GCSE EXAMINERS' REPORTS
MATHEMATICS (NEW)
NOVEMBER 2016
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Unit
Page
Unit 1 - Foundation
1
Unit 1 - Intermediate
5
Unit 1 - Higher
8
Unit 2 - Foundation
12
Unit 2 - Intermediate
15
Unit 2 - Higher
18
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MATHEMATICS (NEW)
General Certificate of Secondary Education
November 2016
UNIT 1 - FOUNDATION
Given that this was the first time candidates have sat this paper, many made good attempts
at many questions. However, there were some topics in the specification which appeared not
to have been learnt by some candidates. Very many candidates did not attempt the question
on rotational symmetry (Q8) or the question on location (Q10). It may be that many
candidates were entered before they were ready to tackle the exam paper with confidence.
The communication part of the OCW question (Q 4) was done reasonably well, though this is
an area where more focused practice would be useful. This is one of the suite of
Mathematics papers so the OC (organisation and communication) part expects a few words
only, stating simply, for example,
Length of side of square = 72  4 cm
= 18 cm
A long, rambling description is wrong in this Mathematics paper and will not gain credit.
Clear, logical statements are expected.
For the W (accuracy of writing) part, it is essential that the units are given appropriately and
correct mathematical form is used. A statement like
72  4 = 18  3 = 54
is mathematically wrong and will not gain credit.
1.
2.
(a)
The curve proved more difficult to draw than the straight lines but there were
many good attempts at drawing the reflection of the given shape. The
reflection of the curve was expected to be within the equivalent set of squares
as the original. This was not always the case.
(b)
A significant number of candidates did not attempt this question, and of those
who did, very many measured the diameter of the circle rather than the
radius.
Despite being asked for the units that the candidate had used, many forgot to
write them down.
Common wrong answers included 90, 180 and particularly 360.
(a)
Almost all candidates attempted this question and very many gave the correct
answer. Candidates needed to work out how many 5p coins Huw had, which
was 6, so the correct answer was unlikely. The most common wrong answer
was likely.
(b)
This was easier to answer as there weren’t any bananas in Catrin’s bag, so
the chance of choosing one was impossible.
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3.
(a)
This question was answered very well.
(b)
There were two possible correct answers: the numbers 1 and 13 or the
numbers 2 and 5. The latter pair was far more common. This question was
also answered very well.
4.
More than a quarter of the candidates did not attempt this question. It might have
helped those who felt they couldn’t engage with it, if they had drawn simple sketches
of the shapes that the question described. This could have suggested to the
candidates that they could find the length of one rod by dividing 72 by 4. Then, it
would be straightforward to find the perimeter of the equilateral triangle.
5.
Candidates were more likely to attempt part (b) rather than part (a).
(a)
A very common wrong answer was 100 as candidates subtracted 20 from
120, rather than correctly dividing 120 by 20.
(b)
Candidates seemed to find this part easier and were more successful with
answering it.
6.
Many candidates were unable to mark the position of A correctly; they were more
successful with marking B correctly. The line given in the question was 10 cm long so
marking every centimetre using their ruler should help candidates to show the
position of A more accurately.
Some placed A at 0 and B at 1, as if to label the line AB. Fortuitously, therefore, they
gained the second mark.
7.
Candidates needed to find how many 15s there are in 204. Most attempted to do this
by adding a long list of 15s until they reached 210, showing them that 14 complete
rows used 210 chairs. However, there were many slips in the addition.
Very few tried a traditional, long division method. This might have been a more
efficient method if the numbers had been different and the total number of chairs
needed was much larger.
8.
Very many candidates did not attempt this question or, if they did, were unable to
answer it correctly.
9.
(a)
Wrong answers included 180, 360 and half turn.
(b)
Many ignored the fact that three of the triangles were coloured differently from
the other three and this limited the order of rotational symmetry to 3. A
frequent wrong answer was 6.
(a)
This was generally well done, though a significant number wrote down the
correct coordinates (5, 4) in the reverse order (4, 5).
(b)
Again, many reversed the numbers in the coordinates so the plots were
wrong and then it was impossible to draw a rectangle using the plotted points.
(c)
If the points in (b) had been plotted correctly, then usually the rectangle could
be drawn. However, the coordinates of D could still be written wrongly in
reverse.
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10.
Only about three-quarters of candidates attempted this question. Of those, very many
marked P at the middle of the line AB. Others drew a line from B. Very many did not
seem to understand what is meant by BAP.
11.
Many candidates chose a number, apparently at random and with no connection to
the numbers given in the question, and wrote that in the answer space without
showing any working at all.
Others thought that the angle on a straight line is 360 or 270 and subtracted the
sum of 105 and 43 from that.
12.
Altogether, this was a difficult question for very many candidates. More practice of
basic arithmetic skills and better learning of appropriate rules would help most
candidates.
(a)
Very common wrong answers were 28 (ignoring the correct position of the
decimal point) and 1.1 (adding 04 and 07).
(b)
Very many did not set out the two decimals one above the other correctly and
then they just subtracted digits randomly.
(c)
Very many wrongly thought that 33 is the same as 33 and that 24 is the same
as 24. So a frequent wrong answer was 9  8 = 1.
Another wrong answer was 1-1.
(d)
The correct answer was seen rarely. Most did not engage with using a
common denominator at all but just gave the answer as 6/5.
