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

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