Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.
com
Q1. Prove that can be written as the fraction
(Total 2 marks)
Q2. Change the recurring decimal to a fraction.
..........................
(Total 2 marks)
Page 1
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
Q3. Prove that the recurring decimal .
(Total 2 marks)
Q4. A company sends every item of mail by second class post.
Each item of mail is either a letter or a packet.
The tables show information about the cost of sending a letter by second class post and
the cost of sending a packet by second class post.
Letter Packet
Weight range Second Class Weight range Second Class
0–100g 32p 0–100g £1.17
101–250g £1.51
251–500g £1.95
501–750g £2.36
751–1000g £2.84
The company sent 420 items by second class post.
The ratio of the number of letters sent to the number of packets sent was 5 : 2.
Page 2
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
of the packets sent were in the weight range 0 – 100 g.
Page 3
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
The other packets sent were in the weight range 101 – 250 g.
Work out the total cost of sending the 420 items by second class post.
£ ............................................................
(Total 5 marks)
Q5. The table shows the costs, per person, of a holiday at two different hotels.
It shows the cost for 5 nights and the cost for each extra night.
It also shows the discount for each child.
Park Palace Dubai Grand
Date holiday starts 5 nights extra night 5 nights extra night
01 Jan – 31 Mar £1169 £150 £849 £86
01 Apr – 09 Apr £1229 £150 £1219 £95
10 Apr – 15 Jul £810 £80 £853 £53
16 Jul – 20 Aug £810 £80 £854 £53
21 Aug – 10 Dec £810 £80 £869 £94
Discount for each child 15% off
off
Page 4
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
There are two adults and two children in the Smith family.
The family want a holiday for 7 nights, starting on 1st August.
One hotel will be cheaper for them than the other hotel.
Work out the cost of the cheaper holiday.
You must show all your working.
£ .................................
(Total 6 marks)
Q6.
u=2 ,v=3
(a) Find the value of f.
.....................................
(3)
Page 5
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
(b) Rearrange
to make u the subject of the formula.
Give your answer in its simplest form.
.....................................
(2)
(Total 5 marks)
Q7.
Diagram NOT
accurately drawn
Page 6
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
ABCD is a rectangle.
X is the midpoint of AB.
Y is the midpoint of BC.
Z is the midpoint of CD.
Page 7
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
What fraction of the total area of ABCD is shaded?
Show clearly how you get your answer.
.....................................
(Total 4 marks)
Page 8
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
M1.
Working Answer Mark Additional Guidance
100x = 47.3737… proof 2 M1 for valid method
x = 0.4737… eg 100x = 47.37373, 1x = 0.4737… and subtract
99x = 46.9
x = 46.9/99 OR 1000x = 473.7373, 10x = 4.737… and subtract
A1 for valid argument leading to
Total for Question: 2 marks
M2.
Working Answer Mark Additional Guidance
100 × 23 99 2 M1 for100 × or 10000 × ...
99 × = 23
A1 for oe
Total for Question: 2 marks
M3.
Page 9
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
Working Answer Mark Additional Guidance
x = 0.1717... Proof 2 M1 for valid method
100x = 17.1717... eg 100x = 17.17…, 1x = 0.1717… and subtract
99x = 17
OR
x= 1000x = 171.7171.., 10x = 1.7171… and subtract
or
1000x = 171.7171…
A1 for valid argument leading to x =
10x = 1.7171…
Alternative method for long division
990x = 170 M1 for identifying 71 and 17 as remainders
x = 17/99 A1 for correct statement
Total for Question: 2 marks
M4.
Working Answer Mark Additional Guidance
420 ÷ 7 = 60 250 5 M1 for 420 ÷ (5 + 2) or 60 seen
5 × 60 = 300 M1 (dep) for 5 × ‘60’ or 2 × ‘60’ or 300
2 × 60 = 120 or 120 seen
M1 for ‘120’ ÷ 3 × 2 oe
120 ÷ 3 × 2 = 80 M1 for 32p × ‘300’ + £1.17 × ‘80’ +
£1.51 × ‘40’
0.32 × 300 + 1.17 × 80 +1.51 × 40 A1 for 250.00 or 250
96 × 93.60 + 60.40
SC B1 for £539
Total for Question: 5 marks
Page 10
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
M5.
Working Answer Mark Additional Guidance
Park Palace: Park Palace 6 M1 for identifying correct week for
£3492 holiday
810 + 80 + 80 = £970 per adult (eg use of 854 for DG, eg circle
1/5 of 970 = 194 correct row)
970 – 194 = £776 per child
970 + 970 + 776 + 776 = £3492 M1 for using 7 nights for at least one
hotel
Dubai Grand:
M2 for complete correct method for
854 + 53 + 53 = £960 per adult reduction of 1/5 and 15% for at
10% + 5% of 960 = 96 + 48 least 5 nights
= 144 (M1 for correct method to get 1/5 or
960 – 144 = £816 per child 15% or 4/5 or 85% of a total for at
960 + 960 + 816 + 816 = £3552 least 5 nights)
A1 for one correct total (3492 or
3552)
A1 for 34 92 and 3552, with Park
Palace (or 3492) indicated as the
best choice.
