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GCSE Mathematics (1380)

November 2011

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November 2011All the material in this publication is copyright© Pearson Education Ltd 2011

PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIER PAPER 1

GENERAL COMMENTS

The absence of working was an issue and many candidates threw marks away simply through not explicitly showing their method; questions 2(b), 6, 8(a), 9(b), 15(b), 17 and 23 often reflected this. Many candidates had problems presenting a solution to a problem in any organised manner and lack of structure and methodology in the presentation of their answers made their working extremely difficult and often impossible to follow. This was particularly evident in questions 2(b) and 17(c).

Once again indifferent arithmetic let many candidates down. This was particularly evident in questions 2(a), 8(a), 15 and 17 and when working with angles in questions 9 and 23.

Despite “Diagram NOT drawn accurately” signposted, some candidates are still measuring the angles in geometry questions.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

Very few errors were seen in part (a).

In part (b) a number of candidates wrote ‘four hundred, or forty thousand and sixty seven’ and some wrote ‘seventy six’. An answer of just ‘tens’ was common in part (c); this gained no marks. In part (d) 1480 and 1400 were not uncommon.

Question 2

Whilst most candidates employed a correct method in part (a), poor arithmetic skills prevented many from gaining full marks. The subtracting of 23 from 960 was particularly poor.

In part (b), a common error was to count the initial 8 30 as one hour, resulting in a total of 8 hours being quoted for the length of the school day. This usually resulted in an answer of 7 hours, gaining 2 of the 3 marks available. However, a significant number of candidates simply offered 7 hours, without any working at all shown, and received no credit. Others treated the times as decimals and offered 5 (8.30 – 3.30) hours as their length of school day.

Many showed a lack of understanding of basic time being 60 minutes in an hour. Several wrote expressions such as 7.00 – 60 = 6.40.

Question 3

All parts to this question were answered well.

In part (b) an answer of 15 or 8 was a common error, while a number of candidates showed their lack of understanding of mode in part (c).

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Question 4

Again all parts to this question proved little challenge to the majority of candidates.

In part (a) some made up their own rule and an answer of 21 was a common error.

In part (b), a number of candidates demonstrated their understanding of the rule by computing subsequent terms in the sequence without actually stating the rule. Also, sloppy writing of the ‘+’ sign sliding into a ‘×’ put marks in jeopardy here. Some were distracted by the rule in part (c) and offered rules such as “×1 + 3” or “+5 – 2”. These, of course, gained full credit.

In part (c), the first two terms, 3 and 7 were often just quoted and sometimes 7 alone. Candidates must make sure they read the questions carefully.

Question 5

This was another question where the majority of candidates were able to pick up most of the available marks. Errors usually stemmed from misreading of the information in the table.

In part (d) the mark was often thrown away with answers such as 3 only.

Question 6

Many candidates failed to read this question carefully enough and simply measured, in cm, the height of the man and length of the bus as shown in the diagram. This gained no credit.

Other attempts often mixed up units and it was common to see the height of the man given in feet and inches with the length of the bus in metres. This could gain full credit if answers fell within the accepted ranges even when the estimated height of the man was never used to estimate the length of the bus.

When using their estimate in (i) to answer (ii) many used an incorrect scale factor of 3 or less.

A very common error was to find the height rather than the length of the bus.

Question 7

Both parts of this question were answered well by candidates.

Question 8

Many candidates, in part (a), were unable to correctly add the two weights 3.45 kg and 1.8 kg. Often 1.8 was read as 1.08 with some candidates explicitly writing 45 + 8 = 53 and as a consequence accuracy marks were lost. Even when added correctly many were unable to subtract 5.25 from 10. Many attempted to find the complement of 5.25, often resulting in 5.75

In part (b) many candidates did not know the conversion factor of litres to millilitres, many divided 300 by 2. It was not uncommon to see a decimal or fraction or even a worded (“6 and a bit”) answer instead of a whole number of glasses.

The build up method of adding 300s until the water had been used up was very common and usually successful.

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Question 9

Although many candidates recognised the equilateral triangle in the diagram and were able to quote an answer of 60 in part (a), there were many who did not. The most common error was to use the angle of 230, subtract it from 360 and halve their answer, usually giving an angle of 65 which many considered to be also the value of the angle x.

This same error was then often continued into part (b) where the base angles of the isosceles triangle were also quoted as 65, leading to a value of y of 50. This was worthy of a method mark if the working was clear, however this was not always the case. Some candidates thought that the whole quadrilateral was a parallelogram and gave an answer of 60 for everything.

Question 10

Although mostly answered well, a significant number of candidates confused congruency with similarity and gave answers of D and F in part (a). A and F was also a common error here.

B and C or A and F were common errors in part (b).

Question 11

This question was generally well done.

Question 12

It appeared that many candidates were anticipating a long multiplication question and saw their chance to demonstrate their skills in this question. Many spent an inordinate amount of time generating an exact answer when a simple estimation was required. The most common correct answer was £95, choosing to work with 19 rather than 20. At times poor arithmetic let some candidates down in simply multiplying 19 by 5. Some candidates estimated an answer of £95 or £100 and deducted a small amount realising that their estimated answer was too large. This was condoned and full marks were still awarded.

Question 13

The vast majority of the candidature gained at least one mark for drawing a rectangle in part (a). Drawing a rectangle of area 20 cm2 was less successful, many producing a 5 by 5 square and many drawing a rectangle of perimeter of 20 cm.

In part (b), an isosceles triangle was often seen but rarely of area 12 cm2. Far too often the product of the base and the perpendicular height was equal to 12. Some candidates did not make good use of the cm. square grid, instead drew triangles using fractions of the sides of the squares.

Question 14

Substituting the correct values into the expression in part (i) was good but many mistakes followed in the evaluation. 2 × was often seen equal to 2 sometimes 1.5 and even when

correctly calculated careless errors were not uncommon. 45 + 2 was another common error here.

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In part (ii), +15 was the most common incorrect answer seen but many candidates were able to secure the mark. It was not uncommon here to get 20 and 1 and then multiply the two together or even just leave the answer as 20 + 1.

Question 15

Whilst many candidates were able to correctly work out the subtraction calculation in part (a), a great many showed weakness in this area. The method of decomposition was the most popular method attempted but this was often poorly executed; 444, 446, 426, 432 and 438 were incorrect answers regularly seen. ‘Build up’ methods often lead to incorrect answers as a result of basic arithmetic errors along the way.

