Principal Examiners’ Report

November 2010

GCSE

GCSE Mathematics (2381)

1

Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH

Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. Through a network of UK and overseas offices, Edexcel’s centres receive the support they need to help them deliver their education and training programmes to learners. For further information, please call our GCE line on 0844 576 0025, our GCSE team on 0844 576 0027, or visit our website at www.edexcel.com.

If you have any subject specific questions about the content of this Examiners’ Report that require the help of a subject specialist, you may find our Ask The Expert email service helpful.

Ask The Expert can be accessed online at the following link:

http://www.edexcel.com/Aboutus/contact-us/

November 2010Publications Code UG025826 All the material in this publication is copyright© Edexcel Ltd 2010Edexcel GCSE Mathematics November 2010.PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIER PAPER 5 (UNIT 1)

3

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 correct materials 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.

4

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 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 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.

5

PRINCIPAL EXAMINER’S REPORT – HIGHER TIER PAPER 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 third 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 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 100 kg was often given.

6

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 mark either for obtaining or or seen as non-

replacement or for or or following replacement.

7

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.

8

PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIER PAPER 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’

9

Question 6

There were not many correct answers to part (a). Common errors were n = 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 of 60.50… 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 at x = 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.

10

PRINCIPAL EXAMINER’S REPORT – HIGHER TIER PAPER 10 (UNIT 2, STAGE 2)

GENERAL COMMENTS

In general there were pleasing aspects to the performance. Standard form 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 correct answer. They either wrote down the answers to the numerator and denominator separately and then finished the calculation off or put in brackets at the correct place or had a calculator into which they could type the whole given expression and then work it out in one operation. Of course, there were still candidates who ended up with 60.50… from just typing all the expression without regard for operator precedence.

Candidates were less successful with part (b) where they had to write their 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 a chance of a decent showing on this paper.

Question 3

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

Question 4

The vast majority of candidates could expand at least one bracket correctly and then go on to collect the terms together. Some, however, could not do this accurately and ended up with the term 5x – 1. A few were confused with what to do with the brackets, ignored the + sign in between them and tried to multiply them out as (3x + 3)(2x − 2).

Part (b) was generally well done as candidates have had plenty of exposure to this type of question. Candidates who got 1 of the 2 marks usually showed x2 + 5x + 6x + 11 at some stage of their working, or got the correct answer of x2 + 5x + 6x + 30, but then made mistakes in the simplification (for example ending up with 11x2 + 30).

Some students gave an answer of x2 + 11 + 11 (or 30) without noticing the obvious error.

11

Question 5

A major stumbling block on this question was that it required candidates to know that distance = speed × time. Students who knew this and wrote down 8 × 104 × 3 × 108 or an equivalent in figures were rewarded. It should then have been a case of picking up the calculator and working it out in standard form. Of course, some students misread their display and wrote down 2.413, although this was comparatively rare. It was pleasing to see students who worked it out mentally as 24 × 1012 and go on to write the correct answer.

Question 6

This question proved to be challenging for many candidates. There were several major deficiencies in solutions. The first was that many could not use mathematical language correctly; for example, they could not use the 3 letter notation to describe an angle. Consequently, candidates who stated ‘the angle at B in equal to the angle at A’ were unlikely to gain any credit, because there were several angles at B. The second was that although must candidates knew there should be a right angle somewhere, often it was marked as the angle CAB or even the angleCBA. The third was that some candidates thought that they had to find a value of x, with 45 and 30 being the favourites. Many candidates could not spot that the triangle was isosceles as two of the sides were radii of the circle. Lastly, there was a real looseness in the vocabulary – a comment needed to be made that the angle between the tangent and the radius is a right angle. All too often comments were written such as ‘the tangent hits the circle at a right angle’.

Question 7

Another proof question, although a standard one. For full marks, candidates had to show correct notation in their proof that the decimals were recurring and that they got to the

fraction, , or equivalent, which they could then cancel down to get the given fraction.

Many candidates seemed to be unaware of this and casually wrote down a few (usually 4) figures. A few candidates could set of a neat proof but in many cases the algebra was confused. The good candidates wrote something along the lines of x = 0.57 followed by the

correct expression for 100x and then 99x = 57 followed by .

Question 8

Answers to this question were very pleasing with many candidates knowing that they had to factorise the numerator and denominator and then follow up by cancelling a common factor. Many got to the correct answer but then spoilt things by cancelling the x terms to end up with an answer of .

