Mathematics: Paper 0626/01 Paper 1 (Core)

Cambridge International General Certificate of Secondary Education (9–1)
0626 Mathematics June 2017

Principal Examiner Report for Teachers
MATHEMATICS
Paper 0626/01
Paper 1 (Core)
Key message
To achieve well in this paper, candidates need to be familiar with all aspects of the core syllabus. The recall
and application of formulae and mathematical facts in varying situations is required as well as the ability to
interpret situations mathematically and problem solve with unstructured questions.
Work should be clearly and concisely expressed with answers written to an appropriate accuracy.
Candidates should be aware that it is inappropriate to leave an answer as a multiple of π or as a surd in a

practical situation unless requested to do so.
Candidates should show full working with their answers to ensure that method marks are considered where
answers are incorrect.
General comments
Candidates appeared to have sufficient time to complete the paper and any omissions were due to lack of
familiarity with the topic or difficulty with the question rather than lack of time. Stronger candidates were able
to attempt all the questions and solutions usually displayed clear methods. However, some candidates
provided solutions with little or no working and, as a consequence, did not earn method marks when the
solution was incorrect. Centres should encourage candidates to show all working clearly in the space
provided in the question paper booklet.
The stronger topics for candidates on this paper included finding fractions of amounts, range, interpreting a
calculator display, use of a calculator, simple scale drawing, currency conversion and simple interest.
Weaker topic areas included ordering fractions, decimals and percentages, forming expressions from a
problem in words, problem solving with algebra in a geometry context, simplifying expressions with indices,
problems with bounds, trigonometry.
Comments on specific questions
Question 1
A straightforward question on finding a fraction of an amount that candidates answered well.
Answer: 462
Question 2
Well answered. Most candidates found the range correctly.
Answer: 16
Question 3
Most were able to interpret the calculator display correctly as £16.99. A few gave £17.00 as the answer.
Answer: 16.99
© 2017
Question 4
Many successfully identified the primes as 17 and 19. There were a number, however, who gave additional
incorrect values such as 15.
Answers: 17, 19
Question 5
This proved difficult for almost all candidates. It was rare to see any working to give part marks here. Those
that had an incorrectly ordered list gained a mark if they had three values in the correct order. A common
error was to give 8.1% as the largest value and 0.18 as the smallest value.
1
Answers: 8.1%, 0.32, , 0.18
8
Question 6
This was well answered generally. Most were able to complete the calculation accurately and round their
answer to three decimal places as required. A few rounded incorrectly and gave answers such as 0.23 or
0.230. Some found the square root of the whole fraction and not just the numerator.
Answer: 0.229
Question 7
The more able candidates answered this well. In part (a), it was common to see two answers such as 16 and
64 or 16 and 27.
Part (b) was answered better than part (a). A few, again, gave two answers such as 5 and 175.
Answers: (a) 64 (b) 175
Question 8
This was well answered. Most were able to interpret the scale and complete the scale drawing. A few were
unable to draw the angle accurately.
Question 9
(a) This was very well answered and most gave an appropriate reason using the correct terminology of
angles on a straight line add up to 180°. A few tried to give a numeric justification such as 180 – 38
which is insufficient as a reason.
(b) Very few gave a correct reason here. Most referred incorrectly to opposite angles. A few gave Z
angles as a reason which is insufficient.
Answers: (a) 142, angles on a straight line add up to 180° (b) Alternate angles are equal.
Question 10
Many were successful with this ‘Show that’ question. The best solutions showed 573 – 384 and 5300 – 3200
before calculating the percentage. A few found 9% of 2100 and showed that it was equal to the difference
189 which was also acceptable. Weaker candidates often made incomplete attempts but understood either
the number of girls or the number of left-handed female students needed to be found.
Question 11
This was answered quite well. The common error was to multiply by the exchange rate rather than dividing.
Answers: 567.37 or 567.38
© 2017
Question 12
Both parts of this question were poorly answered
(a) Some obtained a correct unsimplified expression, but very few went on to simplify correctly as
required. Most tried to deal with the 37 and the h but were unable to set up an expression involving
the overtime.
(b) It was very rare to see any candidate set up an expression that involved the basic rate expressions
and overtime rate expressions added together. A few arrived at the given expression by incorrect
algebra.
Answer: (a) 49h
Question 13
Most candidates who showed working were able to score some marks on this question for a partially correct
method. The main error was in obtaining the correct cost for 0.75 litres of water. Those that obtained the
correct cost usually scored all three marks. Others gained credit for subtracting their cost of water from £1.76
and then dividing the answer by 2.
Answer: 0.46
Question 14
This was poorly answered.
Most candidates were unable to set up a correct equation involving the perimeter of the rectangle.
Candidates were given credit for attempting to solve their incorrect linear equation and so a number obtained
method marks here. The main error was in using two lengths to form the equation rather than considering all
four lengths.
Answer: 15.75
Question 15
(a) Many candidates were successful here and scored all 3 marks. Some calculated the simple interest
only and not the total amount after three years. Weaker candidates struggled to recall the method
to find a percentage of an amount.
(b) This was less well answered than part (a) and the common error was to do a simple interest
calculation rather than compound interest. Some worked in two stages for each year and made
arithmetic errors in the addition.
Answers: (a) 1066.40 (b) 1910.12
Question 16
(a) This question produced mixed responses. Many drew a correct ruled line, others attempted a
freehand line. A common error among some candidates was to draw a dot to dot set of line
segments instead of a line of best fit
(b) This was well answered, most were able to give a reasonable estimate of the height.
(c) (i) The best answers referred to Harry reading a value from the graph and then scaling it up to 24
years old or to extending the line of best fit. A number were vague in their reasons and gave
answers such as ‘He carried on the pattern.’
(ii) This was quite well answered. Most referred to the fact that growth stops at a certain age or that
the scattergraph did not provide data at that age.
© 2017
Question 17
(a) Most were able to complete the table with the required probability. Some did not realise that the
probabilities must sum to 1.
(b) Only a few were successful here and errors appeared to be random and to result from guesswork.
Answers: (a) 0.15 (b) 48
Question 18
(a) Most gave the correct answer. This was sometimes omitted by weaker candidates.
(b) Fewer were successful here. A common error was to add the indices and give y² as the answer.
(c) This was very poorly answered and omitted by many candidates.
x5y 4
Answers: (a) m³ (b) y -8 (c)
7
Question 19
(a) Only the strongest candidates answered this well. Others gave answers such as 13.1 to 13.3.
(b) A number calculated the circumference correctly but were unable to give a correct conclusion.
Many could not recall the formula for circumference and calculated the area instead.
Answers: (a) 13.15, 13.25
Question 20
Most candidates showed little working here so either scored both marks for the two correct values or no
marks at all. Method marks were available for attempting two trials with square numbers in working, but very
few showed this.
Answers: 1936 and 81
Question 21
A number of candidates were well prepared for this question on expanding a pair of brackets and were able
to give the correct answer. It was common however to see an error in the product of one of the terms for
which one mark was available.
Answer: x 2 - 2 x - 35
Question 22
(a) Only the best candidates were able to answer this question involving trigonometry. Some chose the
cosine ratio to solve the problem but were unable to complete the method correctly as it required a
division by the cosine of 27° and not a product.
(b) A very small number were successful here and this part was omitted by many candidates. A few
gained credit for recognition that the shortest distance was the perpendicular from M to LN.
Answers: (a) 95.4 (b) 36.8
© 2017
0626 Cambridge International Mathematics June 2017
MATHEMATICS
Paper 0626/02
Paper 02 (Extended)
Key message
Candidates need to have an understanding of mathematical terminology, as there were a number of

