AS Level Use of Mathematics
Transition activities
The questions in this booklet should be completed, using the Head Start to AS
Maths ook for guidan e ( Head Start to AS Maths Pu lished y CGP (availa le
on Amazon for about £4) ISBN 9781841469935). The material included is all in
the GCSE Maths Higher Syllabus. Answers, with worked solutions, should be
written by hand and brought to your first Maths lesson at the College.
Additional resources that you may find interesting:
+plus magazine (http://plus.maths.org/content/) for interesting articles on application
of mathematics e.g.



The maths of infectious diseases:
Constructing our lives: the mathematics of engineering
Mathematics and the nature of reality
AS Summer Transition Work: AS Use of Maths
1. Indices:
a) What is the value of 16 - 25 + 34 - 43 + 52 - 61?
Simplify the following expressions:
×
b)
f)
Evaluate:
−
×
j)
c)
d)
×
g)
h)
×
l) −
k)
−
×
e)
×
×
i)
×
−
n)
m)
2. Rearranging Formulae
Rearrange the following to make y the subject:
a) x + y = 10
b) 4x + 2y – 6 = 0
c) 4x + y – 5 = 0
d) 3x – y – 7 = 0
e) y – 6x + 9 = 0
f) x – 2y = 10
a) 12 + 6a
b) a2b + ab2
c) x2 – 36
d) x2 + 5x +6
e) x2 – 2x – 24
f) x2 – 6x + 8
g) x2 + 5x – 14
h) x² - 10x + 16
i) y² - 7y + 6
3. Factorise
4. Simultaneous equations
Solve the following pairs of simultaneous equations
a) 3x - y = 1
x+y=3
b) 2x + y = 7
x+y=4
c) 2x +3 y = 9
x + 4y = 7
d) 3x + 4y = 23
2x + 5y = 20
5. Equations
Solve the following equations
a) 5(x + 2) = 2x + 22
b) 2(x - 4) = 3x + 1
c) x² + 8x + 15 = 0
d) x² + 10x + 21 = 0
e) x² - 4x - 21 = 0
f) d² - 9d + 20 = 0
g) x² - 16 = 0
h) x² + 3x - 5 = 0
Example
A car travels at a steady speed of 50mph along a motorway.
The table shows the distances it would go in 1 hour, 2 hours, etc.
Time t hours
Distance d miles
0
0
1
50
2
100
3
150
4
200
Distance/Time Graph
distance (miles)
200
150
100
50
0
0
1
2
3
4
tim e (hours)
The distance can be found from the time by multiplying by 50. The points are on a straight line.
The gradient of the line is 50. The relationship between t and d is linear.
The distance, d, is directly proportional to the time t. [written d  t ]
Task 1
The mass of a cubic centimetre of iron is 8 grams
(a) Copy and complete the table.
Volume cm3
Mass g
1
8
2
16
3
24
4
?
(b) Draw a graph to show the relationship. Check that the points are on a straight line.
(c) What is the gradient of the line?
(d) When the volume is multiplied by 2, what happens to the mass
(e) What is the relationship between the volume and the mass? Write the relationship in
symbols.
 A Resource for Free-standing Mathematics Units
Karen Pittaway, Kingston College Mathematics Division
Task 2
1) Investigate the following relationships (start by drawing the graphs) and determine which are
linear.
Comment on key features and where possible write the relationship in symbols.
(a) The table below shows the frequencies of the notes obtained from a stretched sting
under various tensions.
Tension N
Frequency Hertz
16
200
36
300
49
350
64
400
(b) A small ball is thrown upwards with various initial speeds. The height it goes is
recorded below.
Speed ms-1
Height m
(c)
8
3.2
18
16.2
22
24.2
27
36.45
The current through a resistor when connected to various cells was:
Voltage V Volts
Current I Amperes
1.5
0.3
3
0.6
4.5
0.9
2) Give an example which involves a relationship which is linear.
 A Resource for Free-standing Mathematics Units
Karen Pittaway, Kingston College Mathematics Division
6
1.2