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June 2003

Publications Code UG014129

All the material in this publication is copyright London Qualifications Ltd 2003Contents

Principal Examiners Report Paper 5501.1

Principal Examiners Report Paper 5502.6

Principal Examiners Report Paper 5503.11

Principal Examiners Report Paper 5504. 17

Principal Examiners Report Paper 5505. 22

Principal Examiners Report Paper 5506...27

Principal Moderators Report 5507....32

Statistics and Grade Boundaries 44

1

Principal Examiners Report Paper 5501 (Foundation)

1.1

General Points

1.1.1This paper was accessible and gave candidates the opportunity to demonstrate positive achievement. As intended, the greater number of grade G marks (33) gave weaker candidates more chance to show what they knew and there were relatively few single figure scores. The proportion of high scores (over 65) was also low, although it is likely that this was the result of centres entry policies rather than any intrinsic difficulty of the paper itself.

1.1.2Several questions were very well answered, full marks probably being gained most often on Question 8 (Pictogram) but the success rates on the first four questions, Question 13 (Directed numbers), Question 14 (Number machine) and Question 17 (Two-way table) were also high. At the other extreme, full marks were rare on Question 16 (Frequency table) and, for all but the strongest candidates, the final seven questions on the paper.

1.1.3Inevitably, by failing to show working, many candidates sacrificed the chance to be given credit for their methods, even when their final answers were wrong. This applied particularly to Question 12 (Shopping) and Question 20 (Teddy bears). Of course, when working is shown, it must be comprehensible to examiners. A mass of figures, sometimes at a variety of inclinations to the horizontal, gives candidate and examiner little chance.

1.1.4The only equipment needed for this paper was a ruler and a small minority did not have one. This was a serious handicap on the first two parts of Question 4 (Line and midpoint) but, in the rest of questions which required straight lines to be drawn, careful freehand lines were accepted. Some candidates used their protractors to measure the angles in Question 23, even though it was clearly stated that the diagram was not accurately drawn.

1.2REPORT ON INDIVIDUAL QUESTIONS

1.2.1Question 1

This proved to be a straightforward start to the paper. 40.6 and 6 appeared occasionally in part (a) and the decimal point was sometimes omitted in part (b). 330 and 340 were seen with some regularity in part (c) but, overall, this question caused few problems and many candidates gained full marks.

1.2.2 Question 2

The majority of candidates scored both marks by writing the amounts of money in an acceptable form e.g. 1.60, 1.60p, 1-60, 1,60 and 1 60 but not 1:60. Errors were rare but, when made, were usually either 1.06 for one pound sixty pence or 2.5 or 2.50 for two pounds five pence.

1.2.3Question 3Many candidates gained full marks. In part (a), the most common mistakes were giving a fraction, which was not in its simplest form, or giving the fraction of the shape, which was unshaded. 1 mark out of 2 was awarded for the former but, for the latter to earn a mark, it had to be in its simplest form. If the mark for part (b) was lost, it was usually because or of the shape was shaded.

1.2.4Question 4The majority of candidates were able to draw a line 12cm long, mark its midpoint, and draw a rectangle with the specified dimensions.

1.2.5Question 5Most candidates scored at least one mark, usually for litres, but only a minority managed all three. Grams were quite popular for the weight of a turkey. The fact that millimetres and metres were frequently suggested as sensible imperial units for the width of a page, while ounces and pints appeared as metric units, indicated some confusion about the terms metric and imperial. It was not unusual for candidates to write numbers, instead of units, in the table.

1.2.6Question 6Many candidates demonstrated their knowledge of parallel lines and right angles but the first two parts still proved far from trivial and, for a substantial number of candidates, exposed misunderstanding of at least one of these basic geometrical concepts. Most candidates gave the answer acute for part (c)(i) but, in part (ii), obtuse appeared much more often than the correct answer.

1.2.7Question 7The quality of answers was almost as variable as the spelling. In general, any recognisable attempt received credit. Thus, for example, Sophia was awarded the mark in the first part, for which ball was the popular wrong answer. Part (ii) had the highest success rate of the three, although tube was often seen and, in part (iii), prism appeared frequently. The names of 2-D shapes e.g. circle, triangle and trapezium made regular appearances as well as more intriguing names such as overall (oval?) and tunes (tons?).