mathematical words that candidates did not understand. These included irrational, stratified, inversely and
asymptote.
Full coverage of the syllabus is required if candidates are to be successful. In particular, there was a general
lack of understanding of function notation. These questions are often not difficult once the notation is
understood.
General comments
Candidates were generally well prepared for the paper and demonstrated good understanding and
knowledge across the range of topics tested. Candidates generally attempted all of the questions and were
able to complete the paper within the time. Solutions were well set out and the correct processes chosen and
used efficiently.
Whilst some students found the latter questions on the paper particularly challenging, there were a significant
number of candidates able to demonstrate a high level of mathematical thinking and excellent problem-
solving and algebraic skills in their solutions to these questions.
Question 1
(a) Most candidates completed the table correctly.
(b) Most candidates found the expected number correctly.
Answers: (a) 0.15 (b) 48
Question 2
(a) Many candidates understood the powers of indices had to be added.
(b) Many candidates multiplied the indices together correctly.
(c) The algebraic fraction was generally simplified correctly. However, a common incomplete answer
x6y 4
was . Some candidates gave their answer as 0.143x 5 y 4 which was only awarded 1 mark.
7x
x5 y 4
Answers: (a) m3 (b) y −8 (c)
7
© 2017
Question 3
A variety of answers were seen including 2π and, for example, 38 . Some candidates did not understand
the word irrational and gave decimal answers such as, for example 6.3.
Answer: Any irrational number between 6 and 7.
Question 4
Candidates who evaluated this in one step generally arrived at the correct answer. Some candidates
evaluated the denominator and numerator separately, and because they then did not retain enough decimal
places for these, they sometimes gave an inaccurate final answer. However, these candidates could score 1
mark for correct rounding of their answer to 3 decimal places.
Answer: 8.553
Question 5
(a) Candidates showed a good understanding of upper and lower bounds.
(b) Candidates were able to find the circumference of the wheel, but were not always able to explain
whether or not the rope would be long enough, and in addition, they were required to compare it to
the lower bound.
Answers: (a) 13.15 and 13.25 (b) 13.19 > 13.15
Question 6
(a) Most candidates handled the 3 different conversions required within this question very well. There
was no specific order that the calculations needed to be completed in and candidates were
frequently able to score at least one of the three method marks available. Some candidates were
able to complete the question efficiently using only one calculation, whereas other candidates were
equally successful using a step by step approach.
(b) A variety of answers were seen to this, with most candidates being aware that cars usually travel
faster than 16.8 km/h. Other less common but equally valid comments also scored the mark.
Answers: (a) 16.8 (b) A valid comment
Question 7
It was pleasing to see so many candidates complete this question with ease and a wide variety of systematic
approaches were demonstrated. Candidates who left their answers as 442 and 92 were also awarded the
mark.
Answers: 1936 and 81
Question 8
(a) Most candidates used trigonometry correctly.
(b) Candidates understood that the shortest distance required them to drop a perpendicular line from
M to LN. This was often shown clearly on the diagram. The correct distance was then frequently
obtained.
Answers: (a) 95.4 (b) 38.6
© 2017
Question 9
Whilst many candidates recognised this as a reverse percentage question, the most common error was to
simply increase the 34kg by 15%.
Answer: 40
Question 10
Candidates often struggled to realise that the ratio of the volumes would give them the cube of the scale
1500
factor. Frequently, h was incorrectly found by multiplying 19.8 by .
2592
Answer : 16.5
Question 11
Candidates demonstrated a good understanding of stratified sampling and most calculated the answer as
8.75. To score full marks, this needed to be rounded to a whole number. Common errors included only
considering year 11 students or only considering girls, rather than all of the students.
Answer : 9
Question 12
(a) Candidates understood the process, but common errors included omitting to cube t or not using
inverse proportionality. From a correct formula, the correct answer was usually obtained.
(b) As in part (a), a correct formula usually led to the correct answer.
Answer: (a) 3.2 (b) 10
Question 13
(a) The majority of candidates drew clear sketches of the graph.
(b) Only a minority of candidates were able to write down the equations of the asymptotes, and it was
clear that most did not understand the term ‘asymptote’.
Answer: (b) x = 0 y =0
Question 14
(a) Candidates that understood the notation f f ( x ) usually obtained the correct answer.
Some found f f ( x ) algebraically first and then substituted in x = 5, whereas others found f ( 5 ) = 13
and then f (13 ) .
(b) Not all candidates understood the notation f −1 ( x ) . The question was attempted with various
degrees of success. Some made errors with the rearrangement and others forgot to transpose the
letters. Some of the most able candidates were able to give the correct answer with no working.
(c) Candidates who understood the notation were often able to write the correct answer straight down.
Other candidates produced a lot of working which did not help them progress.
x+2
Answer: (a) 37 (b) (c) x
3
© 2017
Question 15
This question was straightforward for those who understood the concept. A common wrong answer was
y = −3 x.
Answer: y = 3 x
Question 16
Candidates demonstrated clear mathematical problem-solving skills in their solutions to this problem. Some
1
used Pythagoras’ theorem whilst others used ab sin C . After finding the length of one side, most
2
remembered to multiply by 3 for the perimeter.
Answer: 22.8
Question 17
Whilst some candidates had little understanding of vectors, a high level of mathematical thinking and good
knowledge of vectors was frequently seen in solutions to this problem. Candidates used notation clearly and
their chosen route from M to N was often clearly expressed. Candidates were expected to collect like terms
together for the final mark.
1 1 1
Answer: − a + b + c
2 6 3
Question 18
This last question required excellent algebraic skills and awareness that the quadratic formula or completing
the square was necessary. Whilst the weaker students often found the first step difficult, others could not
work out how they could get the different powers of x to combine to be the single subject of a formula. There
were however a number of students who produced faultless rearrangements of the formula.
Answer: x = k ± k 2 − kt
© 2017
MATHEMATICS
Paper 0626/03
Paper 3 (Core)
Key messages
In order to do well in this examination, candidates need to give clear and logical answers to questions, with
sufficient method being shown so that marks can be awarded. Omission of working is not recommended for
any question that requires more than one step in its solution. Candidates who present their work in an orderly
way seem less likely to make simple errors such as misreading their own writing. For a non-calculator paper
in particular, it is useful if candidates check their answers either by assessing how reasonable they are or by
using simple estimation strategies. Also, when solving equations or inequalities, it can be useful to check the
answer by substituting it into the original equation or pair of equations to see if the result expected is
produced. Candidates also need to make sure that they read each question carefully and pay careful
attention to key words and phrases.
General comments
A good number of candidates were clearly well prepared for this examination paper. The use of a calculator
was not allowed and many candidates showed strong arithmetic skills. This was highlighted in Questions 3,
4, 5(b)(i), 11 and 14 in this examination. The most challenging arithmetic question seemed to be Question
11 where candidates were working with directed numbers and needed to consider the order of operations.
The questions that candidates found the least difficult were Questions 4, 7, 8, 9 and 16.
There were several questions which involved candidates making some type of comment to either describe
an assumption or an error in a solution or to justify a solution. For example, in Question 5(b)(ii), candidates
were expected to consider their solutions and indicate any assumption they needed to make. Many
candidates found this quite challenging and did not seem to realise that information they were given in a
question was not something they needed to assume.
All candidates seemed to have sufficient time to answer those questions that were within their capability.
Question 1
Approximately half the candidates answered this question correctly. There were more no responses than
expected for a question of this type, where a list of values to choose from is given. Some candidates were
clearly guessing. It is unclear as to whether the word integer was unknown or whether the integer was not
identified because it was negative. The square root of 5 was most common wrong answer.
Answer: −3
Question 2
A fair number of candidates earned both marks for this question, stating a correct fraction and cancelling
8
down. A small number of candidates gave the fraction and then forgot to cancel down. A fair number of
100
80
candidates gave the fraction and many did write this in its lowest terms. Other candidates gave an
