Year 13

Functions

• Learn - Functions
• 1.1 - Write the equation of a linear function
• 1.2 - Evaluate functions
• 1.3 - Add, subtract, multiply and divide functions
• 1.4 - Composition of functions

Families of functions

• Learn - Family of functions
• 2.1 - Reflections of functions
• 2.2 - Dilations of functions
• 2.3 - Transformations of functions
• 2.4 - Function transformation rules
• 2.5 - Translations of functions
• 2.6 - Functions questions

Polynomials

• Learn - Polynomials
• 3.1 - Write a polynomial from its roots
• 3.2 - Find the roots of factorised polynomials
• 3.3 - Conjugate root theorems
• 3.4 - Fundamental theorem of algebra
• 3.5 - Factorize using a quadratic pattern
• 3.6 - Complex conjugate theorem
• 3.7 - Factoring quadratic polynomials cases

Exponential and logarithmic functions

• Learn - Logarithm
• 4.1 - Convert between exponential and logarithmic form
• 4.2 - Evaluate logarithms
• 4.3 - Product property of logarithms
• 4.4 - Quotient property of logarithms
• 4.5 - Power property of logarithms
• 4.6 - Evaluate logarithms using properties
• 4.7 - Solve logarithmic equations with one logarithm
• 4.8 - Exponential growth and decay: word problems
• 4.9 - Exercise on logarithms
• 4.10 - Logarithmic equations

Radical functions

• Learn - Radical equation
• 5.1 - Solve radical equations

Roots and rational exponents

• Learn - Square roots
• 6.1 - Roots of integers
• 6.2 - Roots of rational numbers
• 6.3 - Find roots using a calculator
• 6.4 - Evaluate rational exponents
• 6.5 - Nth roots
• 6.6 - Simplify radical expressions with variables

Trigonometric functions and identities

• Learn - Complementary angles and trigonometric Identities
• 7.1 - Complementary angle identities

Sequences and series

• Learn - Sequence, recursive and explicit
• 8.1 - Find terms of a sequence
• 8.2 - Identify a sequence as explicit or recursive
• 8.3 - Find terms of a recursive sequence

Probability

• Learn - Sample space and probabilities
• 9.1 - Introduction to probability
• 9.2 - Calculate probabilities of events

Probability distributions

• Learn - Discrete and continuous data
• 10.1 - Identify discrete and continuous random variables

Statistics

• Learn - Biased sample
• 11.1 - Identify biased samples

Introduction to derivatives

• Learn - Average rate of change
• 12.1 - Average rate of change I
• 12.2 - Average rate of change II
• 12.3 - Velocity as a rate of change

Derivative rules

• Learn - Sum and difference rule
• 13.1 - Sum and difference rules
• Learn - Product rule
• 13.2 - Product rule
• Learn - Power rule
• 13.3 - Power rule I
• Learn - Inverse function rule
• 13.4 - Inverse function rule
• 13.5 - Power rule II
• 13.6 - Power rule problems

Derivative strategies

• Learn - Implicit and explicit
• 14.1 - Find derivatives using implicit differentiation
• 14.2 - Find tangent lines using implicit differentiation

Calculate derivatives

• Learn - Derivation of polynomial
• 15.1 - Find derivatives of polynomials
• Learn - Derivation of trigonometry
• 15.2 - Find derivatives of trigonometric functions I
• 15.3 - Find derivatives of trigonometric functions II
• Learn - Derivation of exponential function
• 15.4 - Find derivatives of exponential functions
• Learn - Derivation of logarithmic functions
• 15.5 - Find derivatives of logarithmic functions
• 15.6 - Find derivatives using the product rule
• Learn - Derivation using product rule
• 15.7 - Find derivatives using the chain rule

Rational functions

• 16.1 - Rational functions: asymptotes and excluded values
• Learn - Rational equation
• 16.2 - Solve rational equations
• Learn - Rationalizing the denominator
• 16.3 - Rationalizing the denominator
• 16.4 - Difference rule

Calculate higher derivatives

• Learn - Second derivation
• 17.1 - Find higher derivatives of polynomials
• 17.2 - Find higher derivatives of rational and radical functions
• 17.3 - Find second derivatives of trigonometric, exponential and logarithmic functions
• 17.4 - Find higher derivatives using patterns
• 17.5 - Multiplication and divison of polynomials

Quadratic functions

• Learn - Quadratic equation
• 18.1 - Solve a quadratic equation using square roots
• 18.2 - Solve a quadratic equation by factorizing
• 18.3 - Solve a quadratic equation by completing the square
• 18.4 - Solve a quadratic equation using the quadratic formula
• Learn - Quadratic inequalities
• 18.6 - Quadratic inequalities

Prism

• Learn - Prism
• 19.1 - Volume and area of prism

Inverse functions

• Learn - Inverse functions
• 20.1 - Identify inverse functions
• 20.2 - Find values using function graphs
• 20.3 - Complete a table for a function graph
• 20.4 - Find values of inverse functions from graphs
• 20.5 - Composition and inverse of functions

Domain and range

• Learn - Domain and range
• 21.1 - Domain and range of radical functions

Linear equations

• Learn - Linear equation
• 22.1 - Linear equations
• Learn - Method to solve linear equations
• 22.2 - System of equations

Descartes' rule of signs

• Learn - Descartes' rule of signs
• 23.1 - Descartes' rule of signs

Logarithm law

• Learn - Logarithm law

Division and rationalization of fraction

• Learn - Division and rationalization of fraction
• 25.1 - Fractions of division
• 25.2 - Rationalizing the denominator

Sinusoidal functions

• Learn - Amplitude of sinusoidal functions
• 26.1 - Symmetry and periodicity of trigonometric functions
• 26.2 - Find properties of sine functions
• 26.3 - Find properties of cosine functions
• 26.4 - Find trigonometric functions using a calculator

Double and half identities

• Learn - Double and half identities
• 27.1 - Half and double identities

Partial sums

• Learn - Partial sum of series
• 28.1 - Introduction to partial sums
• 28.2 - Partial sums of arithmetic series
• 28.3 - Partial sums of geometric series
• 28.4 - Partial sums: mixed review

Combinations and permutations

• Learn - Combinations and permutations
• 29.1 - Combinations and permutations
• 29.2 - Find probabilities using combinations and permutations

Addition for probability

• Learn - Addition for probability
• 30.1 - Independence and conditional probability
• 30.2 - Find probabilities using the addition rule
• 30.3 - Probabilities of sum and difference rule

Power rule and derivation

• Learn - Power rule and derivation
• 31.1 - Power rule variables
• Learn - Derivation by limit
• 31.2 - Derivatives using limits

Variance and standard deviation

• Learn - Variance and standard deviation
• 32.1 - Variance and standard deviation

Outlier

• Learn - Outlier
• 33.1 - Identify an outlier
• 33.2 - Identify an outlier and describe the effect of removing it

Correlation coefficient

• Learn - Correlation coefficient
• 34.1 - Calculate correlation coefficients

Regression

• Learn - Regression
• 35.1 - Find the equation of a regression line
• 35.2 - Interpret regression lines
• 35.3 - Analyze a regression line of a data set

Remainder theorem

• Learn - Remainder theorem
• 36.1 - Remainder theorem

Trigonometry

• Learn - Trigonometry
• 37.1 - Fundamental and Pythagorean identities

Discriminant formula

• Learn - Discriminant formula
• 38.1 - Using the discriminant

Pyramid

• Learn - Pyramid
• 39.1 - Area and volume of pyramid