Name
Class
Practice Paper 2
May 2016
Higher Tier
AQA Style
Calculator allowed
Time
2 Hours
Marks Available
105
Commissioned by The PiXL Club Ltd.
1
2
Question 1
Sarah asked 200 students which sport they like best.
They could choose football, hockey or netball.
The two-way tables shows some information about their answers.
Football
Hockey
Male
Netball
Total
15
Female
29
Total
78
57
55
200
Complete the two way table.
(Total 3 marks)
3
Question 2
Here is a list of ingredients to make a Fruit Delight for 6 people.
Fruit Delight- serves 6
225g strawberries
225g raspberries
125 redcurrants
50g caster sugar
30ml water
300ml double cream
2 egg whites
Olivia makes Fruit Delight for 18 people.
(a) Work out how much caster sugar she uses.
…………….. g
(2)
Sarah-Jane makes Fruit Delight.
She uses 75ml of water.
(b) Work out how many people she makes Fruit Delight for.
………………
(2)
(Total 4 marks)
4
Question 3
Use your calculator to work out
14.3 + 6.32
2.61 × 3.89
Write down all the figures on your calculator display.
You must give your answer as a decimal.
……….…………………….
(Total 2 marks)
5
Question 4
Here are the ages of 15 doctors.
35
52
42
27
36
23
31
41
50
34
44
28
45
45
53
Draw an ordered stem and leaf diagram to show this information.
(Total 3 marks)
6
Question 5
The nth term of a number sequence is 𝑛3 + 2
Write down the first three terms of the sequence.
…………………………………………………………………
(Total 2 marks)
7
Question 6
ANB is parallel to CMD.
LMN is a straight line.
Angle LMD = 680
(i)
Work out the size of the angle marked y.
…………………. 0
(ii)
Give reasons for your answer:
….........................................................................................................................................................
.......................................................................................................................................................
.
(Total 3 marks)
8
Question 7
The diagram shows the position of two beacons, A and B.
N
N
B
A
The bearing of a boat C from beacon A is 0500
The bearing of boat C from beacon B is 3200
In the space above, draw and accurate diagram to show the position of boat C.
Mark the position of boat C with a cross (X). Label it C.
(Total 3 marks)
9
Question 8
The equation
𝑥 3 + 19𝑥 = 65
has a solution between 2 and 3.
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
𝑥 = … … … … … … ….
(Total 4 marks)
10
Question 9
Solve 7(b+2) = 4 (b+2)
(Total 2 marks)
11
Question 10
(a) Write 48 as a product of prime factors
……………………..
(2)
(b) Find the Highest Common Factor (HCF) of 48 and 64
……………………..
(2)
(Total 4 marks)
12
Question 11
The tables shows some information about the ages, in years, of 60 people.
Age ( in years)
Frequency
0 to 9
3
10 to 19
5
20 to 29
15
30 to 39
16
40 to 49
13
50 to 59
4
60 to 69
4
On the grid draw a frequency polygon for the information in the table
(2)
(Total 4 marks)
13
Question 12
Sarah, Richard and Allan went on holiday to Los Angeles.
They travelled from London by plane.
The distance from London to Los Angeles is 8760 km.
The plane took 9 hours.
Calculate the average speed of the plane.
……………. km/h
(Total 2 marks)
14
Question 13
Draw the locus of all point which are equidistant from the lines AB and AC.
C
B
A
(Total 2 marks)
15
Question 14
M and N are the vertices of a cuboid.
y
N
3
M
4
x
Diagram NOT
3
drawn accurately
z
(a) Write down the coordinates of point M.
( …….. , ……….. , ………… )
(1)
(b) Write down the coordinates of point N
( …….. , ……….. , ………… )
(1)
(Total 2 marks)
16
Question 15
There are 100 teachers at Bev’s school.
Bev found out the age of every teacher.
The table gives information about her results.
Age ( Y years)
Frequency
20 < Y ≤ 30
25
30 < Y ≤ 40
36
40 < Y ≤ 50
20
50 < Y ≤ 60
14
60 < Y ≤ 70
5
(a) Complete the cumulative frequency table.
Age ( Y years)
Cumulative
Frequency
20 < Y ≤ 30
20 < Y ≤ 40
30 < Y ≤ 50
40 < Y ≤ 60
50 < Y ≤ 70
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
(2)
(c) Use your graph to find an estimate for the median age.
……………….. years
(1)
(d) Use your graph to find an estimate for the number of these teachers who are older than 45
years old.
………………………
(2)
17
Age (Y years)
(Total 6 marks)
18
Question 16
Solve the simultaneous equations.
3𝑥 − 2𝑦 = 8
𝑥 − 3𝑦 = 5
𝑥 = ………………… ,
𝑦 = … … … … … … … ..
(Total 3 marks)
19
Question 17
John invested £2500 for 2 years in a savings account.