In part (b), although a correct answer was the modal answer, many candidates showed a weakness in the knowledge of ‘times tables’, particularly in computing the product of 4 and 7; 21, 24, 25 and 35 were common attempts. A significant number of candidates also struggled to multiply by 5. Few saw the easier option of 4 5 before multiplying by 7.

A few candidates demonstrated a complete lack of understanding by finding 4 7 and 7  5 and adding the products.

Question 16

Part (a) was usually answered correctly, however in part (b) many candidates clearly did take care in viewing the given shape. Often an isosceles triangle was drawn, usually of base 2 and height 5 units.

Question 17

This was one of the most poorly answered questions on the paper, largely because a great many students just could not interpret a mileage chart correctly. In finding a distance between two towns, many calculated the differences between the numbers beneath each town. This was evident immediately in part (a).

In part (b) many, who could read a mileage chart correctly, often correctly selected just two of the 3 required distances.

In part (c), many candidates demonstrated a complete inability to communicate a structured, organised and clear solution to the problem. Calculations dotted about the working space without explanation were rife. A small number of candidates were able to correctly solve the problem fully, many stumbling by incorrect distances from the table but more often the inability to deal with any distance, speed, time calculation. The most common mistake was to assume that 1 mph equated to 1 minute so distances of say 95 miles or 105 miles instantly became times of ‘1 hour 45 minutes’ and ‘1 hour 55 minutes’ respectively. When a total time of travel was found by a reasonable method (usually incorrect however), many candidates were then able to gain credit for correctly attempting to work out the time for the end of the journey.

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Question 18

Very few candidates used any correct algebra to solve this problem. The value of x, Jim’s share of the £23 was often correctly found in part (b) by trial and improvement methods.

It was very rare, in part (a), to see a correct equation formed. Some were able to quote x + 4 and x – 2 as the shares of Gemma and Jo, but could go no further.

In (a), there were many statements like x + 4 – 2 = 23 followed often in (b) by answers of £17.

Question 19

Part (a) was well answered, some left un-simplified and some offered an answer of  with no working.

Part (b) was less successful. Candidates were either able to achieve the full two marks or none. Many stated that 10% = £2 and 5% = £1 but could go no further. Many candidates repeated their efforts in part (a) and gave their answer as a fraction.

In part (c), many candidates were happy to offer incorrect answer which if checked couldn’t possibly be correct. The most common incorrect answer was £6.50 (£10 ÷ 2 + £1.50). Many simply subtracted £1.50 from £10, leaving an answer of £8.50 which they believed to be the final answer.

Question 20

Part (a) was answered correctly more than not, the majority of candidates spotting the patterns of numbers in the table.

Part (b) proved to be more of a challenge and only a small minority were able to complete line 10. Often line 6 or 7 were attempted. Even when the first two columns in line 10 were correct, the final total of 244 was rarely seen; again poor arithmetic skills prevented full credit.

Even fewer candidates were able to spot the connection between part (c) and what had gone before, the vast majority again practicing their long multiplication techniques.

Even when 2 ×10002 + 2 was quoted, the correct answer did not always follow as candidates struggled with squaring 1000.

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Question 21

The majority of candidates knew how to find range although many did not use the key reading the extreme values of the stem and leaf diagram as 52 and 13 and gave 39 instead of 3.9 as their answer in part (a).

Similarly in part (b), 31 was the most common incorrect answer. Many tried to write out the data in order (not realising that this was done in the diagram) and often left out one or more entries.

In part (c) most candidates gained at least one mark and often two. The most common error was .

Question 22

One mark was awarded in part (a) for any correct expanding of a bracketed expression. Many candidates picked up this mark but poor algebraic manipulation prevented further credit. The expression 2x – 2y – 3x – 6y was a common error, showing weakness in dealing with directed numbers.

In part (b), although a correct answer of −2 was often seen, rarely did it result from sound algebra, more often it was the result of a trial and improvement method. Many candidates using this method however seemed unable to consider a negative value.

In part (c), few understood the concept of factorisation and 10x was the most common answer.

Question 23

Only the most able candidates were able to correctly solve this problem although some were able to pick up marks for part solutions, for example in dividing 360 by 6 or showing the exterior angle of a square on the diagram. The interior angles and exterior angles of the hexagon were often confused, many taking 60 as the size of an interior angle.

Several wrote 145 on the answer line again suggesting the use of a protractor.

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Question 24

Plotting of the extra points in part (a) was usually accurately done, although many misread the scale on the axes.

Part (b) was generally answered well. Some candidates attempted to quantify a relationship and got confused; many thought it was a ‘negative’ and some ‘positive’ relationship. Neither response gained any marks.

In the majority of cases, the answer to part (c) was taken directly from the scatter diagram without any consideration of a line of best fit. This was often successful but when not, no marks could be awarded. Students should be encouraged to draw a line of best fit, demonstrating their method.

In part (d) very many candidates referred to a temperature of 100 being too hot or too high instead of relating their response to the constraints of the actual data in the experiment. Explanations such as “the ice would melt too quickly at 100” were rife. Many often thought that the data couldn’t be used because the graph was in minutes not seconds.

Question 25

Misreading of the scale in part (a) prevented a great number of candidates gaining full marks; one mark was awarded for any correct translation.

In part (b) only a very small minority showed any understanding of the line y = x. In fact more candidates gave a correct reflection in the line y = –x which gained one mark. Many just reflected the shape in either x = 0 or y = 0.

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PRINCIPAL EXAMINER’S REPORT – FOUNDATION TIER PAPER 2

GENERAL COMMENTS

There were many good responses. Candidates were particularly good at finding averages and criticising and improving questionnaires.

Simple algebra was also carried out well.

Many candidates still have difficulty calculating with percentages. Too many fell back on ‘build-up’ methods or were unaware of how to find simple percentages.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

In part (i) answers were generally accurate with few errors.

Although many candidates got the correct reading in part (ii), there were common errors of the sort 22, 20.4 and 22.2 and 36 from reading the scale in the wrong direction.

Question 2

This was a simple question designed to assess straightforward calculations of time.

In part (a) many candidates got the correct answer (7:15 p.m. or 19 15). Full marks were also given for alternative non-standard forms where the context made it clear (7.15). Often, candidates did the calculation in their head. Those that did show any work generally used a build up method along the lines of 17:55 18:00 19:00 and 19:15 or more rarely, 17:55, 18:55, 19:00 and 19:15. Of course, having a calculator did lead some astray and they produced answers such as 18:75 (17.55 + 1.20) and 18:35 (17.55 + 80).

