Examiners Notes

8/6/2019 Examiners Notes

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Examiner Notes

These notes are to guide and help teachers as they prepare students for the examinations.

Please note: The views expressed in this section are the author’s own and do not constitute any policy

statements on behalf of the Cambridge International Examination Board. The observations about the

rubric on question papers were correct at the time of going to press but the reader should check exact

conditions for themselves when preparing for an examination. Mark schemes are published by the

examination board and are available on their website.

Accuracy

This is one of the most common areas where students lose marks. Typical problems are:

1 Premature approximation

2 Failure to give answers to the required accuracy

3 Failure to appreciate the needs of special areas of the syllabus

4 Rounding answers to the wrong degree of accuracy

5 Truncating answers

1 Premature approximation

This problem can best be illustrated with an example.

Candidate begins tan 8° =h

1700and the following are typical responses.

Solution 1 Solution 2 Solution 3

h = 1700 × 0.14 h = 1700 × 0.141 h = 1700 × 0.1405

h = 238 h = 239.7 h = 238.85

If they now give their answers to 3 s.f. as required by the instructions on the front cover of the question

paper they will get

h = 238 m h = 240 m (3 s.f.) h = 239 m (3 s.f.)

The correct solution is, of course, h = 1700 tan 8°

= 238.919419…

= 239 m (3 s.f.)




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Students should be encouraged to work either to 4 s.f. or to retain all the figures on their calculator

until the final answer. They need to be especially careful about using this answer if it is needed in a

later part of the question, as the same problem will arise.

2 Required degree of accuracy

The general rubric requires candidates to give all calculated values to 3 significant figures unless the

answer is exact or an angle is being calculated, in which case the rubric specifies 1 d.p.

Examiners often test the ability to round numbers within a question rather than set a specific question

on rounding. If a question asks for an answer to, for example,

• the nearest degree

• 2 decimal places

• nearest 100• 4 significant figures

• some other accuracy

then a mark will be awarded for carrying out that instruction correctly.

Candidates in the examination sometimes ignore these extra instructions.

3 Special areas of the syllabus

(a) Bounds or limits

A length, d cm, is measured as 4.5 cm correct to 1 decimal place.

This means that the measurements are 4.4 4.5 4.6 which gives bounds or

limits of 4.45 4.55

Students should not be working with recurring nines or numbers ending in 4. The questions are

usually written with an answer space with the inequalities written in.

Answer …4.45…..< d < ……4.55……

This takes care of the need to have anything other than a five on the end of each number.

(b) In the extended level, where these bounds are used in problems, it is very important that no

rounding takes place at all.

The side of a square, d cm, is measured as 4.5 cm correct to 1 decimal place. Find the upper and

lower bounds for the area, A cm2, of the square.

We have 4.45 < d < 4.55 and so

4.452 < A < 4.552

= 19.8025 < A < 20.7025

This gives a lower bound of 19.8025 and an upper bound of 20.7025.




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(c) Calculations which test the use of a calculator will often specify that the full calculator display

should be written down. It will not be appropriate to round these answers at all.

(d) Probability

If a question is set in fractions it is wise to work in fractions. If the question is set in decimals thenit is wise to work in decimals. Candidates who change from one to the other often lose accuracy.

The fraction 1

3is often changed to 0.33 or, even worse, to 0.3 and then it is impossible to get to

the correct answer.

(e) Equations

Similar problems exist in this topic as arise in probability. Candidates often lose accuracy marks

by unnecessary conversions.

(f) Drawings and graphs

The normal allowance for drawing angles to scale is ± 1°. The lengths of lines should normally be

accurate to ± 1 mm. For curved graphs the examiners will be working to a tolerance of 1 smallsquare.

(g) Estimating the value of a calculation

This normally requires candidates to work to 1 significant figure as in the example below.