100
4
answer of without showing any other working. It is likely these candidates thought that the fraction was
5
© 2017
80 1
but no credit could be given as the initial unsimplified form had not been shown. The answer was
100 8
very common. Candidates who gave this answer omitted to recall the definition of a percentage as a value
out of 100. Some candidates tried to cancel fractions that were already in their lowest terms.
2
Answer:
25
Question 3
Most candidates applied a correct method and indicated clearly what that method was. A good number of
candidates presented their work neatly and calculated the total accurately. Candidates whose presentation
was more haphazard and less complete often made arithmetic errors. It was common to see £6.39, for
example. Estimating the answer using 3 + 3 + 1.50 may have helped these candidates. Other candidates
giving the answer 6.39 showed no working and therefore were not awarded the method mark.
Answer: £7.39
Question 4
This question was well answered with a good proportion of candidates applying the correct method to find
the mean. A small number of candidates found the median or made arithmetic slips when summing the
numbers given.
Answer: 11
Question 5
(a) Candidates were asked for a number of hours. This question was fairly well answered. Some
candidates did not read the question carefully enough and gave their answer in hours and minutes.
A common wrong answer was 3.30 hours.
(b)(i) A good number of candidates determined that the pictogram represented a total of 30 hours and
carried out the correct calculation. Most of these arrived at the correct answer. Some excellent
arithmetic was seen. Those candidates who misinterpreted the key of the pictogram often realised
that they should attempt to total the number of hours and gained some credit for trying to divide
390 by that. Again, many answers were given without any method having been shown which meant
that method marks could not be awarded when answers were incorrect.
(b)(ii) Candidates needed to comment on what they had assumed when answering part (b)(i). A small
number of candidates understood what they were being asked and gave a sensible answer such
as ‘The hourly rate is the same for each hour’. Some good answers were seen and there was clear
evidence of an understanding of the limitations of what they had calculated. Other candidates
described the method they had used to answer part (b)(i) or the answer they had found.
Answers: (a) 3.5 hours (b) £13 per hour
Question 6
A good number of correct answers were seen and most candidates chose either Credit City or Every. Those
choosing Every had not fully compared the information in the table with the information they were given
about Mary’s requirements.
Answer: Credit City
© 2017
Question 7
(a) This part of the question was very well answered – almost all candidates understood what was
needed and entered the correct values.
(b) Some very good answers were given to this question. Some candidates correctly cancelled their
fraction to lowest terms, though this was not in fact required. Weaker candidates realised that 2
was of significance but often gave this as the answer rather than appreciating it was the numerator
of the fraction required. Some candidates were using words such as unlikely to describe the
probability rather than giving the value required.
2
Answers: (a) (b)
16
4 5 6 7 8
3 4 5 6 7
2 3 4 5 6
1 2 3 4 5
+ 1 2 3 4
Question 8
(a) Most candidates used a pair of compasses to draw a neat and accurate circle. A few freehand
attempts were seen and candidates need to be aware that they are expected to be able to use
compasses when a question requires them to draw an accurate circle.
(b) A very high proportion of candidates plotted the point Q correctly. Those who did not tended to
reverse the co-ordinates.
(c) It was clear that almost all candidates understood what a diameter was and were able to solve the
problem and write down the correct co-ordinates. Those candidates who reversed the co-ordinates
in part (b) usually plotted Q at (3, 6) and then gave the reversed co-ordinates (6, 3) as their
answer. This double error was not credited.
Answers: (a) Circle, centre P, radius 3 cm (c) (6, 3)
Question 9
Almost all candidates gave the correct answer. Very occasionally, the answer 0.4 was given.
Answer: 0.6
Question 10
A high proportion of candidates opted for the mode. Very often candidates gave the reason that this
represented the ‘most common’ as their justification and this was acceptable. Occasionally, the reason given
was not always sufficiently clear for the mark to be awarded or was not quite correct. Some candidates
suggested the mode would indicate how many of each model were sold, which is not the case. Other
candidates suggested the mean was the most suitable as it was the easiest to calculate. These candidates
would have done better had they realised that the data being considered was categorical not numerical and
therefore the mode was the only possible average available.
Answer: Mode with valid supporting comment
Question 11
(a) About half of the candidates offered the correct solution. The remaining candidates generally gave
the answer as −1.
(b) This was very well answered with most candidates giving the correct value. Those who did not
mostly found 32 ÷ 4 incorrectly rather than making a sign error.
© 2017
(c) A good number of candidates realised the need to apply a correct order of operations in this
calculation and did so correctly. Some of these candidates found 4.5 correctly and then made an
arithmetic slip in subtracting it from 8. Commonly 4.5 was given as the answer by these candidates.
Many candidates did not observe that the operations needed to be carried out in the correct order.
These candidates tended to give their final answer as 7.5.
Answers: (a) 11 (b) −4 (c) 3.5
Question 12
(a) A good number of correct answers were seen with candidates who recalled that taking a bearing
from A meant positioning their protractor at point A and measuring clockwise from north, doing so
accurately. About half of candidates gave an acute answer and marked the angle they were
measuring as the bearing of A from B in the anti-clockwise direction.
(b) Again, those who recalled that a bearing is measured in a clockwise direction usually gave a
reasonable explanation of why the bearing of B from C was not 095°. Candidates who measured
the incorrect angle in part (a) usually suggested that it was not 095° because it was 085°.
Answers: (a) 130°
Question 13
(a) A high proportion of candidates recognised the net given as that of a pyramid, with some
candidates even observing that it was, in fact, a square-based pyramid. The most common
incorrect answer seen was triangular prism.
(b) Many candidates stated the calculation 3 × 3 × 3 and then gave the correct answer. On a few
occasions, candidates made the error 3 × 3 = 6 and then gave 6 × 3 = 18. These candidates were
able to earn a method mark whereas candidates who just gave their answer as 18 or 9, without
stating 33 first could not be credited with any marks. Weaker candidates tended to give an answer
of 12, having worked out the perimeter of a 3 by 3 square. These candidates may have done better
if they had attempted to sketch a simple cube and mark on the dimensions.
Answers: (a) Pyramid (b) 27
Question 14
Many candidates answered this question very well. Some well-presented, easy to follow and accurate
3
solutions were seen. Almost all candidates generally managed to find of 640 without difficulty. A fair
8
1
number then misinterpreted the question and went on to find of 240, giving the value they found from that
5
calculation as their answer.
Answer: £80
Question 15
Candidates found this question quite challenging. Those who drew diagrams of triangles or rectangles were
often most successful. Those drawing rectangles simply doubled the given area and from that point it was
easy to see that 9 was the required answer. The answer 4.5 was very common with candidates forgetting to
halve the 10 before dividing. Some gave the general formula for the area of a triangle. Some of these
candidates did not substitute the values given into their formula and, on many occasions carried out an
incorrect sequence of operations, for example (45 ÷ 10) ÷ 2.
Answer: 9 cm
© 2017
Question 16
(a) Good candidates described the error in the solution, often indicating that Sean had not used a
common denominator. Comments such as He cannot just subtract the top and the bottom were not
sufficient to score. Other candidates appreciated that the correct process was to find the Lowest
Common Multiple. Some of these candidates omitted to say of what values the LCM should be
taken. This was necessary. Giving the correct answer in this part was not sufficient as this did not
explain Sean’s error. Some candidates seemed confused between subtraction of and division by a
fraction; these candidates tended to suggest He should have flipped the second fraction.
(b) A good number of correct answers were offered. Some arithmetic slips were seen in finding the
LCM. Weaker candidates suggested that Sean’s solution was correct or did not attempt a solution.
19
Answers: (b)
72
Question 17
In this question, candidates needed to convert a recipe for 4 people to 6 people and convert Imperial to
metric units. A few candidates did manage to do both and usually earned 3 or 4 marks. Many candidates did
one or other of the necessary processes and generally earned 1 of the 4 marks available. A good number of
candidates stated their units and most candidates attempted to answer this question.
Answer: 720 g, 180 g, 1800 ml
Question 18
Candidates found this question challenging. Candidates who rounded all 3 values correct to 1 significant