1.2.8Question 8

This was probably the best answered question on the paper and a high proportion of candidates achieved full marks, some of them because separate half and quarter symbols were accepted as three quarters of a symbol.

1.2.9Question 9The majority had little trouble ordering the natural numbers in the first part but all the remaining parts proved much more demanding. In the second part, only a minority appreciated that 0.067 was the smallest number and, of those who did, many thought that 0.605 was greater than 0.65. The most common error in the third part was to reverse the order of the negative numbers. A large number of candidates scored 1 mark out of 2 in the final part as three of the numbers were in the correct order in their list e.g. but there was rarely any indication that equivalent fractions or conversion to decimals had been used.

1.2.10Question 10Few marks were lost in the first three parts but only stronger candidates had the knowledge of algebra needed for the formula in part (d), for which , m = n and n + 6 were popular wrong answers.

1.2.11Question 11Answers to this varied widely both within and between centres. As far as any pattern was discernible, candidates appeared to be most familiar with multiples and factors and least familiar with cube numbers.

1.2.12Question 12Full marks were awarded quite regularly and much more credit could have been given if candidates had shown their working. Even if the final answer were wrong, 3 of the 4 marks could be scored for the costs of the separate items; if one of these were incorrect, the problem was usually with finding of 72.

A substantial number of candidates simply added 72p, 24p and 25p and then found the change from 5.

1.2.13Question 13This was very well answered, full marks often being gained. It was noticeable that, after answering part (a)(i) correctly, some candidates gave 13 as the answer to part (ii), even when they had drawn a number line. Presumably, they had counted the numbers instead of the steps. The difference between two numbers is regarded as a strictly positive number and so an answer of received no credit.

1.2.14Question 14This was another very well answered question with many candidates scoring full marks. If one error were made, it was most likely to be with the final entry, which was an input.

1.2.15Question 15In part (a), there appeared to be some doubts about the meaning of vertices. From the labelling, some candidates seemed to confuse vertices with edges, while others seemed to confuse them with faces. The success rate on part (b) was very low, wrong answers being seen much more often than the correct answer. The most frequent one was 28, the perimeter of the net, with 38, the sum of the perimeter and the lengths of the internal lines, and 24, the surface area, also appearing regularly. 6, which was occasionally given as the answer, may have been an unsuccessful attempt to evaluate .

1.2.16Question 16A minority of candidates achieved some success with the first two parts but very few made any headway with the last part. In the second part, some of the candidates who had some knowledge of range, albeit imperfect, gave answers such as 29-32 and while, in part (c), the majority of candidates either gave 30 with no working or found the sum of 29, 30, 31 and 32 and then divided their result, usually by 4 and sometimes by 10. Apart from the usual confusion of mean, mode and median, interpreting the table was an additional stumbling block. In recognition of this, one mark was awarded for listing the ten numbers, even if the candidate subsequently attempted to find the median.

1.2.17Question 17Few candidates failed to complete at least the two correct entries in the two-way table needed to score one mark and many scored 2 or 3 marks.

1.2.18Question 18In part (a), most success was achieved on (iii) (), closely followed by (i) , for which also had considerable support. The other two parts proved more difficult. 4p and were often seen in part (ii) while 7rp and 2r5p were popular in part (iv). Part (b) was poorly answered; and, sometimes simplified to 7y, were the most common wrong answers.

1.2.19Question 19This question discriminated well between candidates. A significant proportion shaded both grids correctly and drew the correct conclusion. Correct shading followed by an incorrect conclusion occurred more frequently than might have been expected. Some shaded one of the grids correctly, usually nine squares to represent, while the weakest candidates shaded all fifteen squares, 3 by 5, to represent and six squares, 2 by 3, to represent.

1.2.20Question 20Overall, only a minority of candidates were able to make a meaningful attempt at either part. Those who could, attempted a wide variety of methods in the first part but many made too many computational errors to earn any marks. Methods for evaluating instead of appeared regularly, as did the answer 696, transferred from part (b). In the second part, a small minority completed formal long division accurately but trial and improvement methods were more common. As always, these received credit only if they led to a correct answer. Some misinterpreted the information in the question, thinking the price had remained unchanged at 9.55.

