1
|
NUMBER SETS AND PROPERTIES | |
A
|
Some set language | |
B
|
Number sets | |
C
|
Words used in mathematics | |
D
|
Exponential (index) notation | |
E
|
Factors of natural numbers | |
| Investigation: The sieve of Eratosthenes | ||
F
|
Multiples of natural numbers | |
G
|
Order of operations | |
| Review set 1A | ||
| Review set 1B |
||
2
|
MEASUREMENTS | |
A
|
Time | |
B
|
Temperature | |
C
|
Imperial standard units | |
D
|
Standar form (scientific notation) | |
E
|
Rounding numbers | |
F
|
Rates | |
| Investigation 1: Stopping distances | ||
G
|
Measuring devices and their accuracy | |
| Investigation 2: Measuring devices | ||
| Review set 1B | ||
H
|
Accuracy of measurements | |
I
|
Error and percentage error | |
| Investigation 3: A gram in the hand is worth ... | ||
| Investigation 4: Estimating and accuracy | ||
| Review set 2A | ||
| Review set 2B |
||
3
|
SETS AND VENN DIAGRAMS | |
A
|
Set builder notation | |
B
|
Complements of sets | |
C
|
Venn diagrams | |
D
|
Venn diagram regions | |
E
|
Numbers in regions | |
| Review set 3A | ||
| Review set 3B |
||
4
|
THE RULE OF PYTHAGORAS | |
A
|
The rule of Pythagoras (review) | |
B
|
Pythagoras and geometrical figures | |
C
|
The converse of Pythagoras' rule | |
| Investigation 1: Pythagorean triples spread sheet | ||
D
|
Problem solving | |
E
|
True bearings and navigation | |
| Investigation 2: Shortest distance | ||
F
|
Circle problems | |
G
|
Three-dimensional problems | |
| Review set 4A | ||
| Review set 4B | ||
| Review set 4C |
||
5
|
DESCRIPTIVE STATISTICS | |
A
|
Describing data | |
| Investigation 1: Statistics from the internet | ||
B
|
Presenting and interpreting data | |
C
|
Grouped discrete data | |
| Investigation 2: Taxi Sir? | ||
D
|
Continuous data | |
| Investigation 3: Choosing class intervals | ||
E
|
Frequency distribution tables | |
F
|
Summarising the data | |
| Investigation 4: Effects of outliers | ||
G
|
Measuring the spread of data | |
H
|
Box-and-whisker plots | |
I
|
The standar deviation | |
| Investigation 5: Heart stopper | ||
J
|
Statistics using technology | |
K
|
Parallel boxplots | |
| Investigation 6: How do you like your eggs? | ||
| Review set 5A | ||
| Review set 5B |
||
6
|
LINEAR AND EXPONENTIAL ALGEBRA | |
A
|
Algebraic substitution | |
| Investigation 1: Solving equations | ||
B
|
Linear equations | |
C
|
Practional equations | |
D
|
Problem solving | |
E
|
Formula substitution | |
F
|
Formula rearrangement | |
| Investigation 2: The cycle problem | ||
G
|
Linear simultaneous equations | |
H
|
Problem solving | |
I
|
Index notation (Review) | |
J
|
Negative bases | |
K
|
Index laws | |
L
|
Exponential equations | |
| Review set 6A | ||
| Review set 6B | ||
| Review set 6C |
||
7
|
COORDINATE GEOMETRY | |
A
|
Distance between two points | |
B
|
Gradient | |
C
|
Applications of gradient | |
D
|
Midpoints | |
E
|
Vertical and horizontal lines | |
F
|
Equations of lines | |
G
|
Graphing lines | |
| Investigation: Finding where lines meet using technology | ||
H
|
Midpoints and perpendicular bisectors | |
| Review set 7A | ||
| Review set 7B | ||
| Review set 7C |
||
8
|
QUADRATIC ALGEBRA | |
A
|
Products and expansions | |
| Investigation 1: The product of three consecutive integers | ||
B
|
Further expansions | |
