# 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 view a sample question. 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.1Domain and range
- A.2Identify functions
- A.3Linear functions
- A.4Evaluate functions
- A.5Find values using function graphs
- A.6Complete a table for a function graph
- A.7Add, subtract, multiply and divide functions
- A.8Composition of functions
- A.9Identify inverse functions
- A.10Find values of inverse functions from tables
- A.11Find values of inverse functions from graphs
- A.12Find inverse functions and relations

## Families of functions

## Quadratic functions

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

## Polynomials

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

## Rational functions

## Simultaneous equations

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

## Inequalities and linear programming

## Nonlinear inequalities

## Matrices

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

## Conic sections

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

## Complex numbers

## Argand plane

## Polar form

## Two-dimensional vectors

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

## Three-dimensional vectors

## Sequences and series

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

## Introduction to limits

## Calculate limits

## Limits involving infinity

## Limits and rational functions

## Continuity

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

## Introduction to derivatives

## Calculate derivatives

- W.1Sum and difference rules
- W.2Product rule
- W.3Quotient rule
- W.4Power rule I
- W.5Power rule II
- W.6Find derivatives of polynomials
- W.7Find derivatives of rational functions
- W.8Find derivatives of trigonometric functions
- W.9Chain rule
- W.10Find derivatives using implicit differentiation
- W.11Find tangent lines using implicit differentiation
- W.12Find derivatives of exponential functions
- W.13Find derivatives of logarithmic functions
- W.14Find derivatives using the product rule I
- W.15Find derivatives using the product rule II
- W.16Find derivatives using the quotient rule I
- W.17Find derivatives using the quotient rule II

## Probability

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

## Probability distributions

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

## Statistics

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