# Higher 2 maths

Here is a list of all of the maths skills students learn in higher 2! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. To start practising, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Functions

- A.1 Domain and range
- A.2 Identify functions
- A.3 Find the gradient of a linear function
- A.4 Graph a linear function
- A.5 Write the equation of a linear function
- A.6 Evaluate functions
- A.7 Find values using function graphs
- A.8 Complete a table for a function graph
- A.9 Add, subtract, multiply and divide functions
- A.10 Composition of functions
- A.11 Identify inverse functions
- A.12 Find values of inverse functions from tables
- A.13 Find values of inverse functions from graphs
- A.14 Find inverse functions and relations

## Families of functions

## Quadratic functions

- C.1 Characteristics of quadratic functions
- C.2 Find the maximum or minimum value of a quadratic function
- C.3 Graph a quadratic function
- C.4 Match quadratic functions and graphs
- C.5 Solve a quadratic equation using square roots
- C.6 Solve a quadratic equation by factorising
- C.7 Solve a quadratic equation by completing the square
- C.8 Solve a quadratic equation using the quadratic formula
- C.9 Using the discriminant

## Polynomials

- D.1 Divide polynomials using long division
- D.2 Write a polynomial from its roots
- D.3 Find the roots of factorised polynomials
- D.4 Rational root theorem
- D.5 Complex conjugate theorem
- D.6 Conjugate root theorems
- D.7 Descartes' Rule of Signs
- D.8 Fundamental Theorem of Algebra
- D.9 Match polynomials and graphs
- D.10 Factorise sums and differences of cubes
- D.11 Solve equations with sums and differences of cubes
- D.12 Factorise using a quadratic pattern
- D.13 Solve equations using a quadratic pattern
- D.14 Pascal's triangle
- D.15 Pascal's triangle and the Binomial Theorem
- D.16 Binomial Theorem I
- D.17 Binomial Theorem II

## Rational functions

## Simultaneous equations

- F.1 Solve simultaneous equations by graphing
- F.2 Solve simultaneous equations by graphing: word problems
- F.3 Classify simultaneous equations
- F.4 Solve simultaneous equations using substitution
- F.5 Solve simultaneous equations using substitution: word problems
- F.6 Solve simultaneous equations using elimination
- F.7 Solve simultaneous equations using elimination: word problems
- F.8 Solve simultaneous equations in three variables using substitution
- F.9 Solve simultaneous equations in three variables using elimination
- F.10 Determine the number of solutions to simultaneous equations in three variables

## Inequalities and linear programming

## Nonlinear inequalities

## Matrices

- I.1 Matrix vocabulary
- I.2 Matrix operation rules
- I.3 Add and subtract matrices
- I.4 Multiply a matrix by a scalar
- I.5 Linear combinations of matrices
- I.6 Multiply two matrices
- I.7 Simplify matrix expressions
- I.8 Solve matrix equations
- I.9 Determinant of a matrix
- I.10 Is a matrix invertible?
- I.11 Inverse of a 2 x 2 matrix
- I.12 Inverse of a 3 x 3 matrix
- I.13 Identify inverse matrices
- I.14 Solve matrix equations using inverses

## Conic sections

- J.1 Find properties of parabolas
- J.2 Write equations of parabolas in vertex form
- J.3 Graph parabolas
- J.4 Find properties of circles
- J.5 Write equations of circles in standard form
- J.6 Graph circles
- J.7 Find properties of ellipses
- J.8 Find the eccentricity of an ellipse
- J.9 Write equations of ellipses in standard form
- J.10 Find properties of hyperbolas
- J.11 Find the eccentricity of a hyperbola
- J.12 Write equations of hyperbolas in standard form
- J.13 Convert equations of conic sections from general to standard form

## Complex numbers

## Argand plane

## Polar form

## Two-dimensional vectors

- N.1 Find the magnitude of a vector
- N.2 Find the direction angle of a vector
- N.3 Find the component form of a vector
- N.4 Find the component form of a vector from its magnitude and direction angle
- N.5 Find a unit vector
- N.6 Add and subtract vectors
- N.7 Multiply a vector by a scalar
- N.8 Find the magnitude or direction of a vector scalar multiple
- N.9 Find the magnitude and direction of a vector sum
- N.10 Linear combinations of vectors
- N.11 Graph a resultant vector using the triangle method
- N.12 Graph a resultant vector using the parallelogram method

