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54 questions at your level
Difficulty
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Level 1
Level 2
Level 3
Level 4
Level 5
Pythagoras' theorem
24 questions
Lesson
Not started
Mark as done
3.6
2
+
4.8
2
\sqrt{3.6^2 + 4.8^2}
3.
6
2
+
4.
8
2
Circle your answer.
A
4.2
4.2
4.2
B
6
6
6
C
8.4
8.4
8.4
D
36
36
36
●
●●●●
Level 1
1 mark
Start
→
Mark as done
The diagram shows a right-angled triangle.
9 cm
x
12 cm
Diagram NOT accurately drawn
Work out the length of
x
x
x
.
●●
●●●
Level 2
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
12 cm
5 cm
x
Diagram NOT accurately drawn
Work out the value of
x
x
x
.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
5 cm
12 cm
Diagram NOT accurately drawn
(a)
Work out the length of the hypotenuse. (2 marks)
(b)
Work out the area of the triangle. (1 mark)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
A
B
C
ABC
A
B
C
is a right-angled triangle.
7.4 cm
5.9 cm
A
B
C
Diagram NOT accurately drawn
A
B
=
7.4
AB = 7.4
A
B
=
7.4
cm and
B
C
=
5.9
BC = 5.9
B
C
=
5.9
cm.
Work out the length of
A
C
AC
A
C
.
Give your answer correct to 1 decimal place. (3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
A
A
A
is the point
(
−
2
,
3
)
(-2, 3)
(
−
2
,
3
)
and
B
B
B
is the point
(
4
,
11
)
(4, 11)
(
4
,
11
)
.
(a)
Work out the length of
A
B
AB
A
B
. [3]
(b)
Work out the gradient of the line
A
B
AB
A
B
. [1]
●●
●●●
Level 2
4 marks
Start
→
Mark as done
The diagram shows a circle with centre
O
O
O
and radius
13
13
13
cm.
A
B
AB
A
B
is a chord of length
24
24
24
cm.
24 cm
13 cm
A
B
O
Diagram NOT accurately drawn
Work out the distance from the centre
O
O
O
to the chord
A
B
AB
A
B
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
P
A
PA
P
A
is a tangent to a circle with centre
O
O
O
and radius
8
8
8
cm. The point
A
A
A
is where the tangent touches the circle.
O
P
=
17
OP = 17
O
P
=
17
cm.
Work out the length of
P
A
PA
P
A
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle with hypotenuse
25
25
25
cm.
24 cm
y
25 cm
Diagram NOT accurately drawn
(a)
Work out the length of
y
y
y
.
(b)
Work out the distance between the points
(
−
3
,
2
)
(-3, 2)
(
−
3
,
2
)
and
(
5
,
8
)
(5, 8)
(
5
,
8
)
.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
A ladder leans against a vertical wall. The foot of the ladder is
1.4
1.4
1.4
m from the base of the wall, and the ladder reaches
4.2
4.2
4.2
m up the wall.
4.2 m
1.4 m
ladder
Diagram NOT accurately drawn
Work out the length of the ladder. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
A triangle has sides of length
8
8
8
cm,
15
15
15
cm and
17
17
17
cm. Show that this triangle is right-angled.
(b)
A different triangle has sides of length
7
7
7
cm,
9
9
9
cm and
12
12
12
cm. Determine whether this triangle is right-angled. You must show your working.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A right-angled triangle has hypotenuse
41
41
41
cm and one shorter side of length
40
40
40
cm.
Work out the length of the third side.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
A
A
A
is the point
(
1
,
2
)
(1, 2)
(
1
,
2
)
and
B
B
B
is the point
(
7
,
10
)
(7, 10)
(
7
,
10
)
.
Work out the length of the line segment
A
B
AB
A
B
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A solid cone has base radius
6
6
6
cm and slant height
10
10
10
cm.
6 cm
10 cm
Diagram NOT accurately drawn
Volume of a cone
=
1
3
π
r
2
h
= \dfrac{1}{3}\pi r^2 h
=
3
1
π
r
2
h
Work out the volume of the cone.
Give your answer correct to 3 significant figures. (4 marks)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows trapezium
P
Q
R
S
PQRS
P
QR
S
.
9 cm
6 cm
P
Q
R
S
P
Q
=
9
PQ = 9
P
Q
=
9
cm
P
S
=
6
PS = 6
P
S
=
6
cm
The trapezium has an area of
72
72
72
cm²
Work out the perimeter of the trapezium.
