2) Raw 72 56 48 41 34 27 0



UMS 100 80 70 60 50 40 0 4766 01 S1 – MEI Statistics 1 (AS) Raw 72 61 55 49 43 37 0

UMS 100 80 70 60 50 40 0 4767 01 S2 – MEI Statistics 2 (A2) Raw 72 56 50 45 40 35 0



UMS 100 80 70 60 50 40 0 4771 01 D1 – MEI Decision mathematics 1 (AS) Raw 72 52 46 41 36 31 0

UMS 100 80 70 60 50 40 0 4772 01 D2 – MEI Decision mathematics 2 (A2) Raw 72 53 48 43 39 35 0

UMS 100 80 70 60 50 40 0 4773 01 DC – MEI Decision mathematics computation (A2) Raw 72 46 40 34 29 24 0

UMS 100 80 70 60 50 40 0

4776 01 (NM) MEI Numerical Methods with Coursework: WrittenPaper Raw 72 58 53 48 43 37 0

4776 02 (NM) MEI Numerical Methods with Coursework:Coursework Raw 18 14 12 10 8 7 0

4776 82 (NM) MEI Numerical Methods with Coursework: CarriedForward Coursework Mark Raw 18 14 12 10 8 7 0

UMS 100 80 70 60 50 40 0 4777 01 NC – MEI Numerical computation (A2) Raw 72 55 48 41 34 27 0

http://www.ocr.org.uk/ocr-for/learners-and-parents/getting-your-results


UMS 100 80 70 60 50 40 0 4798 01 FPT - Further pure mathematics with technology (A2) Raw 72 57 49 41 33 26 0

UMS 100 80 70 60 50 40 0

GCE Statistics (MEI) Max Mark a b c d e u G241 01 Statistics 1 MEI (Z1) Raw 72 61 55 49 43 37 0

UMS 100 80 70 60 50 40 0 G242 01 Statistics 2 MEI (Z2) Raw 72 55 48 41 34 27 0

UMS 100 80 70 60 50 40 0 G243 01 Statistics 3 MEI (Z3) Raw 72 56 48 41 34 27 0

UMS 100 80 70 60 50 40 0

GCE Quantitative Methods (MEI) Max Mark a b c d e u G244 01 Introduction to Quantitative Methods MEI Raw 72 58 50 43 36 28 0 G244 02 Introduction to Quantitative Methods MEI Raw 18 14 12 10 8 7 0

UMS 100 80 70 60 50 40 0 G245 01 Statistics 1 MEI Raw 72 61 55 49 43 37 0

UMS 100 80 70 60 50 40 0 G246 01 Decision 1 MEI Raw 72 52 46 41 36 31 0

UMS 100 80 70 60 50 40 0


Level 3 Certificate and FSMQ raw mark grade boundaries June 2017 series

Level 3 Certificate Mathematics for EngineeringMax Mark a* a b c d e u

H860 01 Mathematics for EngineeringH860 02 Mathematics for Engineering

Level 3 Certificate Mathematical Techniques and Applications for EngineersMax Mark a* a b c d e u

H865 01 Component 1 Raw 60 48 42 36 30 24 18 0

Level 3 Certificate Mathematics - Quantitative Reasoning (MEI) (GQ Reform)Max Mark a b c d e u

H866 01 Introduction to quantitative reasoning Raw 72 54 47 40 34 28 0H866 02 Critical maths Raw 60* 48 42 36 30 24 0

*Component 02 is weighted to give marks out of 72 Overall 144 112 97 83 70 57 0

Level 3 Certificate Mathematics - Quantitive Problem Solving (MEI) (GQ Reform)Max Mark a b c d e u

H867 01 Introduction to quantitative reasoning Raw 72 54 47 40 34 28 0H867 02 Statistical problem solving Raw 60* 41 36 31 27 23 0

*Component 02 is weighted to give marks out of 72 Overall 144 103 90 77 66 56 0

Advanced Free Standing Mathematics Qualification (FSMQ)Max Mark a b c d e u

6993 01 Additional Mathematics Raw 100 72 63 55 47 39 0

Intermediate Free Standing Mathematics Qualification (FSMQ)Max Mark a b c d e u

6989 01 Foundations of Advanced Mathematics (MEI) Raw 40 35 30 25 20 16 0

This unit has no entries in June 2017

For more information about results and grade calculations, see www.ocr.org.uk/ocr-for/learners-and-parents/getting-your-results

Documents

Oxford Cambridge and RSA Level 3 Certificate Quantitative ...mei.org.uk/files/papers/H867_01_IQR_2017_June.pdf · Oxford Cambridge and RSA Level 3 Certificate Quantitative Problem