Worked solutions
Pre Public Exam
Paper 2
May 2016
Foundation Tier
AQA Style
Calculator allowed
Time
1 Hour 45 Minutes
Marks Available
105
Commissioned by The PiXL Club Ltd.
Foundation Tier Formula sheet
You must not write on this formulae page.
Anything you write on this formulae page will gain NO credit.
1.
Here are some shapes
H
B
F
D
A
C
G
E
Use the letters inside each shape to help you answer these questions
A, F and H
1M for A and F
1M for H
a) Which shapes are regular?
…………………………………………(2 marks)
A and G
1M each (no extras)
b) Which shapes are hexagons?
…………………………………………(2 marks)
Trapezium
c) What is the name of shape C?
…………………………………………(1 mark)
2.
This bar chart shows the results of the games played by a football team in a season.
F
20
10
0
Win
Lose
Draw
Result
How many points did they get for the season if 3 points are awarded for a win, 1 point for a draw and no
points are awarded if you lose the game?
(4 marks)
Win
11 × 3 = 33
Draw
14 × 1 = 14
Lose
9×0=0
•
•
Total points = 33 + 14 = 47
The team score 47 points
•
•
Attempttofindnumberof
winsanddraws
Readscalescorrectly11
winsand14draws
MultiplyW×3andD×1
Findcorrecttotal47
3.
Look at these shapes made from squares.
How many squares are in the 50th shape?
Sequence is 1, 4, 7, 10,…..
Formula is 3n -2
(2 marks)
n=50, 3n – 2 = 150 – 2 = 148
4.
This diagram shows a rectangle. The length is twice the size of the width.
Length = 3x + 10
Diagram NOT drawn
to scale.
Width = 6x - 31
Use an algebraic method to find the size of the sides.
(5 marks)
3x + 10
9x
x
Length =
=
=
2 (6x – 31)
12x -62
=
=
72
8
34
Width
=
17
……………………………………………………………………………………………………………………………..
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
5.
(a)
Put the numbers below in ascending order.
(i)
-7, 9, 7, 5, -9, -17, -200
-200 -17
-9
-7
5
7
9
…………………………………………
(1 mark)
(ii)
0.65, 0.35, -0.23, 2.056, -3.21, 0.035
-3.21 -0.23 0.035 0.35 0.65 2.056
…………………………………………
(1 mark)
(b)
What is the place value of 3 in the number 5.039?
!
!""
ths
…………………………………………
(1 mark)
(c)
Write the following in descending order:
! !"
68%, ,
! !"
, 0.075
same as:
68 %, 67%, 40%, 7.5%
hence ordered: 0.075,
!" !
, , 68%
!" !
(M1)
(A1)
…………………………………………
(2 mark)
6.
A survey is carried out by asking people entering a cinema to see a film.
part of the questionnaire is reproduced below.
Placeacross(X)inthecorrectbox
1.
2.
(a)
Howoldareyou?
16-25
25-30
31-40
41orolder
Doyouevergotothecinematoseeafilm?
Yes No
Explain why this is a biased survey.
(1 mark)
Only asks people already going to the cinema to see a film
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
(b)
State two criticisms of the first question.
Any two of:
(2 marks)
Under 16s not catered for
25 appears in two boxes
People may object to giving their age
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
7.
2
A square has an area of 5.76 m . Find the length of one side of the square.
(2 marks)
√5.76
(M1)
= 2.4 m
(A1)
……………………..……………………
8
Matt and Jack play a game.
They roll a normal fair die and flip a fair coin.
If the coin lands on heads then the score is twice the score on the die.
If the coin lands on tails then the score is five times the score on the die.
The sample space diagram below shows the possible scores.
1
2
3
4
5
Head
2
4
6
8
10
Tail
5
10
15
20
25
6
12
30
a) Complete the sample space diagram to show the possible scores.
First row correct
Second row correct
(2 marks)
1M
1M
b) What is the probability that you will score
(i)
More than 10
5
(ii)
/12
An even number
9
(iii)
(1 mark)
(2 marks)
/12
1M
=¾
1M
If you get a tail your score will be more than 20
2
/6
1
= /3
1M
1M
(2 marks)
9.
