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# Maths: Year 11 topics

See below for the list of maths topics you can expect  your child to learn in year 11:

Numbers

• Prime or composite
• Identify rational and irrational numbers
• Compare and order rational numbers
• Square roots
• Cube roots
• Add, subtract, multiply and divide rational numbers
• A.7 Order of operations with rational numbers

Exponents

• Exponents review
• Multiplication and division with exponents
• Power rule
• Simplify expressions involving exponents
• Convert between standard and scientific notation
• Multiply, divide and compare numbers written in scientific notation
• Coordinate graphs
• Coordinate graph review
• Midpoints
• Distance between two points

Solve equations

• Solve one- and two-step linear equations
• Solve advanced linear equations
• Solve equations with variables on both sides
• Identities and equations with no solutions
• Solve linear equations: word problems
• Solve linear equations: mixed review

Single-variable inequalities

• Solve one-step linear inequalities
• Graph solutions to one-step linear inequalities
• Solve two-step linear inequalities
• Graph solutions to two-step linear inequalities
• Solve advanced linear inequalities
• Graph solutions to advanced linear inequalities
• Graph compound inequalities
• Write compound inequalities from graphs
• Solve compound inequalities
• Graph solutions to compound inequalities

Relations and functions

• Relations: convert between tables, graphs, mappings and lists of points
• Domain and range of relations
• Identify independent and dependent variables
• Identify functions
• Complete a function table
• Evaluate function rules
• Graph a function
• Write a function rule: word problems
• Find points on a function graph
• Write a rule for a function table

Direct and inverse variation

• Identify proportional relationships
• Find the constant of variation
• Graph a proportional relationship
• Write direct variation equations
• Write and solve direct variation equations
• Write inverse variation equations
• Write and solve inverse variation equations
• Identify direct variation and inverse variation

Linear functions

• Identify linear functions
• Find the slope of a graph
• Find slope from two points
• Slope-intercept form: find slope and y-intercept
• Slope-intercept form: graph an equation
• Slope-intercept form: write an equation from a graph
• Slope-intercept form: write an equation
• Linear function word problems
• Write equations in standard form
• Standard form: find x- and y-intercepts
• Standard form: graph an equation
• Equations of horizontal and vertical lines
• Graph a horizontal or vertical line
• Point-slope form: graph an equation
• Point-slope form: write an equation from a graph
• Point-slope form: write an equation
• Slopes of parallel and perpendicular lines
• Write an equation for a parallel or perpendicular line

Simultaneous equations

• Is (x, y) a solution to the simultaneous equations?
• Solve simultaneous equations by graphing
• Solve simultaneous equations by graphing: word problems
• Find the number of solutions to simultaneous equations by graphing
• Find the number of solutions to simultaneous equations
• Solve simultaneous equations using substitution
• Solve simultaneous equations using substitution: word problems
• Solve simultaneous equations using elimination
• Solve simultaneous equations using elimination: word problems

Exponential functions

• Evaluate an exponential function
• Match exponential functions and graphs
• Exponential growth and decay: word problems

Monomials

• Identify monomials
• Multiply monomials
• Divide monomials
• Multiply and divide monomials
• Powers of monomials

Polynomials

• Polynomial vocabulary
• Model polynomials with algebra tiles
• Add and subtract polynomials using algebra tiles
• Add and subtract polynomials
• Add polynomials to find perimeter
• Multiply a polynomial by a monomial
• Multiply two polynomials using algebra tiles
• Multiply two binomials
• Multiply two binomials: special cases
• Multiply polynomials

Factorising

• GCF of monomials
• Factorise out a monomial
• Factorise quadratics with leading coefficient 1
• Factorise quadratics with other leading coefficients
• Factorise quadratics: special cases
• Factorise by grouping
• Factorise polynomials

Quadratic equations

• Characteristics of quadratic functions
• Complete a function table: quadratic functions
• Solve a quadratic equation using square roots
• Solve an equation using the zero product property
• Solve a quadratic equation by factorising
• Complete the square
• Solve a quadratic equation by completing the square
• Solve a quadratic equation using the quadratic formula

Functions: linear, quadratic, exponential

• Identify linear, quadratic and exponential functions from graphs
• Identify linear, quadratic and exponential functions from tables
• Write linear, quadratic and exponential functions

Families of functions

• Translations of functions
• Reflections of functions
• Dilations of functions
• Transformations of functions

Radical expressions

• Simplify radical expressions
• Simplify radical expressions by rationalising the denominator
• Multiply radical expressions
• Add and subtract radical expressions
• Simplify radical expressions using the distributive property
• Simplify radical expressions: mixed review

Rational exponents

• Evaluate rational exponents
• Multiplication with rational exponents
• Division with rational exponents
• Power rule with rational exponents
• Simplify expressions involving rational exponents I
• Simplify expressions involving rational exponents II

