reception

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Year 8

• Identifying Relations
• Identifying Functions
• Identifying if given relations are functions
• Defining dependent and independent variables
• Identifying domain of a function
• Identifying range of a function
• Types of functions
• Identifying linear functions
• Graphing linear functions
• Completing table of linear functions
• Identifying increasing functions
• Identifying decreasing functions
• Defining sets
• Cardinality of sets
• Types of sets
• Illustrates union of events
• Illustrates intersection of events
• Illustrates mutually exclusive events
• Properties of complementary sets
• Computing probability of mutually exclusive events
• Definition of terms (point, line, plane)
• Describing a point

Year 9

Year 10

• Identifying different types of domains
• Defining Polynomial Functions
• Identifying domain of polynomial functions
• Identifying range of polynomial functions
• Evaluating Polynomial Functions
• Graphing Polynomial Functions
• Solving Problems involving Polynomial Functions
• Defining Hyperbolic Functions
• Identifying Domain of Hyperbolic Functions
• Identifying Range of Hyperbolic Functions
• Evaluating Hyperbolic Functions
• Graphing Hyperbolic Functions
• Solving Problems involving Hyperbolic Functions
• Classifying polynomials
• Addition of Monomials
• Subtraction of Monomials
• Multiplying a monomial and a binomial
• Determining roots of polynomials using Synthetic Division
• Defining functions: mixed review
• Identifying Domain of a function
• Find the domain of the function from the graph
• Find the domain of the function from the table
• Find the domain of the function from the set of ordered pairs
• Identifying Range of a function
• Find the Range of the function from the graph
• Find the Range of the function from the table
• Find the Range of the function from the set of ordered pairs
• Domain and range of function from the table
• Domain and range of function from the graph
• Find values using function equations
• Evaluation of functions
• Operations on functions addition
• Operations on functions multiplication
• Operations on functions division
• Composition of Functions
• Identify types of functions from graphs
• Identify types of functions from equations
• Find the Range of the function from the set of ordered pairs
• Domain and range of function from the table
• Domain and range of function from the graph
• Domain and range of function from the set of ordered pairs
• Find values using function graphs
• Operations on functions subtraction
• Identify linear, affine, quadratic, and cubic functions from graphs
• Identify affine, quadratic, rational and radical functions from graphs
• Identify sine, cosnie, and absolute value functions from graphs
• Identify linear, affine, quadratic, and cubic functions from tables
• Identify linear, quadratic, rational and radical functions from tables
• Identify sine, cosnie, and absolute value functions from tables
• Write linear, affine, quadratic, and cubic functions
• Write linear, quadratic, rational and radical functions
• Write sine, cosnie, and absolute value functions
• Increasing functions
• Decrease functions
• Constante functions
• Identify increase, Increase and constant intervals (Refrence function)
• Finding the Maximum Values of a Function
• Symmetric Functions
• Even functions
• Odd function
• Periodic function
• Identify quadratic function from the equation
• Identify quadratic function from the graph
• Identify quadratic function from the table
• Complete a function table from the equation of quadratic function
• Complete a function table from the graph of quadratic function
• Write quadratic function to solve word problems
• Solving Problems involving quadratic Functions
• Compare quadratic function: graphs, tables and equations
• Write equations in standard form from tables, grahs and mappings and lists of points
• Evaluating quadratic Functions
• Quadratic function over unit intervals
• Identify increase, Increase and constant intervals
• Range of quadratic function
• Identify rational function from the equation
• Identify rational function from the graph
• Identify rational function from the table
• Identify quadratic function from set of ordered pairss
• Domain of rational functions
• Range of rational function
