# 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 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!

## Equations

## Inequalities

- B.1 Graph a linear inequality in one variable
- B.2 Graph a linear inequality in the coordinate plane
- B.3 Write inequalities from graphs
- B.4 Write a linear inequality: word problems
- B.5 Solve linear inequalities
- B.6 Graph solutions to linear inequalities
- B.7 Solve absolute value inequalities
- B.8 Graph solutions to absolute value inequalities
- B.9 Graph solutions to quadratic inequalities
- B.10 Solve quadratic inequalities

## Functions

- C.1 Domain and range
- C.2 Identify functions
- C.3 Evaluate functions
- C.4 Find values using function graphs
- C.5 Complete a table for a function graph
- C.6 Find the gradient of a linear function
- C.7 Gradients of parallel and perpendicular lines
- C.8 Graph a linear function
- C.9 Write linear equations in standard form
- C.10 Write linear equations in point-gradient form
- C.11 Write an equation for a parallel or perpendicular line
- C.12 Linear functions over unit intervals

## Simultaneous equations

- D.1 Is (x, y) a solution to the simultaneous equations?
- D.2 Solve simultaneous equations by graphing
- D.3 Solve simultaneous equations by graphing: word problems
- D.4 Find the number of solutions to simultaneous equations
- D.5 Solve simultaneous equations using substitution
- D.6 Solve simultaneous equations using substitution: word problems
- D.7 Solve simultaneous equations using elimination
- D.8 Solve simultaneous equations using elimination: word problems
- D.9 Solve simultaneous equations using any method
- D.10 Solve simultaneous equations using any method: word problems
- D.11 Solve non-linear simultaneous equations

## Factorising

## Quadratic functions

- F.1 Characteristics of quadratic functions
- F.2 Complete a function table: quadratic functions
- F.3 Find a quadratic function
- F.4 Graph a quadratic function
- F.5 Match quadratic functions and graphs
- F.6 Solve a quadratic equation using square roots
- F.7 Solve a quadratic equation using the zero product property
- F.8 Solve a quadratic equation by factorising
- F.9 Complete the square
- F.10 Solve a quadratic equation using the quadratic formula
- F.11 Using the discriminant

## Polynomials

- G.1 Polynomial vocabulary
- G.2 Add and subtract polynomials
- G.3 Multiply polynomials
- G.4 Divide polynomials using long division
- G.5 Solve polynomial equations
- G.6 Write a polynomial from its roots
- G.7 Find the roots of factorised polynomials
- G.8 Rational root theorem
- G.9 Descartes' Rule of Signs
- G.10 Match polynomials and graphs
- G.11 Fundamental Theorem of Algebra
- G.12 Pascal's triangle
- G.13 Pascal's triangle and the Binomial Theorem
- G.14 Binomial Theorem I
- G.15 Binomial Theorem II

## Radical functions and expressions

- H.1 Roots of integers
- H.2 Roots of rational numbers
- H.3 Find roots using a calculator
- H.4 Nth roots
- H.5 Simplify radical expressions with variables I
- H.6 Simplify radical expressions with variables II
- H.7 Multiply radical expressions
- H.8 Divide radical expressions
- H.9 Add and subtract radical expressions
- H.10 Simplify radical expressions using the distributive property
- H.11 Simplify radical expressions using conjugates
- H.12 Domain and range of radical functions
- H.13 Solve radical equations

## Rational functions and expressions

## Function operations

- K.1 Add and subtract functions
- K.2 Multiply functions
- K.3 Divide functions
- K.4 Composition of linear functions: find a value
- K.5 Composition of linear functions: find an equation
- K.6 Composition of linear and quadratic functions: find a value
- K.7 Composition of linear and quadratic functions: find an equation
- K.8 Identify inverse functions
- K.9 Find values of inverse functions from tables
- K.10 Find values of inverse functions from graphs
- K.11 Find inverse functions and relations

## Families of functions

## Logarithms

- M.1 Convert between exponential and logarithmic form: rational bases
- M.2 Evaluate logarithms
- M.3 Change of base formula
- M.4 Identify properties of logarithms
- M.5 Product property of logarithms
- M.6 Quotient property of logarithms
- M.7 Power property of logarithms
- M.8 Properties of logarithms: mixed review
- M.9 Evaluate logarithms: mixed review

