igureMaths
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50 questions at your level
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Level 5
Angle rules & giving reasons
13 questions
Lesson
Not started
Mark as done
A
B
C
ABC
A
B
C
is a triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
.
B
C
D
BCD
B
C
D
is a straight line.
Angle
A
C
D
=
116
°
ACD = 116°
A
C
D
=
116°
.
116°
A
B
C
D
Diagram NOT accurately drawn
Work out the size of angle
B
A
C
BAC
B
A
C
. Give a reason for each stage of your working.
●●●●●
Level 5
4 marks
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Angles in parallel lines
17 questions
Lesson
Not started
Mark as done
The diagram shows two parallel lines.
X
X
X
lies on the upper line,
Z
Z
Z
lies on the lower line, and
M
M
M
is a point between the lines.
34°
51°
x°
X
M
Z
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. You must give reasons for each stage of your working.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The diagram shows two parallel lines.
X
X
X
lies on the upper line,
Z
Z
Z
lies on the lower line, and
M
M
M
is a point between the lines.
Angle
X
M
Z
=
81
°
XMZ = 81°
X
M
Z
=
81°
.
(2x)°
81°
(3x + 6)°
X
M
Z
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Show your working clearly, giving reasons.
●●●●●
Level 5
4 marks
Start
→
Interior & exterior angles of polygons
22 questions
Lesson
Not started
Mark as done
P
P
P
is a regular polygon with 10 sides.
The interior angle of a regular polygon
Q
Q
Q
is
12
°
12°
12°
greater than the interior angle of
P
P
P
.
Work out the number of sides of
Q
Q
Q
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The diagram shows a regular pentagon
A
B
C
D
E
ABCDE
A
B
C
D
E
. The diagonals
A
C
AC
A
C
and
B
D
BD
B
D
cross at the point
F
F
F
.
x°
A
B
C
D
E
F
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. You must give reasons for each stage of your working.
●●●●●
Level 5
4 marks
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→
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
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Mark as done
The diagram shows a circle, centre
O
O
O
, radius
r
r
r
cm, and two regular octagons.
r cm
O
The sides of the larger octagon are tangents to the circle.
The vertices of the smaller octagon lie on the circle.
By considering perimeters, show that
4
2
−
2
<
π
<
8
(
2
−
1
)
4\sqrt{2 - \sqrt{2}} < \pi < 8(\sqrt{2} - 1)
4
2
−
2
<
π
<
8
(
2
−
1
)
(4 marks)
●●●●●
Level 5
4 marks
Start
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