GCSE Mathematics Modular (Two-Tier)
(Summer Series) 2006
Chief Examiner’s
Report
GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
GCSE MATHEMATICS MODULAR TWO TIER SUMMER 2006
Chief Examiner’s Report
Grade Boundaries: 2006 (GCSE)
Grade
A*
A
B
C
D
E
F
G
U
Mark Range
360
359-320
319-280
279-240
239-200
199-160
159-120
119-80
79-0
Module 1
As the majority of the questions on these papers are common to the three tier Paper 1 the
comments will be the same as for that paper. The candidates were of the same mathematical
ability and attempts at answering the questions produced similar errors. Few of the
candidates achieved over 40 marks on either paper and the examiners involved felt that the
candidates answered Paper 2 much better than Paper 1.
Paper 1
Q.1
Not many of the candidates were able to gain full marks in this question. Quite a few
gave ¼ as the answer to part (a) and many failed to cancel 9/12 to its lowest terms.
Part (b) was not particularly well done and the same applies to part (c). Part (d) was
not well done – many got one correct fraction and then one incorrect answer thus
gaining 0 marks.
Q.2
This question was generally well done but candidates need to be able to express
themselves much better in part (b)(iii). It is insufficient to say 3 without saying what
is to be done with the 3.
Q.3
The majority of candidates completed this question correctly with practically all
candidates gaining at least 1 mark.
Q.4
This question was not very well done particularly part (b). Part (a) had many different
answers some of which were nowhere near the correct acceptable answer of 10 or
11 cm2. Very few candidates were able to calculate the correct volume of the cuboids
and even fewer were able to write down the dimensions of another cuboid of the
same volume. Rearranging 3 × 4 × 6 is not another cuboid. Some candidates again
showed their lack of knowledge by suggesting 9 × 8 as another cuboid.
Q.5
Part (a) of this question brought to light a very worrying aspect of this mathematics
paper – the inability of many candidates to subtract correctly. 420-228 caused great
difficulty for many candidates. Many gave an answer of 208. Part (b) was quite often
omitted and the usual answer to part (c) was 4. Part (d) also proved difficult for many
with a variety of incorrect answers such as 5/12, 5/35 or 6/12. The usual answer to
part (e) was 12 with both parts (f) and (g) being very poorly done.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Q.6
It would appear that some schools have not taught Stem and Leaf diagrams as there
was little evidence that these could be read by the candidates. It was also clear that
candidates did not know what was meant by the terms mode and median.
Q.7
Very few candidates failed to score on this question but sometimes it was only
because they included the units in part (c). Part (a) was usually well done but part (b)
was very disappointing indeed. Only a small number of candidates included the first
0 giving 072°. Finding the correct answer to part (c) was probably hindered by the
usual complaint with this paper – the candidates did not have a ruler with which to
measure the distance required. Some gave the measurement as 5 cm which is 2 across
and 3 up. Teachers: please ensure that all candidates have the required
instruments as listed on the front of the paper.
Q.8
Solving equations is still proving difficult for candidates at this level. Parts (a) and
(b) were well done but parts (c) and (d) proved very difficult.
Q.9
This question proved to be very difficult for all but the best candidates. Most pupils
compared these by looking at the totals sold for each for 7 days. In order to prove
who was best at selling books they needed to find the mean for both sellers.
Q.10
Very poorly done, due to poor geometrical knowledge shown by most candidates.
Many candidates did not seem to know that there are 180° in a triangle to get the
answer to part (a) and then part (b).
Paper 2
Q.1
This question was generally well done. Only a few were unable to answer part (a)
and it was a very rare occasion when a candidate failed to score any marks at all in the
question.
Q.2
This was not well done. Many candidates do not know the properties of geometrical
shapes well enough.
Q.3
Only a few candidates failed to score on this question.
Q.4
Quite a few candidates failed to notice all the factors otherwise quite well done. Part
(b) was usually well done except for part (b)(iii).
Q.5
The first part was usually well done and the obvious answer of 8.2 cm was given for
the answer to part (b) many more times than the correct answer of 7.2 cm
Q.6
In this question all parts were generally well done but once more decimal places and
significant figures have proved difficult for the majority of candidates.