1.2.21Question 21Only the strongest Foundation candidates can realistically be expected to have the competence in basic algebra needed for a question of this type and so it proved. Thus, the answers and were often given for part (a), with and popular for part (b). Every effort was, however, made to reward genuine evidence of understanding. For example, in part (b), one mark was awarded for the appearance of 10y in the expression.

1.2.22Question 22Hardly any candidates made any headway with this question., an attempt to addand , was common, as was, both of them generally unaccompanied by working. Candidates who gaveas the answer were presumably continuing the sequence of fractions.

1.2.23Question 23In parts (a) and (b)(i), a small minority found the size of each angle correctly. Even if part (a) was wrong, candidates who showed how they had used their incorrect x to find y could still gain 2 marks in part (b)(i) but few showed the necessary working. The mark for the reasons in part (b)(ii) was rarely awarded; a statement mentioning the equality of the sides and the equality of the angles was required. If an attempt were made to give reasons, it usually related to the angle sum of a triangle or to the sum of the angles on a straight line. Quite often, the reason given was some variant of either I used my protractor. or, with disarming honesty, I guessed. The regular appearance of parallel in explanations suggested some misinterpretation of the symbols indicating two equal lengths on the diagram

1.2.24Question 24

Very few candidates had the algebraic skills to tackle successfully either part of this question. Some were so suspicious of question setters that, in part (a), they answered that neither Tayub nor Bryani was right.

1.2.25Question 25In the first part, a sizeable minority drew a rectangle with the correct dimensions, which earned 2 marks out of 3, but the hidden detail line required for the final mark was rarely present. In the second part, considerable tolerance was exercised by examiners. Some candidates produced excellent drawings but both marks were awarded for a perspective drawing showing the two key features of the sloping face and the cutout, even if there were errors in the drawing. Consequently, a substantial number of candidates received full marks. Sketches of triangular prisms and, to a lesser extent, pyramids appeared regularly but were not rewarded. Interestingly, there was little correlation between candidates marks on this question, especially the 3-D sketch, and their performance on the paper as a whole.

1.2.26Question 26The answer 20, read directly from the travel graph, appeared much more often than the correct answer in part (a). In part (b), both marks were occasionally awarded but many candidates scored one mark for a line from (45, 20) to the time axis, often (60, 0) or for a line of the correct gradient, usually from (60, 20) to (80, 0).

2

Principal Examiners Report Paper 5502 (Foundation)

2.1

General Points2.1.1The questions on this paper were mostly well understood, with the vast majority of candidates scoring between 20% and 80% of the marks available. Questions on the new specification content were often the most poorly attempted.

2.1.2There was evidence that not all candidates had access to a ruler, protractor or pair of compasses. In fact it was more common to see the circle drawing question attempted freehand!

2.1.3The majority of candidates attempted all of the questions.

2.1.4Questions 2, 3, 5, 8, 9, 13 were answered with the most success.

2.1.5Questions 15, 16, 20, 24, 25, 26 were rarely successfully completed.

2.1.6The pie chart question (No. 21) and the stem and leaf question (No. 24) were poorly answered, in particular there were very few reasonable attempts at the stem and leaf diagram a new topic in the specification for the first time this year.

2 REPORT ON INDIVIDUAL QUESTIONS

2.2.1Question 1

Few candidates gave completely correct answers to this question. About 20% of candidates gained no marks, though the majority of candidates were able to answer one or two parts successfully.

In part (a) common incorrect answers given were and ,

In part (b) incorrect answers of 18 and 18 were often seen.

Part (c) however was correctly answered by about 25% of candidates.

2.2.2Question 2

This question was well understood by most candidates and candidates scored well on this easily accessible question. It is still a great shame that candidates lost marks because they did not have the necessary equipment for the examination and so found it difficult to draw a circle and find the midpoint and length of the line.

2.2.3Question 3

About 95% of candidates gave a fully correct answer to this question and the other 5% scored 2 out of the 3 marks.

2.2.4Question 4

Candidates had variable success with this question.

Part (a) was mostly well understood by all candidates.