12

PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIER PAPER 11 (UNIT 3, NON-CALCULATOR PAPER)

GENERAL COMMENTS

There was no evidence to suggest that candidates had difficulty completing the paper in the given time.

Poor algebra continues to be an issue for many candidates. Candidates should be advised to show their algebraic process on both sides of the equation. Solution of algebraic equations by trial and improvement continues to be an all or nothing strategy for many candidates.

Candidates should be advised to show all the details in their decomposition methods, e.g. 5% = 25, so 1% = 25 ÷ 5

REPORT ON INDIVIDUAL QUESTIONS

Question 1

This question was done quite well. Most candidates were able to complete the missing entries in the bill correctly and use a correct notation for money. Common errors included £5.00 for the de-icer (instead of £6.00), £9.00 for the wiper blade (twice the cost instead of half the cost) and £21.98 for the total cost (an incorrect total cost from a correct entry of £6.00 for the de-icer). Relatively few candidates gave their answers in the form £22.98p or £4.5.

Question 2

Only the first part of this question was done well. Most candidates were able to write down the number of faces of prism, but many were unable to identify the number if edges and the number of vertices of the prism. A common incorrect answer here was to give the number of edges as 8 and the number of vertices as 12 (i.e. the wrong way round).

Question 3

Part (a) was done well. The vast majority of candidates were able to substitute d = 6 and work out the values of the formulas. A relatively small number of candidates gave their answers as 9d and 8d. In part (b), many candidates were able score a mark for substituting f = 2 and g = −1 into the formula, but many were unable to work this out correctly. Common incorrect answers here were 6 + −4 = −10, 6 + −4 = −2, 6 + −4 = 10, 3 × 2 + 4 – 1 = 9 (the wrong order of operations), 3 × 2 + 4×–1 = 9 and 32 + 4 – 1 = 35.

Question 4

Part (a) was done quite well. Most candidates were able to draw the two line of symmetry of the shape, but a significant number of candidates incorrectly drew an extra two ‘diagonals’. A significant number of candidates did not use a ruler to draw the lines of symmetry. In part (b), the many candidates were able to write down the order of rotational symmetry of the shape. A common incorrect answer here was 1.

13

Question 5

This question was done well. The vast majority of candidates were able to read the graph and change Hong Kong dollars to pounds and visa versa though some had difficulty interpreting the pounds scale in part (b). Common incorrect answers in part (b) were £6.7(0) or £6.8(0) and £7.05.

Question 6

This question was done well. The vast majority of candidates were able to write down the mathematical name of each shape. A common error for part (ii) was cuboid. The spelling of technical terms remains an issue for many candidates.

Question 7

This question was not done well. Many candidates were able to write down the value of as a decimal. Of those candidates who realized that a division was required, many did not know whether they should be dividing the 5 by the 3 or the 3 by the 5. Some candidates were able to score a mark for writing 3 ÷ 5 even if they then went on to divide the 5 by the 3. Of those candidates that incorrectly attempted to divide the 5 by the 3 common incorrect answers were 0.12 and 1.2 (presumably 1 remainder 2). A very common incorrect answer for those students who did not realize that a division was required was 0.35 (and in some cases 3.5).

Question 8

This question was generally done well. In part (a), most candidates were able to work out the sum and difference of the given integers. A common incorrect answer in part (ii) was 2. In part (b), most candidates were able to divide and multiply the given integers. A very common incorrect answer in part (ii) was −12.

Question 9

This question was not done well. Algebraic solutions were very rare. The vast majority of candidates simply wrote down the answer or attempted to use a trial and improvement approach.

Many candidates thought that the angle at the bottom left of the triangle was equal to 30 and consequently calculated the value of a as 75, usually by writing (180 – 30) = 150 ÷ 2 = 75 or similar.

Question 10

This question was done well. The vast majority of candidates were able to write down the solutions to the given equations. In part (a), some candidates incorrectly expressed p + p + p = 15 as p3 = 15, but then went on to correctly solve for p.

Question 11

This question was done quite well, but it was evident that many candidates had not brought a pair of compasses and/or a ruler to the examination. Some candidates were unable to draw a complete circle with a constant radius or without gaps. A common incorrect answer in part (b) was to draw a circle with a diameter of 5 cm.

14

Question 12

Many candidates were able to work out the number of tissues taken from the box, i.e. of 150, but a significant number of these did not then go on to find the number of tissues remaining in the box. A small number of candidates converted to 40% and then attempted

to work out 40% of 150, with varying success. Some wrote the fraction as 10 (presumably 5 × 2) to obtain a final answer of 150 – 10 = 140.