| Investigation 2: The expansion of (a + b)^3 | ||
C
|
Factorisation of quadratic expressions | |
D
|
Factorisation of ax^2 + bx +c (a =/1) | |
E
|
Quadratic equations | |
F
|
Completing the square | |
| Investigation 3: The quadratic formula (Extension) | ||
G
|
Problem solving with quadratics | |
| Review set 8A | ||
| Review set 8B | ||
| Review set 8C |
||
9
|
FUNCTION NOTATION AND QUADRATIC FUNCTIONS | |
A
|
Relations and functions | |
B
|
Interval notation, domain and range | |
C
|
Function notation | |
D
|
Function as mappings | |
| Investigation 1: Fluid filling functions | ||
E
|
Linear functions | |
F
|
Quadratic functions | |
G
|
Graph of quadratic functions | |
| Investigation 2: Graph of the form y = x^2 + k | ||
| Investigation 3: Graph of the form y = (x - h)^2 | ||
| Investigation 4: Graph of the form y = (x - h)^2 + k | ||
| Investigation 5: Graph of the form y = x^2 + bx +c | ||
| Investigation 6: Graph of the form y = ax^2 | ||
| Investigation 7: Graph of the form y = a(x - h)^2 + k | ||
H
|
Axes intercepts | |
| Investigation 8: Axes intercepts | ||
I
|
Graph from axes intercepts | |
J
|
Axis of symmetry and vertex | |
| Investigation 9: Solving quadratic equations graphically | ||
K
|
Where functions meet | |
L
|
Quadratic modelling | |
| Graphic calculator investigation: Tunnels and trucks | ||
| Review set 9A | ||
| Review set 9B | ||
| Review set 9C |
||
10
|
NUMERICAL TRIGONOMETRY | |
A
|
Right angled triangle trigonometry | |
B
|
The trigonometric ratios | |
| Investigation 1: Complementary angles | ||
| Investigation 2: Hipparchus and the universe | ||
C
|
Trigonometric problem solving | |
D
|
Constructing trigonometric formulae | |
E
|
3-dimensional problem solving | |
F
|
Areas of triangles | |
G
|
The cosine rule | |
H
|
The sine rule | |
| Investigation 3: The ambiguous case | ||
I
|
Using the sine and cosine rule | |
| Review set 10A | ||
| Review set 10B | ||
| Review set 10C |
||
11
|
PERIMETER, AREA AND VOLUME | |
A
|
Conversion of units | |
B
|
Perimeter | |
C
|
Area | |
D
|
Problem solving with areas | |
| Investigation 1: Rectangles of fixed perimeter | ||
E
|
Surface area | |
F
|
Volume | |
G
|
Capacity | |
| Investigation 2: Minimising material | ||
H
|
Density | |
I
|
Harder applications | |
| Review set 11A | ||
| Review set 11B | ||
| Review set 11C |
||
12
|
SEQUENCES AND SERIES | |
A
|
Number patterns | |
| Spreadsheet Investigation: Number patterns | ||
B
|
Sequences of numbers | |
C
|
Arithmetic sequences | |
D
|
Geometric sequences | |
E
|
Compound interest | |
F
|
Growth and decay | |
G
|
Series | |
| Investigation: Van Koch's snowflake curve | ||
| Review set 12A | ||
| Review set 12B | ||
| Review set 12C |
||
13
|
FINANCIAL MATHEMATICS | |
A
|
Foreign exchange | |
B
|
Simple interest | |
C
|
Compound interest | |
| Investigation 1: Doubling time | ||
D
|
Depreciation | |
E
|
Personal loans | |
| Investigation 2: Buying a car | ||
F
|
The effect of inflation | |
| Review set 13A | ||
| Review set 13B |
||
14
|
PROBABILITY | |
A
|
Experimental probability | |
| Investigation 1: Tossing drawing pins | ||
B
|
Chance investigations | |
| Investigation 2: Coin tossing experiments | ||
| Investigation 3: Dice rolling experiments | ||
C
|
