Mathematics for Australia 12 Mathematical Methods
1 |
FUNCTIONS |
9 |
|
A |
Exponential functions |
10 |
|
B |
Logarithms |
12 |
|
C |
Logarithmic functions |
16 |
|
D |
Trigonometric functions |
22 |
|
|
Review set 1A |
24 |
|
|
Review set 1B |
25 |
|
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|
|
2 |
DIFFERENTIAL CALCULUS |
27 |
|
A |
First principles |
28 |
|
B |
Simple rules of differentiation |
32 |
|
C |
The chain rule |
35 |
|
D |
The product rule |
39 |
|
E |
The quotient rule |
41 |
|
F |
Derivatives of exponential functions |
44 |
|
G |
Derivatives of logarithmic functions |
48 |
|
H |
Derivatives of trigonometric functions |
51 |
|
I |
Second derivatives |
54 |
|
|
Review set 2A |
55 |
|
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Review set 2B |
57 |
|
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|
|
3 |
APPLICATIONS OF DIFFERENTIAL CALCULUS |
59 |
|
A |
Equations of tangents |
61 |
|
B |
Increasing and decreasing functions |
64 |
|
C |
Stationary points |
67 |
|
D |
Inflections and shape |
69 |
|
E |
Kinematics |
79 |
|
F |
Rates of change |
83 |
|
G |
Optimisation |
87 |
|
|
Review set 3A |
92 |
|
|
Review set 3B |
94 |
|
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|
|
4 |
INTEGRATION |
97 |
|
A |
The area under a curve |
98 |
|
B |
Antidifferentiation |
104 |
|
C |
The Fundamental Theorem of Calculus |
106 |
|
D |
Integration |
112 |
|
E |
Rules for integration |
114 |
|
F |
Integrating f(ax + b) |
119 |
|
G |
Definite integrals |
122 |
|
|
Review set 4A |
124 |
|
|
Review set 4B |
125 |
|
|
|
|
5 |
APPLICATIONS OF INTEGRATION |
127 |
|
A |
The area under a curve |
128 |
|
B |
The area between two functions |
133 |
|
C |
Kinematics |
138 |
|
D |
Problem solving by integration |
145 |
|
|
Review set 5A |
148 |
|
|
Review set 5B |
151 |
|
|
|
|
6 |
STATISTICS |
153 |
|
A |
Key statistical concepts |
154 |
|
B |
Measuring the centre of data |
160 |
|
C |
Variance and standard deviation |
172 |
|
|
Review set 6A |
180 |
|
|
Review set 6B |
181 |
|
|
|
|
7 |
DISCRETE RANDOM VARIABLES |
183 |
|
A |
Random variables |
184 |
|
B |
Discrete probability distributions |
187 |
|
C |
Expected value |
192 |
|
D |
Variance and standard deviation |
199 |
|
E |
Properties of aX + b |
202 |
|
F |
The Bernoulli distribution |
204 |
|
G |
The binomial distribution |
207 |
|
|
Review set 7A |
217 |
|
|
Review set 7B |
219 |
|
|
|
|
8 |
CONTINUOUS RANDOM VARIABLES |
221 |
|
A |
Continuous random variables |
222 |
|
B |
Probability density functions |
225 |
|
C |
The normal distribution |
231 |
|
D |
Probabilities using a calculator |
236 |
|
E |
The standard normal distribution (Z-distribution) |
240 |
|
F |
Quantiles |
244 |
|
|
Review set 8A |
249 |
|
|
Review set 8B |
251 |
|
|
|
|
9 |
SAMPLING AND CONFIDENCE INTERVALS |
253 |
|
A |
Sampling distributions |
254 |
|
B |
Distributions of sample means |
258 |
|
C |
The Central Limit Theorem |
263 |
|
D |
Confidence intervals for means |
268 |
|
E |
Sample proportions |
280 |
|
F |
Confidence intervals for proportions |
283 |
|
|
Review set 9A |
291 |
|
|
Review set 9B |
293 |
|
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|
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ANSWERS |
297 |
|
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INDEX |
334 |