## Exponential and logarithmic functions

- N.1 Domain and range of exponential and logarithmic functions
- N.2 Evaluate exponential functions
- N.3 Match exponential functions and graphs
- N.4 Solve exponential equations by factorising
- N.5 Solve exponential equations using common logarithms
- N.6 Solve logarithmic equations I
- N.7 Solve logarithmic equations II
- N.8 Identify linear and exponential functions
- N.9 Exponential functions over unit intervals
- N.10 Describe linear and exponential growth and decay
- N.11 Exponential growth and decay: word problems
- N.12 Compound interest: word problems
- N.13 Continuously compounded interest: word problems

## Parabolas

- O.1 Identify the direction a parabola opens
- O.2 Find the vertex of a parabola
- O.3 Find the focus or directrix of a parabola
- O.4 Find the axis of symmetry of a parabola
- O.5 Write equations of parabolas in vertex form from graphs
- O.6 Write equations of parabolas in vertex form using properties
- O.7 Convert equations of parabolas from general to vertex form
- O.8 Find properties of a parabola from equations in general form
- O.9 Graph parabolas

## Angle measures

## Trigonometry

- Q.1 Pythagoras' Theorem and its converse
- Q.2 Special right triangles
- Q.3 Trigonometric ratios: sin, cos and tan
- Q.4 Trigonometric ratios: csc, sec and cot
- Q.5 Trigonometric ratios in similar right triangles
- Q.6 Find trigonometric ratios using the unit circle
- Q.7 Sin, cos and tan of special angles
- Q.8 Csc, sec and cot of special angles
- Q.9 Find trigonometric functions using a calculator
- Q.10 Inverses of sin, cos and tan
- Q.11 Inverses of csc, sec and cot
- Q.12 Solve trigonometric equations I
- Q.13 Solve trigonometric equations II
- Q.14 Trigonometric ratios: find a side length
- Q.15 Trigonometric ratios: find an angle measure
- Q.16 Solve a right triangle
- Q.17 Law of Sines
- Q.18 Law of Cosines
- Q.19 Solve a triangle
- Q.20 Area of a triangle: sine formula
- Q.21 Area of a triangle: Law of Sines

## Trigonometric functions

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

## Circles

## Circles in the coordinate plane

- U.1 Find the centre of a circle
- U.2 Find the radius or diameter of a circle
- U.3 Write equations of circles in standard form from graphs
- U.4 Write equations of circles in standard form using properties
- U.5 Convert equations of circles from general to standard form
- U.6 Find properties of circles from equations in general form
- U.7 Graph circles

## Sequences and series

- V.1 Classify formulas and sequences
- V.2 Find terms of an arithmetic sequence
- V.3 Find terms of a geometric sequence
- V.4 Find terms of a recursive sequence
- V.5 Evaluate formulas for sequences
- V.6 Write a formula for an arithmetic sequence
- V.7 Write a formula for a geometric sequence
- V.8 Write a formula for a recursive sequence
- V.9 Sequences: mixed review
- V.10 Introduction to sigma notation
- V.11 Identify arithmetic and geometric series
- V.12 Find the sum of a finite arithmetic or geometric series
- V.13 Introduction to partial sums
- V.14 Partial sums of arithmetic series
- V.15 Partial sums of geometric series
- V.16 Partial sums: mixed review
- V.17 Convergent and divergent geometric series
- V.18 Find the value of an infinite geometric series
- V.19 Write a repeating decimal as a fraction

## Probability

- W.1 Introduction to probability
- W.2 Theoretical and experimental probability
- W.3 Compound events: find the number of outcomes
- W.4 Calculate probabilities of events
- W.5 Permutations
- W.6 Counting principle
- W.7 Permutation and combination notation
- W.8 Find probabilities using permutations and combinations
- W.9 Find probabilities using two-way frequency tables
- W.10 Identify independent events
- W.11 Probability of independent and dependent events
- W.12 Geometric probability
- W.13 Find conditional probabilities
- W.14 Independence and conditional probability
- W.15 Find conditional probabilities using two-way frequency tables
- W.16 Find probabilities using the addition rule

## Statistics

## Data and graphs

## Introduction to limits

## Calculate limits

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

## Limits and rational functions

## Continuity

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

## Introduction to derivatives

- DD.1 Average rate of change I
- DD.2 Average rate of change II
- DD.3 Find instantaneous rates of change
- DD.4 Velocity as a rate of change
- DD.5 Find values of derivatives using limits
- DD.6 Find the gradient of a tangent line using limits
- DD.7 Find equations of tangent lines using limits
- DD.8 Power rule I
- DD.9 Power rule II
- DD.10 Find derivatives of polynomials
- DD.11 Find second derivatives of polynomials