Give your answer correct to
3
3
3
significant figures.
(5 marks)
●●●
●●
Level 3
5 marks
Start
→
Mark as done
A circle has centre
O
O
O
and radius
25
25
25
cm.
A
B
AB
A
B
is a chord of length
30
30
30
cm.
(a)
Work out the distance from
O
O
O
to the chord
A
B
AB
A
B
.
(b)
M
M
M
is the midpoint of
A
B
AB
A
B
, and the line
O
M
OM
O
M
is extended to meet the circle at
N
N
N
. Work out the length of
M
N
MN
M
N
.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The diagram shows a cuboid measuring
10
10
10
cm by
6
6
6
cm by
8
8
8
cm.
10 cm
6 cm
8 cm
Diagram NOT accurately drawn
Work out the length of the longest diagonal of the cuboid. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
An isosceles triangle has a base of
16
16
16
cm and two equal sides of
17
17
17
cm.
Work out the
area
of the triangle.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The four vertices of rectangle
P
Q
R
S
PQRS
P
QR
S
lie on a circle, centre
O
O
O
.
11 cm
6.5 cm
P
Q
R
S
O
P
Q
=
11
PQ = 11
P
Q
=
11
cm
Q
R
=
6.5
\qquad QR = 6.5
QR
=
6.5
cm
Work out the circumference of the circle.
Give your answer correct to 3 significant figures.
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A square has a diagonal of length
12
12
12
cm.
(a)
Work out the side length of the square. Give your answer correct to 3 significant figures.
(b)
Work out the
exact
area of the square.
●●●●●
Level 5
3 marks
Start
→
Mark as done
The diagram shows a cuboid measuring
12
12
12
cm by
5
5
5
cm by
9
9
9
cm.
12 cm
9 cm
5 cm
Diagram NOT accurately drawn
Work out the angle between the long diagonal of the cuboid and its base. Give your answer correct to 1 decimal place.
●●●●●
Level 5
3 marks
Start
→
Mark as done
The diagram shows a pyramid with a square base of side
10
10
10
cm. Each sloping edge has length
13
13
13
cm.
10 cm
13 cm
Diagram NOT accurately drawn
(a)
Work out the vertical height of the pyramid. Give your answer correct to 1 decimal place.
(b)
Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.
●●●●●
Level 5
5 marks
Start
→
Mark as done
A
B
C
D
E
F
G
H
ABCDEFGH
A
B
C
D
E
F
G
H
is a cuboid.
12 cm
34°
49°
A
B
C
D
E
F
G
H
A
B
=
12
AB = 12
A
B
=
12
cm \qquad angle
B
A
C
=
34
°
BAC = 34°
B
A
C
=
34°
\qquad angle
G
B
C
=
49
°
GBC = 49°
GB
C
=
49°
Work out the size of the angle between
A
G
AG
A
G
and the plane
A
B
C
D
ABCD
A
B
C
D
.
Give your answer correct to the nearest degree.
(4 marks)
●●●●●
Level 5
4 marks
Start
→
Mark as done
Ten identical regular octagons are joined together as shown in the diagram.
a
S
The octagons enclose the shape
S
S
S
.
Each side of each octagon has length
a
a
a
.
Find an expression, in terms of
a
a
a
, for the area of
S
S
S
.
Give your answer in the form
p
(
5
+
2
2
)
a
2
p(5 + 2\sqrt{2})a^2
p
(
5
+
2
2
)
a
2
where
p
p
p
is an integer.
You must show all your working.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Right-angled trigonometry (SOHCAHTOA)
31 questions
Lesson
Not started
Mark as done
The value of
tan
45
°
\tan 45°
tan
45°
is
Circle your answer.
A
0
0
0
B
1
2
\dfrac{1}{2}
2
1
C
1
1
1
D
3
\sqrt{3}
3
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Here is a right-angled triangle.
8 cm
6 cm
x
Diagram NOT accurately drawn
Work out the size of angle
x
x
x
. Give your answer to 1 decimal place.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
Here is a right-angled triangle.
y
10 cm
30°
Diagram NOT accurately drawn
Work out the length
y
y
y
.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
9.5 cm
6.2 cm
x
P
Q
R
Diagram NOT accurately drawn
P
Q
R
PQR
P
QR
is a right-angled triangle.
