# Year 11 maths

Here is a list of all of the maths skills students learn in year 11! 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!

## Consumer maths

## Scientific notation

## Equations and inequalities

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

## Simultaneous equations

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

## Inequalities and linear programming

## Coordinate plane

## Functions

## Direct variation

## 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.8Properties of matrices
- I.9Solve matrix equations
- I.10Determinant of a matrix
- I.11Is a matrix invertible?
- I.12Inverse of a matrix
- I.13Identify inverse matrices
- I.14Solve matrix equations using inverses

## Complex numbers

## Factorising

## Quadratic functions

- L.1Characteristics of quadratic functions
- L.2Complete a function table: quadratic functions
- L.3Transformations of quadratic functions
- L.4Find a quadratic function
- L.5Graph a quadratic function
- L.6Match quadratic functions and graphs
- L.7Solve a quadratic equation using square roots
- L.8Solve a quadratic equation using the zero product property
- L.9Solve a quadratic equation by factorising
- L.10Complete the square
- L.11Solve a quadratic equation using the quadratic formula
- L.12Using the discriminant

## Polynomials

- M.1Polynomial vocabulary
- M.2Add and subtract polynomials
- M.3Multiply polynomials
- M.4Divide polynomials using long division
- M.5Divide polynomials using synthetic division
- M.6Evaluate polynomials using synthetic division
- M.7Write a polynomial from its roots
- M.8Find the roots of factorised polynomials
- M.9Conjugate roots
- M.10Descartes' Rule of Signs
- M.11Fundamental Theorem of Algebra
- M.12Match polynomials and graphs

## Radical functions and expressions

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

## Rational exponents

## Rational functions and expressions

## Logarithms

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

## Exponential and logarithmic functions

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

## Parabolas

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

## Hyperbolas

- T.1Find the centre of a hyperbola
- T.2Find the vertices of a hyperbola
- T.3Find the length of the transverse or conjugate axes of a hyperbola
- T.4Find the equations for the asymptotes of a hyperbola
- T.5Find the foci of a hyperbola
- T.6Write equations of hyperbolas in standard form from graphs
- T.7Write equations of hyperbolas in standard form using properties
- T.8Convert equations of hyperbolas from general to standard form
- T.9Find properties of hyperbolas from equations in general form

## Angle measures

## Trigonometry

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

## Trigonometric functions

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

## Trigonometric identities

## Area and perimeter

## Surface area and volume

- Z.1Introduction to surface area and volume
- Z.2Surface area of prisms and cylinders
- Z.3Surface area of pyramids and cones
- Z.4Volume of prisms and cylinders
- Z.5Volume of pyramids and cones
- Z.6Surface area and volume of spheres
- Z.7Introduction to similar solids
- Z.8Surface area and volume of similar solids
- Z.9Surface area and volume review

## Quadrilaterals

## Similarity

## Circles

- CC.1Parts of a circle
- CC.2Central angles
- CC.3Arc measure and arc length
- CC.4Area of sectors
- CC.5Circle measurements: mixed review
- CC.6Arcs and chords
- CC.7Tangent lines
- CC.8Perimeter of polygons with an inscribed circle
- CC.9Inscribed angles
- CC.10Angles in inscribed right triangles
- CC.11Angles in inscribed quadrilaterals

## Circles in the coordinate plane

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

## Logic

## Sequences and series

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

## Probability

- GG.1Introduction to probability
- GG.2Theoretical and experimental probability
- GG.3Compound events: find the number of outcomes
- GG.4Calculate probabilities of events
- GG.5Permutations
- GG.6Counting principle
- GG.7Permutation and combination notation
- GG.8Find probabilities using permutations and combinations
- GG.9Find probabilities using two-way frequency tables
- GG.10Identify independent events
- GG.11Probability of independent and dependent events
- GG.12Geometric probability
- GG.13Find conditional probabilities
- GG.14Independence and conditional probability
- GG.15Find conditional probabilities using two-way frequency tables
- GG.16Find probabilities using the addition rule
- GG.17Find probabilities using the normal distribution

## Statistics

## Introduction to limits

## Calculate limits

## Limits and rational functions

## Continuity

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

## Introduction to derivatives

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