13.
This question was answered reasonably well. Candidates should be encouraged to
use the space for working to test some values to work out the answers rather than
guessing.
14.
A common wrong answer was Blue 15 Yellow 10 Red 6.
This obeys only two of the given conditions; i.e. B = Y + 5 and B + Y + R = 31 but
not B = 4R.
Many candidates were able to choose three values which added up to 31, but these
values did not obey either of the other two conditions.
15.
(a)
This was answered very well. Even if they could not do the necessary
calculation of subtracting 7, many candidates recognised that the next term in
the sequence would be found by subtracting 7 from the previous number.
(b)
In contrast, this question proved to be beyond the capabilities of most
candidates. Even if they realised that they needed to combine the x terms
and separately combine the numbers, most candidates failed to equate these
terms. If there was no equation, then neither of the first two marks could be
awarded.
Some candidates worked out that 4y = 32, but failed to go on to find the value
of y.
Many candidates wrote that 13y  5 is the same as 8y, and that 9y + 27 is the
same as 36y and then stopped.
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16.
(a)
This part was generally answered well though some did not follow the
instruction to add the numbers on the two cards.
(b)
A large number of candidates did not seem to understand the phrase ‘more
than 9’. So they included the 9 and wrongly gave the answer as 6/12 rather
than 5/12.
Many candidates did not understand the difference between chance and
probability. The language of chance was not wanted.
(c)
Very many candidates were unable to work this out, certainly if they had given
the answer to (b) as unlikely, say.
The answer needed was 25, not 25/60.
17.
This question was very challenging for very many candidates as there were three
steps which had to be identified to find the solution.
Some who were able to work out the length of CD as 15  9 = 6 cm were unable to
use this as they could not work out the length of BD by dividing 45 by 9.
Not all who got this far remembered the correct formula for the area of a triangle.
Many added up random numbers, apparently trying to find a perimeter.
18.
This question was answered well by many candidates, especially those who tried out
pairs of numbers.
19.
Not all the numbers given as answers lay between 1 and 9 inclusive.
A frequent mistake was writing 6 in the middle box, thinking that that would make it
the median, whatever other numbers were chosen.
Realising that the total of the five numbers needed to be 25 to give the mean as 5,
made the question easier to answer.
© WJEC CBAC Ltd.
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MATHEMATICS (NEW)
General Certificate of Secondary Education
November 2016
UNIT 1 - INTERMEDIATE
This was the first time that candidates sat the new Mathematics GCSE specification.
It appears that perhaps some of the candidates may not have been entered appropriately for
this tier. A larger than usual number of candidates did not attempt some questions which
suggests that they had not yet fully covered the course at the time of the examination.
Hopefully they will have a greater degree of understanding by the summer series of exams.
1.
(a)
The usual error was the misplacement of the decimal point.
Worryingly a number of candidates used the ‘herringbone’ method of
multiplication for essentially multiplying 4 by 7
0
4
0
7
etc.
(b)
Well answered.
(c)
Most candidates gave the correct answer of 11. Some thought 33 – 24
equated to 9 – 8 = 1.
(d)
A few gave the common incorrect answer of 6/5. Most candidates correctly
used a common denominator of 10. Some correctly used a common
denominator of 50.
2.
A mixture of responses with no one particular statement being consistently
misunderstood.
3.
There were more correct answers of ‘Blue = 16, Yellow = 11 and Red = 4’ seen than
incorrect combinations. Most candidates were able to satisfy at least two of the
conditions.
4.
(a)
Well answered.
(b)
The −2f was often given as −8f.
(c)
A correct embedded answer was accepted but candidates should be made
aware that the actual answer has to be seen before a mark is awarded
e.g. 22 = 4 + 3 × 6 is enough to imply that K = 6, but 22 = 4 + 18 alone, would
not gain any marks.
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5.
(a)
The table of scores was usually completed correctly.
(b)
Most of the candidates knew how to present a probability as a fraction.
There was however a high degree of misunderstanding over what was meant
by ‘more than 9’.
Several candidates included the 9 from their table to give an answer of 6/12
rather than 5/12.
(c)
An answer of ‘25’ was required and not ‘25/60’.
6.
Candidates should be made aware of what is taken into consideration when
awarding the OC and W mark.
Responses should be structured with explanations that are clear and logical to the
reader at the point in the solution when they are presented (not a series of
calculations followed at the bottom of the page with a detailed explanation).
Correct mathematical form is required. Units, where appropriate, should be shown.
We do not want to see, for example, ‘Area of a triangle = 6 × 5 = 30/2 = 15’.
Those candidates familiar with the area of simple shapes found the actual question
accessible.
7.
Correctly placed embedded answers were allowed in all three parts of this question.
It is not however a practice that should be encouraged as often the candidate shows
further work which is not mathematically correct.
(a)
Well answered with 2 being the popular wrong answer.
(b)
Well answered with 294 being the popular wrong answer.
(c)
An error was often seen on the right hand side of the first line of solutions with
4y = 22 given instead of 4y = 32.
8.
Well answered.
9.
The condition most often not met was that the numbers should have a median value
of 6.
Many candidates placed a 6 in the middle box thinking this alone would make 6 the
median value.
