GCSE EXAMINERS' REPORTS
APPLICATIONS OF MATHEMATICS
JANUARY 2017
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Unit
Page
4361-01 Unit 1 Foundation
1
4361-02 Unit 1 Higher
3
4362-01 Unit 2 Foundation
5
4362-02 Unit 2 Higher
7
© WJEC CBAC Ltd.
APPLICATIONS OF MATHEMATICS
General Certificate of Secondary Education
January 2017
UNIT 1 – FOUNDATION TIER
Candidates appeared to have had sufficient time to attempt all questions in the given time.
As item level data is available to all centres, by centre and for individual candidates with
comparison of all candidates sitting these examinations, this report will focus on common
errors and misconceptions to aid the interpretation of the data available.
1.
Candidates attempted all parts of this question; however, in (d) some candidates did not
know what a quarter of million is in figures and so could not compare the lower price of the
house with 250000.
2.(a)
Most candidates engaged with this question. Candidates were able to calculate the size of
the third angle even though there wasn’t a diagram drawn for them. Errors occurred with
some candidates not knowing that a 40˚ is an acute one. An obtuse angle was the most
common incorrect answer. Most candidates obtained at least 2 marks for drawing an
accurate diagram. Errors occurred with drawing the 70˚ angles, particularly with the right
hand 70˚ angle.
2. (b)
(c) (d)
Candidates engaged with this question well. Very few errors occurred with swapping of
coordinates in (a). Most candidates were able to identify one net of a cube but the most
common incorrect answer was the bottom left net. Most candidates were able to get the
correct answer of 36 in (d).
3.
This question was very well answered with candidates setting our clear workings for each
party idea. The most common error occurred with finding 1/10 of £240 for the Toots option.
Some interpreted it as 10 pence.
4.
Most candidates could attempt this question. Only a few confused the mean, median,
mode and range.
In (b), most could not give a suitable reason for whether they agreed or disagreed with the
newsagent. Most just stated how they would calculate the average of their choice,
including the mean.
5. (a)
(b)
Very few candidates confused area with perimeter in (a) although many did not give the
correct units for their answer. The most common error in (b) was that a few candidates
only calculated 37 + 15.
5. (c)
Candidates engaged very well with the first part of this question, with many candidates
obtaining at least QWC1. Errors occurred with some candidates calculating the price for 5
days rather than 4. Labels were used by many candidates and very few misused the “=”.
Very few candidates obtained the correct answer in (ii).
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6.
In (a), most candidates were able to obtain the first 3 marks, correctly changing 16 ounces
into grams. However, many candidates did not read the scale and did not find the extra
number of grams needed to make 20 scones.
Part (b) was answered quite well. Most could plot points; however, some did not draw the
line. Most candidates who completed (i) obtained at least the first mark in (ii).
7.
The most common error was in part (d) with these candidates giving their answer as 6x +
8y ÷ 2.
8.
A common question with Higher.
Part (a) was well answered and in (b) most could give the reason of 40 being in 2 boxes.
Very few noticed that the group for 20 – 30 was missing. Candidates made errors with
having overlapping boxes in (c).
9.
A common question with Higher.
Bearings using angle properties is a topic that is not answered well at Foundation Tier.
This was evident in this question. Very few candidates obtained even 1 mark.
10.
(a) (b)
(c)
A common question with Higher.
Relative frequency was not well understood, although a few candidates were able to
complete the table in part (c) and produce a suitable graph.
It is not well known that the best estimate of probability is the one that makes use of all
available results - the final answer in the table. Only a few candidates could give the
correct answer of how they could improve their estimate.
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APPLICATIONS OF MATHEMATICS
General Certificate of Secondary Education
January 2017
UNIT 1 – HIGHER TIER
There was no evidence to suggest that the examination paper was too long for candidates,
as there were clearly responses in later questions.
The paper differentiated well, with different styles of questions and a graduation in the level
of difficulty.
As item level data is available to all centres, by centre and for individual candidates with
comparison of all candidates sitting these examinations, this report will focus on common
errors and misconceptions to aid the interpretation of the data available rather than focus
whether each question was well answered or not.
Question Comments
1
Parts (a) and (b) were generally well answered.
In part (c) many candidates gave boxes to tick, but included overlaps or
gaps.
