June 2009
Paper 3
1)a)
Boy
Girl
Total
Walk
15
22
37
b) P(walk) =
Car
25
8
33
37
100
Other Total
14
54
16
46
30
100
2)
a)
4x + 3y – 2x + 5y = 2x + 8y
b)
2c + 4r
Hint: make up values for c and r and
work out what sum you would need to
do
3)a)
y = 4x – 3
x
y
-2
-11
-1
-7
0
-3
1
1
2
5
3
9
b) Your graph should be a straight line
through all the points with no
‘corners’
On this exam you only got 1 mark for
plotting your points if they were
wrong
4)a) P = 4k – 10 P = 50
50 = 4k – 10
60 = 4k
k = 60 ÷ 4
k = 15
b) y = 4n – 3d
y = 4x2 – 3x5
y = 8 – 15
y = -7
(1 mark)
(1 mark)
n=2
d=5
(1 mark)
(1 mark)
5)a)
5)b)
Translation
(1 mark)
3 right and 1 down
(1 mark)
3
-1
6)
a)
Opposite sides of a rectangle are
equal
b)
4x + 1 = 2x + 12
2x + 1 = 12
2x = 11
x = 5.5
c)
Perimeter = 5.5 + 5.5 + 23 + 23 = 57cm
7)
322 x 48 = 15456
a)
3.22 x 4.8 = 15.456
b)
0.322 x 0.48 = 0.15456
c)
15456 ÷ 4.8 = 3220
8) a)
2x2 =
x2 =
x =
b)
72
36
6
72
36
2
6
2
72 = 2 x 2 x 2 x 3 x 3
= 2 3 x 32
6
3
2
3
9)
9)
10)There are 40 litres of water in a
barrel.
The water flows out of the barrel at a
rate of 125 millilitres per second.
1 litre = 1000 millilitres.
Work out the time it takes for the
barrel to empty completely.
40 litres = 40 000 millilitres
40 000 ÷ 125 = 320 seconds
(40 000 ÷ 125 = 40 x 8)
11)a)
62.5
11)b)
63.5
12)
13) a) What type of magazines do you
read?
Sport
One question
Music
Fashion
1 mark
Tick box options – at least two options
1 mark
13) b) How many magazines have you
read in the last month?
0
1-2
3+
Time period e.g. month, week, year
1 mark
Tick box options – at least three nonoverlapping options
1 mark
14) 6.8 x 191
0.051
7 x 200
0.05
(1 mark for at least
two of these)
1400
0.05
(1 mark)
28000
(1 mark)
(Dividing by 0.05 is the same as
multiplying by 20)
15)a) Write 64 000 in standard form
6.4 x 104
(b) Write 156 x 10-7 in standard form
1.56 x 10-5
16)a) Factorise fully 4x2 – 6xy
2x(2x – 3y)
b) Factorise x2 + 5x – 6
(x + 6)(x – 1)
17)
Use upper
bounds
Join with
a smooth
curve
17)b)
Median is
‘middle
one’
60th value
Mark given
for any
value
between
235 and
245
17)c)
Men spent more money than
women
18)a)
Work out the size of angle AOD
54° (2 marks)
tangent is perpendicular to a radius
angles in a triangle add up to 180°
(reasons not required)
18)b)
Work out the size of angle ABC. Give a
reason for your answer.
27°
(2 marks)
Angle at the centre is twice the angle at
the circumference.
(1 mark)
19)a)
x = 2, y = 3
19b) Find an equation of the straight
line which is parallel to the line
y = ½x + 2 and passes through the
point (0, 4)
y = mx + c
y = ½x + c
y = ½x + 4
20)a)
3t + 1 < t + 12
2t + 1 < 12
2t < 11
t < 5.5
20)b)
t is a whole number.
Write down the largest value
of t that satisfies
3t + 1 < t + 12
t < 5.5
largest value of t is 5
21) M is directly proportional to L3.
When L = 2, M = 160
Find the value of M when L = 3
M = k x L3
160 = k x 23
160 = k x 8
160 = k
8
k = 20
M = 20 x L3
M = 20 x 33
M = 20 x 27 = 540
22)
23)a)
0.5
0.3
0.2
0.5
0.3
0.2
0.2
0.5
0.3
0.2
23)b)
Work out the probability that
Vishi will win both games.
0.5 x 0.5 = 0.25
24)a) AB = AC
(sides of an
equilateral triangle)
AD = AD
(common side)
ADC = ADB = 90°
Therefore ABD and ACD are
congruent (RHS)
24)b) BD = DC
(congruent triangles)
BC = AB
(equilateral triangles)
Therefore BD = ½ AB
25)
1
u
+
1 +
5/
2
2 +
5
4 +
10
1
v
=
1
f
1
10/
3
3
10
3
10
7
10
f
=
1 (1 mark)
f
1
f
1
f
1 (1 mark)
f
7 (1 mark)
10
=
=
=
=
25)
1
u
1
u
1
u
1
u
u
+
1
v
=
=
1 f
v fv
v-f
fv
fv
v-f
=
=
=
1
f
1
v
f
fv
26)
a) Find an equation of the translated curve.
y = f(x – 4)
26)
b)
On the grid, sketch the graph of
y = 3 cos (2x°) for values of x from 0
to 540