###### January 21, 2014

### 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