Plants are sold in different sizes of tray. A tray of 345 plants cost £12.99. A tray of 20 plants cost £5.59. A tray
of 50 plants cost £22.47. Mike wants to buy the best value for money tray. Which size tray of plants should he
buy? You must show all your working outs?
(4 marks)
Tray of 345 plants:
345 plants = £12.99
1 plant = £12.99 / 345 à £0.0377
Tray of 20 plants:
20 plants = £5.59
1 plant = £5.59 / 20 à £0.2795
Tray of 50 plants:
50 plants = £22.47
1 plants = £22.47 / 50 à £0.4494
(M1 each calculation)
A tray of 345 plants cost £12.99 is the best value for money as it offers the cheapest price for 1 plant.
(C1)
10.
Here are the ingredients needed to make Chilli Con Carne for 4 people.
Chilli Con Carne (serves 4)
500g of minced beef
2 tins of tomatoes
6 large chillies
300g of kidney beans
(a)
Work out what weight of kidney beans is needed to feed 10 people Chilli Con Carne
4:10
→
300 x 2.5
(2 marks)
1:2.5
=
750
750g
…………………………………………..
(b)
How many large chillies would be needed to feed 6 people?
4:6
6 x 1.5
→
(2 marks)
1:1.5
=
9
9 large chillies
…………………………………………..
11.
Simplify each of the following.
(a)
8x − 3x + 2x + 10
(2 marks)
7x + 10
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
(b)
6z x 8z
48z
(1 mark)
2
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
(c)
q9
q3
q
(1 mark)
6
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
(d)
6(y + 3)
(1 mark)
6y + 18
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
12.
John bought a new van in Europe. The total cost of the van was £8000 plus VAT at 22%.
He had to pay £2000 deposit when he bought the van, then the rest of the total cost in 12 equal
monthly payments.
Work out the cost of each monthly payment
(5 marks)
8000 x 1.22
=
9760
9760 – 2000
=
7760
7760 ÷ 12
=
646.66666…
Monthly payment is £646.67
…………………………………………..
13.
There is a bus and train service between Onetown and Twoville, and there is only a tram service between
Twoville and Threechester.
Extracts from their timetable are given below.
Bus
Onetown to Twoville
Depart
Onetown
09:10
09:40
10:10
Arrive
Twoville
09:38
10:08
10:38
Train
Onetown to Twoville
Depart
Onetown
08:50
09:50
10:50
Arrive
Twoville
09:10
10:10
11:10
Tram
Twoville to Threechester
Depart
Twoville
10:00
10:45
11:30
Arrive
Threechester
10:40
11:25
12:10
(a)
How long does it take to go by bus from Onetown to Twoville?
(2 marks)
……………09:10 to 09:38 is 28 minutes……………………………………………………………………………..
………………………………………………………………………………………………………………………………
(b)
Ffion lives in Onetown and needs to get to Threechester to watch a film that starts at 12:00.
What time does she need to start? You must give a schedule saying what transport you use, and
what time it runs.
(4 marks)
…latest arrival at Threechester she needs is 11:25, which starts at 10:45………………………
…latest departure from Onetown to get to Twoville for 10:45 is the bus leaving at 10:10
………………………………………………………………………………………………………………………………
Schedule is
Bus leaves Onetown at 10:10, arrives Twoville at10:38.
Tram leaving Twoville 10:45, arriving Threechester at 11:25
14.
(a)
Write 48 as a product of prime factors.
(2 marks)
(M1)
4
=2 x3
(A1)
……………………………………………
(b)
Write 84 and 147 as products of prime factors. Find the HCF and LCM of 84 and 147.
2
84
=
2 x3x7
147
=
3x7
2
HCF = 3 x 7
(4 marks)
(M1)
(A1)
(A1)
2
LCM= 21 x 2 x 7 = 588
(A1)
HCF……………………………………………
LCM……………………………………………
(c)
Amrita blinks her eyes every 6 seconds and Namrita blinks her eyes every 5 seconds. They both
blinked their eyes at 8:00 o’clock. How many times will they both blink at the same time in the next
two minutes?
