1.
(a)
Change
5
to a decimal.
8
.........................
(2)
(b)
Work out
2 1
+
5 7
.........................
(2)
(c)
1 3
Work out 2 × 1
2 5
.........................
(3)
(Total 7 marks)
2.
In 2002, Shorebridge Chess Club’s total income came from a council grant and members’ fees.
Council grant
Members’ fees
(a)
(i)
£50
240 at £5 each.
Work out the total income of the club for the year 2002.
£ .....................................
(ii)
Find the council grant as a fraction of the club’s total income for the year 2002.
Give your answer in its simplest form.
.....................................
(3)
In 2001, the club’s total income was £1000.
The club spent 60% of its total income on a hall.
It spent a further £250 on prizes.
(b)
Work out the ratio
The amount spent on the hall : the amount spent on prizes.
Give your answer in its simplest form.
.....................................
(3)
(Total 6 marks)
3.
2 cm
P
10 cm
Q
3 cm
15 cm
Diagram NOT accurately drawn
Rectangle Q is an enlargement of rectangle P.
(a)
Work out the scale factor of the enlargement.
.........................
(1)
(b)
On the grid, enlarge the shaded shape with a scale factor of 2
(2)
(Total 3 marks)
4.
Julie buys 19 identical calculators.
The total cost is £143.64
Work out the total cost of 31 of these calculators.
£ ................................
(Total 3 marks)
5.
(a)
Use your calculator to work out
4.7
9.4 – 3.5
Write down all the figures on your calculator display.
..........................................................
(2)
(b)
Write these numbers in order of size.
Start with the smallest number.
0.82
4
5
85
2
3
7
8
..............................................................................
(2)
(Total 4 marks)
6.
The table shows information about 40 vehicles crossing a bridge.
Type of vehicle
Number of vehicles
Size of angle
Motorcycle
5
45°
Car
16
Bus
11
Other
8
Complete the pie chart to show this information.
Motorcycle
(Total 3 marks)
7.
The diagram shows three points P, Q and R.
Q
R
P
On the grid, draw the locus of points which are equidistant from PQ and QR.
(Total 2 marks)
8.
Here are some patterns made from dots.
Pattern number 1
Pattern number 2
Pattern number 3
Pattern number 4
Write down a formula for the number of dots, d, in terms of the Pattern number, n.
(Total 2 marks)
9.
(a)
Complete the table of values for
x
y
–1
y = x2 – 4x – 2
0
1
–2
–5
2
3
4
5
–2
3
(2)
(b)
On the grid, draw the graph of
y = x2 – 4x – 2
y
4
2
–1
O
1
2
3
4
5
x
–2
–4
–6
(2)
(c)
Use your graph to estimate the values of x when y = –3
x = .....................................
x = .....................................
(2)
(Total 6 marks)
10.
This is a map of part of Northern England.
Blackpool X
X Preston
X Halifax
N
Wigan
X
X Manchester
Liverpool
X
Chester X
X Stoke-on-Trent
Scale: 1 cm represents 10 km
A radio station in Manchester transmits programmes.
Its programmes can be received anywhere within a distance of 30 km.
On the diagram, shade the region in which the programmes can be received.
(Total 2 marks)
11.
H
G
E
F
3 cm
Diagram NOT
accurately drawn
D
A
C
7 cm
5 cm
B
The diagram represents a cuboid ABCDEFGH.
AB = 5 cm.
BC = 7 cm.
AE = 3 cm.
(a)
Calculate the length of AG.
Give your answer correct to 3 significant figures.
...................................... cm
(2)
(b)
Calculate the size of the angle between AG and the face ABCD.
Give your answer correct to 1 decimal place.
........................................
(2)
(Total 4 marks)
12.
4
Frequency
density
in potatoes
per gram 3
2
1
0
10
20
30
60
50
40
Weight in grams
70
80
90
100
The histogram gives information about the weights of some potatoes.
The shaded bar represents 20 potatoes.
(a)
Work out how many of the potatoes weigh 30 grams or less.
..........................
(1)
(b)
Work out how many of the potatoes weigh more than 45 grams.
..........................
(2)
(Total 3 marks)
13.
Y
4a + 3 b
O
2a+b
X
Diagram NOT accurately drawn
OX = 2a + b
OY = 4a + 3b
(a)
Express the vector XY in terms of a and b
Give your answer in its simplest form.
.....................................
(2)
Z
Y
4a+ 3b
O
2 a +b
X
Diagram NOT accurately drawn
XYZ is a straight line.
