# Year 13 maths

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

## Exponential and logarithmic functions

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

## 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

## Trigonometry

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

## Trigonometric functions

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

## Trigonometric identities

## Conic sections

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

## Complex numbers

## Complex plane

## Polar form

## Sequences and series

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

## Probability

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

## Probability distributions

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

## Statistics

- R.1 Identify biased samples
- R.2 Variance and standard deviation
- R.3 Identify an outlier
- R.4 Identify an outlier and describe the effect of removing it
- R.5 Outliers in scatter plots
- R.6 Match correlation coefficients to scatter plots
- R.7 Calculate correlation coefficients
- R.8 Find the equation of a regression line
- R.9 Interpret regression lines
- R.10 Analyse a regression line of a data set
- R.11 Analyse a regression line using statistics of a data set
- R.12 Find confidence intervals for population means
- R.13 Find confidence intervals for population proportions
- R.14 Interpret confidence intervals for population means
- R.15 Experiment design

## Introduction to limits

## Calculate limits

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

## Limits involving infinity

## Rational functions

## Continuity

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

## Introduction to derivatives

## Derivative rules

## Calculate derivatives

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