• Complete a function table from the equation of rational function
• Complete a function table from the graph of rational function
• Write rational function to solve word problems
• Solving Problems involving rational Functions
• Compare rational function: graphs, tables and equations
• Write equations of rational function in standard form from tables, grahs and mappings and lists of points
• Evaluating rational Functions
• Rational function over unit intervals
• Identify increase, Increase and constant intervals of rational Function
• Rational function Properties
• Identify cubic function from the equation
• Identify cubic function from the graph
• Identify cubic function from the table
• Identify cubic function from set of ordered pairs
• Domain of cubic function
• Range of cubic function
• Complete a function table from the equation of cubic function
• Complete a function table from the graph of cubic function
• Write cubic function to solve word problems
• Solving Problems involving cubic Functions
• Compare cubic function: graphs, tables and equations
• Write equations of cubic function in standard form from tables, grahs and mappings and lists of points
• Evaluating cubic Functions
• Cubic function over unit intervals
• Identify increase, Increase and constant intervals of cubic function
• Cubic function Properties
• Identify radical function from the equation
• Identify radical function from the graph
• Identify radical function from the table
• Identify radical function from set of ordered pairs
• Domain of radical function
• Range of radical function
• Complete a function table from the equation of radical function
• Write radical function to solve word problems
• Solving Problems involving radical Functions
• Write equations in standard form from tables, grahs and mappings and lists of points
• Evaluating radical Functions
• Radical function over unit intervals
• Identify increase, Increase and constant intervals of radical function
• Radical function Properties
• Write radical function to solve word problems
• Solving Problems involving radical Functions
• Compare radical function: graphs, tables and equations
• Solving Problems involving cosine Functions
• Compare cosine function: graphs, tables and equations
• Write equations in standard form from tables, grahs and mappings and lists of points
• Identify absolute value function from the equation
• Identify absolute value function from the graph
• Identify absolute value function from the table
• Identify absolute value function from set of ordered pairs
• Domain of absolute value function
• Range of absolute value function
• Complete a function table from the equation of absolute value function
• Complete a function table from the graph of absolute value function
• Write absolute value function to solve word problems
• Solving Problems involving absolute value Functions
• Compare absolute value function: graphs, tables and equations
• Write equations in standard form from tables, grahs and mappings and lists of points
• Evaluating absolute value Functions
• Absolute value function over unit intervals
• Identify increase, Increase and constant intervals of absolute value function
• Absolute value function Properties
• Identify sine function from the equation
• Identify sine function from the table
• Identify sine function from the table
• Identify sine function from set of ordered pairs
• Domain of sine function
• Range of sine function
• Complete a function table from the equation of quadratic function
• Complete a function table from the graph of sine function
• Write sine function to solve word problems
• Solving Problems involving sine Functions
• Compare sine function: graphs, tables and equations
• Write equations of sine function in standard form from tables, grahs and mappings and lists of points
• Evaluating sine Functions
• Sine function over unit intervals
• Identify increase, Increase and constant intervals of sine function
• Sine function Properties
• Identify cosine functions from the equation
• Identify cosine function from the graph
• Identify cosine function from the table
• Identify cosine function from set of ordered pairs
• Domain of cosine function
• Range of cosine function
• Complete a function table from the equation of cosine function
• Complete a function table from the graph of cosine function
• Write cosine function to solve word problems
