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Mathematical Methods Units 3 &4

591Summary of Topics in Methods

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  • Mathematical Methods Units 3 &4

  • 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

  • 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

  • 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

  • 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