He was paid 3% per annum compound interest.
(a) How much did John have in his savings account after 2 years?
£ ….……………..
(3)
Justin invested £3500 for 𝑛 years in a savings account.
He was paid 6.5% per annum compound interest.
At the end of 𝑛 years he had £4502.63 in the savings account.
(b) Work out the value of 𝑛
………………..
(2)
(Total 5 marks)
20
Question 18
The diagram shows a 6-sided shape.
All corners are right angles.
All the measurements are given in centimetres.
2x -1
Diagram NOT
accurately
drawn
3x
3x +1
The area of the shape is 70 cm2.
(a) Show that
x
9𝑥 2 − 2𝑥 − 70 = 0
(3)
2
(b) (i) Solve
9𝑥 − 2𝑥 − 70 = 0
Give your solutions correct to 3 significant figures.
x = ………………. or x =……………….
(ii)
Hence, work out the length of the shortest side of the 6 sided shape.
…………………. cm
(4)
(Total 7 marks)
21
Question 19
In a sale, normal prices are reduced by 15%.
The sale price of a washing machine is £361.25.
Work out the normal price of the digital camera.
£ ………………
(Total 3 marks)
22
Question 20
Pierre and Jawaad each take a driving test.
The probability that Pierre will pass the test is 0.7
The probability that Jawaad will pass the driving test is 0.8
(a) Complete the probability tree diagram.
Pierre
Jawaad
0.8
Pass
Pass
0.7
….……..
0.8
0.7
….……..
Fail
Pass
Fail
….……..
Fail
(b) Work out the probability that both Pierre and Jawaad will pass the driving test.
…………………………….
(2)
(c) Work out the probability that only one of them will pass the driving test.
……………………………
(3)
(Total 7 marks)
23
Question 21
212 students each play one of three sports.
The table shows information about these students.
Sport played
Football
Netball
Volleyball
Female
27
45
34
Male
52
25
29
A sample stratified by the sport played and by gender, of 50 of the 212 students is taken.
(a) Work out the number of female students who play volleyball in the sample.
……………………………
(2)
(b) Work out the number of male students in the sample.
………………………….
(2)
(Total 4 marks)
24
Question 22
(a) Find the length of PQ.
…………………… cm
(2)
(b) Find the length of AD.
…………………… cm
(2)
(Total 4 marks)
25
Question 23
Q
Diagram NOT
5 cm
5 cm
Accurately drawn
M
R
P
N
5 cm
The diagram shows an equilateral triangle PQR with sides of length 5 cm.
M is the midpoint of QP
N is the mid-point of PR
PMN is a sector of a circle, centre P
Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.
…………………….. cm2
(Total 4 marks)
26
Question 24
Solve
𝟐
𝒙−𝟐
−
𝟒
𝒙+𝟏
=𝟑
(Total 5 marks)
27
Question 25
For all values of𝑥,
𝑥 2 − 8𝑥 + 14 = (𝑥 − 𝑎)2 + 𝑏
(a) Find the value of 𝑎 and the value of 𝑏.
𝑎 = ………… ,
𝑏 = … … … … … ….
(2)
(b) On the axes, draw a sketch of the graph 𝑦 = 𝑥 2 − 8𝑥 + 14
(2)
(Total 4 marks)
28
Question 26
In triangle ABC
Diagram NOT
590
accurately drawn
7.8 cm
12.5
B
C
AB = 12.5 cm
AC = 7.8 cm
Angle BAC = 590.
(a) Calculate the area of traingle ABC.
Give your answer correct to 3 significant figures.
………………….. cm2
(2)
(b) Calculate the length of BC.
Give your answer correct to 3 significant figures.
………………….. cm
(3)
(Total 5 marks)
29
Question 27
There are 13 sweets in a bag.
7 sweets are lemon flavoured.
6 sweets are strawberry flavoured.
Abi takes two sweets out of the bag at random.
Work out the probability that Abi takes a sweet of each flavour.
…………………
(Total 3 marks)
30
Question 28
The incomplete histogram and table give some information about the times, in minutes, that
people waited for a bus.
(a) Use the information in the histogram to complete the frequency table.
Time (t minutes)
Frequency
0<t≤2
11
2<t≤5
5 < t ≤ 10
17
10 < t ≤ 20
20 < t ≤ 40
4
(2)
(b) Use the information in the table to complete the histogram.
(2)
(Total 4 marks)
31
Question 29
Diagram NOT
25 cm
accurately drawn
36 cm
The length of the rectangle is 36 cm correct to the nearest cm.
The width of the rectangle is 25 cm correct to the nearest cm.
Calculate the upper bound for the area of the rectangle.
Write down all the figures on your calculator display.
. . . . . . . . . . . . . . . . . . . . . . . .cm2
(Total 3 marks)
END OF QUESTION PAPER
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