Part (b) proved difficult for a lot of candidates with 3.4 or 0.34 often seen as incorrect answers.

Part (c) was usually correct in about 75% of cases whilst

Part (d) was completed fairly well by 90% of candidates.

2.2.5Question 5

As usual time questions are often misunderstood by Foundation Tier candidates.

About 75% of candidates were able to give correct answers to parts (a) and (c).

In part (b), candidates often found the time taken to travel from Coventry to London, rather than Crewe to London. Many candidates did not appreciate that a length of time should be written in hours and minutes rather than using the same notation as that used in stating a time i.e. 2 hours, 45 minutes rather than 2:45 or 2.45.

2.2.6Question 6

Full marks on this question were rarely seen. Part (a) was generally more successfully answered than part (b). Candidates generally lost marks on part (a) by writing 384 or 38.40. In part (b) the absence of working cost marks, as about 75% of candidates obtained the answer of 3.28, but failed to work out the difference. Difficulties often arose with the use of decimal points and the concept of writing money correctly.

2.2.7Question 7

Part (a) was usually correctly answered though 50,000 was a common incorrect answer.

In part (b) answers of 50,000 or 10,000 were accepted and often seen. This part was not answered as well as part (a). About 25% of candidates gave fractional answers such as thousandths.

2.2.8Question 8

This question was well understood by all candidates and about 50% of candidates were generally successful and scored full marks. The correct reflection was nearly always seen. The confusion between perimeter and area still exists and answers to part (a) and (b) were often transposed.

2.2.9Question 9

For their answers to (a), most candidates could correctly and clearly explain that there was a label missing on the horizontal axis but fewer were able to give a lucid explanation of what was wrong with the frequency axis. Many candidates gave the reason that there was no title. This answer was not accepted.

Nearly all candidates successfully completed the bar chart in part (b) and went on to give the correct answers of blue for the mode in (c) and 14 for the number of teachers in (d). There were very few successful attempts to part (e). The incorrect answer of one third was frequently seen.

2.2.10Question 10

Over half of the candidates found this question difficult. Candidates were more successful in explaining Barrys pattern than Kaths pattern. Common wrong answers for Kaths pattern was that the numbers add up to 7. Some candidates understood the method, but found the ability to explain it very difficult.

2.2.11Question 11

About a quarter of candidates gave entirely numerical answers to this question; most answers given were in terms of n. About half of candidates who sat the paper were able to give 2n or an acceptable equivalent (i.e. 2 n, n 2

or n2) in answer to (a). About 25% of candidates wrote n = 2n and scored no marks. A significant minority of candidates were able to use their expression in (a) + 15 as their answer in part (b), although n + 15 was often seen. Part (c) was successfully answered by about a third of the candidates, and by some that had been unsuccessful in the previous two parts. Some candidates confused their answers by trying to include words or a p (presumably for denoting pence) in their answers.

2.2.12Question 12

Part (a) was well answered by about 75% of candidates. Correct answers for part (b) appeared in only about 25% of cases. Candidates had relative difficulty relating their answers to central tendency with the highest frequency often mistaken for the mode. There was also clear confusion between frequency and the number of cups.

2.2.13Question 13

Parts (a) and (c) of this question were successfully answered by about 50% of candidates. There were a sizeable number who were apparently confused by the placement of the shapes on the diagram, despite the fact that the diagrams were clearly labelled, and gave isosceles for their answer to part (a) and trapezium for part (c).

Correct answers were usually given to parts (b) and (d). Sometimes (2, 3) was given as (3, 2) and more commonly (4, 2) was plotted instead of the (2, 4) given.

2.2.14Question 14

Part (a) was generally more successfully answered than part (b). In part (a) the most common wrong answer was 25000. In part (b) candidates lost a mark because they failed to notice the million written on the answer line and wrote 7000000.

At least 20% of candidates failed to obtain a follow through mark on part (b) because they did not show their working.

2.2.15Question 15

In part (a) almost all candidates gave the correct answer.

In part (b) less than half the candidates wrote down an answer within the acceptable tolerance of 55 ( 03 pounds. Many either misread the graph or, more probably, did not use the graph but applied the rough conversion factor of 1kg to 2 pounds to obtain the answer 5.

