28 questions · 100 marks · ≈ 2 hours
A pattern is made with grey and white squares.
Write down the order of rotational symmetry for this pattern.
A pattern is made with grey and white squares.
Shade, on the grid below, exactly 5 squares to make a pattern with 4 lines of
symmetry.
3
−3 4
3
2
Write down a number from the above list that is
both a rational number and a natural number,
3
−3 4
3
2
Write down a number from the above list that is
an irrational number.
The nth term of a sequence is given by 3
n −
20
2
Find the difference between the 4th term and the 5th term of this sequence.
Using ruler and compasses only and showing all your construction lines, construct the
bisector of angle FGH
Without using a calculator and showing all your working, work out
2 1
11
÷
3
5
Give your answer as a mixed number in its simplest form.
Factorise fully 5
mp
p
−
10
2
Harpreet has been given
red bricks
×
×
×
2
3
5
7
2
5
green bricks
×
×
2
5
7
2
4
2
blue bricks
×
×
×
2
3
5
7
4
2
3
Harpreet is asked to arrange the bricks in rows according to the following rules.
Each row must contain just one colour of brick.
Each row must contain the same number of bricks.
Calculate the maximum number of bricks there can be in a row.
Given that a =
A car travels at an average speed of 80 km/h for 2.5 hours and then travels a further
distance of 25 km in 0.5 hours.
Calculate the average speed, in km/h, of the car for the whole journey.
............................................................................................. km/h
In a survey, 32 students were asked whether they study either History (H) or
Geography (G).
study Geography and 5
x − study History
Given that, of these students, 2
x −
1
5
complete the Venn diagram for this information, giving the missing value in terms
of x
E
G
H
x
2
In a survey, 32 students were asked whether they study either History (H) or
Geography (G).
study Geography and 5
x − study History
Given that, of these students, 2
x −
1
5
Calculate the value of x
x = .............................................................................................
Calculate the mean of the two numbers 4
and 3 6
×
. ×
10100
10101
Give your answer in standard form.
y
8
7
6
5
4
3
2
1
O
x
1
2
3
4
, the line with
The diagram above shows the line L with equation y
mx
c
equation y = 4 and the line with equation x = 3
Find the value of m and the value of c
m = .............................................................................................
c = .............................................................................................
y
8
7
6
5
4
3
2
1
O
x
1
2
3
4
, the line with
The diagram above shows the line L with equation y
mx
c
equation y = 4 and the line with equation x = 3
On the grid, shade and label the region R defined by
≤
≤
≤
≤
≤
and
and
y
x
y
mx
c
0
4
0
3
Simplify
x
x
3
2
2
A bag contains red pens, blue pens, black pens, green pens and purple pens.
A pen is selected at random from the bag.
The table gives information about the probability of the colour of the pen that is
selected.
Tisam draws a pie chart to show the information about the number of pens of each
colour in the bag. The size of the angle of the sector representing green pens is 50.4°
Show that x = 0.14
A bag contains red pens, blue pens, black pens, green pens and purple pens.
A pen is selected at random from the bag.
The table gives information about the probability of the colour of the pen that is
selected.
Tisam draws a pie chart to show the information about the number of pens of each
colour in the bag. The size of the angle of the sector representing green pens is 50.4°
Calculate the value of y
y = .............................................................................................
A bag contains red counters, blue counters and yellow counters such that
= 5 : 2
number of red counters : number of blue counters
number of blue counters : number of yellow counters = 3 : 4
The number of yellow counters in the bag is 56
Calculate the total number of counters in the bag.
Here is hexagon ABCDEF
The perimeter of the hexagon is 40 cm.
Find the area, in cm², of the hexagon.
............................................................................................. cm²
3
1
2
1
B
A
4
3
2
7
Calculate 3A - 2B
10
8
3
1
p
3
7 C
BC
B
32
1
2
4
1
3
1
2
1
B
A
4
3
2
7
Calculate the value of p
p = .............................................................................................
A
B
75°
O
C
OABC is a sector of a circle, centre O, with ∠AOC = 75°
The arc length ABC = 54 cm.
Calculate the area, in cm² to 2 significant figures, of the sector.
............................................................................................. cm²
The diagram shows two mathematically similar solids, A and B
A
B
The volume of solid B is 43% less than the volume of solid A
The total surface area of solid A is 700 cm²
Work out the total surface area, in cm² to 3 significant figures, of solid B
............................................................................................. cm²
X
Diagram NOT
4 cm
accurately drawn
B
5 cm
P
C
A
2 cm
D
A, B, C and D are four points on a circle.
P is the midpoint of AB
APBX is a straight line.
DCX is a straight line.
∠PCX = 115°
BX = 4 cm CX = 5 cm DC = 2 cm
Calculate, in degrees to one decimal place, ∠BPC
.............................................................................................°
BPC
Express 3
2
in the form p x
q
r
where p, q and r are integers to
x
x
(
)
2
6
9
be found.
Hence, or otherwise, solve the equation 3
without using a calculator.
2
x
x
6
9
0
Show your working clearly.
A particle is moving along a straight line. At time t seconds, the displacement, x metres,
of the particle from a fixed point O on the line is given by
3
2
x
t
t
t
2
8
15
At time t seconds, the velocity of the particle is v m/s
Find an expression for v in terms of t
v = .............................................................................................
A particle is moving along a straight line. At time t seconds, the displacement, x metres,
of the particle from a fixed point O on the line is given by
3
2
x
t
t
t
2
8
15
At time t seconds, the velocity of the particle is v m/s
Find the least speed, in m/s, of the particle.
............................................................................................. m/s
C
Diagram NOT
accurately drawn
O
E
102°
54°
A
B
D
In the diagram, A, B, and C are points on a circle, centre O
DBE is the tangent to the circle at the point B
102
54
AOB
EBC
Find, in degrees, the size of ∠OCA
Give reasons for each stage of your working.
............................................................................................. °
OCA
A box contains n buttons.
The buttons are either red or blue such that
number of red buttons : number of blue buttons = 3 : 5
A sample of 2 buttons is taken at random from the bag.
Given that the probability of the 2 buttons being the same colour is 10
19
find the value of n
n = .............................................................................................
Make h the subject of p
=
h
B
60°
A
C
The diagram shows triangle ABC
AB
x
4
6
cm
BC
x
3
cm
AC
x
6
4
cm
ACB
60
Find the area, in cm² to 3 significant figures, of triangle ABC
............................................................................................. cm²
Write
8 in the form a b where a and b are prime numbers.
Without using your calculator and showing all your working
express 6
2 3
where p and q are integers.
in the form
p
q
3 2
8
x
x
x
x
f ( )
12
4
25
14
3
2
=
Use the factor theorem to show that (3x − 4) is not a factor of f(x)
g(x) = f(x) − 2
x
x
x
x
f ( )
12
4
25
14
3
2
=
Factorise fully g(x)
Show clear algebraic working.