(3 marks)
Multiples of 6 = 6, 12, 18, 24, 30, 36
Multiples of 5 = 5, 10 ,15, 20, 25, 30
(M1)
LCM of 5 and 6 = 30 seconds
120 seconds in 2 minutes à 120/30 = 4 times
(M1)
They will both blink at the same time 4 times in the next 2 minutes
(A1)
……………………………………………
15.
Hartlepool
North Sea
Hull
Scale: 1cm represents 20 Km
(a)
It is proposed to build a motorway in a direct line from Harlepool to Hull. What is the distance from
Hartlepool to Hull?
(3 marks)
7.6 cm represents 7.6 x 20 Km.
Distance is 152 Km
……………………………………………………………………
(b)
It is proposed to limit the speed of heavy trucks to 60 Km/hour. Will heavy trucks be able to travel
from Hartlepool to Hull in under two hours? Explain your answer.
(3 marks)
Heavy trucks will travel a maximum of 2 x 60 =120 Km in two hours
120 < 152, so trucks will not be able to travel from Hartlepool to Hull in two hours
……………………………………………………………………
16
Make v the subject of the formula
y=
𝒗
𝟓
+2
(2 marks)
y- 2 =
𝒗
𝟓
v = 5(y – 2)
…………………………………………………………..
17.
This shape is a prism with a pentagonal cross-section.
Side
elevation
(a)
Draw the plan of the prism
1M 5 by 4 rectangle
1M line drawn in middle
(2 marks)
(b)
Draw the side elevation of the prism
1M 5 by 4 rectangle
1M line drawn 1 square
from the top
(2 marks)
18
A restaurant offers a summer menu for a fixed price.
Diners can choose a main course and a dessert.
Main courses – Salmon (S), Beef (B) or Goat’s cheese tart (G).
Dessert – Lemon mousse (L), Chocolate brownie (C) or Ice cream (I)
(a)
Show all the possible meals that diners can choose. Write your answer in the table below.
S
L
S
C
S
I
B
L
B
C
1M
B
I
G
L
G
C
G
I
2M
Exactly9differentmeals
withnorepeats
Atleast6differentmeals
(2 marks)
(b)
Simon decides to choose a meal at random, what is the probability that his main course is Salmon?
(1 mark)
3
/9
1
= /3
(c)
What is the probability that his main course is not Salmon?
2
/3
1M ( 1 – their part b))
(2 marks)
19.
Use this diagram to answer the questions below
b
Notdrawn
accurately
580
c
490
a
Are these statements true or false?
Give a reason for each of your answers.
(a)
a = 73
0
(2 marks)
True because angles in a triangle add up to 180
0
…..……………………………………….. because ……………………………………………………………
…………………………..…………………………………………………………………………………………
(b)
a and b are equal angles because they are alternate angles on parallel lines.
(2 marks)
False because they are corresponding angles
…..……………………………………….. because ……………………………………………………………
…………………………..…………………………………………………………………………………………
(c)
c = 129
0
False because angles on a straight line add up to 180
(2 marks)
0
…..……………………………………….. because ……………………………………………………………
…………………………..…………………………………………………………………………………………
20.
(a)
–3 ≤ n < 2
n is an integer.
Write down all the possible values of n.
(2 marks)
-3, -2, -1, 0, 1
………………………..…………………..
(b)
Solve the inequality
5x < 2x – 6
(3 marks)
3x < -6
x < -2
…………………….………………….
21.
On the grid, draw the graph of x + y = 15 from x = -1 to x = 16
y
15
10
5
x
5
10
15
(3 marks)
22.
Factorise the following expressions.
(a)
2
15y + 35y
(2 marks)
5y (3y + 7)
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
(b)
2
z – 64
(1 mark)
(z – 8) (z + 8)
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
23.
Use this grid to answer the questions below
(a)
Reflect shape A in the line x = 1 and label it shape B.
(1 mark)
(b)
Reflect shape B in the line y = – 1 and label it shape C.
(1 mark)
(c)
Describe fully the transformation that moves shape A onto shape C.
1M Rotation
1M centre ( 1 , – 1 )
(3 marks)
1M 1800
………………………………………………………………………………………………………………………………
…………………………………………………………………/……………………………………………………………
………………………………………………………………………………………………………………………………