• Evaluating Cosine Functions
• Cosine function over unit intervals
• Identify Decrease, Increase and constant intervals
• Cosine function Properties
• Graph sine functions
• Graph cosine functions
• Graph sine and cosine functions
• Writing equation of a parabola in vertex form
• Solving problems involving parabola
• Determining characteristics of a hyperbola
• Writing equation of a hyperbola in standard form
• Writing equation of a hyperbola in vertex form
• Solving problems involving hyperbola
• Determining characteristics of an ellipse
• Writing equation of an ellipse in standard form
• Writing equation of an ellipse in vertex form
• Solving problems involving ellipse
• Determining characteristics of a circle
• Writing equation of a circle in standard form
• Writing equation of a circle in vertex form
• Solving problems involving circle

Year 11

• Function types: mixed review
• Use Function Notation to evaluate functions
• The average rate of change
• Find the Rate of Change over a given interval
• The direction of variation of reference functions
• The table of variation of reference functions
• The sing of reference functions
• Graphing functions using reference functions
• Identify Piecewise-defined function from the equation
• Identify Piecewise-defined function from the graph
• Identify Piecewise-defined function from the table
• Identify Piecewise-defined function from set of ordered pairs
• Domain of Piecewise-defined function
• Complete a function table from the equation of Piecewise-defined function
• Complete a function table from the graph of Piecewise-defined function
• Graph Piecewise-defined functions
• Create and use a Piecewise-defined function from real world data
• Create a Piecewise-defined function from a graph
• Step Functions
• Reference function: mixed review (domains, ranges, graphs, function properties)
• Range Of Piecewise-Defined Function
• Polynomial functions: mixed review (domains, ranges, graphs, function properties)
• Degree of a polynomial functions: mixed review
• Polynomial functions equality
• Add polynomial functions
• Subtract polynomial functions
• Multiply polynomial functions
• Mixed polynomial functions operations
• Mixed polynomial functions operations: word problems
• Simplify polynomial functions
• Composition of polynomial functions
• Identify the root of a polynomial functions
• Find the root of a polynomial functions
• Graph the root of a polynomial functions
• Root of a polynomial functions: word problems
• Factorizing polynomial functions using the factor (x-a)
• Factorizing polynomial functions using roots
• Functions Equality
• Add Function To Real Number (ƒ + k)
• Add Tow Functions (ƒ + g)
• Multiply Function By Real Number (λƒ)
• Multiply Tow Functions (ƒ x g)
• Division Of Tow Functions (ƒ/g)
• Mixed Functions Operations
• Mixed Functions Operations: Word Problems
• Identify The Composition Of Functions
• Find The Composition Of Functions
• Composition Of Functions: Word Problems
• Direction Of Changing Of Function + Real Number (ƒ + k)
• Direct Variation
• Inverse Variation
• Mixed Variation Functions
• Variation Function (ƒ + k)
• Understanding Limit Notation
• Use The Formal Definition Of Limit
• Understanding The Limits Of Functions
• Understanding Left-Hand Limits And Right-Hand Limits
• Learn That A Limit Can Fail To Exist Because Of Unbounded Behavior
• Limits And Oscillating Behavior
• Evaluating Limits Using The Limit Notation ( Estimate A Limit Using A Numerical Approach)
• Find Limits Using The Graphs (Estimate A Limit Using A Graphical Approach)
• Find One-Sided Limits Using Graphs
• One-Sided Limits
• Determine Infinite Limits From The Left
• Determine Infinite Limits From The Right
• Finite And Infinite Limits
• Finite Limit And Infinite Limit At A Real Number
• Finite Limit And Infinite Limit At Infinity
• Evaluate Basic Limits
• Limit Of A Polynomials
• Limit Of A Rational Function
• Limit Of The Sum Of Two Function
• Limit Of The Product Of Two Function
• Limit Of The Ratio Of Two Function
• Limits Of [ F(X) ]2
• Limits Of | F(X) |
• Limits Of √F(X)
• Evaluate Limits Of Function (Limits Of Sum , Product And Composition Of Function)
• Geometric Interpretation Of The Limits
• Understanding The Asymptote
• The Vertical Asymptote
• The Horizontal Asymptote
• The Oblique Asymptote
• The Vertical, Horizontal And Oblique Asymptote