Question 13

This question was not done well. Only the best candidates were able to calculate the simple interest for 2 years. By far the most popular approach was to find 10%, 5%, 1% and then 4% by a process of decomposition. Candidates should be advised to show all the details in their decomposition methods, e.g. 5% = 25, so 1% = 25 ÷ 5. Common mistakes in this question were to calculate the interest for only 1 year, to give the final answer as the interest + the original amount (£540) and to calculate the compound interest for the 2 years. A significant number of candidates having worked out that 5% = 25 then went on to state that 4% = 24.

Question 14

This question was done quite well. Many candidates were able to multiply the two numbers and get the correct answer. Tabular methods were very common. Common errors here were 50 × 20 = 100, 400 × 3 = 120 and 400 × 20 = 6000. Some candidates having obtained all the relevant entries in a table did not then go on to add them all together- typically omitting to add one of the six elements.

Question 15

This question was not done well. Most candidates could find the number of male workers at the factory 300, but only the better candidates were then able to find 15% of this. By far the most popular method here was to decompose 15% into 10% + 5%. A common incorrect answer using this approach was 75 (from 300 ÷ 2 = 150, 150 ÷ 2 = 75).

Question 16

In part (a), few candidates were able to show the inequality using the correct notation. Most simply copied the notation used in the diagram in part (b). In part (b), few candidates were able to write down the inequality shown in the diagram, but many were able to score a mark for −2 < ... By far the most common incorrect answer here was −2 < x < 3, which simply copies the notation used in the inequality in part (a).

In part (c), few candidates were able to give a completely correct answer for the range of values of t, although many were able to find the critical value 4. Most candidates ignored the inequality sign and then tried to solve the equation 3t + 5 = 17, a significant number by trial and improvement. Many candidates continue to use non algebraic methods in their solutions. A common approach here was 17 – 5 = 12, 12 ÷ 3 = 4 (i.e. the correct processes but without any correct algebraic statements). Some candidates, having determined that t > 4, then went on to write 4 on the answer line, thereby losing the accuracy mark. Candidates should be encouraged to use algebra in their solution of equations and inequalities.

Question 17

15

This question was done well. The vast majority of the candidates were able to identify the two nets for the square-based pyramid.

Question 18

This question was done quite well. The majority of candidates were able to write down the required ratio 6 : 18, but a significant number of these were unable to simplify this fully. Common partially simplified answers here were 3 : 9 and 2 : 6. Other common errors include writing the ratio the wrong way round (e.g. 3 : 1) and using 24 to form the ratio (e.g. 6 : 24).

Question 19

This question was not done well. Only the best candidates were able to subtract the two fractions correctly to obtain the required answer. Most candidates were able to score the mark for subtracting the whole number (i.e. for 2), but few were able to express and as fractions with a common denominator. A very common incorrect method here was to subtract both the numerators and both the denominators (to get ). Some candidates were able to score a mark for a correct attempt to change both mixed numbers to top-heavy fractions, but again most were then unable to express these as fractions with a common denominator. A common incorrect answer here was or .

Question 20

Many candidates were able to score at least one mark for this question, usually by drawing a line within the guidelines. In general, most candidates showed their construction lines, whether they were drawn with compasses or otherwise, and many drew a line to bisect both sides of the line AB. A common incorrect answer here was to draw an equilateral triangle or to draw only one pair of intersecting arcs with the mid-point indicated mark on the line AB.

Question 21

Only the best candidates were able to do well in this question. In part (a), a large number of candidates attempted to describe the transformation as a combination of transformations, usually by a rotation followed by a translation. Of those candidates who attempted to describe the transformation as a single rotation, few were able to score all 3 marks. Common errors here include using ‘turn’ for rotation, and to omit to give the centre of the rotation. Candidates should be advised to use the correct notation when describing the coordinates of a point, i.e. to use brackets. In part (b), few candidates were able to translate triangle A by the given vector. Common incorrect answers here were translations downwards or to the left by 3 units, or to reflect the triangle in the x-axis.

16

PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIER PAPER 12 (UNIT 3, CALCULATOR PAPER)

GENERAL COMMENTS

This paper was of a similar demand to recent papers and no question proved to be inaccessible to the great majority of the candidature.

Even though this was a calculator paper, many candidates often worked out calculations ‘long hand’ and ignored their calculators.

The use of a protractor in measuring and drawing angles was poor. This is clearly an issue centres need to address.

