GCSE Mathematics (2381)

Comparison of key skills specifications 2000/2002 with 2004 standardsX015461July 2004Issue 1

GCSE Mathematics (2381)

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November 2010

Publications Code UG025826

All the material in this publication is copyright
© Edexcel Ltd 2010

Edexcel GCSE Mathematics November 2010.

PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIERPAPER 5 (UNIT 1)

GENERAL COMMENTS

The great majority of candidates entered for this paper found it accessible.

The vast majority of candidates attempted nearly all the questions, as blank responses were only rarely seen for any of the questions.

It was good to see that most candidates had the correctmaterials required for the examination.

Questions 1, 2, 3 and 4(a) in Sections A and questions 1, 2(a), 3 in Section B were tackled with the most success.

Questions 4(b) and 5 in Section A were less successfully completed whilst in Section B questions 2(b), 4 and 5 caused the most problems.

REPORT ON INDIVIDUAL QUESTIONS

Question A1

A very well understood question with a success rate of over 95% in parts (a) and (b)(i) though 21% of candidates made an error in trying to find green as the answer to part (b)(ii).

Question A2

Although this type of question is quite common on our papers 12% of candidates could not cope with finding information from a table when three items had to be compared.

Question A3

A well understood question. However though 84% of candidates scored full marks 7% of candidates lost a mark usually for including two boys or two girls in the combination. A few of these candidates also did not write down an additional 5 entries in the list or wrote down up to two wrong combinations.

Question A4

In part (a), ‘pine’ was given as the correct answer by 98% of candidates. Of the 2% of candidates who scored no marks, ‘rowan’ was given as the most popular wrong answer. In part(b) only 48% of candidates scored full marks. Correct working was seldom seen with many candidates writing 720 as their answer doubling the 360º for the sum of the angles around a point.

Question A5

Answers to this question were very mixed.27% of candidates gained full marks for the correct answer of 34. Many candidates did find the midpoint of the group and multiplied the midpoint by the frequency and scored 2 marks. Those who then went on and divided by 30 then scored another mark. Many candidates started with mid-points (or sometimes upper or lower bounds) and attempted to multiply by frequencies (often with errors in mid-points or multiplication) and did gain credit for this approach. Candidates often divided their total by a variety of numbers, with 5 and 150 being the most common wrong ones.Some candidates often started with promise and completed the table correctly but then abandoned their attempts and chose wrong methods such asas a new method or selected the modal class or simply gave wrong answers such as 6. Unfortunately those candidates presenting a choice of solution scored no marks.

Question B1

A well understood question though some candidates were confused with the key when they had to complete the histogram in part (b) with only 86% of candidates gaining both marks.

Question B2

Full marks were gained by 73% of candidates for completing the table correctly with a further 10% gaining the 2 marks for completing 4 or 5 cells correctly. Part (b) was only correctly answered by 52% of candidates. Many candidates gave the answer as 53, the number of people who did not have coffee.

Question B3

A well understood question with 71% of candidates giving the correct answer. It is gratifying to see more candidates giving the answer as a fraction with fewer candidates giving answers such as 3 out of 8 or 3 in 8 etc. These candidates did gain 1 mark in this instance. One mark was also given for giving the correct numerator or denominator as long as the resulting fraction was less than 1 and this one mark was gained by 11% of candidates.

Question B4

This question was only understood by half the candidates with the median often not well understood and where it was, the key was not used in giving the answer as 4 instead of 34 was often seen. In part (b) 50% of candidates were able to correctly explain the lack of use of the stem.

Question B5

The correct relationship in part (a) caused some confusion in candidate’s minds as to marks going up and going down and some who gave the answer as positive without the correlation being present. The line of best fit was correctly drawn by the majority of candidates and the final reading from their graph was also well understood. The most common error seen was in the reading from the scale on the Science axis.

PRINCIPAL EXAMINER’S REPORT – HIGHERTIERPAPER 6 (UNIT 1)

GENERAL COMMENTS

The great majority of candidates entered for this paper found it accessible.

The vast majority of candidates attempted nearly all the questions, as blank responses were only seen in a few questions.

Questions 1, 2 and 3 in Section A and questions 2 and 3 in Section B were tackled with the most success.

The histogram on question 4 in Section A was better answered than in previous seasons. In Section B question 4 and 5 were least well answered.