In part (c) more candidates gave the unacceptable answer of 55 kg rather than the 50 kg (or thereabouts) gained by accurate use of the graph or by using the conversion factor 1 kg ( 22 pounds. Centres are reminded that this fact is stated in the specification as one which candidates are expected to know.

2.2.16Question 16

Many candidates found this multi-step question difficult. Lack of working limited the marks that most candidates scored. In part (a) 5 was often seen which scored 1 mark. In part (b) relatively few candidates scored any marks. Most found it difficult to find 5% of 269.30, of those candidates who did obtain the correct answer a significant number did not round the answer correctly and lost the final accuracy mark.

2.2.17Question 17

There were surprisingly few totally or partially correct responses to this question. The vast majority of candidates doubled rather than squared 41 and went on to give the incorrect answer 8.774. It seemed that few candidates were using the brackets and squaring features often available on calculators. Most candidates did write down all the figures from their calculator display as requested.

2.2.18Question 18

The vast majority of candidates did not understand this question and few correct answers were seen. Part (b) was generally better answered than part (a). Part (c) was the most successful part with about 10% of candidates giving the correct answer. All too often candidates tried to measure the angles.

2.2.19Question 19

About 90% of candidates worked out the income of the club in (a) (i) correctly. However, few went on to write down the correct fraction for (a) (ii).

In part (b) a significant proportion of answers or working shown indicated the successful calculation of 60% of 1000 for which 2 marks were awarded, yet only a small minority (less than 5%) were able to give the correctly and fully simplified ratio 12:5.

2.2.20Question 20

The vast majority of candidates did not understand this question. Many made no attempt at this question. In part (a) 2x was often seen rather than x + 2. Little attempt was made on part (b). A very small minority managed to gain the correct answer in part (c), even though they had not completed part (a) and (b).

2.2.21Question 21

There was some evidence of candidates not having a ruler and/or protractor, or where a protractor was available, it was not used accurately to draw sectors within the 2( tolerance required. This question was often not attempted. Few candidates recorded sector angles in the table or showed any working. The question was attempted less successfully than similar questions set in previous years, with only a small percentage of candidates gaining more than one mark.

2.2.22Question 22

Algebraic manipulation is not well understood by candidates at the Foundation Tier. This question confirmed this again this year. This question proved too difficult for most candidates. Part (a) was better answered than part (b). Quite often candidates simplified the term in p correctly, simplifying q was more difficult. Relatively few candidates made any attempts at part (b).

2.2.23Question 23

A good proportion of candidates were able to complete rows 4 and 8 in the table to gain the first two marks in this question. Few candidates were able to identify the numerical expression needed to answer (c) and of those who successfully did, hardly any worked out its value necessary to gain the mark available here.

2.2.24Question 24

This was a new topic to be tested on the specification. Most candidates had no idea how to answer this question and success was very centre dependent. Most candidates actually drew very artistic plants with stems and leaves. Those candidates who could answer this question usually scored 2 out of the 3 marks available - most losing the mark for not writing a key.

2.2.25Question 25

This question was not well understood and poorly attempted.

It was rare to see candidates attempting to work out the total surface area of the tank or, for that matter, the area of any of the faces. Usually the volume of the tank was calculated, or the three lengths added together. Between 10 and 20% of candidates were awarded one of the five marks given for using their surface area to calculate the cost of paint needed. Only about 1% of the answers seen scored more than one mark.

2.2.26Question 26

This question was again not understood by candidates entered for this tier and it was very poorly answered. Less than 1% of candidates got this question correct. The most commonly seen incorrect answer was 250. No method was shown.

3

Principal Examiners Report Paper 5503 (Intermediate)

3.1GENERAL POINTS3.1.1This was the first year of a new specification. In preparation for the written papers centres have been provided with much information, including a set of specimen and mock papers. It was therefore disappointing to find that candidates were relatively unprepared for questions on the topics that are new to the 2003 specification. Inequalities, geometry of the circle and box & whisker diagrams were questions in which candidates gained very few marks, and there was clear evidence that this was centre-dependent. Centres need to spend more time preparing candidates on the topics that are new to this specification.