20
figure were often unable to evaluate the calculation formed. Commonly, answers of 2 or were given or
3
the answer had a place value error, for example 0.6. Many candidates rounded 0.333 and 2.98 correctly but
did not round 58.6 at all. Some candidates made no attempt to answer. Others rounded 0.333 to 0 and gave
their answer as 0. These candidates needed to check the reasonableness of their answer.
Answer: 6
Question 19
(a) Only the better candidates understood what was needed to answer this question successfully, with
the geometry skills needed to answer this question being beyond many candidates. Some
candidates did find a value for angle x and realised that angle y was half of that value. Other
candidates were measuring angles from the diagram. It is important that candidates understand the
significance of the comment NOT TO SCALE alongside any diagram. Those few candidates who
attempted to find the exterior angle of the hexagon often did not know what to do with what they
had found.
(b) Many candidates were able to explain, using the fact that BE was the hypotenuse of a right-
angled triangle, why BE was longer than AE. Some candidates tried to justify the statement given
by suggesting that it was longer because it was slanting or diagonal.
Answers: (a) 120, 60
Question 20
(a) A small number of candidates solved this inequality successfully. Most candidates tried to solve an
equation and gave the answer as a single numerical value.
(b) As this part of the question depended on the answer to part (a) being an inequality, very few
candidates answered this part successfully. About half of those candidates who had an inequality
as their answer to part (a) were able to represent it successfully on the answer line given.
Answer: (a) x > −4
© 2017
Question 21
Many candidates earned 1 or 2 marks for this question. Often answers were not given in standard form.
Many answers of 3 × 104 or 3 × 10−2 were also seen. Only a few candidates made little or no progress.
Amongst these, answers such as 3−4 were offered.
Answer: 3 × 10−4
Question 22
Many candidates showed some evidence of understanding what was meant by a reciprocal and a fair
number of candidates gave a fully correct solution. Many candidates only attempted to complete one of the
1 1
two necessary steps. Often candidates tried to reciprocate the 2 and the separately and the answer 4
4 2
was not uncommon. Other candidates converted the mixed number to an improper fraction correctly but
seemed to think that was the answer to the question and so did not complete the solution. A few candidates
converted the fraction to a decimal form but made no real progress with this approach.
4
Answer:
9
Question 23
(a) Some good solutions were seen to this question. Often candidates found the value of 106 as 1
million and then realised that this was 1000 × 1000. Weak candidates halved both the 10 and the
power of 6 and the answer of 53 was seen more than once. Some candidates divided 1 million by 2
rather than square rooting it.
(b) About a quarter of candidates understood what was needed and arrived at the correct answer.
Other candidates tended to offer solutions such as 25−1 or −25.
1
Answers: (a) 1000 (b)
5
Question 24
Candidates found this question challenging. A reasonable number of good, neat and clear solutions were
seen. A few solutions had a first correct step. Many candidates did not understand what was needed and
often x and y were simply interchanged in the formula.
y +z
Answer: x =
w
Question 25
About a quarter of candidates used their compasses and accurately constructed the required perpendicular
bisector. Some candidates drew attempts at the bisector with no arcs and often these were not sufficiently
accurate to be rewarded. Many candidates did not seem to understand the term perpendicular bisector and
therefore were unable to offer any solution.
Question 26
Some candidates did find the correct equation. Successful methods were substituting (0, 5) into y = mx + c to
find c and then using (3, −1) to find m or making a sketch of the points given and determining values from
that. Some good candidates omitted to take into account that the gradient of the line was negative and
several answers of y = 2x + 5 were seen. A reasonable number of candidates realised that the value of c
was 5 but were unable to find a gradient.
Answer: y = −2 x + 5
© 2017
Question 27
(a) Many candidates gave a fully correct solution to the calculation. Occasional arithmetic errors were
seen and often these were sign errors. A small number of candidates attempted to work out the
difference of two fractions, having drawn a fraction bar between the components of each vector.
(b) Candidates who understood that the key to the solution was to first find the value of b were almost
always successful in completing the solution. Candidates who were successful used formal
algebra, setting up at least one equation and solving or used trials to find a correct pair of values.
Some candidates corrected sign errors by, very sensibly, checking that their solutions satisfied the
given relationship. Other candidates would have benefitted from undertaking such a check. Those
candidates who thought that they were working with fractions in part (a) tended to repeat that error
in this part.
 17  1
Answers: (a)   (b) a = , b = 4
 − 6  2
Question 28
Candidates used a variety of methods, with varying success. Candidates who chose the method of
substitution often struggled with the algebraic fraction or fractions they had formed. Candidates who used the
method of elimination were usually more successful. Trial and improvement was seen but rarely successful
and is not recommended as a method for solving simultaneous equations as the solutions are often not
integer values. Some candidates would have benefitted greatly from checking their solutions as arithmetic
slips were sometimes made.
Answers: x = 4, y = −3
Question 29
Some very neat and accurate solutions were seen to this problem. A reasonable number of candidates
understood the requirement to draw a pair of accurate circles and shade the left hand crescent formed by
their intersection. Some candidates shaded the left hand section of the smaller circle whilst other candidates
only drew the smaller circle and did not attempt the larger arc. Many candidates did not try this question. It is
not clear if this was because of a lack of knowledge of the topic or a lack of equipment with which to draw.
Question 30
(a) Better candidates looked for, and found, the correct common factors and were usually successful.
A small number of candidates tried to combine the terms in some way. Candidates suggesting the
answer to be 5y(x −42) had misunderstood the meaning of the power of y.
(b) (i) Only the very best candidates were successful with this factorisation using the difference of two
squares. It was clear that some candidates did not recognise the pattern that was being presented
and w(w – 1) was fairly common.
(ii) A very few candidates were successful in this part. Those who used the difference of two squares
in part (b)(i) usually saw the pattern but did not always find the correct value. Some candidates
would have benefited from estimating the answer as the values given as answers were often of
totally incorrect magnitude.
Answers: (a) 5y(x −20y) (b)(i) (w – 1)(w + 1) (b)(ii) 9800
Question 31
Candidates who attempted this question made some reasonable attempts to factorise. Sometimes the signs
were reversed and candidates who did this may have recovered from their error if they had checked that
their values satisfied the given equation.
Answers: x = −6, y = 8
© 2017
MATHEMATICS
Paper 0626/04
Paper 4 (Extended)
Key messages
● Full coverage of the Extended syllabus is needed to access the whole paper.
● Clear, logical steps in working out need to be shown in order to access method marks, when final
answers are incorrect through minor errors.
● For the requirements of the question to be fully understood, careful attention to the key words and
phrases in the question is needed.
● Questions need to be answered fully, and a check made to ensure the requirements of the question
have been met, by re-reading the question before moving on to the next question.
General comments
Many candidates were well prepared for this examination paper. There was evidence of fuller coverage of
the syllabus needed by some.
Good responses were exemplified by clear and logical steps in the working out. Those with minimal or
missing steps were more likely to lose marks in the event of minor errors and a final incorrect answer. Those
with illogical or confusing steps, or untidy writing, were also more likely to lose marks, often as a result of
losing their way through their solution, or misreading their own writing.
This is a non-calculator examination, and arithmetic skills were generally good, although slips were evident
from a significant number of candidates, which more detailed and clearer steps in working out would likely
reduce.
Candidates should be advised to consider the number of marks available in the question when deciding on a
method to adopt, in order to ensure they have understood the requirements of the question.
Question 1
In this estimation question, estimation of the denominator was handled very well, and the square root of 9
was written down as 3 in most cases. Marks were lost due to rounding only two of the figures to 1 significant
figure rather than all three. A common error was to incorrectly round 0.45 to 0 or 1. Rounding 59 to 6, or
leaving it as 59 was another error commonly seen. Squaring 0.5 by some candidates gave an incorrect 2.5,
rather than the 0.25 required.