• Graph The Asymptote
• Prove That The Line Is The Asymptote To The Curve Of The Function
• Find The Asymptote To The Curve Of The Function
• The Relative Position Of The Asymptote To The Curve Of The Function
• Use Vertical Asymptotes To Find Limits (Use Vertical Asymptotes To Help In Determining Limits)
• Understanding Continuity With Functions Graphs
• Identify The Graphs Of Continuous Functions
• Determine Continuity Using Graphs
• Determine One-Sided Continuity Using Graphs
• Continuity On A Closed Interval
• Continuity At A Point
• Properties Of Continuity
• Continuity Theorem
• Properties Of Continuous Functions
• Understanding Average Rate Of Change
• The Average Rate Of Change Formula
• Find The Average Rate Of Change Of A Function
• Find The Average Rate Of Change From The Graph
• Find The Average Rate Of Change From Equation
• Find Instantaneous Rates Of Change
• Velocity As A Rate Of Change
• The Real Limit Of Function When X = 0
• Identify The Derivative Function Of The Function Ƒ
• Find The Derivative Function Of The Function Ƒ
• Derivatives Of Reference Functions
• The Domain Of Derivability
• The Relationship Between A Function And Its Derived Function
• Geometric Interpretation Of The Derived Number
• The Tangent To The Function Graph At A Point
• The Tangent Equation
• The Tangent Slope
• The Tangent To A Parabola
• The Tangent To A Hyperbola
• The Tangent To A Parabola Or A Hyperbola
• Introduction To Linear Approximations
• Determine The Linear Approximation
• Approximation Of A Function Around X = 0
• Approximation Of A Function Around X = A (A Is A Real Number)
• Linearization Of Radical Functions
• Linearization Of Polynomial Functions
• Linearization Of Rational Functions
• Linearization Of Exponential Functions
• Linearization Of Logarithmic Functions
• Linearization Of Trigonometric Functions
• The Derivative Of The Sum Of Two Functions
• The Derivative Function Of The Product Of Two Functions
• The Derivative Function Of The Reciprocal Of A Function
• The Derivative Function Of The Ratio Of Two Functions
• The Derivative Function Of The Function Ƒ(X) = U(Ax + B)
• Basic Derivative Rules
• Functions That Have The Same Derivative
• Graph The Derivative Function
• Exponential Function: Mixed Review (Domains, Ranges, Graphs, Function Properties)
• Key Features Of Exponential Functions By Graphs
• Key Features Of Exponential Functions By Tables
• Key Features Of Exponential Functions By Equations
• Transformations Of Exponential Function Graphs
• Graphs Of Exponential Growth Functions
• Find Growth Factor Of Exponential Growth Functions
• Graphs Of Exponential Decay Functions
• Find Decay Factor Of Exponential Decay Functions
• Rewrite Exponential Functions To Identify Rates
• Use Compound Interest Formula For Fixed Amount Of Time Compounding (Annual, Semi-Annual, Monthly, Etc)
• Use Compound Interest Formula For Continuous Compounding
• Use Compound Interest Formula To Solve For T (Time)
• Construct Exponential Models Given Two Points Or By Using Regression
• Solve Exponential Equations By Graphing
• Exponential Growth And Decay: Word Problems
• Limit Of Exponential Function
• Identify The Logarithms Expressions
• Understand The Inverse Relationship Between Exponents And Logarithms (Find Inverses Of Each Function)
• Rewrite Exponential Functions Into Logarithmic Functions
• Rewrite Logarithmic Functions Into Exponential Functions
• Evaluate Common Logarithms (With And Without Technology)
• Evaluate Natural Logarithms (With And Without Technology)
• Evaluate Logarithms Using Change Of Base Formula
• Key Features Of Logarithmic Functions By Graphs
• Key Features Of Logarithmic Functions By Tables
• Key Features Of Logarithmic Functions By Equations
• Transformations Of Logarithmic Function Graphs
• Solve Logarithmic Equations By Graphing
• Use Properties Of Logarithms To Expand
• Use Properties Of Logarithms To Condense
• Limit Of Logarithmic Function
• Find The Measure Of Directed Angle

Year 12

• Understanding primitive function
• Primitive function of a given function
• The notation for primitive functions
• "Antiderivative" and "Indefinite integral" as synonyms for primitive function
• Properties of primitive function
• Primitive function and continuity
• Primitive functions of elementary functions
• Methods for computing primitive functions
• Calculate a primitive function using the table of usual antiderivatives