The lack of clear working out is still an issue.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

This question was generally well answered. However there were a number of typical errors which prevented candidates gaining full credit. Many candidates correctly worked out the sum of just three items, usually omitting the second pencil, giving an answer of £4.88. Some candidates, not reading the question carefully enough simply found the sum of the 4 items and never attempted to find the change from £10.

Question 2

Most candidates demonstrated an understanding of the term ‘cuboid’ and were able to offer a reasonable sketch of a 3-D configuration. A few drew nets of a cuboid and some weaker candidates attempted to draw other 3-D shapes, cone, cylinder, etc.

Question 3

In part (a), measuring was usually accurate although a great many candidates ignored units and consequently threw a mark away. Most candidates measured the line in centimetres; millimetres was perfectly acceptable. The use of a protractor in parts (b) and (c) was not so good. In part (b) many candidates gave an answer of (132/3) and some were clearly very careless in the positioning of the centre (+) of their protractor, resulting in obscure angles.

In part (c) many candidates drew an angle of 105 at P, again reading the wrong scale on their protractor. Some drew an angle of 65, misreading the correct scale, and some drew their angle at different positions along the line. This was accepted provided that labelling made clear which angle was meant to be 75.

Question 4

Many candidates scored well on this question but often, incorrect units on the answer line prevented many from getting full marks. 0.93 or £0.93 was often the answer given even though there was a strict instruction to give the answer in pence. A significant number of candidates gained no marks by dividing 32 by 29.76.

17

Question 5

In part (a), the great majority of candidates gained full marks for an answer of £87.75 or £87.75p. Part (b) was also well answered although a few candidates mixed the information from the two parts and became confused. Some candidates attempted repeated subtraction (or equivalent) methods, usually unsuccessfully.

Question 6

Generally very well answered indeed. Only a few candidates misplaced the right vertex. This was sometimes a result of carelessness rather than a lack of understanding of the question. A tolerance of ¼ square was allowed.

Question 7

In part (a), the majority of candidates correctly identified as the proportion of girls.

Part (b) was also quite well answered but the most common incorrect answer was .

Question 8

Only a few candidates were not able to correctly identify the two congruent rectangles in part (a). F and G were common errors. In part (b), although well done, many candidates thought the scale factor was 3.

Question 9

In part (b), most candidates gained at least one mark by writing down a fraction equivalent to 20%, usually . Many were then unable to simplify the fraction fully. Some weaker

candidates offered answers of and sometimes . A few candidates converted 20% correctly into a decimal fraction; these gained just one mark.

Question 10

The correct answers of 5 and 3 were most common. Weaker candidates often gave an answer of 24 (30 – 6) in part (a) and 31 (14 + 17) or – 3 (14 – 17) in part (b).

Question 11

Candidates who understood the concept of scale, usually drew a correct 7cm by 4cm rectangle. The most common incorrect rectangles drawn had dimensions 5cm by 1cm (misunderstanding of the given scale) or 5cm by 2.6cm (the dimensions of the given rectangle, which was “NOT accurately drawn”). Some candidates used alternative scales and credit was given for an accurately drawn rectangle, enlarged by scale factor 0.5 or 2.

Question 12

Although it was encouraging to see a good number of candidates solving this multi-step problem, many simply used arithmetic operations on the numbers given without really thinking about the problem.

The most common incorrect approach was to add 5986 and 4176 and then either multiply or, in many cases, divide their answer by 13.9 or, in some cases,13.09. It was also common for candidates to multiply both of the meter readings by 13.9 (one mark so far) but then add the results instead of subtracting them. Many candidates using correct methods to solve the

18

problem often gave an answer in incorrect units or without units.. Many were happy to say that Kumal’s bill was for £25159 without question. A few tried to estimate the answers to their calculations using 14p, etc. This gained no credit.

Question 13

All parts of this question were generally answered correctly, however answers of 1 and –1 in part (b) and 12 in part (c) were common errors made.

Question 14

The vast majority of candidates found the unknown angle to be 65 in part (i). However, a great many fewer were able to offer an acceptable reason in part (ii), ‘because the angles must add up to 360’ was often quoted without any reference to the type of shape. Many just put the mathematical process they used in part (i) in words. A few weaker candidates used 380 as the sum of the angles in a quadrilateral.