## Three-dimensional vectors

- O.1 Find the magnitude of a three-dimensional vector
- O.2 Find the component form of a three-dimensional vector
- O.3 Find a three-dimensional unit vector
- O.4 Add and subtract three-dimensional vectors
- O.5 Scalar multiples of three-dimensional vectors
- O.6 Linear combinations of three-dimensional vectors

## Sequences and series

- P.1 Find terms of a sequence
- P.2 Find terms of a recursive sequence
- P.3 Identify a sequence as explicit or recursive
- P.4 Find a recursive formula
- P.5 Find recursive and explicit formulas
- P.6 Convert a recursive formula to an explicit formula
- P.7 Convert an explicit formula to a recursive formula
- P.8 Convert between explicit and recursive formulas
- P.9 Introduction to sigma notation
- P.10 Identify arithmetic and geometric series
- P.11 Find the sum of a finite arithmetic or geometric series
- P.12 Introduction to partial sums
- P.13 Partial sums of arithmetic series
- P.14 Partial sums of geometric series
- P.15 Partial sums: mixed review
- P.16 Convergent and divergent geometric series
- P.17 Find the value of an infinite geometric series
- P.18 Write a repeating decimal as a fraction

## Introduction to limits

## Calculate limits

- R.1 Find limits using addition, subtraction and multiplication laws
- R.2 Find limits using the division law
- R.3 Find limits using power and root laws
- R.4 Find limits using limit laws
- R.5 Find limits of polynomials and rational functions
- R.6 Find limits involving factorisation and rationalisation
- R.7 Find limits involving absolute value functions
- R.8 Find limits involving trigonometric functions

## Limits involving infinity

## Continuity

- U.1 Identify graphs of continuous functions
- U.2 Determine continuity using graphs
- U.3 Determine one-sided continuity using graphs
- U.4 Find and analyse points of discontinuity using graphs
- U.5 Determine continuity on an interval using graphs
- U.6 Determine the continuity of a piecewise function at a point
- U.7 Make a piecewise function continuous
- U.8 Intermediate Value Theorem

## Introduction to derivatives

## Derivative rules

## Calculate derivatives

- X.1 Find derivatives of polynomials
- X.2 Find derivatives of rational functions
- X.3 Find derivatives of trigonometric functions I
- X.4 Find derivatives of trigonometric functions II
- X.5 Find derivatives of exponential functions
- X.6 Find derivatives of logarithmic functions
- X.7 Find derivatives of inverse trigonometric functions
- X.8 Find derivatives of radical functions
- X.9 Find derivatives using the product rule I
- X.10 Find derivatives using the product rule II
- X.11 Find derivatives using the quotient rule I
- X.12 Find derivatives using the quotient rule II
- X.13 Find derivatives using the chain rule I
- X.14 Find derivatives using the chain rule II

## Derivative strategies

## Calculate higher derivatives

## Probability

- AA.1 Introduction to probability
- AA.2 Calculate probabilities of events
- AA.3 Combinations and permutations
- AA.4 Find probabilities using combinations and permutations
- AA.5 Find probabilities using two-way frequency tables
- AA.6 Identify independent events
- AA.7 Find conditional probabilities
- AA.8 Independence and conditional probability
- AA.9 Find conditional probabilities using two-way frequency tables
- AA.10 Find probabilities using the addition rule

## Probability distributions

- BB.1 Identify discrete and continuous random variables
- BB.2 Write a discrete probability distribution
- BB.3 Graph a discrete probability distribution
- BB.4 Expected values of random variables
- BB.5 Variance of random variables
- BB.6 Standard deviation of random variables
- BB.7 Write the probability distribution for a game of chance
- BB.8 Expected values for a game of chance
- BB.9 Choose the better bet
- BB.10 Find probabilities using the binomial distribution
- BB.11 Mean, variance and standard deviation of binomial distributions
- BB.12 Find probabilities using the normal distribution
- BB.13 Find z-values
- BB.14 Find values of normal variables
- BB.15 Distributions of sample means
- BB.16 The Central Limit Theorem
- BB.17 Use normal distributions to approximate binomial distributions

## Statistics

- CC.1 Identify biased samples
- CC.2 Variance and standard deviation
- CC.3 Identify an outlier
- CC.4 Identify an outlier and describe the effect of removing it
- CC.5 Outliers in scatter plots
- CC.6 Match correlation coefficients to scatter plots
- CC.7 Calculate correlation coefficients
- CC.8 Find the equation of a regression line
- CC.9 Interpret regression lines
- CC.10 Analyse a regression line of a data set
- CC.11 Analyse a regression line using statistics of a data set