• Calculate antiderivatives of the usual functions
• Antiderivatives rules (sum, difference and constan rule)
• Antiderivative power rule
• Calculate antiderivatives of a sum
• Calculate antiderivatives of a subtraction
• Calculate antiderivatives of a rational fraction
• Calculate the antiderivatives of composed functions
• Calculate the antiderivative using integration by parts
• Calculate the primitive using the table of usual antiderivatives
• Antiderivative of trig functions
• Antiderivative of exponential function
• Calculate primitive function of function that takes the value y0 at x0
• Interpretation geometries of primitive function
• Graphing the primitive function
• Calculate the antiderivatives of the addition
• Understanding integration
• Fundamental theorems of integral calculus
• Types of integrals (definite integral and indefinite integral)
• Properties of integral calculus
• Integral calculus formulas
• Methods to find integrals
• Finding integrals by integration by parts
• Finding integrals by substitution method
• Finding integrals by integration by partial fractions
• Interpretation geometries of integration
• Application of integral calculus
• Find accumulation of changes in the function
• Find average change
• Calculate the area
• Calculate the distance
• Calculate the volumes
• Calculate the surface area of revolution
• Calculate the volume of revolution
• Differentiation of Logarithmic Functions
• Understanding differential
• Derivative of function as limits
• Differentiation formulas
• Interpretation geometries of differentiation
• Understanding Differentiation Rules
• Product Rule
• Quotient Rule
• Chain Rule
• Differentiation of Elementary Functions
• Differentiation of Trigonometric Functions
• Differentiation of Special Functions
• The second derivative
• Real-Life Applications of Differentiation
• Understand the relationship between differentiability and continuity
• Distinguish between functions written in implicit form and explicit form
• Use implicit differentiation to find the derivative of a function
• Identify Tangent Functions From The Equation
• Identify Tangent Functions From The Graph
• Identify Tangent Functions From The Table
• Identify Tangent Functions From A Set Of Ordered Pairs
• Domain Of Tangent Functions
• Range Of Tangent Functions
• Complete A Function Table From The Graph Of A Tangent Function
• Write Tangent Functions To Solve Word Problems
• Solve Problems Involving Tangent Functions
• Evaluate Tangent Functions
• Identify Increasing, Decreasing And Constant Intervals Of Tangent Functions
• Determine the period from a sine or cosine function in equation form
• Determine The Amplitude From A Sine Or Cosine Function In Equation Form
• Determine The Period From A Sine Or Cosine Function In Graph Form
• Determine The Amplitude From A Sine Or Cosine Function In Graph Form
• Identify Minimum And Maximum Points Of Sine And Cosine Equations
• Identify Symmetry In The Graphs Of Sine And Cosine
• Graph Sine And Cosine Functions Using Transformations
• Determine The Asymptotes From A Tangent Function In Equation Form
• Determine The Asymptotes From A Tangent Function In Graph Form
• Graph A Tangent Function
• Identify Symmetry In Tangent Graphs
• Graph A Tangent Function Using Transformations
• Determine If Trig Functions Are Odd, Even, Or Neither
• Identify Cosecant Functions From The Equation
• Identify Cosecant Functions From The Graph
• Identify Cosecant Functions From The Table
• Identify Cosecant Functions From A Set Of Ordered Pairs
• Domain Of Cosecant Functions
• Range Of Cosecant Functions
• Identify Secant Functions From The Equation
• Identify Secant Functions From The Graph
• Identify Secant Functions From The Table
• Identify Secant Functions From A Set Of Ordered Pairs
• Domain Of Secant Functions
• Range Of Secant Functions
• Identify Cotangent Functions From The Equation
• Identify Cotangent Functions From The Graph
• Identify Cotangent Functions From The Table
• Identify Cotangent Functions From A Set Of Ordered Pairs
• Domain Of Cotangent Functions
• Range Of Cotangent Functions
• Graph A Cosecant Function
• Graph A Secant Function
• Determine The Period From A Cosecant Or Secant Function In Equation Form
• Determine The Period From A Cosecant Or Secant Function In Graph Form
• Determine The Asymptotes For A Cosecant Function In Equation Form