Of the four possible fully correct combination of numbers, the choice of 1, 3, 6, 7 and
8 was by far the one most candidates opted for.
10.
(a)
A fairly straight forward question that was not well answered. Many thought
that the sum of the exterior angles of a polygon totaled 180° and gave an
answer of 4 sides.
It would be interesting to challenge those who gave an answer of 2 to draw us
their ‘polygon’!
(b)
Very few candidates constructed accurate drawings using only a ruler and a
pair of compasses.
There was little evidence of ‘fake arcs’ but more a case of random arcs drawn
from random centres.
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11.
12.
13.
(a)
Calculating the correct value for y when substituting into the quadratic proved
difficult for many of the candidates.
(b)
There was evidence of misreading of the scale on the y-axis when attempting
to plot their coordinates. Candidates should take care to draw a smooth curve
passing through (not just in the vicinity) all of their plotted points.
(c)
The negative value of one of the points of interception was sometimes
overlooked, resulting in an unnecessary loss of a mark.
(d)
Very few chose the correct equation.
(a)
The popular incorrect choice was 8. Presumably candidates thought ‘six sides
and two faces, so 8 outcomes’.
(b)
The mark scheme allowed for a follow through answer from part (a). So those
who gave an answer of 8 in (a) were given a mark for 1/8 in (b)
(c)
A mixture of responses with no one particular incorrect choice being made.
(a)
Not the most difficult of formula to work with, but still poorly answered.
(b)
Candidates often gave only a partial factorisation.
14.
(a)/(b) A similar type of question was included in the Specimen Assessment
Materials produced prior to this examination. It was disappointing therefore
that so few correct answers were given to these two questions.
15.
This question tested the candidates’ ability to form and solve two simultaneous linear
equations.
It was also one of the questions that addressed Assessment Objective 3 (AO3) in
that candidates had to, ‘interpret and analyse the problem before generating a
strategy to solve it’.
A ‘trial and improvement’ method is not acceptable when solving simultaneous
equations.
16.
(a)
A similar type of question was included in the Specimen Assessment
Materials produced prior to this examination. It was disappointing therefore
that so few correct answers were given.
Most candidates assumed that the branches regarding ‘stopping for a break’
were to be labelled 0·42, 0·58, 0·42 and 0·58.
(b)
A follow through answer using their values for P(Hereford) × P(No) was
allowed. Unfortunately not many candidates seemed to be familiar with the
required rule.
17.
There was a requirement in the question for an inequality to be written down.
Candidates who failed to do so would not gain all of the marks available.
© WJEC CBAC Ltd.
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MATHEMATICS (NEW)
General Certificate of Secondary Education
November 2016
UNIT 1 - HIGHER
This was the first time that candidates had sat the new Mathematics GCSE specification.
As expected, pupils’ performances reflected the increased demand of later questions in the
paper. The majority of candidates attempted every question, and coped well with the variety
of both content and style of question; this suggests that they had mostly been entered for the
appropriate tier, though there were a number of exceptions to this.
Whilst there were plenty of excellent performances, there were also some particular areas in
need of attention:








Question 2(a)(b) - recognising that the graph of a quadratic function should be a
smooth parabola, and that calculated coordinate values should be revisited if this is
not the case;
Question 2(d) - understanding that the intersection of two graphs represents the
solution of an algebraic equation, and knowing how that equation may be obtained;
Question 3(b) - knowledge of standard construction methods using ruler and
compasses;
Question 5 - manipulating numbers in standard form;
Question 13 - recognising when to apply specific circle theorems and quoting them
formally;
Question 15(b) - sketching simple transformations of graphs of trigonometric
functions;
Question 16 - knowledge of the conditions required to prove the congruence of
triangles, and applying them within a formal proof;
Question 17 - manipulating surds.
1.
Most candidates answered this question well, however some incorrectly gave 8 as
their answer to part (a) (presumably from adding six sides and two faces rather than
considering the outcomes of the compound event).
For part (b), the mark scheme allowed for a ‘follow through’ answer from part (a).
Many gave the correct answer for part (c), and of those who were successful, most
employed a written method (either multiplying probabilities or constructing a two-way
table).
2.
There were many excellent responses to parts (a) to (c) of this question.
However, for part (a), some candidates did struggle to calculate the required
coordinate values, particularly when needing to square minus 1.
For part (b), most plotted all the points correctly, coping well with the different scales
on the axes and going on to draw a smooth parabola. (A minority were penalised for
joining their points with straight lines rather than drawing a curve.) When the values
in part (a) were incorrect to the extent that the shape of the graph was not even close
to the correct parabola shape, it was disappointing that candidates did not seem to
question this and revisit their initial calculations. The majority were successful in
part (c), though occasionally the negative value was mis-read as being on the ‘wrong
side’ of minus 1.
© WJEC CBAC Ltd.
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Part (d) was disappointing. A very small minority demonstrated understanding by
equating the quadratic expression to 5 and re-arranging in order to select the correct
equation.
3.
4.
(a)
Well answered, with almost all candidates knowing to divide 45 into 360.
Some used an unnecessarily lengthy (though still valid) method of
considering the total of the interior angles.
(b)
Many candidates did know how to use a ruler and pair of compasses for a
construction, however there was some evidence of ‘fixing’ (drawing fake
arcs). More appeared to know how to bisect an angle than knew how to draw
the initial perpendicular line (appearing to draw the latter by eye or by using a
protractor).