Part (b) was also quite well done. Candidates could use the direct method of counting on from 17 55 to 18 34 or were allowed to work back from the answer to part (a). Some candidates misunderstood and worked out the time until the programme finished (41 minutes).

Question 3

Candidates did well in part (a) although occasionally the 7.01 and the 13.1 were round the wrong way.

Part (b) was answered correctly by nearly all candidates.

In part (c) the brackets proved to be a challenge. (15 – 4) was seen as often as the correct (2 + 1). Many candidates had more than one set of brackets and these were often unmatched.

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Question 4

Many candidates were able to write down the correct answers for part (a), although a significant minority wrote down the coordinates reversed.

For part (b), many plotted where they thought the midpoint was and tried to read off the coordinates and others had an intuitive idea of what to do, often finding the x-coordinate correct but not the y-coordinate, which was often given as 1 instead of the correct 0.5.

Question 5

Many candidates were able to score 1 or 2 marks for answers to the first two parts.

Since the pie chart was drawn accurately it was possible to get a mark for the angle of the sector by giving an answer in the range 103 to 107. However, most candidates calculated their value. The entry for chocolate proved more of a challenge as candidates had to reason proportionally presumably from the entry in the top row by finding one third of 12 and adding on to get 16. This was rarely seen and the answer of 18 was much more common.

Question 6

There was less evidence of confusion between the area and perimeter concepts on this question than has been seen on some past examination papers. This may be due to the fact that the area was much easier to count than the perimeter. Units were generally correct or omitted or occasionally represented just by the power, so 282 was not uncommon. There was the occasional cm3. Some candidates thought they had to calculate the area rather than count squares.

Question 7

Parts (a) and (b) were well answered. Candidates certainly had been trained to measure lengths and angles.

Part (c) was also well done. Most candidates recognised that the angle had to be obtuse and drew it accordingly although there were some who gave the 50 supplementary angle.

Question 8

This was well answered. Most candidates knew what went in the tally column and were then able to summarise that in the frequency column, usually with correct results. Very occasionally, frequencies were put in the tally column with the frequency column left blank or filled with other numbers such as the rankings of the frequencies.

The bar chart was completed well in part (b).

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Question 9

Generally the correct fraction was seen in part (a), although a few candidates wrote .

Part (b) was generally well done, although 0.38 and 3.8 were common errors.

Part (c) was a question which required some independent thought from the candidate. The standard strategies are to convert the fractions to equivalent vulgar fractions with the same denominator or to convert each of the fractions to decimals or percentages. Many candidates did do this and wrote down the correct answer of . Some candidates wrote down this answer without showing any working. They did not score any marks. Other candidates decided to convert the fractions to fourths which meant their fractions had decimal numerators. This was allowed if carried out accurately and the correct conclusion drawn. Other candidates made all the numerators unity in which case the denominators were decimals or divided the denominator into the numerator. These approaches are

mathematically incorrect since and so the difference

depends on the size of a and b, or more simply that 3, 4 and 5 are equally spaced but ,

and are not.

Some candidates drew diagrams to show the fractions, presumably taking the idea from part (a). However, these were not successful as the diagrams did not show a clear enough comparison.

Question 10

There were a variety of responses to part (a) apart from the correct one. A very common response was p6 followed in order of frequency by p + 6 and 6ps.

In part (b), as well as the correct answer, a very common response was 5.

Question 11

In part (a) the table was generally filled well.

Generally points were plotted correctly in part (b) but a substantial number of candidates did not join the points, including those who plotted all the points correctly in a straight line.

In part (c) there were a pleasing number of candidates who scored full marks. Some used the conversion graph they had drawn whilst many others used a correct calculation.

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Question 12

Answer to part (a) were very good, with many candidates ordering their list.

In part (b) there were several misconceptions regarding the range, confusion with one of the other statistics being one of the major issues. Some candidates left their answer as 90 – 99.

There were several misconceptions regarding the mean in part (c), confusion with one of the other statistics being one of the major issues. Some candidates had the correct idea of adding the values and dividing by 10 but sadly forgot about bodmas, ending up with an answer over 800.

Question 13

In part (a) answers were generally good showing that candidates understood the arithmetical equivalence of the equation.

Part (b) was not so good, because of the confusion what to do with the 9 and the 3. Although many candidates did get the correct answer of 27, there were also many who got the answer 3.

Question 14

Most candidates managed to get at least 1 mark in the three parts of the question.

The number of faces in part (ii) was the part best answered.

There was evidence over confusion between the terms ‘edge’ ‘vertex’ and ‘face’ so that often the correct numbers were in the wrong place.

Question 15

Many candidates made a good attempt at this question. They first of all worked out 3 × 1.24 and then subtracted their answer from the total cost of £5.08 to find the cost of the 2 kg of carrots. Candidates then had to divide by 2 to get the cost of 1 kg. Typical errors were those of omission, such as the ×3 when finding the total cost of the potatoes and the ÷2 when finding the cost of a kg of carrots. Generally such mistakes lead to the loss of 2 of the 3 marks.

Question 16

This was very well answered. If there were errors, they tended to come in the final two columns where candidates did not notice that their entries did not add up to the given totals.

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Question 17

Successful candidates worked out the sum of the 3 given angles in the quadrilateral to get 288. They then subtracted this from 360 to get the size of the missing angle (72). The last stage required the subtraction of 72 from 180. Candidates fell at all points with candidates getting to the 288 and stopping, or getting to the 72 and stopping. Some candidates thought that the quadrilateral had two equal angles of 62 and ended with an answer of 118 whilst others simply subtracted the 62 from 180 presumably from a misuse of angles on a straight line.

Question 18

This shape can tessellate in some interesting different ways. The main responses that gained full marks were as shown below, but there were others.

Many candidates did not appreciate that a tessellation requires a repeat of the given shape without any gaps.

Question 19

The typical error was to ignore bodmas, therefore ending with an answer of −1.56. Some candidates used a calculator which was in fixed format so the answer was necessarily inaccurate.

Candidates had difficulty with the last part. There were a variety of incorrect responses, such as failure to round up the 4 to a 5 or to multiplying the answer to (a) by 10 or 100.

Question 20

Simple interest was not well known to candidates. There was little sign of the formula based

expression . Some candidates did work out 2.5% of £3500 correctly but then

did not multiply this by 3. Others did the correct calculation but added on the interest and gave the final amount. Many candidates could not work out 2.5% of 3500 and often worked out 2.5 × 3500. Some candidates decided to compound the interest. There were some signs of the 10%, 5% and 2.5% but often these were carried out incorrectly.

