# Year 12 maths

Here is a list of all of the maths skills students learn in year 12! 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.4Linear functions over unit intervals
- A.5Evaluate functions
- A.6Find values using function graphs
- A.7Complete a table for a function graph
- A.8Add, subtract, multiply and divide functions
- A.9Composition of functions
- A.10Identify inverse functions
- A.11Find values of inverse functions from tables
- A.12Find values of inverse functions from graphs
- A.13Find 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.2Divide polynomials using synthetic division
- D.3Evaluate polynomials using synthetic division
- D.4Write a polynomial from its roots
- D.5Find the roots of factorised polynomials
- D.6Rational root theorem
- D.7Complex conjugate theorem
- D.8Conjugate root theorems
- D.9Descartes' Rule of Signs
- D.10Fundamental Theorem of Algebra
- D.11Match polynomials and graphs
- D.12Factorise sums and differences of cubes
- D.13Solve equations with sums and differences of cubes
- D.14Factorise using a quadratic pattern
- D.15Solve equations using a quadratic pattern
- D.16Pascal's triangle
- D.17Pascal's triangle and the Binomial Theorem
- D.18Binomial Theorem I
- D.19Binomial Theorem II

## Rational functions

## Exponential and logarithmic functions

- F.1Domain and range of exponential and logarithmic functions
- F.2Convert between exponential and logarithmic form
- F.3Evaluate logarithms
- F.4Change of base formula
- F.5Product property of logarithms
- F.6Quotient property of logarithms
- F.7Power property of logarithms
- F.8Evaluate logarithms using properties
- F.9Solve exponential equations by factorising
- F.10Solve exponential equations using logarithms
- F.11Solve logarithmic equations with one logarithm
- F.12Solve logarithmic equations with multiple logarithms
- F.13Identify linear and exponential functions
- F.14Exponential functions over unit intervals
- F.15Describe linear and exponential growth and decay
- F.16Exponential growth and decay: word problems
- F.17Compound interest: word problems

## Radical functions

## Roots and rational exponents

## Simultaneous equations

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

## Inequalities and linear programming

## Matrices

- K.1Matrix vocabulary
- K.2Matrix operation rules
- K.3Add and subtract matrices
- K.4Multiply a matrix by a scalar
- K.5Linear combinations of matrices
- K.6Multiply two matrices
- K.7Simplify matrix expressions
- K.8Solve matrix equations
- K.9Determinant of a matrix
- K.10Is a matrix invertible?
- K.11Inverse of a matrix
- K.12Identify inverse matrices
- K.13Solve matrix equations using inverses
- K.14Identify transformation matrices
- K.15Transformation matrices: write the vertex matrix
- K.16Transformation matrices: graph the image

## Trigonometry

- L.1Convert between radians and degrees
- L.2Radians and arc length
- L.3Quadrants
- L.4Coterminal and reference angles
- L.5Find trigonometric ratios using right triangles
- L.6Find trigonometric ratios using the unit circle
- L.7Find trigonometric ratios using reference angles
- L.8Inverses of trigonometric functions
- L.9Solve trigonometric equations
- L.10Trigonometric ratios: find a side length
- L.11Trigonometric ratios: find an angle measure
- L.12Solve a right triangle
- L.13Law of Sines
- L.14Law of Cosines
- L.15Solve a triangle
- L.16Area of a triangle: sine formula
- L.17Area of a triangle: Heron's formula

## Trigonometric functions

- M.1Find properties of sine functions
- M.2Write equations of sine functions from graphs
- M.3Write equations of sine functions using properties
- M.4Graph sine functions
- M.5Find properties of cosine functions
- M.6Write equations of cosine functions from graphs
- M.7Write equations of cosine functions using properties
- M.8Graph cosine functions
- M.9Graph sine and cosine functions

## Trigonometric identities

## Conic sections

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

## Complex numbers

## Complex plane

## Polar form

## Two-dimensional vectors

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

## Three-dimensional vectors

## Sequences and series

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

## Probability

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

## Probability distributions

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

## Statistics

- X.1Identify biased samples
- X.2Variance and standard deviation
- X.3Identify an outlier
- X.4Identify an outlier and describe the effect of removing it
- X.5Outliers in scatter plots
- X.6Match correlation coefficients to scatter plots
- X.7Calculate correlation coefficients
- X.8Find the equation of a regression line
- X.9Interpret regression lines
- X.10Analyse a regression line of a data set
- X.11Analyse a regression line using statistics of a data set
- X.12Find confidence intervals for population means
- X.13Find confidence intervals for population proportions
- X.14Interpret confidence intervals for population means

## Introduction to derivatives

## Calculate derivatives

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