3.1.2The general standard of arithmetic remains weak, even from those who gained the highest marks on this paper. This was most evident in question 14 and 15, where candidates had great difficulty in multiplying and dividing by factors of 10, and also in questions 6, 11 and 24(iii).

3.1.3The increasing numbers of candidates who work solely in pencil run the risk of their work being illegible, which frequently it is. It is these candidates, far more so than those who work in ink, who also rub out their working, perhaps denying them method marks if their answer is not correct. There are many candidates with a desire to round answers and interim calculations quite discriminatory, rendering a final answer inaccurate. On many occasions this can be compensated, but only if the candidate shows the accurate figure, before rounding. It is also disappointing when candidates give quite absurd answers, such as probabilities more than 1, or monetary answers completely out of the context of the question. Centres are advised to consider how they can help candidates avoid such errors.

3.1.4Work associated with percentages and fractions showed some improvement this year. There was clear evidence of sound percentage calculation in question 15, whilst many candidates used conversion of fractions (frequently to percentages) to assist in ordering in question 3. Indeed, the manipulation of fractions in questions 3, 5 and 9 was encouraging.

3.1.5The concept of explanation of proof was expected to be a good discriminator, and it was. Questions 10 and 25 required the use of geometrical theorem and property, yet many candidates were unable to express their explanation in these terms.

3.1.6There was a continuing improvement in algebraic manipulation. This was evidenced in question 1 and attempts at finding the solutions to equations in question 16. Many candidates showed their misunderstanding of algebraic formulae in question 11, and it was disappointing how few Intermediate candidates could correctly multiply out the bracket in question 27(a). There were some very encouraging responses to a problem on questionnaire design (question 22), demonstrating that some centres have placed a greater emphasis on Data Handling, which is to be encouraged.

3.2REPORT ON INDIVIDUAL QUESTIONS

3.2.1Question 1

The first part to this question was usually well attempted, with most candidates gaining the marks. The common errors were in giving 8g2 and 7rp as the answers, respectively. The second part was also well answered, but the weaker candidates spoilt their answer by writing it as 5y. Whilst most candidates could multiply out the brackets, very few correctly gave the final term as +15. Only partial credit was therefore earned. The collection of terms also caused many candidates some difficulty, far more so than the expansion of the brackets.

3.2.2Question 2

Centres need to ensure that candidates are aware of the difference between giving a formula and giving an expression. Many candidate omitted the m =, and could not therefore be given full marks. n + 6 was a common incorrect answer.

3.2.3Question 3

In general this question was well answered, with part (ii) usually correct. In part (i) some candidates had difficulty in placing 0.605 since they thought 0.065>0.65

In part (iii) most candidates gained at least 1, and many 2, marks. Methods varied, with some using equivalent fractions, and others making the conversion to decimals or percentages. It was very encouraging to see this done with much success.

3.2.4Question 4

Most candidates gained full marks in this question. The only errors appeared to occur in the bottom right of the table.

3.2.5Question 5

Overall many gained full marks. This question enabled most candidates to demonstrate their understanding of fraction size, usually by use of the grids for shading, though more able candidates converted to equivalent fractions or decimals. In the latter case this usually led to approximate answers since candidates prematurely rounded the to a limiting decimal. A common error in use of the grids was to shade 2 out of 3 squares on one grid, and 3 out of 5 on the other.

3.2.6Question 6

This question proved to be a good discriminator. Some candidates wrote out all the values in an attempt to find the median, whilst others stated the mode. A significant number found 302, but then failed to undertake a division. The most common error was the calculation 122 4 or 122 10. It was disappointing when candidates exhibited correct method, flawed by poor summation of fx values.

3.2.7Question 7

Most candidates undertook a rotation in part (a), though there were some errors in the final positioning of the triangle. Those candidates who used tracing paper had much greater success in the correct positioning of the triangle. There were very few correct solutions to part (b). Most candidates chose to draw a triangle of a scale factor 2 rather than ; there were, however, many errors in these attempts, since not all three sides were doubled in length, with a significant number adding cm to each side. It is clear that of all the transformations, enlargement is the one in which candidates are the weakest.