P
Q
=
9.5
PQ = 9.5
P
Q
=
9.5
cm and
Q
R
=
6.2
QR = 6.2
QR
=
6.2
cm.
Work out the size of the angle marked
x
x
x
.
Give your answer correct to 1 decimal place. (3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
A ladder of length
5
5
5
m leans against a vertical wall. The ladder makes an angle of
70
°
70°
70°
with the horizontal ground.
(a)
How far up the wall does the ladder reach? Give your answer correct to 2 decimal places. [2]
(b)
How far is the foot of the ladder from the wall? Give your answer correct to 2 decimal places. [2]
●●
●●●
Level 2
4 marks
Start
→
Mark as done
From a point on level ground
40
40
40
m from the base of a vertical tower, the angle of elevation of the top of the tower is
38
°
38°
38°
.
(a)
Work out the height of the tower. Give your answer correct to 3 significant figures. [2]
(b)
Work out the distance from the point to the top of the tower. Give your answer correct to 3 significant figures. [2]
●●
●●●
Level 2
4 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
x
9.6 cm
38°
Diagram NOT accurately drawn
Work out the length of
x
x
x
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
9.2 cm
6.5 cm
θ
Diagram NOT accurately drawn
Work out the size of the angle marked
θ
\theta
θ
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
x
12 cm
38°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Give your answer correct to 3 significant figures.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
9 cm
14 cm
x
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
x
12 cm
30°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. (2 marks)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
7.2 cm
y
41°
Diagram NOT accurately drawn
Work out the value of
y
y
y
. Give your answer correct to 3 significant figures. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
4.5 cm
7.2 cm
θ
Diagram NOT accurately drawn
Work out the size of angle
θ
\theta
θ
. Give your answer correct to 1 decimal place. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A ship sails
9
9
9
km due East from
P
P
P
to
Q
Q
Q
, and then
5
5
5
km due North from
Q
Q
Q
to
R
R
R
.
9 km
5 km
P
Q
R
N
Diagram NOT accurately drawn
Work out the bearing of
R
R
R
from
P
P
P
. Give your answer correct to the nearest degree.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A helicopter flies
8
8
8
km from
A
A
A
on a bearing of
125
°
125°
125°
to reach
B
B
B
.
(a)
Work out how far East of
A
A
A
the point
B
B
B
is. Give your answer correct to 3 significant figures.
(b)
Work out how far South of
A
A
A
the point
B
B
B
is. Give your answer correct to 3 significant figures.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A phone mast
M
M
M
is
7.4
7.4
7.4
km due West and
3.9
3.9
3.9
km due North of a house
H
H
H
.
(a)
Work out the distance
H
M
HM
H
M
. Give your answer correct to 3 significant figures.
(b)
Work out the bearing of
M
M
M
from
H
H
H
. Give your answer correct to the nearest degree.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
7.5 cm
x
34°
Diagram NOT accurately drawn
Work out the length of
x
x
x
. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
5 cm
x
60°
Diagram NOT accurately drawn
(a)
Write down the exact value of
tan
60
°
\tan 60°
tan
60°
.
(b)
Work out the exact length of
x
x
x
, giving your answer in the form
a
3
a\sqrt{3}
a
3
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
x
11 cm
52°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Give your answer correct to 3 significant figures.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
(a)
Write down the exact value of
sin
30
°
\sin 30°
sin
30°
(b)
A right-angled triangle has hypotenuse
14
14
14
cm, and one of its angles is
30
°
30°
30°
.
Using your answer to part (a), work out the
exact
length of the side opposite the
30
°
30°
30°
angle.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A ship leaves a harbour
H
H
H
and sails
8
8
8
km on a bearing of
060
°
060°
060°
to a point
P
P
P
. It then sails
5
5
5
km on a bearing of
150
°
150°
150°
to a point
Q
Q
Q
.
(a)
Work out the distance
H
Q
HQ
H
Q
. Give your answer correct to 3 significant figures. (3 marks)
(b)
Work out the bearing of
Q
Q
Q
from
H
H
H
. Give your answer correct to the nearest degree. (2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
(a)
A right-angled triangle has hypotenuse
8
8
8
cm and one angle of
60
°
60°
60°
. Work out the exact length of the side opposite the
60
°
60°
60°
angle. [2]
(b)
Another right-angled triangle has hypotenuse
6
2
6\sqrt{2}
6
2
cm and one angle of
45
°
45°
45°
. Work out the exact length of the side adjacent to the
45
°
45°
45°
angle. [2]
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The diagram shows two right-angled triangles.