Candidates attempting the actual calculation rather than an estimation might suspect they are doing too
much work for 2 marks, and re-reading the question carefully should point them in the direction of rounding
the values first.
Answer: 5
Question 2
Some candidates answered this reciprocal question well. Many stopped after the first step of converting the
mixed number to an improper fraction, and gave this as the final answer. Others converted the mixed
number to the decimal 2.25 and gave this as the final answer.
© 2017
Introducing a power of –1 might help those candidates that understood how to find the reciprocal, as it would
remind them to continue to the second step of the solution, if the omission of the final step was an
unintentional slip.
4
Answer:
9
Question 3
This perpendicular bisector construction question was extremely well answered. Most candidates produced
the correct line within tolerance, with good construction arcs. Some candidates would be advised to work to a
bigger scale, to ensure that the intersections are far apart enough to ensure a good line within tolerance.
Proficiency with compasses could be improved by some candidates.
Question 4
(a) This indices question involving a square root was well answered. Many gave a final answer of 103
which needed a further step to evaluate this to 1000 for full marks. Errors involving a factor of 10
too many or too few were seen, which appeared to have been slips rather than a
misunderstanding.
1
(b) This indices question was extremely well answered, with correct answers of , 0.2 and 5–1 seen.
5
(c) Those candidates following the rules for order of operations were generally successful in this
question, barring a few arithmetic errors seen. The most common error was to split the bracket and
attempt to find the cube root of each term separately.
1
Answers: (a) 1000 (b) (c) 3
5
Question 5
This question on finding the linear equation through two points was extremely well answered. Arithmetic
errors resulted in the loss of marks by some candidates, but it was encouraging to see that many worked out
the gradient with clear, logical steps, thus reducing the likelihood of arithmetic errors. Very few candidates
were unable to make some progress and gain marks. Other errors included using a gradient of positive 2;
and some candidates were able to identify the y-intercept as c = 5, but unable to find the gradient.
Answer: y = –2x + 5
Question 6
(a) This vector arithmetic question was extremely well answered, with the most common errors arising
from arithmetic slips. A small number of candidates carried out the calculation in the incorrect
order, or thought they were dealing with fractions.
(b) This was a more challenging vector question, which was very well answered. Candidates mostly
used algebra to arrive at the answers, with many showing clear working out. Those candidates
finding b first often arrived at the correct answer for a too, whilst more convoluted methods had a
greater tendency to make arithmetic slips.
 17  1
Answers: (a)   (b) ,4
 − 6 2
© 2017
Question 7
This simultaneous equation question was extremely well answered. The elimination method was more
popular than the substitution method, but equally successful. Arithmetic slips were the main errors seen, and
some candidates had difficulty in dealing with algebraic fractions when using the substitution method.
Candidates would benefit from checking their values if time allows.
Answer: x = 4, y = –3
Question 8
On both parts of this loci question, candidates would benefit from re-checking the setting of their compasses
to ensure the required measurement has been set correctly, and then check by measurement of the radius of
their arcs. It is evident that some candidates would have benefitted from increasing their proficiency in the
use of their compasses.
(a) Most candidates knew that the locus of points from point A was a circle, and correctly constructed
this.
(b) Many candidates gained both marks for this part. Common errors included inaccuracy in setting
radius, and identifying the incorrect area, which often came from drawing a vertical line between
the two intersections of the arcs.
Question 9
(a) An almost universally well answered question on common factors, with both the numerical and
algebraic factor successfully taken outside of a bracket. Division by the common factor was seen,
and very rarely there was evidence that the candidate was unaware of the process of factorisation.
(b) (i) This difference of two squares question was correctly answered by many candidates.
(ii) Most candidates successful in part (b)(i) gained full marks in this question. The expectation was to
substitute 99 into their factorisation and thus arrive at a simple calculation 98 × 100. Some
candidates gave their final answer as (99 – 1)(99 + 1) and did not make the link to arrive at 9800.
Other errors included long multiplication of 99 x 99 with arithmetic slips, and substituting 99 or 33
rather than 99 into their factorisation from part (b)(i).
Answers: (a) 5y(x – 4y) (b)(i) (w – 1)(w + 1) (ii) 9800
Question 10
This question on solving a quadratic equation was generally well answered. Most candidates factorised
successfully and arrived at the correct solutions. Only a few candidates chose the incorrect factors of –48.
Some candidates used the quadratic formula correctly, but those going down this route often made errors in
the substitution or arithmetic slips in the calculation.
Answer: −6, 8
Question 11
Many candidates chose to convert the mixed numbers to improper fractions, rather than calculating
3 5
43 − 41 = 2 and working with the fractions − and the various alternative methods down this route for
5 6
dealing with the fact that this would result in a negative fraction. This common alternative of working with
improper fractions increased the likelihood of arithmetic errors when dealing with lengthy calculations, and
marks were lost by a significant number of candidates due to errors.
© 2017
The instruction to give their answer as a mixed number was either missed or misunderstood by some
candidates who gave their answer as an improper fraction.
23
Answer: 1
30
Question 12
This rearranging formula question was straightforward and exceptionally well answered. Candidates are
advised to write the complete formula out on the answer line, as many omitted the x =.
y +z
Answer: x =
w
Question 13
Many candidates knew that this was an equation of a circle with centre (0, 0) and correctly drew this. Fewer
candidates correctly labelled the axis intersections. A significant number of candidates gave a quadratic or
linear graph.
Question 14
(a) This histogram question proved a challenging question, with few correct answers seen. Most
candidates treated the histogram as a bar chart, and labelled the vertical axis with the number of
candidates rather than frequency density – there were no part marks for this approach, so most
students gained no marks.
(b) (i) Candidates who treated this as a histogram generally answered this part correctly. Candidates
needed to treat the area as representing the frequency in order to gain marks in this part.
4
(ii) Some candidates realised that the frequency representing of the area between 20 and 25 was
5
required and gained some credit, despite gaining no marks in previous parts. Many candidates
attempted lengthy incorrect calculations which gained no marks with few candidates arriving at a
correct answer.
Answer: (b)(i) 25 (ii) 68
Question 15
This matrix transformations question proved challenging for many candidates.
(a) Many candidates correctly stated the transformation was a reflection. Some were able to correctly
identify the line of reflection. Many candidates gave angles and centres of rotation following a
statement of reflection, which seemed to indicate a confusion between reflection and rotation.
Common errors included giving the transformation as rotation or enlargement.
(b) (i) This matrix transformation question was answered correctly by a small number of candidates.
 0 −1
Answers: (a) Reflection in y = –x (b)  
1 0
Question 16
(a) This simplification of a surd question was very well answered.
(b) Candidates that understood the term ‘rationalise the denominator’ were generaly able to gain full
marks. Many candidates did not rationalise the denominator.
Answers: (a) 5 3
© 2017
Question 17
(a) This question involving exact values of trigonometric ratios was answered well by some
candidates. Sin30 was given as an answer by a significant number of candidates, which required a
further step to ‘work out the value’, as required in the question. Some candidates who were able to
write down the exact values then made errors in handling the surds. Many candidates gave no
evidence that the values were known.
(b) This trigonometric equation was attempted by many candidates. Very few gained both values, and
some candidates gave extra values within the range. Many candidates realised 45° was an answer.
Correct sketches of the sine curve generally led to candidates gaining the second correct value of
135°, of which there were few seen.
1
Answers: (a) (b) 45° and 135°
2
Question 18
(a) This matrix multiplication question was very well answered, with many candidates losing a mark
due to arithmetic slips rather than an incorrect method applied.
(b) (i) This inverse matrix question was well attempted by many candidates. Errors were seen commonly
due to the incorrect rearrangement of the matrix elements, or incorrect calculation of the
determinant.
(ii) This part proved challenging for many candidates. Some candidates successfully wrote down the
identity matrix, whilst many made no attempt, or an incorrect attempt.
 12 −19   0.1 −0.3   1 0