Estimate the value of 19.3 ! 2.789

27.129

Estimate =20! 3

30= 2

4 Rounding off to the wrong degree of accuracy

It is not unknown for candidates to write answers to one decimal place, whatever degree of accuracy

is specified in the question or in the rubric. Candidates should spend any spare time at the end of the

examination checking the accuracy of their answers. This could gain them several marks.

5 Truncating answers

In general it will not be acceptable for a candidate to truncate answers. Candidates are expected to

round answers, following the usual rounding procedure. If a calculated value is 0.146857, it is unlikely

that 0.14 or 0.146 will be acceptable answers.

The one exception to this is probably section 3(c) above.

Marks for showing method

A failure to show working is a critical factor in the loss of marks by some candidates. The example

below illustrates this.




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A TV cost $1600 in Hong Kong and £170 in London when the exchange rate was £1 = $9.30. In which

city did the TV cost less and by how much? [2]

Correct solution

170 × 9.30 = $1581

1600 – 1581 = $19

The TV costs less in London by $19

Incorrect solutions

A candidate shows no working and writes $29. The answer is wrong and there is no working so no

marks.

A candidate writes 170 × 9.30 = $1581 and then gives an answer of $29. The answer is wrong but the

correct working can be seen. This could score one mark.

A candidate writes 170 × 9.30 = $1581 and then $1600 − $1581 = $19 and finally says in the answer space that the answer is $18. This would score two marks as the correct answer has been seen and

the final answer is a transcription error into the answer space.

Graph work

The examiner will give marks as detailed below.

• Correct scales have been used.

• The scales have been applied to the axes with no numbers missing. For example, the scale does

not go 10, 20, 30, 50, 60… if every 10 units has been requested.

• The points are correctly plotted. This can be worth as many as 3 marks if all the points are plotted

correctly. Accuracy of plotting should be to half a small square of the correct position.

• The points are joined with a smooth curve which passes through the plotted points (or the correct

position if a point is missing). The curve is best drawn away from one’s body as the arm functions

more smoothly in that direction.

• Values are correctly read from the graph. The candidate needs to make sure that they have

correctly understood the scale of the graph and know what each mark on the scale represents.

Follow through

In certain circumstances part of a question may depend on a previous answer. If that previous answer

is wrong it is still possible for marks to be scored, provided that the correct method is used and the

answer is calculated to the correct degree of accuracy.




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(a) Calculate the area of cross-section of the triangular prism. [2]

(b) Calculate the volume of the prism. [1]

The candidate writes (a) area = 12 × 5 = 60 cm2

(b) volume = 60 × 20 = 1200 cm3

Part (a) scores no marks as the 1

2is missing from the formula for the area and so the method is

incorrect.Part (b) scores the mark because the correct method is shown and the answer correctly follows

through from that working. It is, therefore, very important that the method is shown.

Presentation

Examiners may be marking a large number of scripts, all in different handwriting and styles. Some

figures can be difficult to distinguish when written in the haste of an examination. It is in the interest of

the student to make sure that their work is legible and clearly presented.

Generally, an examiner will only mark one answer and the work leading to that answer. Candidatesshould avoid giving an examiner two answers to choose from.

When solving equations, for example, it is important that the working is clearly set out and every step

shown, so that an examiner can see where to award marks. It is unwise to leave out working because

if an error is made, the method could still score marks (see above). Sufficient space is allowed on the

question paper for candidate’s working. See the following example.

Solve3 x + 2

5= x ! 6

Now compare the following two solutions:

3 x + 2 = 5( x – 6) 3 x + 2= 5 x – 6

3 x + 2 = 5 x – 6 2 x = 4

3 x = 5 x – 8 x = 2

–2 x = –8

x = 4

Both solutions are incorrect but

the solution on the left can be

seen to have only one error and

might score 2 marks if 3 marks

are available. However, the

solution on the right has only one

correct move to the final line and

probably scores no marks, as all

the important method steps have

been omitted.

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Examiners Notes