Question 15

This was generally well answered with most candidates gaining at least 2 marks. The most common approach was to attempt to find the cost of a single yoghurt from each shop; 0.36p and 0.35p were common sights and provided that units were used consistently the units were largely ignored. This was usually followed by an answer of ‘Jim’s Store’ which gained full marks, however often no explanation was given and indeed, ‘Food Mart’ was also selected by many. Centres must be aware of this in preparing students for examinations in the “new” 2010 specifications when addressing the Quality of Written Communication. A significant number of candidates calculated 5 ÷ 1.80 (= 2.7...) and 3 ÷ 1.05 (= 2.8...) without understanding what their answers represented, thus giving ‘Food Mart’ as their answer. Some candidates found the cost of multiple amounts of yoghurts in each shop. This method often failed particularly when equal numbers were not compared.

Question 16

Very few candidates made any mistake in part (a), misreads of ‘arriving home’ leading to an answer of 3.15 p.m. were the most common errors made. In part (b), 35 (distance from her friend’s home) and 15 (distance from the ‘rest’ period) were the most common errors. In part (c), only weaker candidates failed to score.

Question 17

In part (a) the correct answer of 3.5 was often seen though formal algebra was little used. Weaker candidates often ignored the 3 and seemed to solve the equation 2x = 10 giving 5 as their answer. In part (b), c30 and e3 were common errors. Answers of 11c and 8e were not uncommon.

Question 18

This question was very poorly answered. Only a few candidates recognised the transformation as being a reflection and even fewer were able to adequately define the mirror line; the ‘x-axis at –2’ being the closest incorrect attempt. The correct mirror line was often correctly drawn but this alone scored no marks. Many candidates described a combination of transformations; ‘reflection followed by a translation of 6 units to the right’ or similar was common. Such responses scored no marks since the question required a single transformation to be named.Question 19

19

The most common typical error was to ignore the order of operation, showing no working out, and giving 21.01346457 as the answer. However, many candidates gained at least one mark for showing intermediate working of either 19.56 or 8.0518 Many of these candidates failed, even so, to gain the final mark as a result of a premature approximation, usually of 8.0518. A great number of candidates went on to write their answer to one or two decimal places. This was ignored provided the correct answer had already been seen in the working. Others who failed to show their answer before rounding again lost this final mark.

Question 20

In part (a)(i), the majority of candidates evaluated a correct substitution without error, although 23 = 6 was seen often. In (a)(ii), many struggled with the cubing of the negative value and errors were plentiful. It was pleasing to see a good number of candidates giving the correct value of 4x2 (when x =1.5) in their explanations in part (b). Some others recognised the need to carry out the squaring of 1.5 first before multiplying by 4. Weaker candidates would generally give incorrect alternative vales of 4x2; most often 12, 16 or 24.

Question 21

Here, division by a ratio is showing signs of improvement; many giving the correct answers. 22.5 and 37.5 were accepted in this question. The usual incorrect approach was to divide 60 by 3 and then 5; 20 and 40 being a common wrong answer. Some candidates attempted ‘build-up’ methods were 3 and 5, then 6 and 10 etc were often in evidence. This rarely led to the correct answer but going as far as 21 and 35 (total = 56) did gain one mark.

Question 22

Correct use of Pythagoras’ theorem was patchy. Sight of 92 – 52 usually led to the correct answer although many were happy to leave 56 as the required length. Some rounded their square root of 56 to 7.5 without first writing down the digits from their calculator. This should be discouraged. A significant number showed no working and gave their answer as 7.5 thus gaining no marks. Other candidates, recognising that Pythagoras’ theorem was required, wrote 52 + 92 initially. This gained no credit. A few candidates attempted to find the length of the unknown side by scale drawing. This method is not accepted and gains no credit.

20

PRINCIPAL EXAMINER’S REPORT – HIGHER TIER PAPER 13 (UNIT 3, NON-CALCULATOR PAPER)

GENERAL COMMENTS

There were fewer instances of candidates failing to show working out, but it was clear that too many candidates tried performing calculations in their head, without setting out what they were trying to do.

There was a general weakness in attempts at questions towards the end of the paper. A minority of candidates showed any real understanding of these topics. Whilst it may be the case that they have concentrated on easier topics, it must be discouraging to have to take a paper in which they are unable to gain marks on so many questions.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

Most candidates correctly worked out the answer. Some incorrectly divided by 3.

Question 2

Most candidates understood that they needed to multiply by 200. However, it was disappointing to find so many quoting 1 m = 10 cm or 1 m = 1000 cm. It was also the case that too many candidates failed to give the units with their answer, thereby losing a mark. A correct answer in either cm or m was acceptable.

Question 3

Most candidates gained at least one mark; the most common error was inaccuracy in drawing the angle. Very occasionally triangles were incomplete.

Question 4

Most candidates divided by 5 and multiplied by 3, but some had difficulty in performing this division, with answers of 13 and 14 being seen.