Q.7
A straightforward question which was reasonably well done by the majority of
candidates.
Q.8
Most candidates found this question difficult. It is surprising that the calculations are
not more accurate especially as this is a calculator paper. Some candidates did the
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
calculations correctly but then failed to write down the change received in the correct
notation ie 55p or £0.55 not £0.55p or 55.
Q.9
This was very poorly done by the vast majority of candidates. The candidates did not
seem to know how to find the area of a triangle.
Q.10
This was usually very well done.
Q.11
Candidates must be careful when reading a question. Many candidates calculated
1.15 × 5 then added 2.75 instead of multiplying by 4 and then adding. Similarly in
part (b) they forgot to add the day at the end of their calculations.
Q.12
This question was generally well done with nearly all receiving 1 mark.
Q.13
Scale drawing is an area which needs attention. Not many candidates achieved full
marks. There was very little evidence of compasses being used. (See note on Paper
1.Q.7 re equipment).
Q.14
Again there were not many full marks achieved in this question. Parts (a) and (c)
proved the most difficult for candidates.
Q.15
This was another question which proved difficult for the majority of candidates.
Candidates had difficulty in working backwards in the correct order. This is a
question where working out should be seen to gain part marks but in most cases this
was not seen.
As mentioned earlier the one thing which was noticed this year in comparison to previous
years was the difficulty that many candidates had with subtraction. This, along with stem and
leaf diagrams, three dimensional axes and basic computational skills are all areas which need
attention in the preparations of future candidates.
Module 2
These papers were suitable for all appropriately entered candidates and the majority of
candidates were able to make some attempt to answer most of the questions. Because of the
wider range of grades available on the new Foundation tier, there had to be questions of a
more testing nature at the higher grade level and proper scope for differentiation in the paper
and this meant that there was a wide range of mark totals gained by the candidates. It was
encouraging to see Grade C candidates producing work of a similar standard to that expected
on the traditional terminal papers. Unfortunately there was a large percentage of candidates
who were only able to successfully cope with questions at the lower grade levels. Such will
always be true of grade G and F candidates. The examiners felt that the language appeared to
be at an appropriate level and the questions allowed pupils to respond positively. As many
questions were common to the traditional terminal suite of papers, the comments will be
similar to those for their appropriate counterparts. As usual, a remarkable number of
candidates seem to attend the ‘with calculator’ paper ‘without calculator’, indeed without
ruler, protractor, etc.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Paper 1 (non-calculator)
Q.1
This question on sequence of shapes was generally well answered.
Q.2
In this question on simple fractions, part (a) was reasonably answered but part (b) was
poorly done.
Q.3
This was generally well answered, although too many omitted the 0 in the three figure
bearing.
Q.4
This question involving simple algebraic equations was generally well answered.
Q.5
This question on angles was fairly well answered.
Q.6
Although this was fairly well answered, a number of candidates confused cube and
cube root.
Q.7
This scatter graph question was well answered by many, attempted by most, with
plotting errors too frequent given the simple scales.
Q.8
This was disappointingly answered, with confused attempts in part (a) and very little
understanding of expressing 414 as a percentage of 600 in part (b).
Q.9
While candidates could often spot the pattern, few could find the nth term for either
sequence.
Q.10
Only the most able candidates could answer this question involving calculating the
mean from a frequency table.
Q.11
The basic algebra, ‘expand’ and ‘simplify’ in this question was beyond most of the
candidates.
Q.12
The common denominator was sometimes found, but rarely used completely correctly
in subtracting these fractions.
Paper 2 (with calculator)
Q.1
This flow chart question provided a good start to the paper and was very well
answered.
Q.2
This scale drawing was well done by many candidates.
Q.3
Many candidates made a reasonable attempt at this question.
Q.4
This Stem and Leaf question was fairly well answered.
Q.5
Significant figures were not well understood by candidates on this paper.
Q.6
Candidates were not confident in drawing lines from equations but most gained some
marks for their efforts.
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Q.7
An attempt to solve this problem on money calculations gained some marks for most
candidates but full marks for few.
Q.8
Part (a) on finding a midpoint was generally well answered, but less understanding of
three dimensional coordinates was evident in part (b).
Q.9
Only the best candidates at this level were able to factorise these algebraic
expressions.