Estimating probabilities from data | |
D
|
Sample space | |
E
|
Theoretical probability | |
| Investigation 4: A probability experiment | ||
F
|
Using grids to find probabilities | |
G
|
Compound events | |
| Investigation 5: Probabilities of compound events | ||
| Investigation 6: Revisiting drawing pins | ||
H
|
Using tree diagrams | |
I
|
Sampling with and without replacement | |
| Investigation 7: Sampling simulation | ||
J
|
Probabilities from Venn diagrams | |
K
|
Laws of probability | |
L
|
Independent events revisited | |
| Review set 14A | ||
| Review set 14B | ||
| Review set 14C |
||
15
|
LOGIC | |
A
|
Propositions | |
B
|
Compound propositions | |
C
|
Truth tables and logical equivalence | |
D
|
Truth tables for three propositions | |
E
|
Implication | |
F
|
Converse, inverse, contrapositive | |
G
|
Valid arguments | |
| Investigation: Syllogisms | ||
H
|
Arguments with three propositions | |
| Review set 15A | ||
| Review set 15B | ||
| Review set 15C |
||
16
|
EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS | |
A
|
Evaluating exponential functions | |
B
|
Graphing simple exponential functions | |
| Investigation 1: Exponential graphs | ||
| Investigation 2: Solving exponential equations | ||
C
|
Exponential growth | |
D
|
Exponential decay | |
E
|
Periodic functions | |
F
|
Sine functions | |
| Investigation 3: The family y = A sin x | ||
| Investigation 4: The family y = sin Bx, B > 0 | ||
| Investigation 5: The family y = sin x + C | ||
G
|
Cosine functions | |
H
|
Modelling using sine and cosine functions | |
I
|
Equations involving sine and cosine | |
J
|
Using sine and cosine models | |
| Review set 16A | ||
| Review set 16B | ||
| Review set 16C | ||
| Review set 16D |
||
17
|
MORE FUNCTIONS | |
A
|
Cubic polynomials | |
| Investigation 1: Graphing some families of cubics | ||
| Investigation 2: Cubics in linear factored form | ||
B
|
Quartic polynomials | |
| Investigation 3: Graphing quartics | ||
C
|
The rectangular hyperbola | |
| Investigation 4: The family of curves y = A/x | ||
| Investigation 5: Functions of the form y = A/(x-h) + k | ||
| Investigation 6: Higher order rational functions | ||
D
|
Higher order rational functions | |
E
|
Unfamiliar functions | |
F
|
Where functions meet | |
| Review set 17A | ||
| Review set 17B |
||
18
|
TWO VARIABLE STATISTICS | |
A
|
Correlation | |
B
|
Measuring correlation | |
C
|
Least squares regression | |
| Investigation: Spearman's rank order correlation coefficient | ||
D
|
The x^2 test of independence | |
| Review set 18A | ||
| Review set 18B |
||
19
|
INTRODUCTORY DIFFERENTIAL CALCULUS | |
A
|
Rate of change | |
| Investigation 1: Instantaneous speed | ||
B
|
Derivatives | |
| Investigation 2: The derivative of x^3 | ||
| Investigation 3: The derivative of x^n | ||
C
|
The idea of a limit | |
| Investigation 4: The gradient of a tangent | ||
D
|
The derivative function | |
E
|
Simple rules of differentiation | |
| Investigation 5: Simple rules of differentiation | ||
F
|
Tangent of curves | |
G
|
The second derivative | |
H
|
Changing shape | |
I
|
Stationary points | |
J
|
Rates of change | |
K
|
Optimisation | |
| Review set 19A | ||
| Review set 19B | ||
| Review set 19C |
||
| ANSWERS |
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