(a)
Well-answered, but for the occasional sign error.
(b)
Again, well-answered, but for a minority of partially factorised answers.
5.
Both parts (a) and (b) were usually well-answered, though some failed to observe the
instruction to express the answers in standard form.
In part (b), too many candidates unfortunately gave no consideration to place value,
simply adding 2·3 and 6·4. Also, the powers of 10 were often added here, indicating
confusion between methods for adding or multiplying.
6.
Many excellent solutions were seen for this question. Candidates recognised the
need to set up and solve a pair of simultaneous equations, often going on to do so
successfully. (However, one unexpected error in a significant minority of cases was
evaluating 10/4 to be 0·4 for the value of y.)
Though rarely seen, it is worth noting that use of a trial and improvement method was
not acceptable in this question.
For the OCW requirement of the question, the majority of candidates performed well,
though some needed to engage with the need to ‘communicate’ by explaining where
each of their equations had come from. (This could have been done by simply
labelling the equations as ‘square’ and ‘octagon’.) The quality of written algebra was
good in most cases, as was the arithmetic involved in calculating the second
variable.
7.
There were plenty of excellent solutions seen for both parts of this question.
In part (a), however, it was a concern that a great many candidates did not attempt to
unpick the probability of the compound event (by appropriately dividing 0·42 by 0·7),
opting to write 0·42 on the P(Yes) branch of the tree diagram instead.
For part (b), candidates usually knew to multiply the relevant probabilities (and were
allowed to follow through their answer from part (a)).
8.
Plenty of fully correct solutions were seen here, but too many failed to write down an
inequality (a requirement given in the question).
9.
Both parts were usually well-answered. Again, it is worth noting that those
candidates who wrote down a method appeared to be most successful.
© WJEC CBAC Ltd.
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10.
This question proved difficult for the majority of candidates. Many were able to
deduce the need to equate the volume of a hemisphere and the volume of a cone,
and were often able to do so correctly. Few, however, were able to progress
correctly to a simplified relationship between the common radius and the height of
the cone. Fewer again succeeded in meaningfully producing a final ratio.
Since the relevant formulae (for the volume of a sphere and volume of a cone) were
both printed in the formula list at the start of the paper, it was disappointing that these
were sometimes quoted with incorrect powers of r.
11.
Many candidates gained full marks in this question.
For part (a), however, some showed lack of understanding of ‘inverse’ proportionality,
answering as if it were direct proportion. (Others answered as if y was inversely
proportional to x2 rather than x, indicating a need for more careful reading of the
question).
In part (b), most knew what to do, though some had difficulty in dealing with the given
y value of 1/5.
12.
It was encouraging to observe some secure algebraic skills here, though there was
often a sign error in the last term of the numerator. Weaker candidates were unable
to begin to form a common denominator.
13.
Candidates were often successful in applying the alternate segment theorem (though
it was sometimes incorrectly quoted as ‘alternate angles’), and were then usually
able to progress to finding a correct expression for angle PQR. The main weakness
in this question was a reluctance to formally or adequately quote relevant circle
theorems. It was also of concern that a few candidates misinterpreted lines PQ and
AB as if they were parallel, suggesting that angles PQR and BRQ were equal.
Candidates should be encouraged to simplify their final answer, rather than leaving it
as e.g. 180 – 90 – x.
14.
In part (a), it was necessary to derive the quadratic equation shown. Many
convincing solutions were seen, but those who could not approach it opted to solve
the equation instead (though this was not required until part (b)).
For part (b), the majority of candidates were able to factorise the quadratic
expression and give two solutions, usually explaining correctly that the negative
solution could not represent a length. A minority used the quadratic formula – a more
laborious but still acceptable method. Again, trial and improvement should be
discouraged as a method to solve a quadratic equation. Some candidates
misunderstood the requirement in part (b) to ‘justify any decisions’, interpreting this
as a need to construct the equation (already done in part (a)) or as a need to
substitute answers into the equation to verify them.
15.
Part (a) was usually well-answered, but for part (b), too many candidates simply
sketched the graph of y = cos x, disregarding the need for a vertical translation of 1
unit.
16.
Overall, this was very disappointing. Candidates needed to use the information given
in the question to prove congruence of the triangles (rather than using the symmetry
of the diagram to deduce equal lengths or angles). Many solutions lacked rigour and
necessary justification e.g. stating that AB = AC without explaining why (namely that
the triangle was stated to be isosceles). It is important to note that stating ‘two sides
and an angle’ is not an adequate reason for concluding that triangles are congruent
unless it is made clear that the angle is ‘included’ (which may be implied by quoting
‘SAS’).
© WJEC CBAC Ltd.
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17.
Fluent manipulation of surds was essential in this question. There were some
excellent solutions. Common errors however included misinterpreting (5√3)2 to be
(5 + √3)2 or giving 2√18 to be √36. It was surprising that some candidates stated a
final rational fraction to be ‘irrational’.
18.
This was often well-answered, with many candidates choosing to construct an
appropriate tree diagram. Of those who did not proceed correctly, some tried to state
that 0·8 x 0·8 was 0·16 in order to then multiply by 5.
© WJEC CBAC Ltd.