Q.10
Generally some work was completed on VAT calculations but not many could
complete the whole question without errors of some kind.
Q.11
Many candidates mixed up circumference and area formulae.
Q.12
Some candidates did some factorisation of 40 but not many could find both LCM and
HCF.
Q.13
This discriminator for the top grade proved to be beyond the comprehension of all but
the best candidates.
Q.14
This compound interest problem was quite well answered by a reasonable number of
candidates.
Module 3
There was a vast range in performance on this paper. Some candidates were clearly entered
at the wrong level and struggled to pick up marks, in particular in the latter half of each
paper. The other extreme was where some candidates were clearly very well prepared and
made good attempts at all questions including the more challenging questions at the end of
Paper 1 and in Q.7 and Q.10 on Paper 2. In this upper region some candidates scored full
marks or lost 1 or 2 by carelessness rather than lack of knowledge. There were a large
number of candidates in middle regions who struggled to achieve half marks on these papers,
generally performing better on the non-calculator paper. Some topics simply were not
recognised by the candidates.
Paper 1
Q.1
Q.2
(a)
Quite a large number of candidates misplotted the point (26, 69) interpreting the
height scale incorrectly.
(b)
Too many assume the line of best fit must start at the intercept of the axes,
which was not appropriate in this question.
(a)
The multistep approach in this part caused problems for some with many
candidates not completing the question. However there were a large number of
correct solutions seen.
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(b)
Many knew the method but were unable to complete the numerical calculation.
Few were able to simplify the calculation down to 414/6. This question was a
good discriminator on this paper between the weaker and more able candidates.
Q.3
The majority of candidates picked up marks on this question. Many fully correct
solutions were seen.
Q.4
(a)
The brackets were expanded as 5x − 3 rather than 5x − 15 in many cases.
(b)
This part gave a disappointing response with many candidates not using the
inverse operations when moving terms. For those who did reach 10y = 1 many
then gave the solution as y = 10 instead of y = 1/10.
(a)
Part (a) was reasonably well answered.
(b)
Many candidates expanded the second bracket incorrectly giving −8 as the last
term rather than +8.
Q.5
Q.6
This was a very poorly answered question. Many struggled to recognise any correct
procedure for subtracting fractions. For those who attempted to calculate the whole
parts and fractional parts separately, only the very best were able to deal with the
−3/10 which arose from this method of solution.
Q.7
(a)
Well attempted, though a large number of candidates gave the first term as 7
rather than 8.
(b)
In this part, too many gave either the next term or simply gave n + 11 and n + 4
as the nth terms.
(a)
The bulk of candidates had some idea of what was required but did not have the
technique refined enough to pick up full marks. Common mistakes included
using the upper boundary rather than the midpoint or dividing the total by 6
rather than 100. Many completely incorrect solutions of 100/6 were offered.
For the candidates who did know the correct procedure, many incurred an
arithmetic penalty at some stage.
(b)
This part appeared a mystery to most candidates.
Q.8
Q.9
The bulk of candidates simply subtracted 9 from 12 and added the resulting 3 onto the
7.5 rather than treating this as a ratio question. A disappointing response. Again, the
more able candidates had no difficulty here and achieved full marks.
Q.10
Many assumed that since the second graph was linear the only linear equation was
y = 5x − 5. They did not recognise the alternative format in the equation 5x + 4y = 20
which was the correct solution and hence only picked up half of the available marks.
Q.11
This question was attempted by most but there were very few completely correct
solutions.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Q.12
This was a poorly answered question. Most candidates either equated 70% with £48
or found 70% (or 30%) of £48 and added.
Q.13
(a)
This question on indices was poorly attempted.
(b)
Most candidates commonly gave wrong answers of 6 or 0.
Q.14
A minimal number of candidates recognised the quadratic and the need for two
solutions. Few knew to factorise. Those who did generally got full marks. Many
candidates simply gave x = 1 as the only solution by a trial and error technique.
Paper 2
Q.1
Some candidates appeared not to know the term ‘factorise’; For those who did, only
part (iii) caused problems with candidates not knowing how to deal with the w term
once the w factor had been removed.