2
Part (a) of this question was not well answered, with very little evidence of
the use of construction arcs.
Part (b) of this question was very poorly answered.
A few candidates measured angles, on a diagram which was not drawn to
scale, rather than calculate missing angles using angle facts.
3
Parts (c) and (d) proved to be the more demanding for candidates, with
errors in collecting like terms in (c).
4
A number of candidates incorrectly worked with perimeters rather than areas.
5
Relative frequency was not well understood, although a few candidates were
able to complete the table in part (c) and produce a suitable graph.
It is clearly not well known that the best estimate of probability is the one that
makes use of all available results, the final answer in the table.
6
The most demanding part for candidates to draw and understand proved to
be the ¼ circle arcs on the right hand side.
7
The estimate of the mean was not well understood, with only a few correct
responses.
Candidates did interpret the table accurately in order to answer part (b).
Median and interquartile range was not well answered. It is important to look
for the highest reading on the cumulative frequency axis to work out
quartiles, as using the value 80 to halve and halve again was incorrect,
although very few candidates had an idea how to calculate the interquartile
range.
Some candidates were able to draw a correct box-and-whisker diagram from
the information given, and make valid comparisons for the median, although
often the comparison of the interquartile ranges was not interpreted correctly.
The moving average part of the question was not well answered.
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8
There were many correct responses, although there were also errors in
looking at common factors.
9
This question was not well answered, with many errors in calculations.
10
Very few candidates made worthwhile attempts at many parts of this
question. For example, in part (a) 5 x 40 = 200 metres was a common
incorrect response, incorrectly thinking that the answer was to be found by
working out v x t.
11
Histograms are not well understood. Very few candidates worked with area.
© WJEC CBAC Ltd.
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APPLICATIONS OF MATHEMATICS
General Certificate of Secondary Education
January 2017
UNIT 2 – FOUNDATION TIER
Candidates appeared to have had sufficient time to attempt all questions in the given time.
As item level data is available to all centres, by centre and for individual candidates with
comparison of all candidates sitting these examinations, this report will focus on common
errors and misconceptions to aid the interpretation of the data available.
1.
This question was very well answered by candidates with most getting full marks for the
mathematics. Most candidates obtained at least QWC1. Candidates were able to set up
their workings with units and most labels shown. However; some candidates did not show
why they were buying 4 lots of doughnuts from Doh-Boy Doughnuts and 3 lots of
doughnuts from Benny’s Buns.
2.(a)
(b)
This question was answered very well. Most candidates were able to work out the scale of
the bar chart; although a few used a uniform scale until 50 drinks sold but then used a nonuniform one thereafter. In part (b), errors sometimes occurred with candidates not
subtracting their 20% to find what was left.
2. (c)
This question was not answered well. Many candidates could not draw an accurate pie
chart with many not knowing how to calculate the size of an angle for each sector of the
pie chart.
3.
Very few candidates understood that the volume was the number of metre cubes in the
stage. Some multiplied 2 by 3 by 4. Very few gave m3 as the correct units. Some gave their
answer as cm3. Many candidates were able to give the correct answer to the volume of a
cuboid in part (b) although some did add the dimensions. A few candidates could not round
their answer to 1 decimal place.
4.
This question was quite well answered with many candidates getting at least 3 marks.
Some did not use the correct scale factor of 5. A few candidates used the height of a man
as 5ft 11inches but then did not use this correctly to find the height of the church.
5.
In part (a), not all candidates understood the difference between shapes that had rotational
symmetry and those that had line symmetry. Some candidates did not look at all of the
details within the patterns of the shapes. Only a few candidates gave the order for
rotational symmetry for shapes A and C as 0 instead of 1.
Part (b) was answered very well.
6.
Most candidates thought that David was correct in part (a) because you would get a
negative value for n in Jodie’s equation. In (b), most candidates could solve David’s
equation correctly but made errors with Jodie’s. Some candidates gave the answer of 3.5
for both equations. Very few candidates could correctly explain the error that Jodie had
made in part (c) but could give the correct value of n.
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7.
Most candidates were able to correctly draw a congruent shape and attempted to draw a
similar one. However, errors often occurred with the dimensions of the shape candidates
had drawn for Q not being correct for both the length and width.