11
MATHEMATICS (NEW)
General Certificate of Secondary Education
November 2016
UNIT 2 - FOUNDATION
This was the first time that candidates sat the new Mathematics GCSE specification. It
appears that the majority of candidates who were entered were working at F/G grade. A
large number of candidates did not attempt the intermediate crossover questions which
suggests that they had not yet fully covered the course at the time of the examination.
Hopefully they will have a greater degree of understanding by the summer series of exams.
1.
(a)
This part was generally well answered – common errors were putting the
decimal point in the wrong place or omitting it altogether.
(b)
This part was generally well answered, though a common incorrect answer
was 109.9, where candidates ignored the final value was in pence not
pounds. Both rounding parts were well answered.
2.
This question was not well answered by candidates. As it’s a true and false question
you’re unable to fully understand the candidates reasoning for their selections,
though it was clear that they were confusing pentagons and hexagons, diameters
and radii, and the names of triangles.
3.
Candidates should be made aware of what is taken into consideration when
awarding the OC and W mark.
Responses should be structured with explanations that are clear and logical to the
reader at the point in the solution when they are presented (not a series of
calculations followed at the bottom of the page with a detailed explanation).
This question was not well answered by candidates. Candidates who engaged with
the question were generally able to identify the factors of 20, though they often
struggled to fulfil the other conditions - identifying the factors which sum to greater
than 10 but less than 15.
4.
This question was answered well by over half of the candidates. Incorrect answers
were usually as a result of candidates confusing mode, median and mean.
5.
(a)
This part was well answered by over half of the candidates. The most
common incorrect answer was 9a.
(b)
This part was answered slightly better, though some candidates failed to gain
the second mark for identifying the rule – writing “plus 4” was the common
incorrect answer.
6.
This question wasn’t answered well. Many candidates were able to find one of the
extra values (nearly always 17), but not the second value (1) – gaining two out of the
three marks.
© WJEC CBAC Ltd.
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7.
8.
9.
(a)
Some candidates were able to list all of the possible outcomes in part (i), with
some able to calculate the probability in part (ii). Common incorrect answers
were just listing the outcomes involving Heads, totally ignoring those involving
Tails. This prevented them from gaining any marks in (ii) because candidates
needed at least 4 additional outcomes in part (i) to gain any marks in (ii).
(b)
This part wasn’t well answered, with candidates commonly stating that both
outcomes had an even (as opposed to equal) chance of occurring.
Overall this question wasn’t well answered by candidates.
(a)
57 was a common incorrect answer.
(b)
43 was not accepted unless 64 was also shown.
(c)
186 ÷ 3 was not accepted unless 62 was also shown.
(d)
7·25 × 8 was not accepted unless 58 was also shown.
(a)
This part wasn’t answered well by candidates, with the most common
incorrect answers being 120° and 60°.
(b)
This was answered considerably better than part (a).
10.
This question was poorly answered by candidates. Reflecting the shapes in the
horizontal line was a very common error.
11.
This question was poorly answered by candidates - most simply calculated 360 –
(117 + 74 + 125) and gained no marks as the ‘125°’ was the only value that was not
allowed as a follow through of what should have been 55°.
12.
(a)
A correctly placed embedded answer was allowed. It is not however a
practice that should be encouraged as often the candidate shows further
work which is not mathematically correct.
(b)
Some candidates mistook the process involved in a number machine with that
of the hierarchy of number operations by writing −2 + 5 × 7 = 33.
(c)
This part was answered poorly – most candidates didn’t attempt this part, with
those that attempted it often answering 2x + 3.
13.
This question was poorly answered. Very few candidates gained full marks, with
many stating it was true with no or little (normally incorrect) calculations. Some
candidates gained 2 marks for increasing by 10% but were unable to correctly
decrease by 10%.
14.
This question was poorly answered. Whilst the candidates can recognize congruent
shapes and are familiar with simple 2-D shapes, they obviously found it difficult to
visualise the shapes and relate the statements to the concept of congruency.
15.
This question was well answered, though some candidates thought that the missing
value for Newport was 0°C.
© WJEC CBAC Ltd.
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16.
Those candidates familiar with the formula for the circumference of a circle found the
actual question accessible, however they were few and far between, with some using
the formula for area, whilst others not being able to progress further than calculating
the diameter of the circle.
17.
(a)
Very poorly answered – most candidates simply reflected in the x or y-axis.
(b)
This part was poorly answered. The question asked for the description of a
single transformation. Those descriptions indicating more than one step (the
‘and then’) gained no marks. All four components were required
(anticlockwise rotation of 90° about the origin).
Obviously a ‘clockwise rotation of 270°’ would be equivalent. Allowances were
made as regards the description of ‘the origin’ but the word ‘turn’ was not
accepted for ‘rotation’.
Very few candidates identified all four components (most identified only two) the component most often left out was ‘about the origin’.
© WJEC CBAC Ltd.
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MATHEMATICS (NEW)
General Certificate of Secondary Education
November 2016
UNIT 2 - INTERMEDIATE
This was the first time that candidates sat the new Mathematics GCSE specification. It
appears that perhaps some of the candidates would have been better suited if they had
been entered at a different tier. A larger than usual number of candidates did not attempt
some questions which suggests that they had not yet fully covered the course at the time of
the examination. Hopefully they will have a greater degree of understanding by the summer
series of exams.
