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Mathematical Methods Units 3 &4
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FUNCTIONS AND GRAPHS
Functions and Relations
a. Number Theory and Set Notation
b. Domain and Range
c. Odd and Even Functions
d. Modulus Function
e. Composite Functions
f. Inverse Functions
Polynomial Functions
a. Equating Coefficients
b. Division of Polynomials
c. Remainder and Factor Theorems
d. Quadratic Functions
e. Cubic Functions
f. Higher Degree Polynomials
g. Determining the Rule for Graphs
Families of Functions
a. Functions with the Rule =
b. Functions with the Rule =
c. Transformations and Mapping
d. Determining the Rule for Functions
e. Addition of Ordinates
f. Graphing Inverse Functions
Functions Revisited
a. More Composite Functions
b. More Inverse Functions
c. Sums and Products and Addition of Ordinates
d. Curve Fitting
e. Modeling Data
f. Linear Representation of Non-Linear Relations
Exponential and Logarithmic Functions
a. Graphing Exponential Functions
b. Exponential Equations
c. Index Laws
d. Logarithmic Functions
e. Logarithmic Equations
f. Logarithm Laws
g. Graphing Logarithmic Functions
h. Change of Base Rule
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i. Inverses
j. Exponential Models and Applications
Circular Functions
a. Radians and Degrees
b. Sine, Cosine and Tangent
c. Symmetry of the Unit Circle
d. Complementary Angles
e. Exact Values
f. Basic Graphs of Circular Functions
g. Solving Trigonometric Equations
h. Solving Inequalities
i. Addition of Ordinates
j. Using Derivatives
k. Tangent Function
l. Pythagorean Identities
m. Applications of Circular Functions
CALCULUS
Differentiation of Polynomials, Power Functions and Rational
Functions
a. First Principles of Differentiation
b. The Derived Function
c. Chain Rule
d. Product Rule
e. Quotient Rule
f. Graphs of the Gradient Function
g. Limit Theorems
h. Discontinuous Functions
i. Differentiating the Absolute Value Function
Differentiation of Transcendental Functions
a. Differentiation of Exponential Functions
b. Differentiation of Logarithmic Functions
c. Applications of Differentiation of Exponential and
Logarithmic Functions
d. Differentiation of Circular Functions
e. Applications of Differentiation of Circular Functions
f. Extra Chain Rule Operations
Applications of Differentiation
a. Tangents and Normals
b. Linear Approximation
c. Sketching Graphs
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d. Maxima and Minima Problems
e. Rates of Change
f. Kinematics
g. Related Rates of Change
Further Applications of Differentiation
a. More Linear Approximation
b. More Related Rates of Change
c. Applications of Transcendental Functions
Integration
a. Integration of Rational Exponents
b. Integration of ( + )
c. Integration of Exponential Functions
d. Definite Integral
e. Properties of Definite Integrals
f. Area Under a Curve
g. Integration of Circular Functions
h. Integration by Recognition
i. Area Between Curves
j. Approximating the Area Under a Curve
k. Area Between a Curve and the Y-axis
PROBABILITY
Discrete Random Variables
a. Lattice Diagrams
b. Set Notation
c. Venn Diagrams
d. Tree Diagrams
e. Probability Tables (Karnaugh Maps)
f. Mutually Exclusive Events
g. Addition Law
h. Conditional Probability
i. Independent Events
j. Discrete Probability Distributions
k. Measures of Centre (Mean, Median and Mode)
l. Measures of Spread (Variance and Standard Deviation)
Binomial Distribution
a. Binomial Theorem
b. Bernoulli Sequences
c. Markov Chains
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d. Binomial Probability Distributions
e. Graph of the Binomial Probability Distribution Function
f. Expectation and Variance
Continuous Random Variables
a. Common Types of Continuous Distributions
b. Cumulative Distribution Functions
c. Properties of Continuous Distribution Function
d. Mean, Mode and Median
e. Percentiles (Quantiles)
f. Measures of Spread (Variance, Standard Deviation, Range and
Interquartile
Range)
g. Properties of Mean and Variance
h. Sums of Independent Random Variables
Normal Distribution
a. Features of the Normal Distribution
b. 68-95-99.7% Rule
c. Determining Normal Probabilities
d. Applications of the Normal Distribution