XY : YZ = 2 : 3
(b)
Express the vector OZ in terms of a and b
Give your answer in its simplest form.
.....................................
(3)
(Total 5 marks)
14.
y
5
4
3
2
1
–5
–4
–3
–2
–1 O
2
1
3
4
5
x
–1
–2
–3
A
–4
–5
Enlarge triangle A by scale factor –
1
, centre (–1, –2).
2
Label your triangle B.
(Total 3 marks)
15.
The density of juice is 4 grams per cm3.
The density of water is 1 gram per cm3.
315 cm3 of drink is made by mixing 15 cm3 of juice with 300 cm3 of water.
Work out the density of the drink.
....................................... grams per cm3
(Total 3 marks)
16.
Diagram NOT
accurately drawn
R
c
S
a
Q
P
PQRS is a trapezium.
QP is parallel to RS.
QP = 3RS.
QR  a , RS  c
Express in terms of a and/or c
(i)
QP
QP = ..............................
(ii)
SP
SP = ..............................
(Total 3 marks)
17.
Verity records the heights of the girls in her class.
The height of the shortest girl is 1.38 m.
The height of the tallest girl is 1.81 m.
The median height is 1.63 m.
The lower quartile is 1.54 m.
The interquartile range is 0.14 m.
(a)
On the grid, draw a box plot for this information.
1.30
1.40
1.50
1.60
1.70
1.80
1.90
Girls’ height (m)
(3)
The box plot below shows information about the heights of the boys in Verity’s class.
1.30
1.40
1.50
1.60
1.70
1.80
1.90
Girls’ height (m)
(b)
Compare the distributions of the boys’ heights and the girls’ heights.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 5 marks)
18.
Here are four cumulative frequency diagrams.
B
A
D
C
Here are four box plots.
P
Q
R
S
For each box plot, write down the letter of the appropriate cumulative
frequency diagram.
P and .....................................
Q and .....................................
R and .....................................
S and .....................................
(Total 2 marks)
19.
A teacher asked some students how much time they spent using a mobile phone one week.
The histogram was drawn from this information.
Frequency
density
(students
per
hour)
30
20
10
0
1
2
3
4
5
Time
(hours)
Use the histogram to complete the table.
Time (t) hours
0t<
1
2
Frequency
1
2
t<1
1t<2
30
2t<3
3t<5
(Total 2 marks)
20.
The histogram shows information about the lifetime of some batteries.
Frequency
density
1.5
2
2.5
3
3.5
4
4.5
5
Two of the batteries had a lifetime of between 1.5 and 2.5 years.
Find the total number of batteries.
.....................................
(Total 2 marks)
21.
A lighthouse, L, is 3.2 km due West of a port, P.
A ship, S, is 1.9 km due North of the lighthouse, L.
(a)
Calculate the size of the angle marked x.
Give your answer correct to 3 significant figures.
x = ……………….. °
(3)
(b)
Find the bearing of the port, P, from the ship, S.
Give your answer correct to 3 significant figures.
…………………... 
(1)
(Total 4 marks)
22.
y
100
y = a – bcos(kt)
80
60
40
20
t
O
30
60
90
120
The graph of y = a – bcos(kt), for values of t between 0° and 120°, is drawn on the grid.
Use the graph to find an estimate for the value of
(i)
a,
.....................................
(ii)
b,
....................................
(iii)
k.
....................................
(Total 3 marks)
23.
Diagram NOT accurately drawn
The lengths of the sides of a triangle are 4.2 cm, 5.3 cm and 7.6 cm.
(a)
Calculate the size of the largest angle of the triangle.
Give your answer correct to 1 decimal place.
....................................°
(3)
(b)
Calculate the area of the triangle.
Give your answer correct to 3 significant figures.
............................... cm2
(3)
(Total 6 marks)
24.
A
X
Diagram NOT
accurately drawn
8 cm
C
70°
15 cm
B
In triangle ABC,
AC = 8 cm,
CB = 15 cm,
Angle ACB = 70°.
(a)
Calculate the area of triangle ABC.
Give your answer correct to 3 significant figures.
............................... cm2
(2)
X is the point on AB such that angle CXB = 90°.
(b)
Calculate the length of CX.
Give your answer correct to 3 significant figures.
................................ cm
(4)
(Total 6 marks)
25.
The table shows some rows of a number pattern.
Row 1
1
=
1 2
2
Row 2
1+2
=
23
2
Row 3
1+2+3
=
3 4
2
Row 4
1+2+3+4
Row 8
(a)
In the table, complete row 4 of the number pattern.