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Question 21

In part (a)(i) most candidates knew what a factor was and were able to write down at least 4 factors. Fully successful candidates could list all 8 factors or give 4 factor pairs. Some tried a factor tree, but were unable to use it to give a complete list.

There was a pleasing number of correct answers in part (a)(ii). In many cases wrong answers were actually common factors, just not the highest one.

In part (b) many candidates were able to make a start by listing successive multiples of 4, 5 and 6 respectively. In order to get to the lowest common multiple there have to be 15 multiples of 4, so many candidates failed to write their lists as far as 60. Appearances of 120 found from 4 × 5 × 6 were relatively rare, but the answer ‘1’ was all too frequently seen.

Question 22

This proved to be a challenging question. Many candidates were able to derive the given result y = 3x + 40 by adding 2x − 10 to x + 50, although there was no evidence that they were aware of the exterior angle property of a triangle.

In part (b)(i) many candidates took the short cut of 180 – 145 without justification although many were able to solve the equation 3x + 40 = 180 using a small amount of algebraic manipulation.

In (b)(ii) many candidates did substitute their value found in (b)(i) to work out two of the angles in the triangle and the other one was found from 180 – 145. Few were able to carry out the full calculation and select the largest angle.

Question 23

There were two approaches to the simplification. One was to use the calculator and work out the value of the three powers either by writing out in full or by using the power key. Those candidates generally, if successful, produced an answer of 216 but were unable to express this as a power of 6. The other was to work directly with the powers of 6. Many candidates who tried this route misused the index laws writing 610 as the numerator for example.

Question 24

Many candidates were reasonably successful in part (a). Most wrote down integers for example, although there was confusion about the correct end points of the list of numbers, so –1, 0, 1, 2, 3, 4 and 5 was a common wrong answer.

In part (b) candidates either knew how to apply this rule or did not. A few candidates were able to produce something that was a proper four-term binomial expansion and even fewer were able to simplify by collecting terms to a correct three-term expansion.

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Question 25

In part (a) many candidates could not calculate 12% of £140. The use of multipliers was very rare. Many candidates who did calculate 12% of £140 forgot to add their answer on to £140. Candidates who tried a build up method such as 10% = 14 and 1% = 1.4 were occasionally successful, but often had problems with place value when adding the decimals to the whole numbers.

Part (b)(i) was far better answered than (b)(ii). Many candidates thought that the correct answers were 10 kg (or 10.0) and 11 kg (but not 12 kg) respectively. Part (b)(ii) was rarely answered correctly, although there were a few answers of 11.5 seen. A significant number of candidates thought that 11.4 was the maximum possible.

Question 26

This was a complex problem involving ratio and fractions. Many candidates who had some idea of sharing in a given ratio were disconcerted by the fact that the divisor was larger than the sum of money to be divided. Nevertheless, many candidates were able to find two thirds of £9.60 or the equivalent.

Question 27

This was a standard question of its type. Many candidates were able to identify (the several) errors in the question and response boxes and also to make a good attempt at an improved question. Most candidates were able to state that the response boxes overlap or that there was a box missing for ‘I don’t listen to music’. However, a substantial number gave answers such as ‘it’s not accurate’ or ‘the question is too vague.’ These answers do not earn any marks.

Question 28

This was a multistep question involving Pythagoras’ theorem and area of a triangle. There were many candidates who did not know the use of Pythagoras or used it wrongly. Errors that occurred frequently included adding the squares (122 + 62), failing to find the square root (108) or forgetting to work out the area of the triangle after finding the square root, or just using base × height when attempting to find the area of the triangle.

Question 29

This fascinating question produced some interesting responses. A good minority of candidates were able to visualise a possible placement of the disks as just touching and to calculate the total number (32) from 8 × 4. However, some found the 8 and the 4 and then added. Other sensible strategies included dividing the total area by 64 and dividing the total area by the area of 1 disc. The optimal answer of 36 was very rarely seen.

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PRINCIPAL EXAMINER’S REPORT – HIGHER TIER PAPER 3

GENERAL COMMENTS

Many candidates struggled with basic arithmetic processes on many questions.

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

It was encouraging to note that most candidates did try to show their working. This led to method marks being awarded in questions 2(c), 3, 6 and 9 when the final answer was incorrect. However, some candidates produced such a jumble of numbers that it was hard to distinguish correct working from a choice of methods which would score no marks.

It is advisable for candidates to draw lines on the graph as part of their working to score method marks on these questions when their answer is incorrect. This might have proved very useful on question 11, 14 and 15(d). Candidates should be advised to ensure that all lines drawn are clearly visible to the examiner.

It is also advisable to fill in angles on diagrams that involve geometric calculations. This might have proved very useful on question 3, 10 and 19.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

Part (a) proved to be a good starter question with over 80% of the candidates scoring both marks. Some candidates failed to cancel their fraction to its simplest form. It was pleasing to note that only 8% of the candidates failed to score.

The most common error in part (b) was to give their answer as a fraction although 65% of the candidates could provide the correct answer of 30%. Many found 10% to be £2, but then were often not able to write 30% for £6.

Part (c) was poorly answered with over 68% of the candidates failing to score. A large proportion halved 10 then added £1.50 to get £6.50 whilst others managed to subtract £1.50 from £10 but then went no further. Only a small handful of candidates used the approach of setting up an equation. There were many attempts at trial and improvement. Candidates need to be encouraged to check their answers; had they done so they would have realised that £6.50 and £3.50 do not have a difference of £1.50. Only 29% scored both marks.

Question 2

Nearly all candidates got part (a) correct and many were able to get at least two of the three required columns in part (b) correct. The most common error was to provide Line Number 5 rather than Line Number 10. An incorrect calculation for 244 was the most common error where common wrong answers were 246 (wrong order of operations) or 144 (just squaring the 12). Square numbers were occasionally confused with doubles and 112 and 122 were clearly not known. 43% of candidates scored all 3 marks for the first two parts with a further 28% scoring 2 marks.

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Over 66% of the candidates failed to spot the pattern in part (c). Many of these tried to calculate 9992 + 1001² using long multiplication techniques, rarely meeting with success or continued the table to 62 + 82.

Some did attempt 2 × 10002 + 2, though a surprising number could not calculate the square correctly, giving answers of 2000, 10 000, 100 000 as well as 4000 after multiplying by 2 before calculating the square. Others failed to correctly square 1000, double their result or forgot to add 2. Only 22% of the candidates scored both marks.