Question 5

Nearly all candidates gave the answer of B, but some gave an incorrect shape of D as their second shape.

Question 6

Many recognised that a rotation had taken place but many spoiled their response by describing an additional transformation in their explanation, usually a translation. The angle of rotation was usually given, but the centre less frequently.

Question 7

21

There were many attempts at finding 17.5% of £6000 using 10%, 5%, etc., although some candidates incorrectly stated that 10% of 6000 was 60. Those candidates who tried to calculate 0.175×6000 or 1.175×6000 often made errors in their calculations,. Of those who gained the method mark for finding the VAT, many gained the next method mark for adding the VAT to £6000 and were able to complete their solution competently. However, a significant number of candidates subtracted the £3000 initially and tried to find 17.5% of £3000 and therefore could only be awarded credit for the division by 10.

Question 8

This was well answered by many. The two most common errors made were either to divide 180° by 5, or to write 360° as the sum of angle of a triangle.

Question 9

In part (a) there was much confusion as to whether the circle was to be shaded in, or not. It was not uncommon to see circles over 0 or 3.In part (b) the confusion was over which signs to use, though -2 and 3 were seen regularly.In part (c) many candidates progressed the solution through to the number 4, many writing the answer as t=4, or t<4.

Question 10

Many correctly rad off the graph and knew the figures 16 and 30 were needed to calculate the speed, but some incorrectly used 30÷16. Those candidates who established a connection between 16 and ½ often made an error in 16 ÷ ½ = 8, a common incorrect answer.

Question 11

In part (a) two distinct methods were seen. Some candidates who chose to deal with the whole numbers first. Some subtracted numerators and denominators to give an incorrect answer. Other candidates chose to convert the mixed numbers into improper fractions. Many established a common denominator, but then found it difficult to find a numerator to match. In part (b) a minority of candidates were unsuccessful as they tried to deal with the whole

numbers first, often leading to an answer of . Many correctly converted one of the mixed

numbers to an improper fraction, but again the problem was then matching numerators and denominators.

Question 12

In part (a) there were many incorrect attempts at Pythagoras. Other candidates appeared to guess a value for DC so they could have a value to work with in part (b). Others established a connection between the 10 and the 5 and decided that the scale factor was 2, thereby stating DC=16cm. In part (b) candidates lost possible marks by not showing sufficient working. Follow-through marks from (a) were only available when the working was clear. Some worked on the diagram; many split the trapezium into a rectangle and a triangle but often made an error when calculating the area of the triangle.

22

Question 13

Most candidates tried to make the coefficients of x or y the same, with only minor errors, usually involving the number term. However a significant number of candidates then chose the wrong operation leading to, in most cases, 0 marks. Of those who chose to eliminate the y term, the majority stated 26x=13, only for some to incorrectly state that x=2.

Question 14

The incorrect factorisation of (x + 8)(x – 1) was seen frequently. Some tried to use the quadratic formula but a small number earned full marks. Those who used trial and improvement could only find the solution x=1. Of those who arrived at the correct factors, it was not uncommon to see the bracketed terms left on the answer line rather than the solutions.

Question 15

This question was poorly answered, with little understanding shown of an “inverse proportion”; the most common incorrect expression seen was P=v-3.

Question 16

This was not well answered. Very few candidates stated that OP=a+b. Some wrote a+b÷21 on the answer line, which was ambiguous. Some gained some credit in part (b), following through an incorrect answer in part (a). Attempts at Pythagoras gained no marks.

Question 17

Only a few recognised x2+y2=9 as the equation of a circle. Circles with a radius of 3 were seen occasionally, some drawn freehand and not always within normal tolerance. Attempts at drawing parabolas were seen but it was more usual to see the straight line x + y = 3.In part (b) attempts to draw the line x + y = 1 were more successful but many variations were seen.

23

PRINCIPAL EXAMINER’S REPORT – HIGHER PAPER 14 (UNIT 3, CALCULATOR PAPER)

GENERAL COMMENTS

The paper proved to be accessible to most candidates with the majority of the candidates attempting all questions.

Candidates appeared to be able to complete the paper in the allotted time.

Candidates are advised to make sure that their pencil marks in constructions and diagrams are clearly visible, particularly when the paper is marked online. At times it was hard to see the lines drawn in question 8.

