Download Pre Public Exam June 2016 Paper 3F Foundation Tier Edexcel Style

Name
Class
Worked Solutions
Pre Public Exam
June 2016
Paper 3F
Foundation Tier
Edexcel Style
Calculator
Time 1 hour 30 minutes
Marks Available
80
Commissioned by The PiXL Club Ltd.
1
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Question 1.
Write 34 669 to the nearest thousand
34 669
34 thousand 669
Closer to 35 thousand
35 000
(Total 1 mark)
Question 2.
(a) Simplify 9𝑎 − 3𝑎 + 5𝑎
11a
(1)
(b) Simplify 2𝑥 ×3𝑦
6xy
(1)
(Total 2 marks)
Question 3.
Fiona buys a 200g bar of chocolate.
110 grams of the chocolate bar is sugar.
27 grams of the chocolate bar is saturates.
30% of the bar is fat
The remainder of the bar is salt.
Work out how many grams of salt the chocolate bar contains.
3 × 10% of 200g
=
3 × 20g = 60g
200 – (110 + 27 + 60) = 200 – 197 = 3
3 grams
(Total 3 marks)
2
Question 4.
Here is a grid showing points P, Q and R.
Q
S
R
T
P
(a) Write down the coordinates of the point R.
(3, 2)
(1)
(b) On the grid, mark with a cross (×) the point (5, 1).
Label this point T.
See diagram
(1)
(c) On the grid, mark with a cross (×) a point S, so that the quadrilateral PQRS is a parallelogram.
(1)
(Total 3 marks)
Question 5.
Christine buys a washing machine for £455.
She pays a deposit of £65.
She pays the rest in 12 equal monthly payments.
Work out the cost of each monthly payment.
455 – 65 = 390
390 ÷ 12 = 32.5
£32.50
(Total 3 marks)
3
Question 6.
The bar chart below gives information about the favourite fruits of some students at Stoney Mount School.
(a) What fraction of the students who preferred bananas are boys?
10 girls + 12 boys = 22 students like bananas.
12 boys out of 22
𝟏𝟐
…………….𝟐𝟐
(2)
Chris says,
“More boys than girls prefer grapes and apples”
(b) Is Chris correct?
You must give a reason for your answer.
15+7 = 22 girls like grapes and apples
17+6 = 23 boys like grapes and apples
Yes, he is correct since 23 is more than 22.
(2)
4
The pie-chart gives the same information about the favourite fruits of the same students at Stoney
Mount School.
Number of students at Stoney Mount School
Gabriella says,
“It is more difficult to find out the number of students who prefer apples from the pie-chart than from
the bar chart.”
(c) Is Gabriella correct?
You must give a reason for your answer.
Yes, since you don’t know how many students are represented on the pie-chart.
You can only see that it is a small proportion, not the number of boys, whereas on the bar
chart you can see exactly how many boys prefer apples.
(1)
(Total 5 marks)
5
Question 7.
Here is a number machine.
Input
÷ 2
+6
output
(a) Work out the output when the input is 20
20 ÷ 2 = 10
10 + 6 = 16
16
(1)
(b) Work out the input when the output is 11
11 – 6 = 5
5 × 2 = 10
10
(2)
(c) Here is another number machine.
The numbers in the machines are missing.
Input
× ?
− ?
output
When the input is 10, the output is 16.
What numbers could be missing from the number machines?
10 × 2 = 20
20 – 4 = 16
Could also be others eg 10 × 3 = 30
30 – 14 = 16 ie 3, -14
2, 4
(2)
(Total 5 marks)
6
Question 8.
1 foot is 12 inches.
5 cm is approximately 2 inches.
Work out an approximation for the number of cm in 4 feet.
4 feet = 4 x 12 inches = 48 inches
Every 2 inches is 5 cm
48 ÷ 2 = 24
24 × 5cm = 120cm
120 cm
(Total 3 marks)
Question 9.
A gym has 360 members.
Members have either peak or off peak membership.
35% of the members have peak membership.
Work out the number of peak members.
35% × 360 = 0.35 × 360 = 126
126
(Total 2 marks)
Question 10.
Write the numbers below in order of size.
Start with the smallest number.
!
!
0.125
!
14%
0.14
!"