Most candidates could explain the difference between congruent and similar shapes in
part (b).
8.
This question was very well answered.
9.
This question was not well answered. Many candidates did not know how to find the
number of units used and just multiplied 8449 and 6107 by 5.4 pence without subtracting
their answers. Many candidates were able to find the cost of the 90 days. Some
candidates mixed the units of pence and pounds when finding their total cost of the bill.
Some candidates confused giving their answer to the nearest penny with giving their
answer to the nearest pound.
10.
(a)
A common question with Higher.
In part (a), (i) and (ii) were often answered correctly, as the values on the scatter diagram
were on grid lines that did not require much in the way of working with the linear scale.
However, some candidates gave the answer of 35000 as 30500. There were many errors
in the misinterpretation of the scale in (iv).
In part (b), very few candidates engaged with the idea of comparison considering lifetime
of the tyres. Candidates generally worked accurately in costing the tyres.
11.
A common question with Higher.
The first part of (a) was often answered correctly, but not the second part. The most
common incorrect answer was 3.
In part (b)(i), although many candidates could convert accurately from pounds to Dirhams,
very few candidates understood the concept of buying currency when only certain notes
were available. Very few candidates were able to obtain marks in in (ii), however a few
candidates used the alternative method to answer this question.
© WJEC CBAC Ltd.
6
APPLICATIONS OF MATHEMATICS
General Certificate of Secondary Education
January 2017
UNIT 2 – HIGHER TIER
There was no evidence to suggest that the examination paper was too long for candidates,
as there were clearly responses in later questions.
The paper differentiated well, with different styles of questions and a graduation in the level
of difficulty.
As item level data is available to all centres, by centre and for individual candidates with
comparison of all candidates sitting these examinations, this report will focus on common
errors and misconceptions to aid the interpretation of the data available rather than focus
whether each question was well answered or not.
Question Comments
1
Parts (a) and (b) were often answered correctly. Candidates found part (c)
the most demanding part of the question, not understanding how to express
the percentage profit.
2
In part (a), (i) and (ii) were often answered correctly, as the values on the
scatter diagram were on grid lines that did not require much in the way of
working with the linear scale. There were many errors in the
misinterpretation of the scale in (iii).
In part (b)(i), very, very few candidates (of this small entry) engaged with the
idea of comparison considering lifetime of the tyres. Candidates generally
worked accurately in costing the tyres.
In part (b)(ii), it seemed that the working with percentage was again an issue.
Candidates seemed to have insecure knowledge regarding using the full
price as the baseline.
3
The majority of candidates engaged with the idea of this question.
4
Very, very few candidates knew a conversion of metres to miles, so part (a)(i)
was not well answered. The first part of (ii) was often answered correctly, but
not the second part.
In part (b), although many candidates could convert accurately from pounds
to Dirhams, very few candidates understood the concept of buying currency
when only certain notes were available.
5
Part (a) was not well attempted, with very few candidates having an idea of
unitary g per m2 for a fabric of a constant width.
In part (b), very few candidates progressed beyond looking at the difference
between heights and the lengths of the new skis.
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6
Very few candidates were able to visualise the situation in a sketch, in order
to make progress.
7
Very few candidates used the idea of bounds to solve the problem, even
though the reminder was given twice in bold type within the question.
8
Many candidates answered part (a) correctly.
Very few candidates were able to reason through the cell information in part
(b). However, there were a few sketches showing the cell labels.
9
Candidates either could not work with algebraic fractions or had little or no
idea of how to solve simultaneous equations.
10
This question was not well answered. The part that candidates found least
demanding within this question was part (b). Candidates were not able to
visualise in three dimensions in part (a), even though a diagram was given.
Part (c) involved percentage work, which had already been highlighted as a
weakness of the small entry of candidates. Very few candidates drew
diagrams or wrote formulae in part (d).
11
Part (a) was attempted by most candidates; who did seem to have some
experience of working with the AER formula.
Part (b) was not well answered.
12
Similarity beyond working with linear measures is not well understood. And
in this case not recognised as similar figures. The volume of a cone was
attempted, but candidates gave up as soon as they came across the missing
height, not equating the formula to the volume given.
GCSE Applications of Mathematics Report January 2017
© WJEC CBAC Ltd.
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