Total for Question: 6 marks
M6.
Working Answer Mark Additional Guidance
(a) 3
M1
M1 correct addition of the fractions to get oe
A1 for oe
Page 11
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
(b) 2
M1 oe or vf + uf = uv oe or
or u = or u =
A1 u = or u =
Total for Question: 5 marks
M7.
Working Answer Mark Additional Guidance
Page 12
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
Let AB = x, AD = y 4 M1 a full method to find the unshaded area and
subtracting from 1
Area of rectangle = xy
B1 area of AXD = area of ABCD ÷ 4
B1 area of CYZ = area of ABCD ÷ 8
A1 cao
OR
Diagram
M1 for dividing left into 2 congruent triangles
for dividing right into 4 congruent triangles
Page 13
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
Total for Question: 4 marks
Page 14
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
E1. The majority of candidates divided 469 by 990 on their calculator and cited this as
sufficient justification in this question. However, there were some excellent clear and
concise proofs from more able candidates. Many candidates had remembered some
aspects of the technique required in this proof but failed to put an accurate, complete and
convincing argument together.
E2. Candidates who answered this question fell into two categories they could either write
down the answer with or without working, showing a well practised response, or the most
common wrong answer of 23/100 was written without any working at all. About a quarter
of all solutions were correct and about half of the solutions fell into the 23 out of a hundred
category.
E3. Just over a quarter of candidates were able to give a full, clear and correct proof to
gain both marks. This needed to include multiplying by an appropriate power or
appropriate powers of 10 and subtracting, and then linking this with 17/99. Many
candidates gave answers suggesting they had remembered some elements of the
necessary proof but not enough to convince examiners to give them any credit.
Many candidates tried to “fudge” their proof or simply stated that when 17 is divided by 99
using a calculator the required recurring decimal is given. Long division was carried out by
a small number of candidates. Where this method was employed it was often possible to
award one mark where enough remainders were clearly shown, but candidates rarely tried
to explain why the decimal would recur.
##
Thirty per cent of candidates were awarded full marks for their response to this question.
Unfortunately, a surprising number of candidates did not take into account the ratio of the
number of letters to the number of packets thereby simplifying the question. These candidates
Page 15
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
could be given little credit for their attempts as they restricted their working to finding a simple
fraction of a quantity followed by the calculation of a simple bill. Candidates who did realise the
significance of the ratio often failed to show their working in a coherent way. This may have
inhibited their ability to think through the processes involved and execute them accurately in the
correct logical sequence.
##
Nearly all candidates were able to access this question by scoring at least one mark.
However, the element of functionality proved very difficult for many candidates with very
few fully correct answers seen with just under 10% scoring all 6 marks and just over 7%
scoring 5 marks. Although many had a basic idea of what to do, there were too many
variables that caused them problems. Centres need to be aware that they need to be
developing these skills. The vast majority of candidates scored 2 or 3 marks, generally for
selecting the correct week, demonstrating they had calculated for 7 nights and either
finding 20% discount for Park Palace or 15% discount for Dubai Grand.
Unfortunately there were many poorly presented solutions with scribbles all over the two
pages including in the margins. This sometimes made it difficult for examiners to award
marks.
Some confusion was caused by the wording “discount for each child”. It was quite
common to see 2/5 or 30% calculated – doubling the discount as there were 2 children.
Many struggled with the arithmetic with many candidates unable to divide by 5 or add or
subtract correctly. Others thought one fifth was 25% or 5%. Where candidates did find the
discount, many then failed to subtract this discount from their adult total. Errors also
occurred when trying to work out the cost of 2 adults with 810 × 2 + 80 × 2 (instead of 4)
frequently seen.
E6. Many candidates gained one mark in part (a) for a correct substitution but very few
were able to progress any further. Most went on to add 2½ to 3⅓ and then gave either
5 or the reciprocal of it as the final answer. Some candidates attempted to use a
common denominator of 2½ × 3⅓ but frequently made errors in their calculations. A small
number of candidates converted the fractions to and respectively and obtained
easily but some then forgot to invert.
Many candidates showed considerable working which was often poorly set out and
difficult to follow. Only the very best candidates were successful in part (b). Most were
unable to manipulate the terms correctly. Some simply inverted everything and u + v = f
became u = f – v. Others attempted to clear the fractions but forgot to multiply all the
terms by f (or v or u). Those who managed to get to 1/u = 1/f – 1/v sometimes went on to
gain one mark for u = 1/(1/f – 1/v).
Page 16
Edexcel Maths GCSE - Fractions (H) PhysicsAndMathsTutor.com
Page 17