(1)
(b)
In the table, complete row 8 of the number pattern.
(1)
(c)
Work out the sum of the first 100 whole numbers.
.....................................
(1)
(Total 3 marks)
26.
(a)
Calculate the size of angle a in this right-angled triangle.
Give your answer correct to 3 significant figures.
Diagram NOT accurately drawn
5m
a
6m
.....................................
(3)
(b)
Calculate the length of the side x in this right-angled triangle.
Give your answer correct to 3 significant figures.
Diagram NOT accurately drawn
10 m
x
40°
..................................... cm
(3)
(Total 6 marks)
27.
A
7 cm
B
8 cm
C
Diagram NOT accurately drawn
ABC is a right-angled triangle.
AB = 7 cm,
BC = 8 cm.
(a)
Work out the area of the triangle.
............................ cm2
(2)
(b)
Work out the length of AC.
Give your answer correct to 2 decimal places.
.............................. cm
(3)
D
32 mm
y
F
46 mm
E
Diagram NOT accurately drawn
DEF is another right-angled triangle.
DE = 32 mm,
FE = 46 mm.
(c)
Calculate the size of angle y.
Give your answer correct to 1 decimal place.
................................. °
(3)
(Total 8 marks)
28.
y
10
B(2, 8)
8
6
4
2
A(0.5, 1)
–4
–2
O
2
4
x
The diagram shows a sketch of the graph y = abx
The curve passes through the points A (0.5, 1) and B (2, 8).
The point C (–0.5, k) lies on the curve.
Find the value of k.
.....................................
(Total 4 marks)
29.
y
A
O
B
x
y
D
O
O
O
E
x
y
G
C
F
x
y
O
x
y
x
O
I
x
y
O
x
y
O
H
x
y
y
x
O
Write down the letter of the graph which could have the equation
(i)
y = 3x – 2
……………
(ii)
y = 2x2 + 5x – 3
……………
(iii)
y=
3
x
……………
(Total 3 marks)
30.
The equation x3 + 10x = 21
has a solution between 1 and 2
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)
31.
x
x
A cuboid has a square base of side x cm.
The height of the cuboid is 1 cm more than the length x cm.
The volume of the cuboid is 230 cm3.
(a)
Show that
x3 + x2 = 230
(2)
The equation
x3 + x2 = 230
has a solution between x = 5 and x = 6.
(b)
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
x = ...........................
(4)
(Total 6 marks)
32.
Tarish says,
‘The sum of two prime numbers is always an even number’.
He is wrong.
Explain why.
...............................................................................................................................................
...............................................................................................................................................
(Total 2 marks)
33.
y
(4, 320)
Diagram NOT
accurately drawn
(1, 5)
0
x
The sketch graph shows a curve with equation y = pqx
The curve passes through the points (1, 5) and (4, 320).
Calculate the value of p and the value of q.
p = .....................................
q = .....................................
(Total 3 marks)
34.
A = 24 × 32 × 7
B = 23 × 34 × 5
A and B are numbers written as the product of their prime factors.
Find
(i)
the highest common factor of A and B,
............................................
(ii)
the lowest common multiple of A and B.
............................................
(Total 3 marks)
35.
r is inversely proportional to t.
r = 12 when t = 0.2
Calculate the value of r when t = 4.
……………………………
(Total 3 marks)
36.
Here are the first five terms of an arithmetic sequence.
3
5
7
9
11
Find, in terms of n, an expression for the nth term of the sequence.
.....................................
(Total 2 marks)
y2 =
37.
ab
ab
a = 3 × 108
b = 2 × 107
Find y.
Give your answer in standard form correct to 2 significant figures.
y = ...................................
(Total 3 marks)
38.
In a spring, the tension (T newtons) is directly proportional to its extension (x cm).
When the tension is 150 newtons, the extension is 6 cm.
(a)
Find a formula for T in terms of x.
T = .................................
(3)
(b)
Calculate the tension, in newtons, when the extension is 15 cm.
................................. newtons
(1)
(c)
Calculate the extension, in cm, when the tension is 600 newtons.
................................. cm
(1)
(Total 5 marks)
39.
The number of atoms in one kilogram of helium is 1.51 × 1026
Calculate the number of atoms in 20 kilograms of helium.
Give your answer in standard form.
..............................................
(Total 2 marks)
40.
Prove that,
(n + 1)2 – (n – 1)2
is a multiple of 4, for all positive integer values of n.
(Total 3 marks)