10
16
y
C (9,7)
NOT TO
SCALE
A (1,3)
O
x
B (3,0)
The co-ordinates of A, B and C are shown on the diagram, which is not to scale.
(a) Find the length of the line AB.
Answer(a) AB =
[3]
Answer(b)
[3]
(b) Find the equation of the line AC.
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2
1
Javed says that his eyes will blink 415 000 000 times in 79 years.
(a) Write 415 000 000 in standard form.
Answer (a) ......................................................
[1]
(b) One year is approximately 526 000 minutes.
Calculate, correct to the nearest whole number, the average number of times his eyes will blink
per minute.
Answer (b) ......................................................
2
[1]
Luis and Hans both have their birthdays on January 1st.
In 2002 Luis is 13 and Hans is 17 years old.
(a) Which is the next year after 2002 when both their ages will be prime numbers?
Answer (a) ......................................................
[1]
(b) In which year was Hans twice as old as Luis?
Answer (b) ......................................................
3
Ᏹ
[1]
Ᏹ
B
A
D
C
Diagram 2
Diagram 1
(a) In Diagram 1, shade the area which represents A傼B′.
[1]
(b) Describe in set notation the shaded area in Diagram 2.
Answer (b) ......................................................
0580/2, 0581/2 Jun02
[1]
75
2
x°
NOT TO
SCALE
52°
A straight line intersects two parallel lines as shown in the diagram.
Find the value of x.
[1]
Answer x =
9
A
2x°
C
5x°
x°
B
NOT TO
SCALE
D
AB is parallel to CD.
Calculate the value of x.
Answer x =
[3]
105
© UCLES 2011
0580/12/M/J/11
7
14
y
13
NOT TO
SCALE
1
x
0
3
The diagram shows the straight line which passes through the points (0, 1) and (3, 13).
Find the equation of the straight line.
Answer
[3]
Answer
cm [3]
15 A cylinder has a height of 12 cm and a volume of 920 cm3.
Calculate the radius of the base of the cylinder.
© UCLES 2011
0580/23/M/J/11
109
7
5
(a) The table below shows how many sides different polygons have.
Complete the table.
Name of polygon
Number of sides
3
Quadrilateral
4
5
Hexagon
6
Heptagon
7
8
9
Nonagon
[3]
(b) Two sides, AB and BC, of a regular nonagon are shown in the diagram below.
C
NOT TO
SCALE
x°
A
B
(i) Work out the value of x, the exterior angle.
Answer(b)(i) x =
[2]
(ii) Find the value of angle ABC, the interior angle of a regular nonagon.
Answer(b)(ii) Angle ABC =
© UCLES 2011
0580/32/M/J/11
[1]
[Turn over
112
10
6
(a)
C
NOT TO
SCALE
140°
p°
B
D
A
The diagram shows a triangle ABC with BA extended to D.
AB = AC and angle CAD = 140°.
Find the value of p.
Answer(a) p =
[2]
(b)
72°
NOT TO
SCALE
q°
Find the value of q.
Answer(b) q =
[2]
(c)
108°
104°
94°
NOT TO
SCALE
x°
Find the value of x.
Answer(c) x =
© UCLES 2011
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[1]
113
17
(b)
F
G
2x°
(x + 15)°
H
J
NOT TO
SCALE
75°
E
EFG is a triangle.
HJ is parallel to FG.
Angle FEG = 75°.
Angle EFG = 2x° and angle FGE = (x + 15)°.
(i) Find the value of x.
Answer(b)(i) x =
[2]
Answer(b)(ii) Angle HJG =
[1]
(ii) Find angle HJG.
© UCLES 2011
0580/43/M/J/11
117
8
19
y
NOT TO
SCALE
5
l
x
0
10
(a) Calculate the gradient of the line l.
Answer(a)
[2]
Answer(b)
[2]
(b) Write down the equation of the line l.
© UCLES 2005
0580/02, 0581/02 Nov 2005
127
8
18
y
NOT TO
SCALE
8
0
x
10
l
The line l passes through the points (10, 0) and (0, 8) as shown in the diagram.
(a) Find the gradient of the line as a fraction in its simplest form.
Answer(a)
[1]
(b) Write down the equation of the line parallel to l which passes through the origin.
Answer(b)
[1]
(c) Find the equation of the line parallel to l which passes through the point (3, 1).
Answer(c) y =
© UCLES 2007
0580/02/O/N/07
[2]
132
8
18
y
NOT TO
SCALE
y = 2x + 4
y = mx + c
A
B
x
6 units
The line y = mx + c is parallel to the line y = 2x + 4.
The distance AB is 6 units.
Find the value of m and the value of c.
Answer m =
© UCLES 2009
0580/21/O/N/09
and c =
[4]
135
4
9
topicAngleproperties
NOT TO
SCALE
t°
104°
117°
91°
t°
In the pentagon the two angles labelled t° are equal.
Calculate the value of t.
Answer t = ......................................................
[3]
topicEquationsandInequalities
topicNumbersetnotationandlanguage
0580/2 W00
146
6
14
NOT TO
SCALE
r
2r
The sphere of radius r fits exactly inside the cylinder of radius r and height 2r.
Calculate the percentage of the cylinder occupied by the sphere.
[The volume, V, of a sphere with radius r is V =
4
3
πr3.]
Answer
% [3]
ap = px + c
15
Write p in terms of a, c and x.
Answer p =
© UCLES 2011
0580/23/O/N/11
[3]
148
6
NOT TO
SCALE
13 cm
7 cm
The diagram shows a solid made up of a hemisphere and a cone.
The base radius of the cone and the radius of the hemisphere are each 7 cm.
The height of the cone is 13 cm.
(a) (i) Calculate the total volume of the solid.
[The volume of a hemisphere of radius r is given by V =
2
3
3
πr .]
[The volume of a cone of radius r and height h is given by V = 13 πr h .]
[2]
(ii) The solid is made of wood and 1 cm3 of this wood has a mass of 0.94 g.
Calculate the mass of the solid, in kilograms, correct to 1 decimal place.
[3]
2
(b) Calculate the curved surface area of the cone.
[The curved surface area of a cone of radius r and sloping edge l is given by A = πrl .]
[3]
(c) The cost of covering all the solid with gold plate is $411.58.
Calculate the cost of this gold plate per square centimetre.
2
[The curved surface area of a hemisphere is given by A = 2 πr .]
Ó UCLES 2004
[5]
0580/4, 0581/4 Jun/04
162
17
NOT TO
SCALE
20 cm
10 cm
9 cm
d cm
The diagrams show two mathematically similar containers.
The larger container has a base with diameter 9 cm and a height 20 cm.
The smaller container has a base with diameter d cm and a height 10 cm.
(a) Find the value of d.
Answer(a) d =
[1]
Answer(b)
ml [2]
(b) The larger container has a capacity of 1600 ml.
Calculate the capacity of the smaller container.
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