# NOTE: make sure you can get your hands on as many of these ...

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16 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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NOTE: make sure you can get your hands on as many of these textbooks as
possible! They definitely solidify your understandings of course concepts!

MATHEMATICS 3C/3D

Textbooks used:

A.J. Sadler Mathematics 3C

A.J. Sadler Mathematics 3D

Mathematics 3CD

Mathematics 3CD WACE Study Guide Academic Associates Greg Hill

Mathematics 3CD WACE Trial Examination Papers Academic Associates
Greg Hill

Creelman Exam Questions Mathematics 3CD Academic Taskforce G&K
Williams

T
opics (in chronological order):

We did 3C concepts in first semester and 3D concepts in second semester.

3C:

1.

Partial Fractions (not in 3C or in 3D but helps for difficult integration questions
and
some of the algebraic manipulation questions in 3D).

2.

Compos
ite Functions

a.

Domain and range

b.

g(f(x)) and f(g(x))

3.

Counting Techniques

a.

Combinations

b.

Permutations

4.

Differentiation

a.

Basic differentiation (e.g. equation to tangents, gradient at a point on
graph)

b.

Product Rule

c.

Quotient Rule

d.

Chain Rule

5.

Applications of
Differentiation

a.

Drawing f’(x) and f’’(x) graphs by looking at a graph of f(x)

b.

Locating points of inflection and second derivative test

c.

Optimisation

d.

Marginal Rates

e.

Incremental Formula (and small percentage changes)

f.

Total change

6.

Integration

a.

Basic integration

methods

b.

Integrating “happy” equations (i.e. in the form of

(

)
(

(

)
)

)

c.

Area under a curve

7.

Probability

a.

Tree diagrams

b.

Probabilities with combinations

c.

Independent Events

d.

Mutually Exclusive Events

8.

Exponential Function

a.

Growth and Decay using the
derivative of an exponential curve

b.

Finding the derivative of exponential functions

c.

Integrating exponential functions

9.

Probability Distributions

a.

Piecewise probability functions

b.

Binomial probability distribution

c.

Graphs for binomial distributions

d.

Uniform
distribution

e.

Integrals of uniform distribution

f.

Normal distribution

3
D
:

1.

Algebraic Equations

a.

Solving algebraic equations and fractions

b.

Inequalities

c.

Deriving three formulae from a paragraph of information

d.

Solving these three formulae simultaneously using the
Echelon matrix
method

e.

Solving 3x1 matrices for: no solutions, infinite solutions and unique
solutions

2.

Linear programming

a.

Deriving all constraints of a linear programming question

b.

Finding the maximum and minimum optimum solution

c.

Sensitivity of maximum/minim
um points

3.

Calculus

a.

Fundamental theorem of calculus

i.

When there are no functions within the limits

ii.

When a function is the upper limit

iii.

When a function is the lower limit

4.

Applications of calculus

a.

Related rates

b.

Volume of revolution

i.

Rotating about the x
-
axis

ii.

Ro
tating about the y
-
axis

iii.

-
axis with a distance between axis and object

iv.

-
axis with a distance between axis and object

v.

Demonstrating that volumes of shapes using this method also
equal its generic equation

c.

Rectilinear motion

5.

Proofs

a.

Algebraic proofs

i.

Examining parity of numbers (i.e. even and odd)

ii.

Checking an equation is divisible by integer, n

iii.

Proof by exhaustion

b.

Geometric proofs

i.

Revising year 10 geometry axioms (such as alternate angles etc.)

ii.

Similar triangles

iii.

Congruent triang
les

iv.

Angles in circles

v.

Tangents to circles

6.

Probability

a.

Theoretical application of what does a normally distributed set of data
resemble

b.

Possible interchange of using a binomial model on data

7.

Central Limit theorem

a.

Sample sizes

b.

Central limit theorem

c.

Confidenc
e intervals

d.

Choosing sample size

PHYSICS 3A/3B

NOTE: many current physics textbooks have some of the “old content” in them
(e.g. series and parallel circuits and parsecs) so don’t do them, not going to be
tested in WACE.

Textbooks used:

Heinemann Physics
3A 3B Pearson Education

STAWA Physics Stage 3

Physics 3AB

Sarath Chandran

Physics 3AB WACE Study Guide Academic Associates Michael Lucarelli

Physics 3AB WACE Trial Examination Papers Academic Associates Chris
Kolomyjec

Cr
eelman Exam Questions Physics 3AB Academic Taskforce Dr R Skinner

Topics (in chronological order):

We did 3A concepts in first semester and 3B concepts in second semester.

3A:

1.

Motion and Forces in a Gravitational Field:

a.

Difference between centre of mass an
d centre of gravity

b.

Year 11 Scalar/Vector quantities revision

and kinetic/gravitational potential
energy

c.

Resolving a Vector

d.

Projectile Motion

e.

Circular motion in a horizontal plane

f.

Circular motion in a vertical plane

g.

Gravitation

h.

Satellites in motion

i.

Attrac
tion force between two objects

j.

Torque

i.

Tension in cables

ii.

Force of compression

2.

Electricity and Magnetism:

a.

Magnetic domains

b.

Earth’s magnetic field

c.

Conventional, DC and AC current

d.

Flemming’s left hand rule

e.

AC motors (slip rings)

f.

DC motors (split ring
commutator)

g.

Force on conductor in magnetic field

h.

Induced currents and generating electricity

i.

ii.

Lenz’s law

i.

Electric fields

j.

Electromotive force

k.

Transformers

l.

Power Transmission

3
B
:

3.

Particles, Waves and Quanta (such a big topic!):

a.

Waves, wave
graphs, wave equation

b.

Particles, light and Young’s Double Slit experiment

c.

Wave/Particle Duality (photons)

d.

Diffraction

e.

Superposition

i.

Constructive Interference

ii.

Destructive Interference

iii.

Interference from two sources

f.

Beats

g.

Natural and Forced vibrations

i.

Resonance

ii.

Tacoma Narrows Bridge

iii.

Standing Waves

iv.

Waves in string

v.

Standing waves in open pipes

vi.

Standing waves in closed pipes

h.

i.

The visible spectrum

j.

Continuous spectrum

k.

Absorption spectra

l.

Emission spectra

m.

The photoelectric effect

n.

Fluor
escence and phosphorescence

o.

Energy levels and excitation

p.

Properties of X
-
rays

q.

Properties of matter

r.

Quarks, protons, electrons and neutrons

s.

Big Bang Theory

t.

Hubble’s Law

u.

Doppler Effect

v.

Red shift and blue shift

w.

Frames of reference and Newton’s theory of Rela
tivity

x.

Time Dilation equation

y.

Mass Increase equation

z.

Length Contraction equation

aa.

Speed of light

bb.

Mass and energy equivalence (i.e. E = mc^2)

4.

Motion and Forces in Electric and Magnetic Fields (much smaller than the
previous section!):

a.

Charged particles in
electric fields

b.

Electric fields in metal conductor

c.

Electric field strength between parallel plates

d.

Charged particles in magnetic fields

e.

The Cathode Ray Oscilloscope (CRO)

f.

Effects of Combining Electric and Magnetic Fields

g.

The Velocity Selector

h.

The Mass Spec
trometer

i.

Particle Accelerators

At the end of the year, we also did some practice on questions regarding:

o

Inkjet printers

o

Polarization of light and the concentration of sugar solution

o

Higg’s boson

o

“Gold leaf” experiment

o

The Large Hadron Collider (LHC)