It was encouraging to note that most candidates did try to show their working out and this led to many method marks being scored in questions 15, 16 and18 when the answer was incorrect. However in question 5 candidates often did not show partial calculations which could have scored a mark if their answer was incorrect.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

This proved to be a good starter question with over 80% of the candidates scoring all 4 marks. Those who did not score all 4 marks tended to lose 2 marks in (b) by working out 2 ÷ ½ reaching an answer of 4 people.

Question 2

Part (a) was generally done very well with nearly 70% of candidates scoring both marks.Those that were incorrect tended to have no idea of how to reflect in a horizontal line. These candidates would be best advised to rotate the exam paper 45° so that the mirror line is vertical.Over 80% of candidates scored at least 2 marks generally for a correct enlargement scale factor 3. However many filed to use the correct centre. As a result only 32% scored all 3 marks.

Question 3

88% of candidates scored both available marks in a variety of ways. 8 ÷ 20 × 100 was seldom seen with various partitioning methods preferred.

Question 4

Part (a) was answered very well with over 90% of candidates gaining full marks. It was pleasing to note that most tried to rearrange the equation rather than use trial & improvement. There were several candidates whose 1st step was 2x = 10 + 3 whilst others divided by 2 first. This was extremely well answered with over 91% writing c11.

24

This part was almost as successful as part (b) with over 87% writing e8. e3 was the most common incorrect response.

Question 5

Although a pleasing 82% scored both marks it was noticeable that the 9% of candidates who scored no marks tended to show no working thereby not accessing a mark for 19.56 or 8.0518 seen. Any candidate with a calculator should have no difficulty scoring at least one mark on this question.

Question 6

This was well answered with nearly 78% scoring both marks. Only 10% failed to score. This was generally for an answer of –3, –2, –1, 0, 1

Question 7

Writing down expressions and a formula was very well done with 48% scoring all 3 marks. A further 33% scored 2 marks generally for parts (a) and (b). The most common incorrect response in (c) was T = x + y. A few made careless errors by using the letter x in both parts (a) and (b).

Question 8

Most candidates gained full marks for drawing the front elevation. For those who did not, the errors included:adding an extra column or occasionally an extra row,adding an extra square at the top,drawing a 3 dimensional diagram,drawing from a different orientation.

This was also done well. A significant number attempted to draw a net of the shape or a 3 dimensional diagram. A minority drew a rectangle of different proportions (most only one square longer or shorter but occasionally long enough to fit the whole space). A minority of candidates transposed parts (a) and (b).Overall, nearly 70% of candidates scored all 4 marks with a further 24% scoring 2 or 3 marks.

Question 9

This was well answered with 73% scoring both marks and only 14% failing to score.. Common errors included incorrectly removing the bracket, subtracting 15 from 24 instead of adding, and leaving the answer embedded in the equation. Only a few candidates divided through by 3 as their 1st step. Some attempted trial and improvement methods but were usually unsuccessful.

Question 10

25

This question was tackled in a variety of ways. Many started with 14.56 × 10–16 and then either stopped or went on to write 1.456 × 10m17. Others converted the two parts to ordinary numbers and then either forgot to put their final answer back into standard form or did not convert one of the numbers correctly. Overall, 50% of the candidates scored both marks with a further 20% scoring 1 mark.

Question 11

Most candidates just wrote 1, 2, 3, 4 or 4, 3, 2, 1. This did not manage to score any marks! Overall, 30% scored both marks with a further 35% scoring 1 mark.

Question 12

It was really pleasing to see how candidates attempted this question with only 12% of candidates failing to score. Many did the calculations correctly but then did not write any explanation or sufficiently explain why only 92 cups could be filled. As a result 29% of candidates scored 2 marks. There were some errors in converting between ml and litres in about 10% of the responses. Nearly half the candidates got this question fully correct.

Question 13

A majority of candidates completed the table correctly. (–2, –15) was the most likely point to be incorrect. Some chose points to make the graph fit a straight line after joining (3, 20) and (–1, –8)! A few candidates made errors on the table, then clearly realised their mistake while drawing the graph, but did not alter their error on the table.A significant number of candidates joined their points with a ruler losing a mark in (b) and a few did not join the points at all. Other candidates clearly used a scale of 1 mm = 1 unit for y. Overall it was pleasing to find that over half the candidates scored all 4 marks with a further 29% scoring 3 marks.

Question 14

This question was not done at all well with over 65% of the candidates failing to score. 52° was commonly seen but it was nearly always not seen in angle ADC on the diagram and often seen as the answer. Many others gave an answer of 128°. A few candidates gained a mark for 128 × 2 or 256 seen but only 24% reached the correct answer of 104°.