Question 3

There seemed to be much confusion over interior and exterior angles. Many correct angles were seen but the method used to achieve them was not always very clear. Having obtained 150° a few went on to calculate 360 – 150 = 210 as their final result. Indicating angles on the diagram may have helped to identify the required angle.

There were many instances of dividing 360 by 5 rather than by 6. Others calculated 60 but indicated this on the diagram as the interior angle of the hexagon.

25% of the candidates got the correct answer from valid methods with a further 22% scoring 2 or 3 marks. It was disappointing to find that over 40% failed to score.

Question 4

Many candidates located the correct item, knowing the 11th value, but were unable to interpret the key correctly, thus 31 or 1 was a very common incorrect answer. Some confused median with mode and therefore thought 35 or 3.5 was the answer. Another common error was 21 ÷ 2 = 10.5th term, with average of 29 and 31 given. Many candidates wasted time rewriting all the numbers out below the table even though they were provided with an ordered table. Overall 32% of the candidates gave the correct answer with a further 34% scoring 1 mark.

Question 5

64% of the candidates scored 1 mark for any translation of the given shape in part (a) with a further 21% translating the shape correctly. The scale seemed to confuse candidates with many moving 8 squares to the left and 2 squares down rather than using the scales on the axes. Candidates might have realised something was amiss when their final shape ended up partly off the grid.

Part (b) was less successfully done with over 70% of the candidates failing to score.

8% of the candidates did score a mark for correctly drawing the line y = x or producing a correct reflection in the line y = –x. Translations and reflections in the x-axis or y-axis were common incorrect responses.

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Question 6

Using the information in the distance table appeared to cause some difficulty. Most seemed to add distances together but not always the correct ones or not just the 3 required distances. The alternative approach using individual times was dealt with no better. In some cases 2 p.m. appeared on the answer space without any method shown. This is a risky strategy as it denies the award of method marks should the answer be incorrect.

A few confused abbreviations of miles and minutes, using m for both, which resulted in adding a combination of times and distances eg adding the distances onto their 9 a.m. and 3 hours or changing the 3 hours for the meeting into 150 miles! There was a spread of marks awarded with 28% scoring all 4 marks and 34% failing to score. 21% scored exactly one mark generally for adding 3 appropriate distances or working out one of the times correctly.

Question 7

Part (a) was a seemingly innocent algebra question which if attempted in logical steps yielded the correct value of x. Unfortunately many missed the correct expansion of the left hand side of the equation and floundered in further simplification with only 48% of the candidates scoring all 3 marks. 18% of the candidates did manage to score 1 mark for either expanding the bracket correctly or rearranging their equation with at least the terms in x or the constant terms isolated correctly. However a significant number made mistakes with signs when rearranging ending up with 8t or 0 rather than 4t and 24. 25% failed to score.

In part (b) 57% scored one mark as large numbers of students failed to correctly expand the 2nd term of the 2nd bracket with –3x – 6y seen rather than –x + 6y. Most managed to expand the first bracket correctly. A significant minority treated the question as expanding double brackets to obtain a quadratic equation. Only 21% of the candidates expanded and simplified correctly.

Part (c) was generally well done with 43% getting it fully correct and a further 24% scoring one mark for either writing down 4 correct terms with incorrect signs or 3 correct terms out of 4 with the correct signs. Many students used the grid method which generally resulted in at least one mark. There are still many candidates who do not realise that the expansion should contain a term in x2 and there were many who combined the constant terms to get +2 or –2 rather than –35.

Question 8

65% of candidates scored 1 mark. They were able to show they had used 0.5 or 0.6 but gave the final answer as 0.9 rather than 0.09. Others tried to calculate rather than estimate or rounded 0.61 to 1. Only 10% of the candidates gave an answer of 0.09.

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Question 9

Not many candidates took the easiest route of using 22 % – 17 % and then finding 5% of £180. Numerous different attempts were seen, some of which were productive. Most candidates made a good attempt at this question and encouragingly lots of working was shown with 43% scoring all 3 marks.

However a high proportion of candidates made arithmetic errors in their calculations. The most common method used to find the percentages was to break them down to 10%, 5%, 2%, 1% and %. Mistakes came from an error in this or an error when adding them. 26% of candidates failed to score.

Workings were too often slanted on the page and scattered everywhere. A more organised approach should be encouraged.

Question 10

Many misread the isosceles triangle thinking that the base angles were CBE and BEC leading incorrectly to state CBE = 48. The follow through applied to angle ABC meant all was not lost with 23% scoring 1 mark in this situation. It was disappointing to note that 54% failed to score. Candidates should be encouraged to write their calculated angles on the diagram particularly as they find it hard to express angles in 3 letter notation. Only 14% were able to write 42 on the answer line.

Question 11

In part (a) many candidates plotted the two points correctly and then went on to provide an acceptable description of the relationship between the 2 variables. 64% of candidates got both part (a) and part (b) correct with only 6% failing to score.

Many lost a mark in (b) by only writing ‘negative’ rather than ‘negative correlation’.

In part (c) many found the approximate value without drawing a line of best fit on the diagram. Whilst this was not penalised, candidates risked losing all the marks if they wrote down an incorrect value.

In part (d) many statements referred to the physical attributes of the situation. There was not a great appreciation that correct comments had to refer to the data stopping at 70° or a reference to the line of best fit extending to negative time, not the laws of physics. Some candidates gave irrelevant information about the graph needing to be in seconds or information about the boiling point of water rather than answer the actual question which concerned why Suzy’s data cannot be used. There were many interesting, unacceptable comments which referred to ice cubes melting and water boiling at 100°. Only a quarter of the candidates were successful in both parts (c) and (d) with around half the candidates not scoring in part(d).

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Question 12

There were some good starting points with the realisation that the equations needed multiplying to make either the x or y terms the same. Nearly 30% of the candidates continued to find both correct values. It was encouraging to note that the majority appreciate they are being asked to perform algebraically rather than an endless testing of values. However, many candidates had no idea what to do or added their new equations rather than subtract. As a result 58% of candidates did not score on this question.

Elimination followed by substitution was the favoured method but there were lots of arithmetic errors when multiplying through the equations and difficulties when trying to eliminate one of the variables. There was confusion over whether to add or subtract the equations. If subtraction was chosen then some could not cope with the solution of –y = –32 and went on to substitute y = –32.