Q.2
(a)
Many achieved full marks on this question. Unfortunately too many candidates
were unable to distinguish between the required formulae for area and for
circumference inserting the answers in the wrong places.
(b)
Some candidates lost a mark by not including appropriate units in their answer.
Q.3
Many candidates were able to pick up full marks on this question. Simple rounding
errors or not using appropriate currency cost some candidates a mark. Some
candidates did not read the question carefully enough and proceeded to add the VAT
on to the second price also. In a few cases candidates worked in the reverse way
trying to take the VAT off the second price. This would not be considered usual
procedure in such a question.
Q.4
(a)
This was successfully answered by the majority of candidates with a very few
confusing the positioning of the coordinates in the answer space.
(b)
This question on three-dimensional coordinates was reasonably well answered.
Q.5
Whilst this question was not difficult, many ignored the requirement to give an
equation and rather than work algebraically they chose to provide a basic numerical
solution. For those who did work with an equation some gave the answer as 0.62p or
£0.62p incurring a penalty with respect to notation of currency.
Q.6
In many cases HCF and LCM were mixed up. Few candidates appeared comfortable
with applying the method of product of primes to reach the required answers. More
often listing of factors and multiples was used.
Q.7
This question was the best discriminator for differentiating between candidates on this
paper. Firstly some candidates did not recognise the need for the use of Pythagoras to
find the diameter and often chose to work with just 30 or 15 as the radius. Those who
did calculate the diameter correctly often forgot to half it to get the radius for
progressing with the question. A variety of formulae were then offered for the
volume of a cylinder. Finally some did not convert from cm3 to litres. There were
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
many totally blank responses to this question. Few completed it to the end.
Candidates must be encouraged to break more complex questions into simpler steps
and aim for some attempt in order to pick up marks on multistep questions.
Q.8
This was generally very good. The most common mistakes were when candidates
only did simply interest or where rounding errors were incurred.
Q.9
This was generally well answered. Many completely correct solutions were seen. For
many candidates, marks were lost through careless/inaccurate readings rather than
lack of understanding of the topic.
Q.10
This was very poorly answered. Many of the less able candidates made no attempt.
Only the very best achieved full marks in this coordinate geometry question.
Q.11
Many arrived at cos = 8/11 but were unable to complete using the inverse
trigonometry function on the calculator.
Q.12
The poor response to this question was a result of using a variety of wrong formulae.
This was astounding, considering the required formula was given at the front of the
question paper and basically the requirement for the candidates was to substitute in
the numerical values and key in to a calculator. An easy 2 marks were lost by a large
number of candidates. For those who did make the correct substitution too many
rounded 4/3 to 1.3 rather than keying directly into calculator.
Module 4
Both papers demonstrated a considerable range of ability from the candidates. Many centres
entered students who were clearly not well prepared and scored less than 20 marks. A
disappointing small proportion of the entry contained very able candidates many of whom
scored 35 marks or better on each paper. There were very few centres where candidates
scored a range of the marks available.
Paper 1
Q.1
(a)
The better students immediately identified angles standing on the same arc.
There were many poor answers of 90°.
(b)
Again the more able entrants spotted facing angles in a cyclic quadrilateral.
However the answer 100° did appear far too frequently.
(c)
Virtually every candidate identified that z was twice the size of y. Even though
the diagram was not drawn accurately, many followed through their wrong
answer in (b) and responded with z = 200° even though the angle did appear to
be obtuse.
Q.2
Well answered by most candidates who all correctly identified £48 = 30% as their
starting point. It was disappointing to see a large number of misreads and incorrect
logic of the type 70% = £48 and finding 30% of £48 and adding it on to £48.
Q.3
(a)
This was generally well answered.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Q.4
Q.5
(b)
Again a very good response.
(a)
Most candidates had no trouble in identifying the correct factors and hence
obtaining the correct solutions. Poor responses including (x + 14)(x − 1) = 0,
(x − 15)(x + 1) = 0 and weak attempts at a formula method. The weaker
candidates tended to begin with x2 + 14x = 15 and generally go no further.
(b)
Probably the best answered question on the paper. It was very clear that
candidates had practised this type of question and there were many correct
solutions.
(a)
This was easily done by most candidates.