Answers: (a)   (b)(i)   (ii)  
 −16 17   0.2 0.4   0 1
Question 19
This circle geometry question was extremely well answered. A thorough understanding of the isosceles
triangles within a circle was evident. The preferred method was to work with ‘tangent meets radius’, then
isosceles triangle OML to find b, and use ‘angle at centre is twice angle at circumference’ to find a. Less
popular was the route using the alternate segment theorem. Errors made were mainly due to arithmetic slips
rather than method. Some candidates had assumed symmetry of the diagram through OM, which was not
the case.
Answer: a = 24, b = 32
Question 20
(a) (i) This probability question was answered with varying degrees of success. Many candidates realised
that it was a ‘without replacement’ type of question. Tree diagrams were used with varying degrees
of success. Common errors included using a denominator of 10 in all three probabilities to be
multiplied; using 0.6 for all three fractions; and addition of three fractions rather than multiplication.
(ii) Few candidates made the link to 1 – part (a)(i). Those candidates with lengthy calculations to arrive
at an answer ought to have noticed that it was only worth 1 mark, and perhaps consider a different
approach.
(b) (i) Many candidates correctly answered this question. There was evidence that some candidates had
not understood the event described, so were unable to provide a meaningful attempt. A common
error was to add two fractions, rather than multiply.
(ii) Many candidates attempted this but few candidates arrived at the correct expression. Greater
success would have been achieved if they had considered how the expression varied with
increasing values of n, beginning with n = 1, 2, 3, etc., rather than writing down an expression with
no pattern established. Of those candidates that understood the pattern, there were many that
© 2017
incorrectly expressed it in terms of n, and commonly wrote down (n − 1) as a multiplier rather than
a power.
n −1
1 5 5 5 1
Answers: (a)(i) (ii) (b)(i) (ii)   ×
6 6 36 6 6
Question 21
This cubic expansion was very well answered, with some candidates clearly understanding the method, and
losing marks due to making arithmetic slips. Better setting out of working would benefit some candidates, in
order that partial marks can be awarded in cases of arithmetic slips. Some candidates arrived at the correct
answer, and then continued on to an incorrect answer, through incorrect attempts to factorise, or miscopying
their working. A few candidates only partially expanded the brackets, leaving the answer written as a
quadratic factor and linear factor.
Answer: x3 + 2x2 – 9x –18
Question 22
Many candidates were able to differentiate the function correctly, with few errors made in the two term
derivative. Errors following this step were usually from arithmetic slips or candidates not sure what to do after
differentiating. Many candidates made little or no attempt. This question elicited a wide variety of incorrect
methods too, with a significant number of candidates not differentiating the function at all, but trying to
substitute into f(x).
Answer: a = 2, b = 54
© 2017
MATHEMATICS
Paper 0626/05
Paper 5 (Core)
Key messages
To succeed in this paper, candidates need to have covered all of the Core syllabus content. They should be
able to apply their mathematics to everyday situations and combine mathematical skills in solving problems.
General comments
The question paper included a range of questions: some routine tasks, some set in familiar contexts and
others that required application of a range of skills in contexts that were less familiar. In general, candidates
performed well on the more routine questions but were less proficient when they needed to identify the
mathematics required.
In many cases, candidates showed insufficient method which meant that part marks could not be awarded if
the final answer was not correct. When candidates are required to show a result it is important to set out
steps logically and include all relevant working.
It was evident that a number of candidates were unfamiliar with stem and leaf diagrams and similar triangles.
Question 1
(a) Most candidates answered this part correctly.
(b) (i) Many correct answers were seen in this part. Some candidates were unable to convert 575 g to
kilograms.
(ii) Candidates who had reached an answer less than £20 in part (i) usually calculated the correct
change.
(c) Good responses to this question involved candidates calculating the cost per egg for each pack
and this usually led to identifying that the pack of 10 was better value. Some candidates worked out
the cost of two packs of six eggs, for example, and compared this cost with the cost of a pack of 10
which was not an acceptable strategy. Only methods involving comparison of the same numbers of
eggs were acceptable.
(d) Many candidates were able to calculate the reduced price of a cake. A small number of candidates
just calculated 25% of the cost rather than reducing the price by 25%.
Answers: (a) £8.26 (b)(i) £3.91 (ii) £16.09 (c) Pack of 10 with 0.289 and 0.295 (d) £2.85
Question 2
(a) (i) Most candidates read the time correctly from the timetable.
(ii) Most candidates calculated the correct length of time for the journey.
(b) Most candidates identified which train would be needed and found the correct departure time.
© 2017
(c) Many candidates were able to work out that the time taken was 1 hour 15 minutes, which some
correctly converted to 75 minutes. Although many candidates knew that speed is calculated by
dividing distance by time, few were able to convert the time to 1.25 hours and use this to calculate
the speed correctly. It was common to see division by either 75 or by 1.15.
(d) This question required candidates to show the given saving. However, few candidates showed a
clear set of correct calculations leading to the required result. Many could correctly calculate the
cost of an adult ticket using the railcard. The calculation of 35% of £48 was found to be much more
challenging. It was common to see candidates attempting 35% of £24 from a misinterpretation of
the railcard price for a child’s ticket. Some clearly set out and well annotated correct solutions were
seen.
Answers: (a)(i) 10 15 (ii) 47 minutes (b) 12 05 (c) 52 mph
Question 3
Many candidates were able to use the given information to calculate the costs correctly using each plan and
make the correct decision about which plan should be chosen. Many candidates clearly labelled their
calculations Plan A and Plan B. A small number of candidates worked out the number of kilowatt hours used
each day and compared these costs which was also acceptable. Some candidates were confused about the
daily charge for Plan B and this was sometimes only added once for the whole 90 days or was omitted
completely.
Answer: Plan B with £109.23 and £122.88
Question 4
(a) (i) Most candidates could correctly find the output from the function machine.
(ii) Many candidates correctly reversed the function machine. Common errors were to calculate
12.7 + 4.8 ÷ 2.5 rather than (12.7 + 4.8) ÷ 2.5 or to calculate (12.7 – 4.8) × 2.5.
(b) Candidates found this problem more challenging and many did not attempt it. Those that did
attempt it often identified that q = 5 but did not know how to find the value of p. Some candidates
showed correct algebraic working although many appeared to reach the correct result using a trial
and improvement approach.
Answers: (a)(i) 5.2 (ii) 7 (b) p = 3.5, q = 5
Question 5
(a) (i) Candidates completed the frequency graph correctly. Some did not use a ruler to draw the bars.
(ii) Many candidates found the correct values of 13 and 67 to use in their answer and a correct fraction
was usually given. Some answers were given as ratios which is not acceptable for probability.
(b) (i) Most candidates were able to work out that the sector angle for cars was 200° and they often also
calculated that 8° represented one person. Not all candidates could then combine this information
to calculate the number of people who travelled by car.
(ii) Few candidates were able to give an acceptable reason in this part and those reasons that were
accepted were usually related to not all employees answering the question in the original survey.
Very few candidates were able to identify that the responses to this survey might not be
representative of the new company.
(c) (i) Many candidates were unfamiliar with stem and leaf diagrams. However, some successfully
identified the highest number in the diagram.
(ii) Fewer candidates were able to find the mode from the stem and leaf diagram and this part was
often omitted.
© 2017
(iii) Very few candidates were able to find the median and most attempts involved writing out a list of
numbers, often omitting the stems, rather than finding the middle pair in the stem and leaf diagram.
Some candidates found the mean rather than the median.
13
Answers: (a)(ii) (b) (i) 25 (c)(i) 58 (ii) 27 (iii) 32.5
67
Question 6
(a) Many candidates divided 16.5 in the ratio 2 : 9 correctly. The common error was to multiply 16.5 by
2 and by 9.
(b) Many good answers to this part were seen with candidates able to identify that one quarter of the
mix is cement or that if one third was cement the ratio would be 1 : 2.
(c) This part of the question was more challenging and many candidates were not able to make any
attempt. Those candidates who identified that 22.6 kg was 2 parts from the ratio usually reached
the correct answer. Common errors were to treat 22.6 kg as either 1 part or 7 parts.
Answers: (a) cement 3 kg, sand 13.5 kg (c) 79.1 kg
Question 7
(a) (i) Many candidates were able to explain that he should have added 2 to both sides rather than
subtracting in his first step.
(ii) Candidates often reached the correct answer.
(b) (i) Candidates who attempted this part usually expanded at least one of the brackets correctly. A
common error was to write –21 rather than +21.
(ii) Although a number of correct answers to this part were seen, it was clear that many candidates did
not relate this part to the expansion they had done in the previous part and they did the working
again in this part. Some correct answers were reached using a trial and improvement approach
rather than solving algebraically.
Answers: (a)(ii) 2.2 (b)(i) 8x – 36 – 3x + 21 (ii) 3
Question 8
(a) Many candidates were unsure what was required in this part of the question although those that
attempted it usually showed enough to be given credit. They were required to add the expressions
for the thinking distance and braking distance given in the information at the top of the page to
show that this was the same as the given formula.
(b) Many candidates were able to substitute 45 into the given formula; however, not all could correctly
evaluate the result.
(c) This part was found to be very challenging as it required a combination of two formulas to be used.
Some correctly substituted 210 into the braking distance formula but then were uncertain how to
proceed. Again some candidates were unable to evaluate the stopping distance once they had
correctly substituted the speed into the formula.
Answers: (b) 146.25 feet (c) 275 feet
Question 9
(a) Many candidates identified that the transformation was a rotation. Complete descriptions were
seldom seen with either the centre or the direction or both omitted.
(b) Correct reflections were often seen, although reflections in x = 3.5 were also common.
© 2017
(c) Candidates were unfamiliar with enlargements with a fractional scale factor and two times
1
enlargements were common. Those that used the scale factor were often unable to use the
2
given centre of enlargement and rays from this point were rarely seen.
Answers: (a) Rotation, centre (2, 5), 90° clockwise
Question 10