1.
2.
All parts of this question were well answered.
(a)
57 was a common incorrect answer.
(b)
43 was not accepted unless 64 was also shown.
(c)
186 ÷ 3 was not accepted unless 62 was also shown.
(d)
7·25 × 8 was not accepted unless 58 was also shown.
(a)
There were nearly as many answers of 120° or 60° as there were of the
correct 30°.
(b)
Very well answered.
(c)
Well answered although a significant number chose 90°, presumably having
turned anticlockwise.
3.
Reflecting the shapes in the horizontal line was a very common error.
4.
(a)
A correctly placed embedded answer was allowed. It is not however a
practice that should be encouraged as often the candidate shows further
work which is not mathematically correct.
(b)
(i)
Several candidates mistook the process involved in a number
machine with that of the hierarchy of number operations by
writing −2 + 5 × 7 = 33.
(ii)
The most frequent error was to omit brackets around the n + 5. A few
are uncomfortable with leaving an expression as an expression, but
continue to solve an imaginary equation.
5.
Well answered although a number of candidates thought that the missing value for
Newport was 0°C.
© WJEC CBAC Ltd.
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6.
The weaker candidates simply calculated 360 – (117 + 74 + 125) and gained no
marks as the ‘125°’was the only value that was not allowed as a follow through of
what should have been 55°.
7.
Well explained and clear reasoning shown with accurate calculations to prove that
the statement was incorrect. Some chose ‘interesting’ start values.
‘87·6 × 1·1 = 96·36 followed by 96·36 × 0·9 = 86·724 so false’ is one that sticks in
the mind!
8.
Many of the candidates failed to choose the correct response to each of the four
statements.
Whilst at a lower level of testing they can recognize congruent shapes and are
familiar with simple 2-D shapes, they obviously found it difficult to visualise the
shapes and relate the statements to the concept of congruency.
9.
Candidates should be made aware of what is taken into consideration when
awarding the OC and W mark.
Responses should be structured with explanations that are clear and logical to the
reader at the point in the solution when they are presented (not a series of
calculations followed at the bottom of the page with a detailed explanation).
Correct mathematical form is required. Units, where appropriate, should be shown.
We do not want to see, for example, ‘Circumference = π × 40 = 125·6 ÷ 2 = 62·8’.
Those candidates familiar with the formula for the circumference of a circle found the
actual question accessible.
10.
(a)
Common incorrect answers were ‘n + 1’ and ‘3n + 1’.
(b)
(i)
Not as well answered as expected at this level. There was no obvious
consistent misunderstanding shown by the answers given.
(ii)
Initially converting the problem into an inequality ‘n2 + 7 > 85’ would
have very much simplified the question. Unfortunately very few began
their solution with this initial step.
11.
(a)
A disappointing response to a relatively straightforward question on reflection.
There was no obvious consistent misunderstanding shown by the answers
given.
(b)
The question asked for the description of a single transformation. Those
descriptions indicating more than one step (the ‘and then’) gained no marks.
All four components were required (anticlockwise rotation of 90° about the
origin).
Obviously a ‘clockwise rotation of 270°’ would be equivalent. Allowances were
made as regards the description of ‘the origin’ but the word ‘turn’ was not
accepted for ‘rotation’.
The component most often left out was ‘about the origin’.
(c)
(i)/(ii) A similar type of question was included in the Specimen Assessment
Materials produced prior to this examination. It was disappointing
therefore that so few correct answers were given to these two
questions. Candidates need to be aware that a column vector requires
the brackets to be in place and that a ‘fraction’ e.g. 5/4 is not
acceptable.
© WJEC CBAC Ltd.
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12.
(a)
Common incorrect answer was x18.
(b)
Common incorrect answer was (4x – 3y).
(c)
By far the answer given by most candidates was x/30. Often accompanied by
an explanation that ‘speed = distance / time’!
13.
Those candidates familiar with this type of question usually gained all four marks.
Some did not carry out the necessary check required (e.g. looking at 2·25) to
establish that the answer was 2·3 and not 2·2 and therefore only gained two marks.
14.
(a)
Well answered although a number of candidates decided that the extra 4
students required in the Chemistry set should go alongside the 1, 2 or 6
already shown in the Venn diagram.
(b)
Many gave the incorrect answer of 8, having wrongly included the six
students who studied all three subjects.
(c)
Well answered.
15.
This topic was not well understood.
(a)
(b)
16.
(i)
Few knew how to find the gradient, and some of those who did know,
misread the (different) scaling on the two axes.
(ii)
The instruction to write the equation of the line in the form y = mx + c
was ignored by many of the candidates.
Despite the mark scheme generously trying to give some credit for any
understanding of gradients of equations and the connection with parallel lines,
very few gained marks on this part of the question.
Another topic not well understood.
(a)
More often than not, the answer given was simply 0·05.
(b)
Little of what was written made any sense! Many focused on the greater
number of defective sockets there were, rather than the best estimate of the
probability of selecting at random a defective socket.
17.
It was one of the questions that addressed Assessment Objective 3 (AO3) in that
candidates had to, ‘interpret and analyse the problem before generating a strategy to
solve it’.
Many having correctly identified angle BDC = 28° and angle BCD = 90°, then used
an incorrect trig ratio when attempting to calculate the length of BD. This was
probably because line CD was a ‘sloping line’ and of course for some ‘the
hypotenuse is the sloping line’!