(b)
Only those who realised that the question could be rewritten as 321/5 managed
to obtain the correct answer.
(c) & (d) These were answered only by the very good students and generally
correctly.
It was noticeable that weaker candidates were giving answers such as (a) 18, (b) 6.4,
(c) 12 and (d) −822/3, clearly demonstrating no knowledge of rational indices.
Q.6
(a)
Generally this was well answered with many students easily identifying the
correct ration required.
2
(b)
Q.7
⎛4⎞
Only the better students realised that ⎜ ⎟ was required to give the area ratio.
⎝3⎠
There were several alternative approaches involving scaling up the height of the
small triangle.
(a)
A standard variable width histogram answered correctly by those candidates
who had practised the technique. Many bar charts were produced by the
weaker students.
(b)
Correctly identifying the fact that the sampling method suggested was not
random earned easy marks here.
(c)
A question answered correctly only by the very best candidates who correctly
used the given information to identify these plants between 9 and 10 cm using
proportions.
Many simply assumed that half the interval were greater than 9 cm.
Q.8
(a)
There were few problems here as most candidates gave correct factors.
(b)
Virtually everyone reached the stage 3(a2 − 9d2) but only the good candidates
continued on to 3(a + 3d)(a − 3d).
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Q.9
A standard question of this type of equation. Correctly using the correct common
denominator and expanding and simplifying gave the correct quadratic equation
which factorised. Many trivial errors were made in the algebraic work leading to
incorrect quadratic equations which failed to factorise. An important point to note
here is that candidates using the quadratic formula for their equation and leaving their
answers in surd form did achieve 3 follow-on marks.
Q.10
A very poor response with only a small number of correct answers. Clearly many
candidates had not seen an ‘identity’ of this type. The method of ‘completing the
square’ was correctly used by only a very small number.
Paper 2
Q.1
A straightforward question with many correct responses.
(a)
Using the 150th (or 150½th) measure gave easy answers.
(b)
The 75th and 225th measures were easily identified and correctly subtracted by
most candidates.
(c)
Some confusion here with many not realising that all that was required was the
280th measure.
In general too many careless mistakes were made reading the answers as incorrectly
drawn vertical lines led to incorrect measurements. It should be easier to take the
reading on the graph at the point required.
Q.2
(a)
A disappointing number of candidates showed very little knowledge of how
gradient should be calculated with many incorrect values appearing. In fairness
most used y = mx + c correctly identifying c with ease.
(b)
An easy variation on the answer to (a) with many obtaining follow through
marks from their answer in (a).
(c)
Only the better candidates correctly identified the gradient required and using
substitution of the given point calculated the corresponding value of c.
Many of the weaker students made no response to this question at all.
Q.3
An easy question with only elementary trigonometry being required. Many correct
responses were obtained.
Q.4
Given that the relevant formula was given on page 2 this was only a calculator
exercise to produce the correct solution. Many forgot to give the correct units and lost
4
3
a mark. Incredibly formulae such as πr 2 , πr 3 and 4πr2 were seen all too
3
4
frequently.
Q.5
Another straightforward question with many correct answers obtained. Sadly there
were many careless errors seen in multiplying and subtracting the equations.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Q.6
(a)
Those who had studied this topic had little difficulty in obtaining the length of
OG.
(b)
Here the ∆ GOA had to be used to find ∠GOA. Many tried to find ∠GOB and
∠BOA and then attempted to add them to get ∠GOA.
Q.7
A standard proof which many had learned correctly.
Q.8
(a)
Very few candidates could produce the quadratic equation required.
(b)
It was an easy task to find the values of x required and most students correctly
applied the quadratic formula.
(a)
Using the graph was the method required despite the fact that many used a
calculator and obtained no credit. Reading the scales again gave many students
problems.
(b)
Rewriting the given equation as Cos x = 0.625 proved too difficult for many.
Q.9
Q.10
A disappointing response was obtained to this question. Many failed to correctly
identify the correct triangle or even the fact that the distance from Start to Ben was 7
km.
The students who produced correct solutions easily managed to rearrange the Cosine
Rule to find the necessary angle and hence the required bearing.
Q.11
Of those students who had practised this type of question many used y = 5 − 1½x and
gave themselves some tricky working in trying to simplify x2 + 4(5 − 1½x)2 = 10.