0.12
0.15 0.12
0.12,
𝟏
𝟖
, 14%,
𝟑
𝟐𝟎
(2)
(Total 2 marks)
7
Question 11.
Write down three different factors of 20 that add together to give a prime number.
Factors of 20: 1, 2, 4, 5, 10, 20
1 + 2 + 4 = 7 7 is a prime number
Could have
4, 5, 10 or 1, 2, 20 or 1, 2, 4 or 2, 4, 5 or 1, 2, 10 or 2, 5, 10 or 1, 10, 20
1, 2, 4
(Total 2 marks)
Question 12.
The length of a boat is 12.3 metres.
Suzie makes a scale model of the boat.
She uses a scale of 1cm to 30cm.
Work out the length of the scale model of the boat.
Give your answer in cm.
12.3 metres = 12.3 × 100 = 1 230 cm in real life
1 230 ÷ 30 = 41
41 cm
(Total 2 marks)
8
Question 13.
ABC is a right-angled triangle.
M is a point on AC
N is a point on BC.
CM = CN
(a) (i)Work out the size of the angle marked a.
180 - 90 - 64 = 180 - 154
26 0
(1)
(ii) Give a reason for your answer
Angles in a triangle add up to 1800
(1)
(b) Work out the size of angle CMN.
CMN = CNM= (180 – 26) ÷ 2 = 154 ÷ 2 = 770
770
(2)
(Total 4 marks)
9
Question 14.
The cost of 3 portions of fish and 4 portions of chips is £18.10
The cost of 5 portions of chips is £8.00
Work out the cost of 1 portion of fish and 1 portion of fish.
£8.00 ÷ 5 = £1.60 = cost of 1 portion of chips
3 portions of fish (3 ×f) and 4 portions of chips (4× c) : £18.10 = 3× f + 4 ×1.60 =
£18.10 = 3 × f + £6.40
£18.10 – £6.40 = 3 × f
£11.70 = 3 × f so cost of 1 portion of fish is £11.70 ÷ 3 = £3.90
Cost of 1 portion of fish and 1 portion of chips = £3.90 + £1.60 = £5.50
(Total 4 marks)
Question 15.
Sally has 28 green marbles and 36 black marbles.
!
!
of the green marbles are chipped and
!
!
of the black marbles are chipped.
Sally places the chipped marbles in a bag.
Sally picks at a random, a marble from the bag.
Work out the probability that this marble is green.
𝟏
𝟒
𝟐
𝟑
× 28 = 7
7 green marbles are chipped
× 36 = 24
24 black marbles are chipped
Total number of chipped marbles: 7 + 24 =31
𝟕
P (chipped green marble) = 𝟑𝟏
(Total 3 marks)
10
Question 16.
Change 30 m/s into km/h
30 m/ s = 30 × 60 × 60 m/h
= 108 000 m/h
1km = 1000m
108 km/h
108 km/h
(Total 3 marks)
11
Question 17.
Here is a wooden board.
3a
b
The measurements in the diagram are in metres.
Four of these rectangles are put together to make a frame for a flower bed.
The perimeter of the inside if the frame is M metres.
(a) Show that M = 12a - 4b
3a- 2b +3a + 3a –2b + 3a = 12a - 4b
(2)
Katie says,
‘When a and b are whole numbers, M is always an even number’
(b) Is Katie correct?
You must give a reason for your answer.
12a - 4b = 2(6a – 2b)
Since it is a multiple of 2, it is an even number.
(2)
(Total 4 marks)
12
Question 18.
The diagram shows a trapezium PQRS and two identical semicircles.
Q
P
R
S
18cm
The centre of each circle is on PQ.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
Area of trapezium =
𝟏𝟔
𝟐
(14+18) = 8 × 32 = 256 cm2
Radius of each semi-circle = 14 ÷ 4 = 3.5
Area of two semi-circles 𝑨 = 𝝅 × 𝟑. 𝟓𝟐 = 38.48451001
Area of shaded region = 256- 38.48451001 = 217.51549 = 218 3sf
(Total 4 marks)
13
Question 19.
Sanjay is going on holiday to America.
The exchange rate is £1 = $1.45075
Sanjay changes £675 to dollars.
(a) Work out how many dollars he should get.
Give your answer correct to the nearest dollar.