Question 15

The majority of candidates realised they needed to use a trigonometric ratio but many chose the wrong one). Those who did choose to use the cosine ratio generally got the correct answer with just over 40% of the candidates scoring all 3 marks. Many used the sine rule but then did not continue with Pythagoras to find AB so no marks could be scored. Overall 55% of candidates failed to score any marks on this straightforward trig question.

Question 16

This question on bounds had a higher success rate than usual with over 40% of the candidates scoring all 3 marks. Where the candidate knew that the upper bounds of the lengths were 35.5 and 26.5 they often went on to achieve full marks. Those that did not usually had little idea as to how to approach the question at all. Unfortunately, nearly half the candidates failed to score. The most common error was to simply do 35 × 26 and then use the 910 to give an upper bound of 910.5 or something similar. A number of candidates considered 26.4 and 35.4 to be suitable bounds.

26

Question 17

35% of candidates gained full marks but nearly 60% of the candidates failed to score. A significant number of candidates showed no awareness of the need to find a common denominator.

Other common errors included: using 5 as the denominator,ignoring the denominator ( after correctly using 6),arriving at 5x = 8,multiplying only one of the terms on the LHS by 2 or 3,not equating the correct expression to 8

Question 18

Over 80% of the candidates failed to score on this question even though the first mark was awarded for any attempt to multiply both sides by 3 + n even if it was not quite accurately done. 10% of the candidates were able to do this and a further 5% went on to rearrange their equation correctly isolating the terms in n. However, factorising the terms in n proved a stumbling block for all except the most able.

Question 19

Generally candidates were more successful with part (a) than part (b) though 15% of candidates did gain all 5 marks. A significant number made no use of either the sine or cosine rules. Others clearly attempted to do so but appeared to forget to use at least one element – often the sine/cosine element! Several candidates used straightforward trig ratios or Pythagoras, as if the triangle were right angled. The most common error in (b) was to evaluate (179.14 – 174.3) × cos 62°. Overall, nearly 60% of the candidates failed to score any marks on this final question on the paper.

27

STATISTICS

MARK RANGES AND AWARD OF GRADE

Unit/ComponentMaximum

Mark Mean MarkStandardDeviation

% Contribution

to Award5381F/05 30 21.5 5.8 205381H/06 30 17.3 7.1 205382F/07 25 15.7 4.1 155382H/08 25 14.8 5.5 155383F/09 25 13.4 5.2 155383H/10 25 15.4 5.6 155384F/11F 60 33.2 10.5 255384F/12F 60 39.4 11.5 255384H/13H 60 28.8 11.8 255384H/14H 60 37.6 10.6 25

GCSE Mathematics Grade Boundaries for 2381– November 2010

The table below gives the lowest raw marks for the award of the stated uniform marks (UMS).

Unit 1 – 5381

A* A B C D E F GUMS (max:

55) 48 40 32 24 16Paper 5381F 27 22 18 14 10UMS (max:

80) 72 64 56 48 40 36Paper 5381H 29 24 17 11 7 5

Unit 2 Stage 1 – 5382

A* A B C D E F GUMS (max: 41

) 36 30 24 18 12Paper 5382F 21 17 14 11 8

UMS (max: 60 ) 54 48 42 36 30 27

28

Paper 5382H 23 19 15 11 9 8

Unit 2 Stage 2 – 5383

A* A B C D E F GUMS (max: 41

) 36 30 24 18 12Paper 5383F 19 15 11 8 5

UMS (max: 60 ) 54 48 42 36 30 27

Paper 5383H 24 21 16 12 8 6

Unit 3– 5384

A* A B C D E F G5384F_11F 41 33 25 17 95384F_12F 49 40 31 23 155384H_13H 51 40 29 19 10 55384H_14H 58 48 38 29 17 11

A* A B C D E F GUMS (max:

139 ) 120 100 80 60 405384F 90 73 56 40 24

UMS (max: 200) 180 160 140 120 100 90

5384H 108 88 68 48 27

UMS BOUNDARIES

Maximum Uniform mark

A* A B C D E F G

28 24 20 16

29

400 360

320 0 0 0 0

120 80

Further copies of this publication are available fromEdexcel Publications, Adamsway, Mansfield, Notts, NG18 4FNTelephone 01623 467467Fax 01623 450481Email publications@linneydirect.comOrder Code UG025826 November 2010

For more information on Edexcel qualifications, please visit www.edexcel.com/quals

30

Edexcel Limited. Registered in England and Wales no.4496750Registered Office: One90 High Holborn, London, WC1V 7BH

31