The very good students noted that 4y2 = (2y)2 and produced quick and elegant
solutions.
Module 5
Principal Moderator’s Report
The majority of centres are to be commended for the preparation of their candidates for the
management and the assessment of the set ‘estimation’ task. Centres that used the
Coursework Support Clinics benefited from this service and CCEA will continue to offer this
support in addition to the Agreement Trials in the autumn term. Centres will be notified of
the dates in the autumn and spring terms that the Coursework Support Clinics will be taking
place.
Observations on the Use of the Given Data
All but a few centres used some or all of the given data. The candidates in the few centres
that did not make any use of the given data generally did not achieve as well as candidates in
centres where the given data was used. It may have been because the candidates did not
consider the given data that they began by listing hypotheses. This is a practice that we have
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
advised against as it limits the number of marks which can be attained. Candidates are
expected to link their hypotheses, with each new hypothesis emerging through reflection and
evaluation of the outcome of testing the previous hypothesis.
The purposes of the given data are to:
•
enable weaker candidates to access assessment criteria in the first two mark bands;
•
provide opportunities for candidates to satisfy the criteria for Application of Number up
to Level 2;
•
provide a stimulus for candidates to set up their own task and to prompt them to identify
the factors they need to take into account when planning and collecting data. Factors
should be limited to 3 and could be age, gender or whether the estimation is non-sensory,
visual or tactile.
There were examples of coursework where candidates carried out an extensive analysis of the
given data and used statistical techniques which were inappropriate because of the small
sample sizes. Extreme examples of this were the use of box and whisker or cumulative
frequency diagrams with 10 pieces of data. Candidates should be advised not to use these
statistical techniques until they have collected sufficient data.
Observations on Collecting the Data
It is inevitable that teachers will have a role in managing the collection of data but candidates
must describe in their own words how the data was collected. More able candidates must
explain how the method of collection eliminates bias, why they are going to collect identified
data and why they have selected the target groups to collect it from. If this is well done it
will satisfy the sampling criteria and it will not be necessary to sub-sample unless to assist the
manageability of the analysis of data if candidates are demonstrating Application of Number
criteria.
Observations on Using Statistical Techniques
Candidates used a good range of statistical techniques in processing and representing the
given and their collected data. ICT was used appropriately and candidates seeking an
Application of Number Level demonstrated the techniques manually although many of these
candidates did not carry out checks on the accuracy of their calculations. It should however
be pointed out that statistical techniques that are not used for any conclusion are redundant.
There were examples of candidates executing a statistical technique (manually or using ICT)
without an appropriate level of understanding to enable them to apply the outcome
meaningfully to the task. The mark awarded to a particular technique should reflect the
quality of use and understanding. It was good to see many candidates use the absolute
percentage errors in estimations and it was even better to see candidates explain why they did
this.
Observations on Reflecting and Evaluating
This is an area in which candidates were weakest with many focusing on the ‘doing’ of the
task and not taking time to reflect on their results from processing and representing their data.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
This needs to, at least, happen following the testing of each hypothesis and at the end of the
task.
Examples of good practice observed where:
•
a candidate who stated a strength for using the collected data ~ “you can mark the actual
measurement on the box and whisker diagram letting you see how close it is to the
median”;
•
a candidate stated a weakness for using the collected data ~ “the size of the error is likely
to be bigger for longer lengths and will make comparison difficult”;
•
a candidate who stated that “my conclusions are valid only for the two lines I have used”;
•
a candidate who stated “the correlation between the estimates of the length of the straight
line and the curved line is weak; maybe it is because Year 8 are not good at estimating”;
•
a candidate who stated “I have used a cumulative frequency curve to make my Box Plot
as I measured the data”.
It will be necessary to continue to encourage candidates to state strengths and weaknesses in
their strategy which includes the collection of data and the statistical techniques selected for
use. It is important that these are in the context of the task and not a list of theoretical
strengths and weaknesses from a text book or internet.
The standard of coursework was encouraging for the first year of the pilot and the moderation
team commends centres for providing quality work which can be used for training new
centres and teachers.