Question 13

Most candidates had an idea of what to do in part (a) although 29% only scored 1 mark for either leaving the answer as 24 × 1015 or 24 000 000 000 000 000. A significant minority managed to get the 24 × 1015 but then incorrectly changed this to 2.4 ×1014. It was not uncommon to see both numbers converted to ordinary numbers but all too often candidates were let down by their inability to multiply these. 23% got part (a) fully correct.

In part (b) 67% failed to score. Some gained one mark for writing out the 2 numbers and attempting to add. However, there were place value issues with many adding the 6 to the 4 resulting in 100000000 or equivalent. Only 18% wrote the correct answer.

Question 14

Many candidates that attempted the question did not seem to have any idea what was required. Only 11% of the candidates were able to find an estimate for the solutions to (a)(i) and 10% to a(ii). Attempts were seen at solving the equation by factorisation and some crude, unsuccessful attempts to use the quadratic formula. Those candidates that were able to use the graph to find the solutions to x2 – 5x – 3 = 6 generally gained full marks, reading the graph correctly to within the tolerance of ±0.2; marks were not lost by inaccuracy. The line y = 6 was seldom seen.

In part (b) drawing the line y = x – 4 on the graph was not handled well with many unable to produce a worthwhile attempt. Not all the attempted lines drawn actually intersected the given curve thus making the solutions of the equations somewhat alien. 91% of candidates failed to score. If the line was drawn correctly points of intersection were often identified, although many candidates failed to appreciate the difference in scales. Many responses only gave x values instead of the co-ordinate pair, failing to appreciate that they were solving simultaneous equations.

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Question 15

66% of candidates spotted the correct class. Some candidates lost the mark by giving the frequency that corresponds to the correct class. There were also incomplete answers when candidates gave the lower or the upper limit of the class.

71% of the candidates completed the cumulative frequency table correctly. The most popular incorrect answer to (b) was to use the frequency in each group as the cumulative frequency. Some made an error with one or more additions and followed that through to give various incorrect final values. A few thought that the first cumulative frequency value had to be zero whilst others used multiples of 10 for the cumulative frequencies.

On the whole part (c) was well done with most candidates correctly plotting their values from an acceptable cumulative frequency table correctly, mostly at the top of the class intervals. Common errors were not joining the points together and not placing points at the ends of intervals. Bar charts were also evident and there were many lines of best fit drawn. In part (d) many candidates did not subtract their reading from 50 to get the correct answer. Just under 20% of the candidates got parts (c) and (d) fully correct with 30% failing to score in either part.

Question 16

Many candidates split their cross-sectional area into triangles and a rectangle, some doing it successfully and completing the question. Few could remember or correctly apply the formula for the area of a trapezium, or multiplied all the numbers they could see (or a selection of) or found the total surface area. For some, the step by step requirements of the question prevented them from following any sort of logical process, with the cross-sectional area just being the first hurdle. This was evident in the written work which was often chaotic and lacked any methodical approach. Many gained the latter two marks for correctly multiplying their volume by 5 and then converting correctly to kg by dividing by 1000. However, there were equally as many candidates who tried to convert g to kg by dividing by 100 or 10, or who tried to find the mass by dividing by 5. Only 9% of candidates scored full marks on this question with 68% failing to score any marks.

Question 17

Even at this level, in part (a) many struggled to square –5 in the context of the question. 68% of the candidates failed to score. It was clear that a number of candidates had a poor knowledge of the order of operations. 10 + 150 = 140 or –140 were common incorrect responses. Overall only 17% of candidates were able to work out that y = –160.

In part (b) most candidates found the changing of the subject of the formula quite challenging. Recognition that the term in x needed to be isolated was not always seen as the first step. Addition and subtraction took preference over division in subsequent working. Many students ‘lost’ the minus sign on the –2qx2 although some were able to carry on and successfully divide by 2q, then square root their answer. In the more successful processing, methods dealing with the introduction of the square root presented further challenges. Many only placed the square root round the numerator. 78% of candidates failed to score with the percentage of candidates scoring 1, 2 or 3 marks evenly spread.

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Question 18

It was pleasing to see that many less able candidates were able to write down the value of 20 with 59% of the candidates getting this correct. The most frequent incorrect answers were 0 and 2. There were a few more creative individuals who gave other answers such as , 20 and 0.2

It was quite evident that very few candidates understood what they were being asked to find in part (b) as the most common response was a nil response. 86% of candidates were not able to write down the value of y.

There were some confident approaches amongst the more able candidates in part (c) with almost 20% of the candidates scoring at least 1 mark. Dealing with the negative sign in the power tended to be the first priority in these cases. Even if the final answer did not appear, marks were being gained by writing down the stages in the working.

Question 19

Many candidates were able to give the correct response of 45, but few gave valid reasons for their answers. Many started with angle CBD = 90° rather than starting with angle ACB being 90° as it was an angle in a semicircle. The reasons given were often missing or incomplete and few were correctly able to cite the necessary circle theorem rule. Many students spotted the isosceles triangle, though several referred to the triangle incorrectly as equilateral. Many picked up a mark for an answer of 45°.

Correct angle notation was not widely used and many reasons were not well written so candidates should be encouraged to annotate diagrams as much as possible. Overall 54% scored 0 marks, 17% scored 1 mark and 5% scored all 4 marks.

Question 20

Candidates answered part (a) quite poorly without a clear understanding of how to factorise. Some candidates had an idea and put two empty brackets or had put 2x in one of the brackets. On a positive note, where (2x…..)(x……) was shown, they were nearly always correct. 85% failed to score and 14% scored both marks in part (a).

In part (b) candidates who achieved marks usually attempted to expand the right-hand side of the equation; only on very rare occasions did the answer from part (a) appear and then only really to produce x = –3 since (2x – 1) was cancelled on both sides and not equated to zero. Expanding (2x – 1)2 often led to 4x2 + 1 or 4x2 – 1 which then prevented any further marks. 80% of candidates could not make any headway in this part with only 2% arriving at both correct solutions.

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Question 21

An application of Pythagoras Theorem was required to find the height of the right-angled triangle. Most realised this but did not always apply it correctly. A few assumed that k was the height of the triangle and went on to give the area as k 2√3 resulting in an immediate dead-end. In others there was a reluctance to show much working with just the value 6 on the answer line. As a proof was required this could not score any marks. 88% failed to score with 5% scoring 1 mark for a valid statement of Pythagoras or adding rather than subtracting the squares of the two sides and reaching √48. Many were unable to square 2√3. Of the candidates who successfully used Pythagoras a number forgot to divide by 2 for the area of the triangle.