(a) Many candidates were able to calculate the percentage increase correctly.
(b) In this part, many candidates identified the calculation required and started by finding the difference
between the two populations. A common error was to divide by the new population rather than by
the original population.
(c) Not all candidates were familiar with standard form, but those who were generally gave the correct
answer.
(d) There were several stages required in this part and many candidates calculated the difference
correctly. They were not always able to round this to three significant figures or to write it in
standard form. It was common to see the numbers written out in full for the subtraction suggesting
that candidates were not able to enter numbers into their calculator in standard form which would
have been a more efficient method.
Answers: (a) 75 400 (b) 13.7% (c) 1.073 × 106 (d) 1.22 × 109
Question 11
(a) Some candidates identified that the diameter of the circle was 9 cm, but they were not always able
to use this to calculate the area of the circle correctly. Some used either 9 or 3 as the radius and
others used the circumference formula.
(b) (i) Very few candidates were able to write an expression for the areas of the square and the circle so
could not then show the ratio of 4 : π.
(ii) Very few candidates could answer this part and those who did generally calculated the radius of
the circle using the area formula and used this to find the area of the square rather than using the
ratio found in the previous part.
Answers: (a) 63.6 cm2 (b)(ii) 22.5 cm2
Question 12
(a) Many candidates were unfamiliar with similar triangles. Some did find the scale factor of 1.25 but
very few were able to use this to find the missing length.
(b) Some candidates were able to access this challenging problem which involved the use of
Pythagoras’s theorem or trigonometry and similar triangles. Clear and correct method was seen in
some cases leading to the correct answer, although some candidates were able to calculate the
length of AQ and then make no further progress.
Answers: (a) 7.5 cm (b) 31.25 cm
© 2017
Question 13
(a) (i) Most candidates were able to find the next term of the sequence.
(ii) Some candidates were able to find a correct expression for the nth term of the sequence. Common
incorrect answers were n + 6 and 7n + 6.
(b) Candidates who started by creating the equation 3n2 + 2 = 110 were often able to reach n = 6.
They did not always then identify that they needed to substitute 7 into the expression for the nth
term to find the required answer, and often an answer of 116 was seen. It was also common to see
110 substituted as the value of n in the expression as a starting point. Many candidates omitted this
part.
Answers: (a)(i) 31 (ii) 6n + 1 (b) 149
© 2017
MATHEMATICS
Paper 0626/06
Paper 6 (Extended)
Key messages
To succeed in this paper, candidates need to have covered all of the Extended syllabus content. They
should ensure that all working is shown, especially in ‘Show that’ questions.
General comments:
All questions except the last one were accessible and nearly all of the candidates attempted most of the
questions. There was no evidence that candidates were not able to complete the paper because of a lack of
time.
Candidates generally showed a detailed method, which is essential on the longer problem solving type
questions. A small error on questions of this type with no working shown will lead to a significant loss of
possible marks. When candidates are required to show a result it is important that they show a detailed
method showing every step of their working.
Some questions required an explanation; when answering this type of question, candidates must relate their
answer to the information given or found in the question rather than give vague responses or responses with
a lack of detail.
Comments on specific questions:
Question 1
(a) Most candidates successfully found the mean. A small number just added the five different
numbers of chocolates and divided by 5.
(b) Most candidates gave a sensible answer either justifying or rejecting the claim.
Answers: (a) 30.6
Question 2
(a) Most candidates found the correct acceleration. An infrequent error was to divide the time by the
speed.
(b) The method of calculating the distance from a speed-time graph was well understood with most
candidates finding the correct answer.
Answers: (a) 1.5 m/s2 (b) 252 m
Question 3
(a) (i) The fact that the masses of the planet were given in standard form did not deter candidates from
using the correct method to find the mass of Mercury as a percentage of the mass of Mars, with
most giving a correct response.
(ii) A few candidates were put off by the wording of this question and multiplied by 8.7 instead of
dividing, but many found the correct answer.
© 2017
(b) There were three stages to this question and some candidates only completed two, either
forgetting to multiply by three quarters or one thousand. A few divided the masses of the two
planets rather than multiplying. Nearly all candidates were adept at using their calculators to
perform operations in standard form. There was a fair proportion of correct responses.
Answers: (a)(i) 51.6% (ii) 7.36 × 1022 kg (b) 9 × 1056
Question 4
Candidates were generally aware of the overall principles involved when working through this question. Most
found the area of the trapezium successfully, but there were errors finding the area of the circle with some
using the diameter rather than the radius in the formula. Most then went on successfully to find the number of
bags needed for their area. Few found the amount of grass seed left over successfully.
Answers: 13 bags with 668 g left over
Question 5
(a) Most candidates knew how to find the inter-quartile range and carried out this process correctly.
(b) There was some problem solving required to find the highest mark and the quartiles in this question
and, as a result, many scored part marks on this question. Nearly all plotted the median correctly
and many found the correct highest mark.
(c) Generally candidates did not know what was required of them on this question. They compared the
results of the two classes by comparing, for instance, the two medians but they did not then go on
to give a reason for this comparison by interpreting their result in the context of the question.
Answers: (a) 17
Question 6
(a) Candidates generally knew how to compute compound and simple interest correctly and many
obtained full marks. Candidates need to be aware that on questions of this nature where they are
asked to show a result, they must give a clear step by step method showing all their working to
achieve the required result.
(b) Many candidates did not know how to proceed on this question, although there were some good
responses. Some candidates tried to use an algebraic method but did not have the necessary skills
to complete their attempt.
Answers: (b) 37
Question 7
(a) (i) Although there were candidates who were able to mark and label an external angle, some were
confused as to what was required.
(ii) Some candidates tried to use some sort of formula to answer this question but were not able to
apply it to find the number of sides of the polygon. Candidates who thought the problem through
from first principles were often more successful.
(b) (i) Some candidates were able to identify an error in the proof.
(ii) Although most candidates attempted this, many were confused as how to proceed and few gained
both the available marks.
Answers: (a)(ii) 30 sides (b)(i) Reflection symmetry not a valid reason or RHS not a valid
© 2017
Question 8
(a) There was a good understanding of how to draw the graph of this linear equation with many
candidates gaining both marks.
(b) (i) Most candidates attempted this question and many successfully drew the line of y = 3. Some
candidates did not realise that y = 3 needed to be a dashed line as y = 3 was not included. Most
candidates who had drawn their linear lines correctly identified the correct region.
(ii) There were a few fair attempts to identify the integer co-ordinates in their region. Some included
points with y co-ordinate 3, forgetting that y < 3.
Answers: (b)(ii) (1, 1), (1, 2), (2, 2)
Question 9
Candidates were well versed in using algebra in questions of this type to find the correct value of x. Some
candidates stopped at this point, not knowing how to proceed. Those that did carry on usually made a fair
attempt showing that the quadrilateral was cyclic, although some did not give the full geometrical reason of
opposite angles in a cyclic quadrilateral adding up to 180°or equivalent.
Question 10
(a) (i) Responses to this were mixed with candidates having some idea as to how to fill in the Venn
Diagram but not giving a fully correct answer; consequently, one mark only was often awarded.
(ii) Most candidates answered this correctly.
(iii) Many candidates did not understand how to apply this case of conditional probability. An answer of
12
was a common error.
80
(b) Most candidates attempted to fill in these Venn Diagrams with three sets. There were many correct
responses.
12
Answers: (a)(ii) 61 (iii)
38
Question 11
(a) This question was answered well with many candidates showing a good understanding of how to
add these algebraic fractions.
(b) There were many good attempts at this question. Most candidates successfully wrote down and
simplified an algebraic expression for the area of the shape. Some then had problems in
manipulating this expression to give an answer in the required form. There were several fully
correct responses with just a few candidates losing a mark from not showing all the required stages
in their response.
(c) Candidates showed a good understanding of powers involving negative numbers and fractions with
many finding the correct answer.
17 x + 12
Answers: (a) (b) 6(2 x + y )(2 x - y ) (c) –4
5( x + 1)
© 2017
Question 12
(a) Some candidates tried to solve this problem using geometrical reasoning and were, inevitably,
unsuccessful in this. There were many who appreciated that the cosine rule was needed and, of
these, many were able to find the correct response, Common errors were to misapply the rule or to
use an incorrect value for angle PQR.
(b) There were very few fully correct responses to this question. Some candidates were able to find
further angles using the sine rule, but were unable to identify which angle was required to be found
to calculate the bearing of P from Q.
Answers: (a) 15.3 (b) 296
Question 13
This question was found to be very difficult for nearly all candidates, who could not connect the information
given in the question with the problems posed in the questions.
(a) Few related the equation of the quadratic in its completed square form to finding the minimum point
of the curve. There were a few candidates who successfully gave the x co-ordinate in terms of p
and r and were awarded a mark for this.
(b) Again this part of the question was found to be challenging. A few candidates used their x co-
ordinate from part (a) to successfully write down an acceptable equation.
(c) Very few candidates were able to relate the information given in the question to giving a sensible
answer.
(d) As candidates were asked to do something specific, many candidates did attempt this part of the
question and many scored part marks. Few gave a fully correct response as they did not realise the
implications of using the negative value when finding a square root.
(e) There were very few correct responses for this part.
(f) There were very few correct responses for this part.
(g) (i) There were very few correct responses for this part.
(ii) There were some reasonable attempts at this part of the question with a few correct answers.
p+r
Answers: (a) (c, – d) (b) x = c or x = (c) (x – p)(x – r) (f) pr (g) (ii) 9
2
© 2017