2x + 3
15
10
x + 3
a
b
All lengths are measured in centimetres.
Given that
sin
a
=
tan
b
\sin a = \tan b
sin
a
=
tan
b
work out the value of
x
x
x
.
(3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
P
Q
R
PQR
P
QR
is a triangle.
S
S
S
is a point on
Q
R
QR
QR
.
9.6 cm
47°
29°
P
Q
R
S
P
Q
=
9.6
PQ = 9.6
P
Q
=
9.6
cm \qquad angle
P
Q
S
=
47
°
PQS = 47°
P
QS
=
47°
\qquad angle
P
R
S
=
29
°
PRS = 29°
P
R
S
=
29°
Work out the length of
P
R
PR
P
R
.
Give your answer correct to 1 decimal place.
(3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A yacht sails from
P
P
P
on a bearing of
070
°
070°
070°
for
12
12
12
km to reach
Q
Q
Q
. It then sails on a bearing of
160
°
160°
160°
for
9
9
9
km to reach
R
R
R
.
12 km
9 km
P
Q
R
N
N
Diagram NOT accurately drawn
(a)
Show that angle
P
Q
R
PQR
P
QR
is a right angle.
(b)
Work out the distance
P
R
PR
P
R
.
(c)
Work out the bearing of
R
R
R
from
P
P
P
. Give your answer correct to the nearest degree.
●●●●●
Level 5
7 marks
Start
→
Mark as done
A ship leaves a harbour
H
H
H
and sails
15
15
15
km on a bearing of
048
°
048°
048°
to a point
A
A
A
.
It then sails
25
25
25
km due South to a point
B
B
B
.
(a)
Work out the distance
H
B
HB
H
B
. Give your answer correct to 1 decimal place.
(b)
Work out the bearing of
B
B
B
from
H
H
H
. Give your answer correct to the nearest degree.
●●●●●
Level 5
7 marks
Start
→
Mark as done
Priya stands
45
45
45
m from the foot of a tower on level ground. From her eye, the angle of elevation of the top of the tower is
27
°
27°
27°
.
Priya's eyes are
1.6
1.6
1.6
m above the ground.
Work out the height of the tower. Give your answer correct to 1 decimal place.
●●●●●
Level 5
4 marks
Start
→
Mark as done
A boat is
130
130
130
m from the base of a vertical cliff of height
58
58
58
m.
Work out the angle of
depression
of the boat from the top of the cliff. Give your answer correct to 1 decimal place.
●●●●●
Level 5
3 marks
Start
→
Mark as done
P
Q
R
PQR
P
QR
is a right-angled triangle.
5.2 cm
7.4 cm
x
P
Q
R
P
Q
=
7.4
PQ = 7.4
P
Q
=
7.4
cm correct to the nearest mm.
Q
R
=
5.2
QR = 5.2
QR
=
5.2
cm correct to the nearest mm.
Calculate the upper bound for the size of the angle marked
x
x
x
.
You must show all your working.
(3 marks)
●●●●●
Level 5
3 marks
Start
→
Mark as done
A
B
C
D
E
F
G
H
ABCDEFGH
A
B
C
D
E
F
G
H
is a cuboid.
A
B
C
D
E
F
G
H
A
C
=
7.5
AC = 7.5
A
C
=
7.5
cm \qquad
A
G
=
15
AG = 15
A
G
=
15
cm
Work out the size of the angle between
A
G
AG
A
G
and the plane
A
B
C
D
ABCD
A
B
C
D
.
(2 marks)
●●●●●
Level 5
2 marks
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Mark as done
A
B
C
D
E
F
G
H
ABCDEFGH
A
B
C
D
E
F
G
H
is a cuboid.
12 cm
34°
49°
A
B
C
D
E
F
G
H
A
B
=
12
AB = 12
A
B
=
12
cm \qquad angle
B
A
C
=
34
°
BAC = 34°
B
A
C
=
34°
\qquad angle
G
B
C
=
49
°
GBC = 49°
GB
C
=
49°
Work out the size of the angle between
A
G
AG
A
G
and the plane
A
B
C
D
ABCD
A
B
C
D
.
Give your answer correct to the nearest degree.
(4 marks)
●●●●●
Level 5
4 marks
Start
→