18.
(a)
A standard question that was poorly answered. It was disappointing to see so
many attempting to use a ‘trial and improvement’ method.
(b)
A similar type of question was included in the Specimen Assessment
Materials produced prior to this examination. It was disappointing therefore
that so few correct solutions were seen.
© WJEC CBAC Ltd.
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MATHEMATICS (NEW)
General Certificate of Secondary Education
November 2016
UNIT 2 - HIGHER
This was the first time that candidates had sat this paper. However, it appeared that most
candidates did attempt most questions, although it was evident that some of their subject
knowledge was lacking towards the end of the paper. Candidates still need to be reminded
to show their workings, even when not directed to do so within the question.
1.
(a)
Not answered as well as expected for the first question. The majority of
candidates could draw the line 𝑦 = 𝑥, but failed to reflect the triangle correctly.
A common mistake was a rotation of 180° about the vertex that touches the
reflection line, ie. 𝑦 = 𝑥. Occasionally the triangle was reflected on the 𝑥-axis
even though 𝑦 = 𝑥 was correctly drawn.
(b)
(i)
Occasionally the error here was incorrectly assigning the column
vector numbers with the 𝑥 direction and the 𝑦 direction.
(ii)
Generally well answered, although not all candidates were conversant
with the column vector form – either giving their answers incorrectly in
the form of a fraction (with or without brackets) or as coordinates.
2.
Well answered on the whole, with some slips in working from time to time.
3.
(a)
Well answered. Occasionally, the incorrect answer seen was 𝑥 18 .
(b)
The misconception many candidates made was incorrectly expanding the
second bracket, i.e. −(3𝑥 + 2𝑦) expanded to −3𝑥 + 2𝑦 (instead of the correct
−3𝑥 − 2𝑦) leading to the incorrect answer of 4𝑥 − 3𝑦.
(c)
This part was not as well answered, with 30 being the most popular answer.
Candidates had failed to see the need to convert the minutes into hours.
𝑥
4.
The majority of candidates answered this question well, with a significant number
gaining full marks. Apart from the obvious error of not testing to find the answer
correct to 1 decimal place (usually by trialling x = 2.25), other slips seen was not
finding values correct to 1 dp either side of 0, or not using the given formula correctly.
5.
Although Venn diagrams is a new topic, candidates answered this question well.
(a)
Generally full marks were awarded. The occasional error was placing the 4 in
the wrong region, usually in the area specific to chemistry.
(b)
The incorrect answer of 8, presumably by adding 5, 2 and 1 together of the
top regions was occasionally seen.
(c)
Very well answered. However many candidates did superfluous work;
simplifying the fraction even though it was not required.
© WJEC CBAC Ltd.
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6.
7.
8.
(a)
(i)
The different scale on each of the axes contributed to the failure of a
number of candidates on this part of the question, the gradient of 1
being a common answer. Some candidates failed to appreciate that it
is only the coefficient which is the gradient, resulting in 2𝑥 being
offered rather than 2.
(ii)
Reasonably well answered. Most candidates followed through their
gradient correctly, and generally, the 𝑚 and the 𝑐 were not incorrectly
interchanged. Infrequently the ‘𝑦 =’ was omitted.
(b)
This was one of the first questions on the paper which was poorly answered.
Although many were able to either double or halve one of the given equations
(although many candidates only focussed on the 𝑥 and 𝑦 coefficients and
forgot to halve or double the constant term), they were unable to justify why
the lines were parallel. They needed to be able to explain why the gradients
would be the same – showing an understanding, that was often lacking.
Those candidates who correctly rearranged the equations to the form
y = mx + c were able to gain both marks, if they commented on the equal
gradients or not.
(a)
This question was not as well answered as expected, with many candidates
not offering the correct method and answer. Many candidates only offered the
relative frequency for 3000 sockets tested, whilst others offered a sum of the
defective sockets for 1000, 2000 and 3000, amongst other answers. A
number of candidates incorrectly read the relative frequency for 3000 as 0.5.
Also, some candidates just wrote down 0.05 as their answer.
(b)
More candidates knew that the best estimate would be gained from reading
from the graph at 5000 sockets tested – the greatest number tested. The
probability was often given as a fraction 240/5000, although only the reading
of the relative frequency at 5000 was required.
The OCW question in this paper.
̂ C and furthermore
A considerable number of candidates could evaluate angle B𝐷
BĈD correctly quoting the circle theorems. Of these candidates many then did
realise that trigonometry should be employed but some candidates used the incorrect
ratio because they labelled the sides incorrectly (tan 28° was often seen as an error).
Some candidates also correctly used the sine rule to work out side BD. Another error
4.7
was incorrectly solving, sin 28 = 𝐵𝐷, i.e. the unknown as the denominator of the
equation.
Focussing on the OCW marks, many candidates did not write down the fact that
B𝐶̂ D = 90°, although they may have shown it on the diagram, or implied it within their
working (by correct use of trigonometry) – they often lost the mark for the Writing
element within the OCW marks in this case.
In the OC element of the OCW marks, candidates were expected to present their
working in a structured way, explaining each step of their answer. Unfortunately, a
number of candidates are still writing a short account of their process, writing it
separately from their calculations. For the W element, apart from not stating
B𝐶̂ D = 90°, candidates also need to remember to use correct mathematical form, and
to include the units in their working and answers (° and cm here).
