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Higher 2 Maths Topics

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Functions

Function notation

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Inequalities of combined functions

Inverse functions

One to one functions

Difference quotient: applications of functions

Transformations of Functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Even and odd functions

Quadratic Functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing parabolas for given quadratic functions

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic Equations and Inequalities

Solving quadratic equations by factorising

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solving quadratic inequalities

Polynomial Functions

What is a polynomial function?

Polynomial long division

Polynomial synthetic division

Remainder theorem

Factor theorem

Rational zero theorem

Characteristics of polynomial graphs

Multiplicities of polynomials

Imaginary zeros of polynomials

Determining the equation of a polynomial function

Applications of polynomial functions

Solving polynomial inequalities

Fundamental theorem of algebra

Descartes' rule of signs

Rational Functions

What is a rational function?

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Solving equations with algebraic fractions

Solving rational inequalities

Solving Simultaneous Equations

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving simultaneous equations by elimination

Solving simultaneous equations by substitution

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Inequalities in two variables

Graphing linear inequalities in two variables

Graphing simultaneous linear inequalities

Graphing quadratic inequalities in two variables

Graphing simultaneous quadratic inequalities

Applications of inequalities

What is linear programming?

Linear programming word problems

Introduction to Matrices

Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

Determinants and Inverses of Matrices

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

Conics

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

Imaginary and Complex Numbers

Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

Vectors

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

Scalar multiplication

Equivalent vectors

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

Unit Vector

Word problems on vectors

Sequences and Series

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

Limits

Finding limits from graphs

Continuity

Finding limits algebraically - direct substitution

Finding limits algebraically - when direct substitution is not possible

Infinite limits - vertical asymptotes

Limits at infinity - horizontal asymptotes

Intermediate value theorem

Squeeze theorem

Derivatives

Definition of derivative

Power rule

Gradient and equation of tangent line

Chain rule

Derivative of trigonometric functions

Derivative of exponential functions

Product rule

Quotient rule

Implicit differentiation

Derivative of inverse trigonometric functions

Derivative of logarithmic functions

Higher order derivatives

Probability

Addition rule for "OR"

Multiplication rule for "AND"

Conditional probability

Probability with permutations and combinations

Law of total probability

Bayes' rule

Probability with Venn diagrams

Permutations and Combinations

Fundamental counting principle

Factorial notation

Path counting problems

Permutation vs. Combination

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Binomial theorem

Data Interpretation

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Bivariate, scatter plots and correlation

Regression analysis

Equation of the best fit line

Discrete Probabilities

Probability distribution - histogram, mean, variance & standard deviation

Binomial distribution

Mean and standard deviation of binomial distribution

Poisson distribution

Geometric distribution

Negative binomial distribution

Hypergeometric distribution

Properties of expectation

Normal Distribution and Z-score

Introduction to normal distribution

Normal distribution and continuous random variable

Z-scores and random continuous variables

Sampling distributions

Central limit theorem

Rare event rule

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