675 × 1.45075 = 979.25625 = $979 to nearest dollar
979 dollars
(2)
Sanjay sees a pair of trainers in America.
The trainers cost $135.
Sanjay does not have a calculator.
He uses £2 = $3 to work out the approximate cost of the trainers in pounds.
(b) Use £2 = $3 to show that the approximate cost of the trainers is £90.
$135 ÷ 3 = 45
45 × 2 = 90
(2)
(c) Is using £2 = $3 instead of using £1 = $ 1.45075 a sensible way for Sanjay to work out the cost of
the trainers in pounds?
You must give a reason for your answer.
Yes it is.
It makes it much easier to calculate the cost of something to the nearest pound without using a
calculator. Using $1.5 instead of $1.45075 makes sense.
(1)
(Total 5 marks)
14
Question 20.
Here are the first five terms of a Fibonacci sequence.
1
3
4
7
11
The rule for the sequence is:
‘The next term is the sum of the previous two terms.’
(a) Find the 8th term of this sequence.
6th term: 7+11 = 18
7th term: 11 + 18 = 29
8th term: 29 + 18= 47
47
(1)
The first three terms of a different sequence which follows the same rule are:
m
2n
m + 2n
(b) Show that the 6th term of this sequence is 3m +10n
4th term: m + 2n + 2n = m + 4n
5th term: m + 4n + m + 2n = 2m + 6n
6th term: 2m + 6n + m + 4n = 3m + 10n
(2)
Given that the 3rd term is 5 and the 6th term is 23,
(c) Find the value of m and the value of n
3m +10n = 23
3m +10n = 23
m + 2n = 5
×3
3m + 6n = 15
-
4n = 8
n=2
m + 2n = 5
m + 4 = 5 so m = 1
m=1
n=2
(3)
(Total 6 marks)
15
Question 21.
= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
A = 𝑥: 𝑥 is a factor of 12
1, 2, 3, 4, 6
B = 𝑥: 𝒙 is a multiple of 3 3, 6, 9
(a) Complete the Venn diagram to show the elements of each set.
A
5
2
7
10
4
B
1
3
6
9
(3)
(b) A is changed to A = 𝑥: 𝑥 is a factor of 15 .
James says that the number of elements in A U B stays the same.
Is James right?
Give a reason why.
NO, it doesn’t stay the same, since 6 is not a factor of 15
(1)
(Total 4 marks)
16
Question 22.
Julie is thinking of having a water meter.
These are the two ways she can pay for the water she uses.
Watermeter
Nowatermeter
Afixedchargeof£104.82
Plus
£1.95foreverycubicmetreofwaterused
Achargeof£283peryear
1cubicmetre=1000litres
Julie uses on average, 140 litres of water each day.
Use the information above to determine whether or not Julie should have a water meter.
With the water meter cost would be:
140 litres = 0.140 cubic metres
Cost of 0.140 cubic metre per day: 0.140 × £1.95 = £0.273
Cost over 365 days: 365 × £0.273 = £99.645
Total cost £104.82 + £99.645 = £204.465 which is approx £205
Since £205 is less than £283- it is cheaper for Julie to have a water meter.
(Total 5 marks)
17
Question 23.
The table below shows some information about the sales of two companies and the number of workers for
each company in 2005 and 2015.
Company A
Sales
(£ millions)
Company B
Number of
workers
Sales
(£ millions)
Number of
workers
2005
310
2760
64
505
2015
418
3120
82
560
(a) Work out the percentage increase in sales from 2005 to 2015 for Company A.
Amount increase 418-310 = 108
𝟏𝟎𝟖
as a percentage: 𝟑𝟏𝟎 ×𝟏𝟎𝟎% = 34.8387 …..
= 35%
35%
(2)
(b) Which company had the most sales per worker in 2015, Company A or company B?
Company A:
Company B:
𝟒𝟏𝟖 𝟎𝟎𝟎 𝟎𝟎𝟎
𝟑𝟏𝟐𝟎
𝟖𝟐 𝟎𝟎𝟎 𝟎𝟎𝟎
𝟓𝟔𝟎
= 133 974.359
approx. 134 000
= 146 428.571… approx. 146 000
Company B
(3)
(Total 5 marks)
TOTAL FOR PAPER IS 80 MARKS
18