© WJEC CBAC Ltd.
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9.
(a)
This question was well answered, especially the follow through to give the
values for 𝑥 from the candidates’ brackets whether it was correctly factorised
or not. Incorrect signs in the brackets was the common error seen in the
factorising.
(b)
A fair number of candidates gained full marks. Generally the marks lost were
from errors in expanding after the denominators were changed to be common
in all the terms. For example (7𝑥 + 1) incorrectly doubled to 14𝑥 + 1 was
often seen. Once the equation was simplified to have no denominators a
number of candidates made arithmetical errors with directed numbers or
incorrectly rearranged the equation to solve for 𝑥. Also the numerator being
multiplied by its respective denominator was seen on occasion.
10.
This question was not answered particularly well. There were numerous errors seen
within the scripts, ranging from using a positive enlargement (sometimes fractional),
a negative enlargement using the incorrect scale factor, or using the incorrect centre
of enlargement. Many candidates made more than one of these errors gaining few, if
any, marks.
11.
This question was very well answered. The only occasional error was multiplying a
lower bound by an upper bound.
12.
(a)
Not well answered. Candidates did not realise that they could factorise the
brackets (x – 7) leading to a simple and elegant solution. Many candidates
expanded the brackets, and collected the terms, before factorising to give the
required answer. However, many slips were seen when employing this
method leading to scoring either 1 or no marks. It was surprising that many
candidates who expanded the expression correctly, i.e. 𝑥 2 − 12𝑥 + 35, did not
proceed to factorise it, this being a relatively simple B grade question with the
𝑥 2 coefficient equalling 1.
(b)
Again, this question was poorly answered. The majority of candidates who
did gain any marks here gained only the first mark for 3(4x2 – 9y2). Few were
able to go further, although some other partial factorisations were also seen
e.g. (2x – 3y)(6x + 9y).
13.
The majority of candidates gained the first mark for expanding the single brackets
correctly. From there onwards numerous, fundamental errors were made showing a
clear lack of understanding of the process involved of collecting subject terms on one
side, factorising and then dividing. Numerous candidates would (incorrectly) divide
the equation by each 𝑥 term coefficient, not appreciating that this process would
affect all terms. Surprisingly at this level, signs of terms were not inverted correctly
when collecting on one side of the equation.
14.
(a)
Most candidates found it difficult to get started on this question, due to having
to work back from knowing the area of the sector to find the angle at the
centre. A few were able to start by calculating the area of the complete circle
𝜃
65
and then stating that
=
. If they got as far as this, they were often
360
𝜋×102
able to go on to find the required angle.
© WJEC CBAC Ltd.
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(b)
This part of the question was often left unattempted, especially if they had
had difficulty in (a). Those candidates who gained all 3 marks in (a) usually
gained both marks in (b). A few candidates, who had got an incorrect answer
in part (a), were, however, also able to go on to gain these 2 marks for the arc
length, bearing in mind that an incorrect angle could be used as a follow
through.
15.
This question was not well answered, with no pattern to the answers offered. It would
be beneficial to candidates, and schools, to not only concentrate on the shape of
different graphs, but also on recognising the intercepts of equations of different
graphs on each of the x and y axes.
16.
Many unforeseen errors were made by the majority of candidates whilst expanding
the expressions on either side of this equation, meaning that they normally gained
one of the three marks available for setting up the equation in the form
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0. For their equation, many candidates made slips in substituting
−𝑏±√𝑏2 −4𝑎𝑐
their values of a, b and c into
, which meant that only M1 was available. A
2𝑎
common error was incorrectly evaluating the 𝑏 2 in the discriminant to be negative
when 𝑏 is itself negative. A number of candidates failed to duplicate the formula
correctly, even though it is given on the Formula list, within the front cover, meaning
they lost the last three marks.
17.
This question, when attempted, seemed to gain candidates either no marks or full
marks. If they knew to find the linear scale factor, from stating, or calculating, the
ratio of the areas, then they usually went on to find the perimeter of the larger shape
correctly. The remaining candidates simply wrote that the scale factor to be
700/140 = 5, without considering this to be ratio of the areas – they gained no marks.
18.
(a)
This question on the whole was not answered well, even though the majority
of candidates attempted the question. The important step of needing to find
the angle within the triangle, at the centre of the star, was imperative, and the
majority of candidates failed to recognise this. Instead, the majority of
candidates incorrectly imagined that each triangle was right-angled, and
immediately lost all marks for part (a). However, a fair number of students
gained some marks for correctly using the cosine rule with their derived
angle. An error made by a number of candidates who did employ the cosine
rule was the failure to appreciate the order of operations in the calculation.
They calculated 𝑏 2 + 𝑐 2 correctly to be 149, but then proceeded to subtract
2𝑏𝑐 (equalling 140) before multiplying by the cosine of their angle.
(b)
Had the candidates found an angle, correct or otherwise, at the centre of the
star, then a significant number of candidates were able to gain marks here for
1
employing A = 2ab sin C . On the other hand, those candidates who had
imagined the triangle to be right-angled in (a), continued to do so in (b), and
again lost the marks.
© WJEC CBAC Ltd.
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