Module 6
Completion Test
Foundation Tier
The quality of responses in this completion test, tested for the first time, was very mixed with
candidates in general scoring much higher in Paper 2 where a calculator was available. Many
candidates who sat Module M1 as well as those who sat Module M2 were sitting this
completion module for the first time. The paper proved to be accessible in some form to
virtually all the candidates who sat at this level with varying degrees of mathematical skills
demonstrated.
Weaker candidates performed quite well in the earlier questions in both papers while there
was sufficient scope in the latter part of the papers to challenge the more able. Many
candidates were lacking in the mathematical skills to deal with a variety of topics particularly
estimation, planes of symmetry, drawing plans and the use of algebra in equations,
inequations and indices. There was no indication that the students did not have sufficient
time to complete the paper.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Paper 1
Q.1
This question on reading scales was generally well done by all candidates.
Q.2
There was a very large number of poor responses. The ability to estimate is a skill
which was not in evidence in the work of a large number of entrants for this
examination.
Qs. 3 & 4
These questions were generally well done but the precedence of operators was
ignored in many cases.
Q.5
Symmetry is one topic at which nearly all candidates excelled – generally overall
excellent responses.
Q.6
The train timetable proved to be difficult for many candidates who failed to spot a
change of trains at Central Station.
Q.7
Most candidates received part marks for enlarging the triangle by the proper scale
factor but only the better candidates had the triangle in the correct position.
Q.8
Candidates were well prepared for the conversion graph and many scored full marks
though a significant number ignored the minus sign in part (b).
Q.9
There were good responses to part (a) but only the very best candidates gave the
negative square root as well as the positive.
Q.10
Generally well attempted by all but the weakest candidates.
Q.11
This question on probability and relative frequency was a good discriminator with
nearly all candidates getting some reward and only the more able completing the
question successfully.
Q.12
Again, most candidates experienced some degree of success although explanations in
part (b) were vague in some cases.
Q.13
There were few totally correct responses on planes of symmetry.
Q.14
As with Q.2, the ability to estimate is weak in many cases, and most candidates did
not seem to understand the term ‘reciprocal’.
Q.15
Only the very best candidates derived any marks in this question. The concept of
‘plan’ was not well understood across a wide range of centres.
Q.16
Rearranging a relatively straightforward formula proved beyond the scope of many
candidates sitting at this level.
Q.17
Most candidates with mathematical equipment were able to bisect the line but few
coped with the construction required in the second half of the question.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Q.18
Most candidates failed to formulate an expression in terms of x for the areas of the
circles and hence only the very able at this level experienced any success with this
question.
Paper 2
Qs.1 & 2
There were good responses to both these opening questions on the calculator
paper.
Q.3
Weaker candidates tended to respond similarly to parts (a) and (b) leading to a loss in
marks but part (c) was universally well received.
Q.4
Imperial units caused difficulty for many candidates at this level.
Q.5
Nearly all candidates received reward in this financial problem but only the better
candidates solved the problem correctly.
Q.6
Many good responses to this question requiring candidates to insert the correct values
into the algebraic equations.
Q.7
Most candidates had success in this question but in many centres, candidates seemed
unable to express a probability in a correct notation.
Q.8
There were many good responses to this question on currency exchange.
Q.9
Nearly all candidates gave good responses to this question involving ratio and
proportion.
Q.10
There were many disappointing responses despite the fact that the formula for the area
of the trapezium was given on page 2. Only the very best candidates gave their result
to an appropriate degree of accuracy.
Q.11
This question was a good discriminator with all candidates experiencing at least some
success in coping with the various transformations in the Cartesian plane.
Q.12
There were many good responses to probability and relative frequency.
Q.13
Some candidates seemed unable to cope with the conversion to hours but generally
this question received many positive responses. Most centres had prepared well for
the problem involving ratio.
Q.14
Most candidates received merit in parts (a) to (c) but the final part differentiated
between candidates of differing abilities with only the very best gaining full marks.
Q.15
There were many poor responses to the inequality but most candidates gained some
merit in simplifying the algebraic indices.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
Higher Tier
There were good responses to both papers with many high totals being achieved. A few
candidates were entered at the wrong level and would have had a better experience doing the
Foundation papers. Candidates generally achieved a higher total on the calculator paper.
Paper 1
Q.1
Probability and its use were well understood.