Mathematics: Paper 0626/01 Paper 1 (Core)

Uploaded by

Copyright:

Available Formats

Mathematics: Paper 0626/01 Paper 1 (Core)

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Mathematics: Paper 0626/01 Paper 1 (Core)

Uploaded by

Copyright:

Available Formats

Cambridge International General Certificate of Secondary Education (9–1)

0626 Mathematics June 2017

Candidates should be aware that it is inappropriate to leave an answer as a multiple of π or as a surd in a

Comments on specific questions

A straightforward question on finding a fraction of an amount that candidates answered well.

Well answered. Most candidates found the range correctly.

Answers: (a) 64 (b) 175

Answers: 567.37 or 567.38

Both parts of this question were poorly answered

Answer: (a) 49h

This was poorly answered.

Answers: (a) 1066.40 (b) 1910.12

Answers: (a) 0.15 (b) 48

Answers: (a) 13.15, 13.25

Answers: 1936 and 81

Answers: (a) 95.4 (b) 36.8

Candidates need to have an understanding of mathematical terminology, as there were a number of

Comments on specific questions

(a) Most candidates completed the table correctly.

(b) Most candidates found the expected number correctly.

Answers: (a) 0.15 (b) 48

(a) Many candidates understood the powers of indices had to be added.

(b) Many candidates multiplied the indices together correctly.

Answer: Any irrational number between 6 and 7.

(a) Candidates showed a good understanding of upper and lower bounds.

Answers: (a) 13.15 and 13.25 (b) 13.19 > 13.15

Answers: (a) 16.8 (b) A valid comment

Answers: 1936 and 81

(a) Most candidates used trigonometry correctly.

Answers: (a) 95.4 (b) 38.6

Answer: (a) 3.2 (b) 10

(a) The majority of candidates drew clear sketches of the graph.

Comments on specific questions

Answers: (a) 3.5 hours (b) £13 per hour

Answer: Credit City

Answers: (a) Circle, centre P, radius 3 cm (c) (6, 3)

Answer: Mode with valid supporting comment

Answers: (a) 11 (b) −4 (c) 3.5

Answers: (a) 130°

Answers: (a) Pyramid (b) 27

Answer: 720 g, 180 g, 1800 ml

Answers: (a) 120, 60

Answer: (a) x > −4

Answers: (a) 5y(x −20y) (b)(i) (w – 1)(w + 1) (b)(ii) 9800

Comments on specific questions

Answers: (a) 5y(x – 4y) (b)(i) (w – 1)(w + 1) (ii) 9800

Answer: (b)(i) 25 (ii) 68

This matrix transformations question proved challenging for many candidates.

(a) This simplification of a surd question was very well answered.

 12 −19   0.1 −0.3   1 0

Answer: x3 + 2x2 – 9x –18

Comments on specific questions

(a) Most candidates answered this part correctly.

Answers: (a)(i) 10 15 (ii) 47 minutes (b) 12 05 (c) 52 mph

Answer: Plan B with £109.23 and £122.88

Answers: (a)(i) 5.2 (ii) 7 (b) p = 3.5, q = 5

Answers: (a) cement 3 kg, sand 13.5 kg (c) 79.1 kg

(ii) Candidates often reached the correct answer.

Answers: (a)(ii) 2.2 (b)(i) 8x – 36 – 3x + 21 (ii) 3