2
1
1 Calculate (1 - cos 48°) .
2
................................................... [1]
2 Factorise completely.
4x2 - 8xy
................................................... [2]
3 Find the lowest common multiple (LCM) of 20 and 24.
................................................... [2]
4 Make a the subject of the formula.
x = y+ a
a = ............................................ [2]
5 Calculate the volume of a hemisphere with radius 3.2 cm.
4
[The volume, V, of a sphere with radius r is V = rr 3 .]
3
............................................cm3 [2]
3
2
6 The probability that Pedro scores a goal in any match is .
5
Calculate the probability that Pedro scores a goal in each of the next two matches.
................................................... [2]
7 y is inversely proportional to x2.
When x = 2, y = 8.
Find y in terms of x.
y = ............................................ [2]
8 Simplify.
1
c 12 m
8 3
a
................................................... [2]
4
9
y
14
12
10
x
–2 0 2 4 6 8 10 12 14 16 18 20 22
–2
By shading the unwanted regions of the grid above, find and label the region R that satisfies the following
four inequalities.
xH0 x+yH7 yHx x + 2y G 20
[3]
10 f(x) = 3 + 4x g(x) = 6x + 7
Find, in its simplest form,
(a) f(3x),
................................................... [1]
(b) fg(x).
................................................... [2]
5
11 Two bottles and their labels are mathematically similar.
The smaller bottle contains 0.512 litres of water and has a label with area 96 cm2.
The larger bottle contains 1 litre of water.
Calculate the area of the larger label.
............................................cm2 [3]
12 Write the recurring decimal 0.6 3 as a fraction in its lowest terms.
You must show all your
working.
................................................... [3]
13
39 cm NOT TO
SCALE
x°
24 cm
71.8°
Find the value of x.
x = ............................................ [3]
6
14 (a) Solve the inequality.
x + 13 H 3x + 7
................................................... [2]
(b) List the positive integers that satisfy the inequality in part (a).
................................................... [1]
................................................... [3]
7
15 The diagram shows a speed-time graph for the journey of a car.
12.5
NOT TO
SCALE
Speed
(m/s)
0
0 20 220 280
Time (s)
Calculate the total distance travelled.
............................................... m [3]
- c - m.
11 3 2
16 Without using your calculator, work out
12 4 3
You must show all your working and give your answer as a fraction in its simplest form.
.............................................. [4]
8
17 Simplify.
(a) 6w0
.............................................. [1]
(b) 5x3 − 3x3
.............................................. [1]
(c) 3y6 # 5y-2
.............................................. [2]
9
18 The diagram shows a cube ABCDEFGH of side length 26 cm.
H G
E F NOT TO
SCALE
D
C
A B
Calculate the angle between AG and the base of the cube.
................................................... [4]
19 (a) Simplify.
4 (x - 6) 2
(x - 6)
................................................... [1]
(b) Expand the brackets and simplify.
(x + 4) 2 + 5 (3x + 2)
................................................... [3]
10
20 Marcel invests $2500 for 3 years at a rate of 1.6% per year simple interest.
Jacques invests $2000 for 3 years at a rate of x% per year compound interest.
At the end of the 3 years Marcel and Jacques receive the same amount of interest.
Calculate the value of x correct to 3 significant figures.
x = ............................................ [5]