The standard of literacy seen in ‘explain’ questions was very poor and it is hoped that teachers will work on this so that overall performance can be improved.

REPORT ON INDIVIDUAL QUESTIONS

Question A1

Question 1 was very well understood with 95% gaining full marks and a further 1% gaining one mark for showing correct working leading to an incorrect answer.

Question A2

Part (a) of this question was well understood and correctly answered by 78% of candidates whilst part (b) was less well understood with 67% of candidates gaining the mark.The mistakes that were made usually came from incorrect interpretation of the average asked for or for writing the frequency rather than the group. In part (c) answers were very mixed.About a thirdof candidates gained full marks for the correct answer of 34. Many candidates did find the midpoint of the group and multiplied the midpoint by the frequency and scored 2 marks.Those who then went on and divided by 30 then scored another mark.Many candidates started with mid-points (or sometimes upper or lower bounds) and attempted to multiply by frequencies (often with errors in mid-points or multiplication) and did gain credit for this approach.Candidates often divided their total by a variety of numbers, with 5 and 150 being the most common wrong ones.Some candidates often started with promise and completed the table correctly but then abandoned their attempts and chose wrong methods such as as a new method or selected the modal class or simply gave wrong answers such as 6. Unfortunately those candidates presenting a choice of solution scored no marks.

Question A3

This question was well answered with only 14% of candidates scoring no marks.In part (a) candidates often tried to calculate the median rather than the interquartile range whilst in part(b) they gave the number of members who weighed less than 100kg was often given.

Question A4

Candidates performance in drawing histograms is improving over time with 43% of candidates gaining full marks.When candidates made mistakes it was usually with the frequency density as this was often calculated the wrong way round but the most common mistake was to draw a bar chart.Candidates would also help themselves if they used an HB pencil or softer when drawing graphs.

Question B1

Some candidates had not realised that the key elements to this question were to have a time scale in the demand to the question and that the response boxes should contain non-overlapping but continuous sums of money that include zero and a more than box.Unfortunately only 43% of candidates gained all four marks in this type of question that is a regular visitor to these papers.

Question B2

The correct relationship in part (a) caused some confusion in candidate’s minds as to marks going up and going down and some who gave the answer as positive without the correlation being present.The line of best fit was correctly drawn by the majority of candidates and the final reading from their graph was also well understood.The most common error seen was in the reading from the scale on the Science axis.Interestingly only 55% of candidates gained all 3 marks in this routine question.

Question B3

This question was very well understood with 45% of candidates gaining both marks. 21% of candidates gained one mark for showing that they understood how to work out a 4-week moving average and only 34% of candidates gained no marks.

Question B4

Candidates often read off the values from the box plots but did not compare them and so forfeited the marks.Many candidates lost marks because they talked about the number of girls and boys rather than using some statistical measures to compare the distributions, e.g. using the word average without the word median, or spread instead of range. 28% of candidates gained both marks because they compared an individual measure as well as a measure of spread. A further 37% gained one mark for giving one of these statistical pieces of information.The remaining 35% of candidates did not gain any marks.

Question B5

Only 16% of candidates gained all 4 marks in this question.Many candidates misread the question and worked out the probability of taking exactly one jar of honey rather than at least one jar of honey but a large number of candidates treated the question as one with replacement rather than non replacement and so could only gain a maximum of two marks.

21% of candidates gained one markeither for obtaining or or seen as non- replacement or for or or following replacement.

16% of candidates gained two marks for obtaining or or or for following replacement.

Three marks were obtained by 4% of candidates when was seen. The alternative method of 1 minus the probability of two jars of jam was rarely seen.

PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIERPAPER 9 (UNIT 2, STAGE 2)

GENERAL COMMENTS

This paper is constructed on the premise that students have access to a calculator they are familiar with. It was clear that some candidates did not or were not. It is of some concern that a significant number of candidates cannot write money properly.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

Students who had brought a calculator with them generally did well enough and got at least as far as 35.5. Many went on to write the correct £35.50 or the allowable £35.50p. Many had no access to a calculator and could not multiply a decimal by 10 (there were very few 3.550) but had to resort to laboriously writing out 10 lots of 3.55 and adding up. These attempts were often not successful. Some candidates got themselves confused between 35.50 and 35.05.