3.2.8Question 8

This question was well answered by most candidates; the only common error in part (a) was 12 + x, given by a minority of candidates. There were many correct solutions in part (b), but a significant number of candidates spoilt their final answer by incorrectly simplifying further, sometimes giving the response 22xy.

3.2.9Question 9

The weaker candidates thought that was , but then usually went on to give as their answer. Candidates who attempted a conversion into decimals gave approximated conversions for , thereby losing any accuracy in their final answer. There were some candidates who attempted a conversion to equivalent fractions, and those who did so correctly usually went on to gain full marks. Overall it was encouraging to see most candidates make an attempt at this question, and despite the fact that many struggled with the fraction work, the quality of fraction work in this question surpassed similar attempts at such questions in the past.

3.2.10Question 10

The numerical work in this question was usually well done, with full marks being gained. A few candidates persist in thinking there are 360 in a triangle. The final mark in (b)(ii) was not usually awarded since many candidates merely described the process of calculation followed; in many cases this had already been demonstrated. The marks on the two equal sides of the triangle were frequently misinterpreted to mean parallel lines, though this type of geometrical notation is universal. Candidates gained the final mark for using references to isosceles triangles, or establishing the link between the two equal sides with the two equal. Centres need to be aware that geometrical reasoning and explanation will in future require sound mathematical communication and use of geometrical properties, and that candidates need to be better prepared to give such explanations and justification of numerical work undertaken.

3.2.11Question 11

The choice between Tayub and Bryani was evenly split, but in both cases full explanations were usually given. It was disappointing to see a significant number of able candidates gaining full marks in part (a), to then make a common error in part (b) of calculating (4(x + 1))2. Overall correct answers to part (b) were rare, with 169 a common incorrect answer.

3.2.12Question 12

Reponses to this question were centre-dependent. Most candidates obtained 2 marks for a correctly drawn rectangle outline. It was very rare to see the hidden (usually dashed) line shown. It is hoped that candidates will have greater success once this becomes a more familiar topic. It was encouraging to see the many attempts at the 3-D sketch, most earning full marks. Common errors included a failure to show the depression on both sides of the sketch, or a failure to show a sloping edge. A minority of candidates drew 3-D shapes that failed to relate to the elevation, such as cylinders, triangular prisms or pyramids.

3.2.13Question 13

In part (a) the conversion to km/h was beyond most candidates, with many merely multiplying 20 by 30. This resulted in some answers given as 600km/h or 60km/h. Few candidates related 30 minutes to 0.5 hour in order to perform the correct calculation. In part (b) most candidates realised that their line had to arrive back on the horizontal axis, but only a minority attempted to calculate the necessary gradient.3.2.14Question 14

Many candidates tried to use long multiplication and division methods. The three parts discriminated well, in that most candidates obtained the first part, but then met decreasing success through parts (ii) and (iii). There was little evidence that candidates understood the relationship between place value and the position of the decimal points.

3.2.15Question 15

A significant number of candidates merely assumed this could be calculated using simple interest methods. Whilst many knew that they had to calculate 10% of 12000, and even wrote this out as 12000 , it was disappointing how many such calculations resulted in an answer of 120. When both of these errors occurred, no credit was earned. Some credit could have been earned if candidates demonstrated, by their working out, that a compound, rather than simple interest method was being used. More able candidates had little difficulty in obtaining the correct answer.

3.2.16Question 16

Weaker candidates attempted to use trial and improvement methods; inevitably these failed to lead to a correct answer. Those candidates who could perform some manipulation of algebra gained some credit, and usually arrived at the correct answer. In part (b) some credit was gained when candidates multiplied out the bracket, but the majority then failed to perform the correct manipulation, usually giving 2r = 22, or 2r = 18. Negative signs were frequently lost in the course of the manipulation. There was little evidence that candidates took the time to check their answers to the equations.

3.2.17Question 17

Many able candidates gained full marks. The most common incorrect answer was n + 5. Some candidates extended the sequence, giving 31 as their answer. It was discouraging to see candidates spoiling their answer by writing the incorrect statement n = n + 5.

3.2.18Question 18

Most candidates gained at least 1 mark in part (a), though attempts were not quite as good as in previous years. There was clear confusion between and