5
6
A
8
B
A
B
D
C
O
6
D
C
Diagram I
Diagram II
ABCD is a rectangle in which AB # 8 cm and BC # 6 cm.
A circular piece of wire, centre O, passes through the vertices of the rectangle as shown in
Diagram I.
(a) Show that the radius of the circular wire is 5 cm.
[1]
(b) Show that angle AOB # 106.3°, correct to 1 decimal place.
[2]
(c) Calculate the area of the shaded segment.
[3]
(d) The circular wire is cut at A, B, C and D, and the four pieces joined to form the shape shown in
Diagram II.
Calculate the area enclosed by the wires in Diagram II.
4024/02 O/N03
[3]
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For
Examinerʼs
Use
For
Examinerʼs
Use
8
14
In the diagram, ABCD is a diameter of the circle centre P.
AB = BC = CD = 2x centimetres.
(a) Find an expression, in terms of x and π, for the
circumference of this circle.
A
2x
B
(b) The perimeter of the shaded region consists of
two semicircles whose diameters are AB and CD,
and two semicircles whose diameters are AC and BD.
P
2x
2x
D
C
Find an expression, in terms of x and π, for the
area of the shaded region.
Answer (a) .............................................cm [1]
(b) ........................................... cm2 [2]
15
A
In the diagram, BCDE is a trapezium, and the sides
CD and BE are produced to meet at A.
CB = 12 cm, DE = 9 cm and the perpendicular
distance from D to CB is 4 cm.
Calculate
(a) the area of BCDE,
(b) the perpendicular distance from A to CB.
9
D
E
4
C
12
B
Answer (a) ............................................ cm2 [1]
(b) ..............................................cm [2]
© UCLES 2007
4024/01/M/J/07
13
A
18 OAB is the sector of a circle of radius r cm.
AÔB = 60°.
For
Examiner’s
Use
Find, in its simplest form, an expression in terms of r and π for
O
(a) the area of the sector,
60°
r
B
Answer (a) .............................. cm2 [1]
(b) the perimeter of the sector.
Answer (b) ............................... cm [2]
19 A =
冢–13 12冣
and B =
冢–10 23冣 .
Find
(a) A – B,
Answer (a)
冢
冣
[1]
Answer (b)
冢
冣
[2]
(b) B–1.
© UCLES 2010
4024/12/M/J/10
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4
5
c=
冢32冣
d=
冢–86 冣
(a) Calculate 2c – d .
Answer
冢 冣
[1]
(b) Calculate 兩 d 兩 .
Answer
........................................ [1]
6
A
6
B
9
C
ABC is a right-angled triangle with AB = 6 cm and BC = 9 cm.
A semicircle of diameter 6 cm is joined to the triangle along AB.
Find an expression, in the form a + bπ, for the total area of the shape.
Answer
© UCLES 2011
4024/12/M/J/11
................................. cm2 [2]
4
5
y is inversely proportional to the square of x.
For
Examiner’s
Use
Given that y = 2 when x = 6, find the value of y when x = 2.
Answer y = ............................... [2]
6
A circle of diameter 6 cm is cut from a square of side 8 cm.
Find an expression, in the form a – bπ , for the shaded area.
6
Answer
© UCLES 2012
4024/12/M/J/12
8
..............................cm2 [2]
14
19 The diagram shows the metal cover for a circular drain.
Water drains out through the shaded sections.
For
Examiner’s
Use
B
A
O
D
C
O is the centre of circles with radii 1 cm, 2 cm, 3 cm, 4 cm and 5 cm.
t = 40°.
The cover has rotational symmetry of order 6 and BOC
(a) Calculate the area of the shaded section ABCD, giving your answer in terms of π.
Answer
© UCLES 2013
4024/11/M/J/13
.....................................cm2 [2]
15
(b) The total area of the metal (unshaded) sections of the cover is
55
π cm2.
3
For
Examiner’s
Use
(i) Calculate the total area of the shaded sections, giving your answer in terms of π.
Answer
.....................................cm2 [1]
(ii) Calculate the fraction of the total area of the cover that is metal (unshaded).
Give your answer in its simplest form.
Answer
............................................ [1]
Answer
............................................ [1]
Answer
............................................ [1]
Answer
............................................ [1]
20 (a) Evaluate
(i) 50 + 52,
1
(ii)
36 2 ,
^2 3h .
2
(iii)
6
k
1
(b) c m = 9
3
Find the value of k.
Answer k = ...................................... [1]
© UCLES 2013
4024/11/M/J/13
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13
17
For
Examiner’s
Use
45°
45°
3
2
The diagram shows part of an earring�
It is in the shape of a sector of a circle of radius 3 cm and angle 45°,
from which a sector of radius 2 cm and angle 45° has been removed�
(a) Calculate the shaded area�
Give your answer in the form
aπ
, where a and b are integers and as small as possible�
b
Answer
�������������������������������������cm2 [2]
(b) The earring is cut from a sheet of silver�
The mass of 1 cm2 of the silver sheet is 1�6 g�
By taking the value of π to be 3, estimate the mass of the earring�
Answer
© UCLES 2013
4024/12/M/J/13
����������������������������������������� g [1]
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5
7
A thin piece of wire is shaped into a figure five as shown.
5.25
4.8
3
280°
The shape has two straight sections of length 5.25 cm and 4.8 cm.
The curved part is the arc of the major sector of a circle, radius 3 cm.
The angle of the major sector is 280°.
The total length of wire needed to make the figure is ^a + brh cm.
Find the values of a and b.
Answer
a = ....................................................
b = .................................................... [2]
© UCLES 2014
4024/11/M/J/14
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