Download 1. Evaluate [2] 2. Multiply out the brackets and simplify [3] 3. Solve

Prelim Practice
Non-Calculator
1.
Evaluate
1 3
+ ÷2
3 4
[2]
2.
Multiply out the brackets and simplify
5 x 2 − 2 x(3 x − 5) − 6 x
3.
[3]
Solve the pair of equations
5 x − 2 y = 16 and 3x + 5 y = −9
4.
5.
[4]
9x 2 − 4 y 2
Factorise
[1]
Find the equation of the straight line passing through A(-2, 3) and B(1, 12).
Give your answer in its simplest form.
[3]
a = b 2 c + 7 to 'b'.
6.
Change the subject of the formula
7.
A group of 18 men were asked to perform as many press-ups as they could in
one minute. The results were as follows:
42
16
25
21
30
24
19
32
25
35
30
29
38
22
28
16
(a)
Calculate the median and quartiles of these data.
(b)
Draw a boxplot which illustrates this information.
[3]
25
39.
[2]
[4]
8.
(a)
(b)
9.
Simplify
Evaluate
Simplify
m5
m −3
8
−
2
3
72 + 2 2 − 32
[1]
[2]
[3]
Calculator
1.
A patient in hospital is given 200mg of a drug at 09:00. 12% of the amount of the
drug at the beginning of each hour is lost, through natural body processes, by the
end of that hour.
How many mg of the drug will be lost by 12:00?
2.
David bought 4 cream eggs and 5 flakes in a sweet shop. They cost him £3.88.
(a)
(b)
(c)
3.
[4]
Taking the cost of a cream egg to be ‘x’ pence and the cost of a flake to
be ‘y’ pence, construct an equation in x and y to show the above information.
[1]
Given that Carly bought 3 cream eggs and 2 flakes and paid a total of £2.14,
construct a second equation.
[1]
Gavin bought 2 cream eggs and a flake. How much did he pay?
[4]
During the 2004 Athens Olympic games the BBC recorded audience figures
for different events.
1∙07 × 107 people watched Paula Radcliffe compete in the marathon.
8∙8 × 106 people watched Kelly Holmes win in the 800 metres.
(a)
How many more people watched the marathon than the 800 metres?
Answer in scientific notation.
(b)
Express this as a percentage of the 800 metres audience to the nearest percent.
[2]
[2]
4.
A young child was given a slab of moulding clay. It was a cuboid and measured
15∙2cm by 4∙8cm by 3∙4cm.
(a)
Calculate the volume of the cuboid rounding your answer to 2 significant
figures.
[1]
The clay was made into 25 identical spheres.
(b) Using your answer from part (a), calculate the radius of one of the
spheres.
[4]
5.
Find the mean and standard deviation of these data, showing appropriate working:
23
6.
7.
35
21
26
32
3 tan x° − 4 = 0
Solve the equation
34.
0 ≤ x ≤ 360
[4]
[3]
Solve the following equation giving your answer correct to 2 significant figures.
2 x 2 − 5x − 5 = 0 .
[5]
8.
P and Q are points on the circumference of a circle centre O and diameter AB.
.
A
P
O
Q
o
42
42o
B
If ∠ ABP = 42o and AP = AQ, calculate the size of ∠ PAQ.
9.
[2]
Calculate the area of the sector shown in the diagram, given that it has radius 6∙8cm.
[2]
135
Oo
42o
10.
Sparks Electrical are having their annual clearance sale where everything is reduced
by 40%.
A Flat screen TV cost £480 in the sale.
How much did the TV originally cost?
[3]
A selection of the number of games won and the total points gained by teams in the
Scottish Premier League were plotted on this scattergraph and the line of best fit was
drawn.
P
80
70
60
50
Points
11.
40
30
20
10
4
8
12
Wins
16
20
W
(a)
Find the equation of the line of best fit.
[3]
(b)
Use your equation to calculate the points gained by a team who won 27
matches.
[1]
12.
A ship is at position A. Lighthouse L is on a bearing of 050o from the ship.
L
N
50o
A
N
60 km
B
The ship then travels 60 kilometres on a bearing of 130o to position B.
From position B the captain now observes the lighthouse on a bearing of 340o.
Calculate the distance between the ship and the lighthouse when the ship is at
position B.
[5]