Q.2
The value of R was usually calculated correctly and 5n − 2 recognised and explained
as being possibly odd or even.
Q.3
Planes of symmetry were understood with some errors, the sphere causing least
difficulty.
Q.4
Values were rounded correctly to form an estimate but the reciprocal was often left as
1/0.02 or 100/2.
Q.5
The correct plan was recognised by the better candidates, and many others got part
marks for a correct position or shape or aligning the tower block and water tank
correctly.
Q.6
The formula was usually arranged correctly although a few candidates then cancelled
the 10 into the 30.
Q.7
There were accurate constructions for the bisector in part (a), although some
candidates only used arcs above, with a line which stopped at AB. In part (b) few
arcs of radius 6 cm appeared and the incorrect side of the bisector was often used.
Q.8
A common error was to equate the area of the four circles to 1600 cm2 but follow
through marks could be obtained.
Q.9
The expression was generally proved equivalent to 5n. Some calculation errors
occurred, the most serious being the omission of the square when multiplying n by n.
Q.10
The higher level probability was again well understood and answered.
Q.11
In a few cases the incorrect answer 0.7777 appeared in part (a). The appropriate
method for eliminating the repeated digits was used correctly in the majority of cases.
Q.12
Many candidates did not choose sufficient points to obtain a good quadratic curve and
many errors occurred when calculating values of y for a negative value of x. Only the
best candidates found the correct line to draw in part (c), others just substituted into
the given expression.
Q.13
Many cases of direct variation appeared, the word ‘inversely’ being ignored.
Q.14
Surprisingly few candidates realised that all that was required was to factorise each
bracket and get 8(n + 1)(n + 2)(n + 3). Most students started the laborious task of
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
multiplying out all the brackets and few achieved the correct result. Others just
substituted a few values into the given expression.
Q.15
A good understanding of surds was demonstrated in part (a) by the better candidates.
However, most of these did not rearrange their values or rationalise correctly to find
q.
Q.16
Vectors were understood but errors occurred when arrows showing direction were not
drawn on the diagram. Candidates should be trained to write down the path taken and
to ensure that the final answer is simplified.
Paper 2
Q.1
Proportion was understood and used correctly.
Q.2
Transformations were drawn correctly by many candidates. Often (0, 0) was not used
for the rotation and a pair of transformations were used to describe the mapping of
shape S onto shape W.
Q.3
Again, probability was used correctly, although twelve thousand was sometimes
written as 1200.
Q.4
(a)
Average speed was understood but often left in km/min or calculated by using
3.3 hours.
(b)
Ratio was usually used correctly.
Q.5
Graphs were usually correct with the values at y = 12 found correctly. Of those who
calculated the value at −1 incorrectly, few were concerned at the shape of what should
have been a quadratic curve. Only a few candidates found the correct equation in part
(d).
Q.6
Inequalities and indices were generally dealt with correctly. Occasionally part (b)(iii)
was not fully simplified.
Q.7
Many inaccurate readings of the time were taken from the graph.
Q.8
Calculator form instead of standard form sometimes appeared.
Q.9
The surface area was calculated correctly but it was not generally recognised that
12076.28, 12076 or 12070 was not an appropriate degree of accuracy.
Q.10
Most candidates could get at least some of the dimensions correct.
Q.11
(a)
Various lines/angles which were/were not equal were listed without answering
whether the triangles were congruent or not. Many candidates wrote that the
side of 4 cm was unequal to the side of 6 cm but did not realise that the angle of
90° had to be taken into account.
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GCSE MATHEMATICS MODULAR (TWO-TIER) (SUMMER SERIES) 2006
(b)
Common errors were to omit the curved surface area of the cylinder or to
subtract it, to subtract two volumes or to calculate the area of the top surface
only.
Q.12
A few incorrect tree diagrams occurred and the probability of getting yellow and pink
appeared without the probability of pink and yellow.
Q.13
(a)
The crossing points on the x-axis were often kept at 1 and 7.
(b)
Here the crossing points on the x-axis were not kept at 1 and 7.
Q.14
In this probability question, some answers using the replacement of the green crayon
were given.
Q.15
There was some excellent algebra produced by some very well prepared candidates.
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