Question 22

The first branches on the probability tree were nearly always correct but the second branches caused much more difficulty starting with exactly how many there were of each colour in the boxes. The most common error in the second branch was to use 10 as the denominator rather than 11. It is disappointing at this level to see how many candidates just put a single number on each branch, e.g. 6, 4 on the first branch followed by 7, 3, 7, 3. This would not score any marks.

Part (b) made use of the values on the probability tree but using this information correctly involved a clear understanding of the question which was frequently not the case. Some, after writing the incorrect probabilities, did go on to multiply across the correct branches and even to add their totals, thus securing method marks and showing recognition of BB or WW.

However, there was a lot of confusion with some multiplying across all branches and adding all totals, others thinking that the required combination was BW and WB rather than BB and WW. Overall half the candidates failed to score on this question with a further 28% scoring one mark, generally for the first branch in part (a). Just over 6% of the candidates got the question fully correct.

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PRINCIPAL EXAMINER’S REPORT – HIGHER TIER PAPER 4

GENERAL COMMENTS

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

Candidates made a good effort to attempt questions that involved more than one stage in the working, for example, questions 5 and 7 but were often let down by a lack of standard techniques, for example finding the area of a right-angled triangle and knowing which order to carry out a division sum.

Candidates need to ensure that they can recall standard formulae such as those needed for finding the circumference of a circle and the area of a triangle.

When asked to give reasons in geometry questions then geometric reasons should be given rather than working.

Candidates need practice in giving clearly expressed written answers, particularly when interpreting data.

REPORT ON INDIVIDUAL QUESTIONS

Question 1

The majority of candidates were able to give the correct answer to the calculation in part (a). Candidates who choose to work out the numerator and denominator separately before carrying out the division would be well advised to retain accuracy until the final operation. Some who took this approach then divided the denominator by the numerator rather than the other way round. A value of –1.56055013 was the most popular incorrect answer seen, coming from the wrong order of operations.

Part (b) was well done although a common error was to round to one rather than two decimal places.

Question 2

This question asked for the total amount of simple interest earned. Common errors were to give the total amount in the account and/or to use compound interest. Those who did use compound interest could gain a maximum of 2 marks out of 3. The calculation of 2.5% was generally well done although errors were frequently seen from candidates using the ‘build up’ approach. Candidates sometimes confused 2.5% with 25% when converting to decimals.

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Question 3

In part (a) two of the three possible problems – no time frame, overlapping boxes, no box for zero – were given by the majority of candidates. Stating that the ranges under two of the boxes were different was not accepted.

In part (b) most candidates started with a question that included a time frame, although this was still missing in some answers. Giving either exhaustive or non-overlapping response boxes was enough to gain the second mark. The use of inequalities in conjunction with response boxes on a questionnaire is not accepted, though inequalities were seen on only a small minority of scripts.

Question 4

Part (a) was well answered.

In part (b) the usual confusion between LCM and HCF was evident in responses with 1 given as a common incorrect answer. Candidates who listed multiples of the three given numbers were generally more successful in finding the correct LCM than those who wrote each number as a product of its prime factors. Those who gave a common multiple rather than the LCM were able to gain one of the two marks.

Question 5

Many correct responses were seen. Those candidates who were able to divide the money into the given ratio successfully generally went onto gain full marks. There were, however, a significant number of candidates who either ignored the final statement in the question or who were unable to find of £9.60. Some candidates simply found and did not subtract.

The initial stage in the calculation to divide £28 in the ratio 13: 12: 10 confused a number of candidates who divided 35 by 28 rather than the other way round. Candidates who made this early error were still able to gain 2 out of 4 marks provided they went on to complete the question correctly with their incorrect amounts. The focus in this question was on technique so an answer of £6.4 was accepted but candidates should be reminded that this isn’t always the case, they should ensure that any answer involving money should have two decimal places when appropriate.

Question 6

When asked to ‘show’ that a statement is true it is important that this is shown explicitly. In this question the sum of the two algebraic expressions was frequently seen but, in most cases, this was never equated to y. Reasons were often omitted or, if present, were incomplete. It is not sufficient to say ‘line is 180’ – the full statement ‘angles on a straight line sum to 180’ should be given.

Part (b) was generally answered better than part (a) although the correct answer was not always given in (b)(ii) despite being evaluated. Candidates would sometimes correctly work out the size of all three angles but then give, for example, 60 rather than 85 as their final answer. A very small minority of candidates named the largest angle in the final part rather than giving its value.

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Question 7

The overall method needed to solve this problem was clearly understood by the vast majority of candidates. Problems occurred firstly when many candidates were unable to work out the area of the triangle correctly, the most common error being forgetting to halve the product of the perpendicular sides. The other most common error was for candidates to use the perimeter rather than the area of the rectangle.

Question 8

The formulae for the circumference and area of a circle are still either frequently confused by candidates or not known. Candidates who used the correct formula in part (a) generally scored full marks in this part.

From those candidates who attempted part (b) the most popular method, unfortunately incorrect, was to attempt to divide the area of the rectangle by the area of the circle. However, those who did this correctly and then gave their answer as the integer 44 were given one mark. Unfortunately, the majority of candidates who took this route divided the area of the rectangle by the circumference of the circle. Those candidates who realised that part (b) could be answered by considering the diameter of the circle alongside the length and width of the rectangle were more successful. The main error when using this method was to fail to round to integer values before multiplying to find the total number of circles.

Question 9

There was a lot of confusion with exchange rates demonstrated in candidates’ answers to this question. The common way to attempt to answer the question was to take an amount of money, usually in pounds, and then use the two exchange rates to convert to Euros. Unfortunately, the majority of candidates using this method with an amount in pounds generally multiplied by both exchange rates rather than multiplying by the exchange rate in London and dividing by the exchange rate in Paris. A minority of candidates realised that all that was needed was to divide 1 by either of the rates given and then compare with the other rate. The most sophisticated correct method seen was to convert from pounds to euros using the London rate and then back into pounds using the Paris rate. It was, however, clear that some candidates using this approach did not necessarily understand their answer as their conclusion was frequently incorrect. It was also noted that many students failed to use units in their working, so it was often unclear what they were attempting to calculate.

Question 10

Those candidates that understand the method needed to estimate the mean from a frequency table were generally successful. The most common error seen here, however, was to divide by 6 rather than by 60. Other errors were mostly arithmetical. There are still many candidates who divide the total of the frequency column by the number of classes or find the mid interval values and sum these before dividing by either the frequency of number of class intervals.

