Download Answer ALL questions

Name
Class
………………………………………………………………
………………………………………………………………
TIME ALLOWED
1 hour 30 minutes
INSTRUCTIONS TO CANDIDATES
 Answer all the questions.
 Read each question carefully. Make sure you know what you have to
do before starting your answer.
 You are permitted to use a calculator in this paper.
 Do all rough work in this book.
INFORMATION FOR CANDIDATES
 The number of marks is given in brackets [ ] at the end of each
question or part question on the Question Paper.
 You are reminded of the need for clear presentation in your
answers.
 The total number of marks for this paper is 80.
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This resource is strictly for the use of member schools for as long as they remain members of The
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membership ceases. Until such time it may be freely used within the member school. All opinions
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Out of
Mark
Question
Pre Public Examination
GCSE Mathematics (Edexcel style)
March 2017
Foundation Tier
Paper 2F
Worked Solutions
1
1
2
1
3
1
4
1
5
2
6
2
7
2
8
3
9
2
10
3
11
3
12
3
13
3
14
2
15
3
16
6
17
3
18
1
19
2
20
3
21
3
22
4
23
4
24
4
25
2
26
4
27
5
28
3
29
4
Total
80
Answer ALL questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
Question 1.
Work out
2.33
12.167 B1
(Total 1 mark)
Question 2.
There are only toffee sweets and caramel sweets in a bag.
3
8
of the sweets are toffee.
Write down the ratio of toffee sweets to caramel sweets.
3:5 B1
(Total 1 mark)
Question 3.
Draw a sector on this circle
B1
(Total 1 mark)
Question 4.
On the grid, complete the diagram of a kite.
B1
(Total 1 mark)
2
Question 5.
A café sells the following sandwiches and crisps.
Sanwiches
Cheese and Ham
Crisps
Cheese and Onion
Tuna and Sweetcorn
Prawn Cocktail
Cheese and Tomato
Barbeque Beef
Chicken and Salad
Ready Salted
Samantha orders a sandwich and a packet of crisps.
Write down all the possible combinations of sandwiches and crisps that Samantha could have.
CH,CO; CH,PC; CH,BB; CH,RS; TS,CO; TS,PC; TS,BB; TS,RS; CT,CO; CT,PC; CT,BB; CT,RS;
CS,CO; CS,PC; CS,BB; CS,RS;
B1 for 8 correct combinations; B1 for all correct combinations.
(Total 2 marks)
Question 6.
The nth term of a sequence of numbers is 7n + 3
(a) Is 227 a term of the sequence?
You must explain your answer.
Yes, it is the 32 term of the sequence. (227 – 3)÷7=32 C1
(1)
(b) Rizvana says,
“No terms of the sequence are multiples of 3”
Give an example to show Rizvana is wrong.
(7x3)+3 =24 which is a multiple of 3 B1
(1)
(Total 2 marks)
3
Question 7.
A pattern is made using identical rectangular tiles.
Find the total area of the pattern.
4 + 4 + 3 =11
4 + 3 =7
P1
Therefore lengths are 3cm and 4cm
(4×3) × 4 = 48cm2 A1
(Total 2 marks)
Question 8.
A road map has a scale of 1 : 70 000
The length of a road on the map is 6.25cm.
Work out the length of the real road in kilometres.
70000 x 6.25 P1
70000 x 6.25 = 437500
437500 ÷ 100000 = 4.375 M1
4.375km A1
(Total 3 marks)
4
Question 9.
A
123°
58°
B
C
Aiysha says,
“ABC cannot be a straight line.”
Explain why Aiysha is correct.
123 + 58 = 181 P1
The two angles add to more than 180 and therefore ABC cannot be a straight line. C1
(Total 2 marks)
Question 10.
Uzma is planning a dinner party for 12 adults.
She is planning to give each adult a 425g chicken fillet.
1 kg of chicken costs £3.25.
Work out how much Uzma will have to pay for the chicken.
425 x 12 = 5100 P1
5100 ÷ 1000 = 5.1 B1
5.1 x 3.25
£16.58 A1
(Total 3 marks)
5
Question 11.
Ameena thinks of a whole number.
She multiplies the number by 4.
Ameena’s answer is 53.
(a) Explain how you know Ameena’s answer is wrong.
The answer cannot be an odd number because any number times by 4 gives an even number answer.