Rational functions and expressions

• Rational functions: asymptotes and excluded values
• Simplify complex fractions
• Simplify rational expressions
• Multiply and divide rational expressions
• Divide polynomials
• Add and subtract rational expressions
• Solve rational equations

Introduction to triangles

• Classify triangles
• Triangle Angle-Sum Theorem
• Exterior Angle Theorem
• Two-dimensional figures
• Polygon vocabulary
• Interior angles of polygons
• Exterior angles of polygons
• Review: interior and exterior angles of polygons

Three-dimensional figures

• Three-dimensional figure vocabulary
• Parts of three-dimensional figures
• Nets and drawings of three-dimensional figures
• Cross-sections of three-dimensional figures
• Solids of revolution

Introduction to congruent figures

• Congruence statements and corresponding parts
• Solve problems involving corresponding parts
• Identify congruent figures

Congruent triangles

• SSS and SAS Theorems
• ASA and AAS Theorems
• SSS, SAS, ASA and AAS Theorems
• Congruency in isosceles and equilateral triangles
• Hypotenuse-Leg Theorem

Triangles

• Midsegments of triangles
• Triangles and bisectors
• Identify medians, altitudes, angle bisectors and perpendicular bisectors
• Angle-side relationships in triangles
• Triangle Inequality Theorem

Quadrilaterals

• Z.1 Classify quadrilaterals
• Z.2 Properties of parallelograms
• Z.3 Proving a quadrilateral is a parallelogram
• Z.4 Properties of rhombuses
• Z.5 Properties of squares and rectangles
• Z.6 Properties of trapezoids
• Z.7 Properties of kites
• Z.8 Review: properties of quadrilaterals

Transformations

• Translations: graph the image
• Translations: find the coordinates
• Translations: write the rule
• Reflections: graph the image
• Reflections: find the coordinates
• Rotate polygons about a point
• Rotations: graph the image
• Rotations: find the coordinates
• Classify congruence transformations
• Compositions of congruence transformations: graph the image
• Transformations that carry a polygon onto itself
• Congruence transformations: mixed review
• Dilations: graph the image
• Dilations: find the coordinates
• Dilations: scale factor and classification
• Dilations and parallel lines

Similarity

• Identify similar figures
• Similarity ratios
• Similarity statements
• Side lengths and angle measures in similar figures
• Similar triangles and indirect measurement
• Perimeters of similar figures
• Similarity rules for triangles
• Similar triangles and similarity transformations
• Areas of similar figures

Right triangles

• Pythagorean Theorem
• Converse of the Pythagorean theorem
• Pythagorean Inequality Theorems
• Special right triangles

Trigonometry

• Trigonometric ratios: sin, cos and tan
• Trigonometric ratios: csc, sec and cot
• Find trigonometric functions of special angles
• Find trigonometric functions using a calculator
• Inverses of trigonometric functions
• Trigonometric ratios: find a side length
• Trigonometric ratios: find an angle measure
• Solve a right triangle

Area and perimeter

• Perimeter
• Area of triangles and quadrilaterals
• Area and perimeter in the coordinate plane I
• Area and perimeter in the coordinate plane II
• Area and circumference of circles
• Area of compound figures
• Area between two shapes
• Area and perimeter of similar figures

Circles

• Parts of a circle
• Central angles
• Arc measure and arc length
• Area of sectors
• Circle measurements: mixed review
• Arcs and chords
• Tangent lines
• Perimeter of polygons with an inscribed circle
• Inscribed angles
• Angles in inscribed right triangles
• Angles in inscribed quadrilaterals

Surface area and volume

• Introduction to surface area and volume
• Surface area of prisms and cylinders
• Surface area of pyramids and cones
• Volume of prisms and cylinders
• Volume of pyramids and cones
• Surface area and volume of spheres
• Introduction to similar solids
• Surface area and volume of similar solids
• Surface area and volume review

Problem solving

• Consecutive integer problems
• Rate of travel: word problems
• Weighted averages: word problems

Measurement

• Convert rates and measurements
• Metric mixed units
• Imperial mixed units
• Convert between metric and imperial units
• Precision
• Greatest possible error
• Minimum and maximum area and volume
• Percent error
• Percent error: area and volume

Probability

• Theoretical probability
• Experimental probability
• Compound events: find the number of outcomes
• Identify independent and dependent events
• Probability of independent and dependent events
• Geometric probability

Statistics

• Mean, median, mode and range
• Quartiles
• Mean absolute deviation
• Variance and standard deviation
• Identifying biased samples
• Data and graphs
• Interpret histograms
• Create histograms
• Interpret stem-and-leaf plots
• Interpret box-and-whisker plots
• Interpret a scatter plot
• Scatter plots: line of best fit

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