Question 2

On part (a), most candidates could draw a fairly decent radius although some were clearly confused between a diameter and a radius. It was pleasing to see that many candidates could recognise a semi-circle when they saw one. The sensible ‘half-circle’ is not, however, a mathematical term, although ‘sector’ was acceptable.

Question 3

On part (a) most candidates were able to recognise and write down a square number and 9 was more popular than 16. A minority wrote down 3 possibly thinking of 3 squared = 9. Part(b) proved to be more of a challenge with 3 again being a popular, but incorrect answer.

Question 4

This was a standard money calculation question and it was surprising to see so many wrong answers. Again, candidates hurt their chances by not having a calculator, so they added up the correct five items, but got the wrong answer. If they showed a subtraction from 20 of their wrong answer, then they could at least have picked up a method mark. Many did not. The other errors were mainly of omission – some candidates found the total price of 1 medal and 1 trophy, whilst others found the correct total but then failed to subtract this from the £20.

Question 5

The candidates who wrote down ‘hours’ for part (a) certainly had a point, but the acceptable answer was ‘miles’ – which most candidates put down. There was some confusion between which was which out of ‘miles’ and ‘kilometres’

Question 6

There were not many correct answers to part (a). Common errors weren = 6, 1n, n = 6 and 6n=n. The latter cannot be considered correct because it is not an algebraic expression. Part(b) was even more poorly answered although there was a follow through from part (a) if they had an expression which was 3 less than the expression in part (a).

Question 7

This proved to be pleasingly answered by those who had a calculator. Sensibly many worked out the numerator and denominator separately and wrote them down before finishing the calculation. They gained 1 mark. Interestingly, a minority of candidates carried out the wrong operation with their two answers – addition and subtraction were both seen. There were many cases of plug the numbers and signs into the calculator and write down what came about. This led to an answer of60.50… which was frequently seen. The question did ask for all figures on the calculator display to be written down.Some candidates ignored this showing working of which scored no marks.

In part (b) the idea of significant figures proved an elusive one.

Question 8

This proved to be beyond most candidates at this tier. There was little evidence that many understood the concept of multiplying the terms inside by the term outside. If they did then often 2x was substituted for x2.

Question 9

At least one or two values in the grid were calculated correctly in many cases. The odd one out was usually the value of y when x =−1. Many candidates went on to plot their values correctly and join them up. Some pleasingly spotted that their point atx = 1 was ‘odd’ and ignored it by drawing the correct straight line. They got both the marks. At the other extreme were the candidates who completed the table correctly, plotted the points correctly, but did not join them up. This has been a recurrent theme for several years. Just as mysterious are those candidates who calculate the values in the table correctly but cannot link the table with the grid and so leave the grid blank.

Question 10

Many candidates did not know how to work out the volume of a cuboid so it is hardly surprising that they performed poorly on part (a) of this question. Some sensibly did a sort of trial and improvement method by using the 5 and the 4 to get the 60. They got the marks if they wrote down 3 on the answer line. Many did 60 – 20. Part (b) was very poorly answered with few candidates knowing the relationship between the three variables.

PRINCIPAL EXAMINER’S REPORT – HIGHER TIERPAPER 10 (UNIT2, STAGE2)

GENERAL COMMENTS

In general there were pleasing aspects to the performance. Standardform was generally well understood, as was expansion of brackets.Simplification of algebraic fractions has also improved.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

Most candidates at this tier had no difficulty in getting the correctanswer. They either wrote down the answers to the numerator anddenominator separately and then finished the calculation off or put inbrackets at the correct place or had a calculator into which they couldtype the whole given expression and then work it out in one operation.Of course, there were still candidates who ended up with 60.50… fromjust typing all the expression without regard for operator precedence.

Candidates were less successful with part (b) where they had to writetheir answer correct to 1 significant figure. Many wrote down 3 figures(force of habit?) or 1 decimal place.

Question 2

This question was generally efficiently done – as it needs to be for students to have achance of a decent showing on this paper.

Question 3

Although part (a) was well done, there were still a surprising number ofcandidates who either did not know the expression ‘height × width ×length’ or could not apply it when one of the measurements was missingand the volume given. There were many cases of 60 – 20 and use of halfthe cross-sectional area. Part (b) was also well answered but not withthe success of part (a). Candidates made more sophisticated errors thanthose seen on the corresponding question on the Foundation tier. Forexample, some candidates thought that there had to a cube or cube rootsomewhere.