C1
(1)
Here is a number machine.
-5
×9
Mariyam says that when the output is 45 the input is 450
Here is her working.
45 + 5 = 50
50 × 9 = 450
Mariyam is wrong.
(b) Explain what she has done wrong.
45 ÷ 9 = 5; 5 + 5 = 10 B1
She should have divided by 9 first and then added 5 C1
(2)
(Total 3 marks)
Question 12.
Work out the value of
√3.2 + 7.4
5.6 − 2.9
Give your answer correct to 2 decimal places.
9.188854…÷ 2.7 M1
= 3.403279401 M1
3.40 A1
(Total 3 marks)
6
Question 13.
Adam is learning to drive.
He plans on taking 19 lessons before he takes his driving test.
He sees the offer below on the internet.
Lessons – 1 hour each
£16 per lesson
Special Offer
£168 for 12 lessons
Work out the most money that Adam can save by using the Special Offer.
16 × 19 = 304 P1
19 – 12 = 7
7 × 16 = 112
168 + 112 = 280 M1
304 – 280 = 24 A1
£24 A1
(Total 3 marks)
Question 14.
Describe fully the single transformation that maps shape A onto shape B.
𝟒
) B1
−𝟑
Translation (B1) by the vector (
(Total 2 marks)
7
Question 15.
11
40
of the people at a wedding celebration are men.
34% of the people at the wedding are women.
The rest of the people at the wedding are children.
Works out what percentage of the people at the wedding celebration are children.
𝟏𝟏
𝟒𝟎
× 100 = 27.5%
34 + 27.5 = 61.5%
100 – 61.5 =
P1
M1
38.5% A1
(Total 3 marks)
Question 16.
Bob, Bill and Ben are triplets. They decide to paint their bedroom in the school holidays.
The total area of the wall space that needs painting is 96m2
The paint that the triplets buy costs £3.60 per tin and each tin covers 9m2.
(a) Calculate the total cost of painting the bedroom.
96 ÷ 9 P1
= 10.6666667
11 × 3.6 M1
£39.60 A1
(3)
The triplet’s friend Fred says he can get the job done in 3 hours.
Fred offers to paint the room for £14 per hour which includes the cost of the paint he will use.
The triplets want to spend as little money as possible.
(b) Should they hire Fred or do the job themselves?
You must explain your answer clearly showing your workings.
3 × 14 P1
3 × 14 = 42 M1
42 – 39.60 = £2.40
They should do the job themselves because they will save £2.40 C1
(3)
(Total 6 marks)
8
Question 17.
In January David invested £345 in his bank account.
At the end of February he had a total of £505 in his bank account.
In March David invested some more money in his bank account.
The total interest he made by the end of April was 15% greater than the total interest he made in January and
February.
In May David wants to pay a bill of £25.
David thinks that the 15% extra interest he made in March and April will be enough to pay this bill.
Is David correct?
You must show all your working.
505 – 345 = 160 P1
𝟏𝟓
𝟏𝟎𝟎
× 160 = 24
P1
No, he is £1 short
C1
(Total 3 marks)
Question 18.
Solve
9=
324
𝑥
324 ÷ 9 = x
x = 36 A1
(Total 1 mark)
Question 19.
Write an integer in the box to make the statement true.
5
Explain why the statement is true.
8
≥
10
Integer ≥ 16 B1
𝟓
𝟖
= 0.625 and
𝟏𝟎
𝟏𝟕
= 0.58823529 hence
𝟓
𝟖
is greater than
𝟏𝟎
𝟏𝟕
C1
(Total 2 marks)
9
Question 20.
A laptop has a normal price of £1035.
In a sale the price is reduced by 41%.
Work out the price of the laptop in the sale.
100 – 41 = 59
59 ÷ 100 = 0.59 M1
1035 × 0.59 M1
£610.65 A1
(Total 3 marks)
Question 21.
The diagrams show two identical squares.
Diagram A shows a quarter of a circle shaded inside the square.
Diagram B shows four identical quarter circles shaded inside the square.
Show that the area of the region shaded in diagram A is equal to the area of the region shaded in diagram B.
Radius of A = x and B = x/2 P1
𝟏
𝟒
𝟏
𝟒
𝟏
πx2 or 4 × × π (x/2)2 M1
𝟒
𝟏
πx2 = πx2 hence both areas are the same C1
𝟒
(Total 3 marks)
10
Question 22.
