# Grade 11 maths

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

## Numbers

## Consumer maths

## Scientific notation

## Equations

## Inequalities

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

## Functions

## Simultaneous equations

- G.1Is (x, y) a solution to the simultaneous equations?
- G.2Solve simultaneous equations by graphing
- G.3Solve simultaneous equations by graphing: word problems
- G.4Find the number of solutions to simultaneous equations
- G.5Solve simultaneous equations using substitution
- G.6Solve simultaneous equations using substitution: word problems
- G.7Solve simultaneous equations using elimination
- G.8Solve simultaneous equations using elimination: word problems
- G.9Solve simultaneous equations using any method
- G.10Solve simultaneous equations using any method: word problems
- G.11Solve simultaneous equations in three variables using substitution
- G.12Solve simultaneous equations in three variables using elimination
- G.13Determine the number of solutions to a system of equations in three variables
- G.14Solve non-linear simultaneous equations

## Inequalities and linear programming

## Complex numbers

## Argand plane

## Factorising

## Quadratic functions

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

## Parabolas

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

## Polynomials

- N.1Polynomial vocabulary
- N.2Add and subtract polynomials
- N.3Multiply polynomials
- N.4Divide polynomials using long division
- N.5Divide polynomials using synthetic division
- N.6Evaluate polynomials using synthetic division
- N.7Solve polynomial equations
- N.8Write a polynomial from its roots
- N.9Find the roots of factorised polynomials
- N.10Rational root theorem
- N.11Complex conjugate theorem
- N.12Conjugate root theorems
- N.13Match polynomials and graphs
- N.14Pascal's triangle
- N.15Pascal's triangle and the Binomial Theorem
- N.16Binomial Theorem I
- N.17Binomial Theorem II

## Radical functions and expressions

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

## Rational exponents

## Rational functions and expressions

## Function operations

- R.1Add and subtract functions
- R.2Multiply functions
- R.3Divide functions
- R.4Composition of linear functions
- R.5Composition of linear and quadratic functions
- R.6Identify inverse functions
- R.7Find values of inverse functions from tables
- R.8Find values of inverse functions from graphs
- R.9Find inverse functions and relations

## Logarithms

- S.1Convert between exponential and logarithmic form: rational bases
- S.2Convert between natural exponential and logarithmic form
- S.3Convert between exponential and logarithmic form: all bases
- S.4Evaluate logarithms
- S.5Evaluate natural logarithms
- S.6Change of base formula
- S.7Identify properties of logarithms
- S.8Product property of logarithms
- S.9Quotient property of logarithms
- S.10Power property of logarithms
- S.11Properties of logarithms: mixed review
- S.12Evaluate logarithms: mixed review

## Exponential and logarithmic functions

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

## 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

## Similarity

- Z.1Identify similar figures
- Z.2Similarity ratios
- Z.3Similarity statements
- Z.4Side lengths and angle measures in similar figures
- Z.5Similar triangles and indirect measurement
- Z.6Perimeters of similar figures
- Z.7Similarity rules for triangles
- Z.8Similar triangles and similarity transformations
- Z.9Similarity of circles
- Z.10Triangle Proportionality Theorem
- Z.11Areas of similar figures

## Two-dimensional figures

- AA.1Polygon vocabulary
- AA.2Perimeter
- AA.3Area of triangles and quadrilaterals
- AA.4Area and perimeter in the coordinate plane I
- AA.5Area and perimeter in the coordinate plane II
- AA.6Area and circumference of circles
- AA.7Area of compound figures
- AA.8Area between two shapes
- AA.9Area and perimeter of similar figures

## Circles

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

## Circles in the coordinate plane

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

## Surface area and volume

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

## 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.17Expected values of random variables
- GG.18Write the probability distribution for a game of chance
- GG.19Expected values for a game of chance
- GG.20Choose the better bet
- GG.21Find probabilities using the binomial distribution

## Statistics

## Data and graphs

## Constructions

- JJ.1Construct the midpoint or perpendicular bisector of a segment
- JJ.2Construct an angle bisector
- JJ.3Construct a congruent angle
- JJ.4Construct a perpendicular line
- JJ.5Construct parallel lines
- JJ.6Construct an equilateral triangle or regular hexagon
- JJ.7Construct a square
- JJ.8Construct a tangent line to a circle
- JJ.9Construct the circumcenter or incenter of a triangle
- JJ.10Construct the inscribed or circumscribed circle of a triangle
- JJ.11Construct the centroid or orthocenter of a triangle