Revised
Additional Mathematics syllabus
• Set Language and notation
• Vectors(Relative Velocity)
•Permutations and
Combinations
• Matrices
•Calculus
Revised Additional Mathematics syllabus
Syllabus Aims
To enable students to





consolidate and extend elementary mathematical skills;
further develop their knowledge of mathematical concepts and principles;
appreciate the interconnectedness of mathematical knowledge;
acquire a suitable foundation in mathematics for further study;
devise mathematical arguments and use and present them precisely and
logically;
integrate information technology to enhance the mathematical
experience;
conduct independent and/or cooperative enquiry and experiment.
develop the confidence to apply their mathematical skills in appropriate
situations;
develop creativity and perseverance in the approach to problem solving;
derive enjoyment and satisfaction from engaging in mathematical
pursuits, and gain an appreciation of the beauty, power and usefulness of
mathematics.
 appreciate the
interconnectedness of
mathematical knowledge;
 acquire a suitable foundation
in mathematics for further
study;





Revised Additional Mathematics syllabus
We aim to
Continue to build on
the five inter-related
aspects of the
pentagon framework
Revised Additional Mathematics syllabus
Appreciation
Interest
Confidence
Perseverance
Estimation and
Approximation
Mental Calculation
Communication
Use of mathematical
tools
Arithmetic manipulation
Algebraic manipulation
Handling data
Monitoring one’s
own thinking
Mathematical
PROBLEM
SOLVING
Numerical
Geometrical
Algebraic
Statistical
Thinking
skills
Heuristics
Revised Additional Mathematics syllabus
To continue to underscore the
importance of the affective
aspects of mathematics learning
Meaningfu
 confidence in applying mathematics,
l
 enjoyment of mathematical
pursuits,
 appreciation ofactivities
the power and
beauty of mathematics
 perseverance in problem solving
Revised Additional Mathematics syllabus
Set Language and notation
Permutations and Combinations
Matrices
 Vectors (Relative Velocity)
Rich
 Calculus
Learning
environmen
Using and applying mathematics
t
 in practical tasks
 real life problems
 within mathematics itself
Example 1 on p1
Relative Velocity
200 m min-1
3 mins A
400 m
2 mins A
1 min
A
Start
A
600 m
200 m
N
P2
Relative Velocity
Velocity vector
 200   200   0 






(displacement
vector)
=
(velocity
vector)

(time
elapsed)
0
200
200
of B relative to A 
 
 

=
(velocity
vector
of
B)
(Velocity
vector
of
A)
metres
A
600
B
400
200
Start


200 400 600 metres
Example 2 on p2
Relative Velocity
N
North Bank
C
D
D
C
D
C
D
C
60 m
South Bank
River boat & The Plane and the wind - notes and animation http://www.glenbrook.k12.il.us/gbssci/phys/class/vectors/u3l1f.html
Relative Motion (Frame of reference) http://www.physics.gatech.edu/academics/tutorial/phys2121/Java%
20Applets/ntnujava/relativeVelocity/relativeVelocity.html
Learning about Properties of
vectors and Vector sums,
Components of a vector http://www.standards.nctm.org/doc
ument/eexamples/chap7/7.1/index.
htm
Example 4 on p4
'true'
velocity of the boat
Relative Velocity
(velocity ofof
boat
relative
to water)
= combination
the
rower's
effort
(velocity
water)
+ the effect
ofofthe
current.
North Bank
Final result:
travelling diagonally
‘True’
across the river

2
Rower's
effort
N
3
Effect of
the current
How far downstream
did he land?
Relative Velocity
Example 4 on p4
The current makes no
difference
his crossing time!
North to
Bank
Final result:
travelling diagonally
across the river
‘True’

2
Rower's
effort
N
3
Effect of
the current
Page 5
Relative Velocity
Points of View
‘the velocity of A relative to B’
refers to velocity of A from the point view of a
(sometimes imaginary) person who is moving
with B.
The velocity of a swimmer
relative to the water is her speed
and direction of motion as seen
by someone in a boat which is
drifting with the current.
Page 5
Points of View
At what speed does it actually travel?
(velocity
From theofpoint
boatof
relative
view of
tosomeone
bank) =
Boat/bank = boat/water + water/bank
(velocity
on the ground
of boatorrelative
dry land,
to water)
i.e.
+relative
(velocity
toof
the
water
Earth.
relative to bank)
Probe/Jupiter = probe/Earth + Earth/Jupiter
(velocity
probe
relative
Jupiter) =
Can weoftalk
about
theto‘actual’
(velocity
of of
probe
relativeat
to all?
Earth)
velocity
an object
+ every
(velocity
of Earth
relative
to Jupiter)
velocity
is relative
to something
Example 5 on p 6
Relative Velocity
‘Aiming off’ Q 1000m P
An aircraft wishes to travel from point P to point Q which
is due west of P. If wind is blowing from the south-west,
in which direction must the pilot head? How long will the
journey take?

Aircraft is not
travelling westward
100
Win
d
45
500
Velocity of aircraft
relative to wind
Example 5 on p 6
‘Aiming off’
Win
d
100

Aircraft is not
travelling westward
45
500
Wind
Aircraft is
travelling
westward
Velocity of aircraft
relative to wind
45
100

500
Aircraft is
'aiming off'
somewhat south
Two canoeists A and B each paddle in still water at
5m/s. They both leave at the same time from the
same point on the rive bank. The river flows at 3m/s
between straight parallel bank, 240m apart.
Canoeist A paddles in the direction that enables him
to cross the river in the shortest distance. Canoeist
B paddles in such a direction that he lands 240m
downstream of the point where A lands.
Determine, with full working whether A or B lands
first.