There are 180 members of the swimming club.
The pie chart shows the proportion of men and the proportion of women in the club.
Diagram Not to Scale
There are 13 more women in the badminton club than in the swimming club.
There are 27 fewer men in the badminton club than in the swimming club.
Brian draws a pie chart to show the proportion of men and the proportion of women in the badminton club.
Work out the angle of the sector in Brian’s pie chart that represents women in the Badminton club.
𝟏𝟖𝟔
𝟑𝟔𝟎
× 180 = 93 P1
180 + 13 − 27 = 166 P1
𝟗𝟑+𝟏𝟑
𝟏𝟔𝟔
× 360 M1;
= 230° A1
(Total 4 marks)
Question 23.
Here is a number line.
A1
(a) On this number line, show the inequality –3 ≤ x < 1 M1
(2)
(b) Solve 4n + 5 > 22
4n > 22 – 5;
Therefore
4n > 17 M1
n > 17 ÷ 4
n > 4.25 A1
(2)
(Total 4 marks)
11
Question 24.
Here is a Venn diagram.
(a) Write down the numbers that are in set
(i) A ∪ B
10, 12, 14, 15, 16, 18 B1
(ii) A ∩ B
12, 18 B1
(2)
One of the numbers in the diagram is chosen at random.
(b) Find the probability that the number is in set A'
10, 14, 16, 11, 13, 17, 19 M1
𝟕
𝟏𝟎
A1
(2)
(Total 4 marks)
12
Question 25.
Katie measured the length and the width of each of 10 pine cones from the same tree.
She used her results to draw this scatter graph.
9
(a) Describe one improvement Katie can make to her scatter graph.
Not start at (0, 0) or change scale size C1
(1)
The point representing the results for one of the pine cones is an outlier.
(b) Explain how the results for this pine cone differ from the results for the other pine cones.
Pine cone has very short width for length C1
(1)
(Total 2 marks)
13
Question 26.
Triangle ABC has perimeter 20 cm.
AB = 7 cm.
BC = 4 cm.
By calculation, deduce whether triangle ABC is a right–angled triangle.
20 – (7 + 4) = 9 P1
Length AC is 9 cm. This must be the hypotenuse if it is right angled.
If right angled, by Pythagoras 72 + 42 = 92 M1
49 + 16 = 65 M1
65 is not equal to 81 so it is not right angled. C1
(Total 4 marks)
Question 27.
The Singh family and the Peterson family go to the cinema.
The Singh family buy 2 adult tickets and 3 child tickets.
They pay £28.20 for the tickets.
The Peterson family buy 3 adult tickets and 5 child tickets.
They pay £44.75 for the tickets.
Find the cost of each adult ticket and each child ticket.
Simultaneous Equations:
2a + 3c = 28.2
2a + 3c = 28.2 (×3)
3a + 5c = 44.75 P1
3a + 5c = 44.75 (×2)
6a + 9c = 84.6
6a + 10c = 89.5 (subtract) M1
c = 4.90
2a + 14.7 = 28.2;
2a = 13.5;
a= 6.75
a = £6.75 or c = £4.90 A1
Adult ticket is £6.75 and Child ticket is £4.90 C1
(Total 5 marks)
14
Question 28.
On the grid, draw the graph of y =
1
for values of x from 1 to 7
𝑥
x
1
2
3
4
5
6
7
y
1
0.5
0.333…
0.25
0.2
0.1666…
0.1428…
M1 for at least 4 correct values
X
X
X
X
X
X
X
B1 for plotting at least 4 correct points; B1 for correct graph
(Total 3 marks)
15
Question 29.
Asif is going on holiday to Turkey.
The exchange rate is £1 = 3.5601 lira.
Asif changes £550 to lira.
(a) Work out how many lira he should get.
Give your answer to the nearest lira.
550 × 3.5601 M1
1958 lira A1
(2)
Asif sees a pair of shoes in Turkey.
The shoes cost 210 lira.
Asif does not have a calculator.
He uses £2 = 7 lira to work out the approximate cost of the shoes in pounds.
(b) Use £2 = 7 lira to show that the approximate cost of the shoes is £60
(210÷7) × 2 M1
30 × 2 = £60 C1
(2)
(Total 4 marks)
TOTAL FOR PAPER IS 80 MARKS
16