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Question 11

Part (a) was answered better by candidates than part (b).

In part (c) common incorrect answers which gained some credit were 2n12, 8n12 and 16n7. Very occasionally 16 + n12 was seen. A common incorrect answer seen was 2n7.

Question 12

In part (a) the majority of candidates recognised the need to provide a list of integers. Many correct answers were seen, common errors were including 5 or omitting –2 and sometimes 0.

In part (b) 2.5 was seen in the vast majority of scripts but the correct final answer of x > 2.5 was not always present. When the requirement of the question is to solve an inequality then the final answer must be the correct inequality.

Question 13

Despite the form of the equation given, part (a) was generally well answered. Weaker candidates did struggle with using the equation.

Success in part (a) generally led to a correct graph in part (b).

However, part (c) was frequently not attempted. When using the graph to find the gradient, the different scales on the axes caused some problems. Those candidates who chose to rearrange the given equation were more successful in finding the correct answer although the answer was often given as y = –1.5x.

Question 14

The instruction to factorise an expression is still not understood by a number of candidates. Success was more evident in the easier part (a).

In part (b) candidates had to take out at least two common factors correctly before any marks were awarded. Many answers were left partially factorised; provided this had been done correctly using two factors then the method mark was awarded. A number of candidates tried to factorise into two brackets.

Question 15

The common error from those candidates who knew how to find a moving average was an incorrect use of their calculator with the division button being used before the sum of the relevant three numbers had been found. Although, it is fair to say that this error was not as evident as it has been in previous series.

A common incorrect answer in part (a) was for the candidate to continue what they believed to be an arithmetic sequence with the numbers 41 and 47.

In part (b) the requirement was to describe the trend. Therefore no credit was awarded to answers that appeared to be attempting to describe a correlation either by the use of the word positive or in a general. Neither was credit awarded to answers that concluded more cars are sold in colder months.

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Question 16

The vast majority of candidates could write down the median from the given box plot. There was less success with finding the interquartile range. Errors included just writing down the value of the lower or upper quartile, using an incorrect value for either the lower or upper quartile and leaving the answer as 70 – 47.

There were few errors seen in drawing the box plot in part (c), the most common error was in plotting the median, usually at 64 rather than at 62. When asked to compare distributions it is expected that candidates will compare one value (e.g. the median) and one measure of spread (e.g. the range). Many statements given did not answer the question as candidates often tried to provide an answer along the lines as to which group provided the best guess rather than comparing the distributions or just stated values without any comparison.

Question 17

A popular incorrect answer was to find the scale factor 2.5 and then use this to multiply 12.5 to give a final incorrect value of 31.25. Candidates who used the scale factor were more successful in generating the correct answer. Many candidates found the value of 5 which is the difference between the two lines using but failed to add this to the 12.5 cm ignoring the obvious fact that the line must be longer than 12.5 cm.

Question 18

The most popular (incorrect) answer seen was 90 showing that candidates still fail to grasp the connection between square units.

Question 19

Candidates who were able to make a start on this question by multiplying through by x were few and far between. Once the correct quadratic equation was obtained however this generally led to the correct solutions. Once exact solutions were seen any attempts to find decimal equivalents were ignored. Candidates who opted to use a trial and improvement method of solution generally gained no marks unless they were successful in finding both solutions to at least three significant figures in which case 2 marks were awarded. A few candidates successfully completed the square to get exact answers. Many candidates seem unaware that their answer involving a surd and fraction was the correct answer.

Question 20

A correct trigonometric statement in part (a) was then often rearranged incorrectly to give no further marks.

Some candidates picked up a mark in part (b) for correctly identifying angle RPQ as 62 but that was as far as most candidates got. The few that did go onto use the cosine rule or some other two stage method were generally successful. Some candidates clearly had their calculator set in grad or rad mode throughout this question. Common errors were to assume angle PRQ was 90 or that SR was 7cm.

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Question 21

Those candidates who understood the concept of histograms generally gained full marks. An incorrect answer of 32 (instead of 34) was occasionally seen in the frequency table, possibly arising from a mis-reading of the scale on the vertical axis.

Question 22

Proof involving congruent triangles is not well understood. The best solutions were clearly set out with a reason accompanying each statement and the final reason (e.g. SSS) for congruency given. Some candidates were able to pick up a mark for such statements as AM = MC. One common incorrect method was to show that all three pairs of corresponding angles are equal and then incorrectly believing that this was a proof for congruent triangles.

Question 23

It was encouraging to see a number of candidates make a start to part (a) by providing a partial factorisation of the expressions but this was often then left as x(x + p) + q(x + p) or x(x + p) q(x + p) omitting the required addition sign.

The more able candidates were generally able to gain two marks in part (c) but being unable to cope with the negative sign meant that many incorrect solutions followed on from gaining the two method marks.

Question 24

The formula for the surface area of a sphere was occasionally quoted incorrectly, usually with r3 rather than r2. Candidates who provided the correct formula for the surface area of a sphere generally then went on to score 1 mark, frequently the area of the top surface was ignored.

Question 25

Common incorrect calculations included 645 × 400 and 640 × 395 Some candidates were able to gain a method mark for showing that they were attempting to multiply two lower bounds together but rarely were these the correct lower bounds.

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GRADE BOUNDARIES

GCSE Linear Mathematics 1380November 2011

1380 A* A B C D E F G1380F Foundation tier Paper 1F 64 52 39 27 15

1380F Foundation tier Paper 2F 65 52 40 28 161380H Higher tier Paper 3H 76 57 40 22 15 12

1380H Higher tier Paper 4H 84 64 44 25 17 12

(Marks for papers 1F, 2F, 3H and 4H are each out of 100.)

1380 A* A B C D E F G1380F Foundation tier 129 104 79 55 31

1380H Higher tier 160 121 84 47 32 24

(Marks for 1380F and 1380H are each out of 200.)

Grades for GCSE on the Higher tier papers are set by examiners at A, C and D by looking at the work of candidates and using statistical evidence. Once that has been done, the boundaries for grade B are set to be midway between A and C. A* is then calculated arithmetically so that the boundary for grade A falls midway between those for A* and B.

The percentages of students gaining each grade is thus set for A to E, but the Ofqual Code of Practice allows us to adjust the overall A* boundary in the light of statistical evidence to maintain standards over time. The examiners decided that a boundary of 159 would not have given a consistent percentage of A* grades this year, so it was adjusted to 160 to allow 4.4% of A* grades.

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