• Determine The Asymptotes For Secant Function In Equation Form
• Determine The Asymptotes For A Cosecant Function In Graph Form
• Determine The Asymptotes For Secant Function In Graph Form
• Identify Symmetry In Cosecant Graphs
• Identify Symmetry In Secant Graphs
• Graph A Cotangent Function
• Determine The Period From A Cotangent Function In Equation Form
• Determine The Period From A Cotangent Function In Graph Form
• Determine The Asymptotes From A Cotangent Function In Equation Form
• Determine The Asymptotes From A Cotangent Function In Graph Form
• Identify Symmetry Of Cotangent Graphs
• Determine If Reciprocal Trig Functions Are Odd, Even, Or Neither
• Understand That Arcsine, Arccosine, And Arctangent Represent The Inverse Of A Sine, Cosine, And Tangent Function Respectively
• Evaluate Arcsine Functions Using Unit Circle Knowledge
• Evaluate Arcsine Functions Using A Calculator
• Graph The Arcsine Functions
• Evaluate Arccosine Functions Using Unit Circle Knowledge
• Evaluate Arccosine Functions Using A Calculator
• Graph Arccosine Functions
• Domain Of Arcsine And Arccosine Functions
• Range Of Arcsine Functions
• Range Of Arccosine Functions
• Evaluate Arctangent Functions Using Unit Circle Knowledge
• Evaluate Arctangent Functions Using A Calculator
• Graph Arctangent Functions
• Domain Of Arctangent Functions
• Range Of Arctangent Functions
• Properties Of Inverse Trig Functions
• Rewrite A Trigonometric Expression Using Trig Identities
• Use Reciprocal Identities To Evaluate Trig Functions
• Use Quotient Identities To Evaluate Trig Functions
• Use Pythagorean Identities To Evaluate Trig Functions
• Use Cofunction Identities To Evaluate Trig Functions
• Use Even/Odd Identities To Evaluate Trig Functions
• Simplify A Trigonometric Expression Using Trig Identities
• Factor A Trigonometric Expression Using Trig Identities
• Add And Subtract Trigonometric Expressions Using Trig Identities
• Trigonometric Substitution
• Rewrite A Logarithmic Expression Using Trig Identities
• Verify Trigonometric Identities
• Use The Sum And Difference Formulas For Sine To Evaluate A Trigonometric Function
• Use The Sum And Difference Formulas For Cosine To Evaluate A Trigonometric Function
• Use The Sum And Difference Formulas For Tangent To Evaluate A Trigonometric Function
• Use Sum And Difference Formulas To Verify Identities
• Use Sum And Difference Formulas To Solve A Trigonometric Equation
• Use Multiple-Angle Formulas To Rewrite Trigonometric Functions
• Use Multiple-Angle Formulas To Evaluate Trigonometric Functions
• Use Double-Angle Formulas To Rewrite Trigonometric Functions
• Use Double-Angle Formulas To Evaluate Trigonometric Functions
• Use Power-Reducing Formulas To Rewrite Trigonometric Functions
• Use Half-Angle Formulas To Rewrite Trigonometric Functions
• Use Half-Angle Formulas To Evaluate Trigonometric Functions
• Use Product-To-Sum Formulas To Rewrite Trigonometric Functions
• Use Product-To-Sum Formulas To Evaluate Trigonometric Functions
• Use Sum-To-Product Formulas To Rewrite Trigonometric Functions
• Use Sum-To-Product Formulas To Evaluate Trigonometric Functions
• Use Trigonometric Formulas To Rewrite Real Life Models
• Solve A Right Triangle For Any Missing Angles Using Trigonometry
• Simple Harmonic Motion
• Combining Like Terms Using Trigonometric Functions
• Extract Square Roots From Trigonometric Equation
• Solve A Right Triangle For Any Missing Sides Using Trigonometry
• Find An Angle Of Depression
• Find Directions In Terms Of Bearings
• Solve Trigonometric Equations Of Quadratic Type
• Rewrite Trigonometric Equations Of Quadratic Type To Get A Single Trig Function
• Squaring And Converting To Quadratic Types
• Use The Quadratic Formula To Solve Trigonometric Equations Of Quadratic Type
• Use Inverse Functions To Solve Trigonometric Equations Of Quadratic Type
• Solving A Multiple-Angle Equation
• Estimate A Limit Using A Numerical Approach
• Estimate A Limit Using A Graphical Approach
• Estimate A Limit Using An Analytic Approach
• Learn That A Limit Can Fail To Exist When Behavior Differs From The Right And From The Left
• Learn That A Limit Can Fail To Exist Because Of Unbounded Behavior
• Limits And Oscillating Behavior
• Use A Formal Definition Of Limit
• Evaluate Basic Limits
• Limit Of A Polynomial
• Limit Of A Rational Function
• Limit Of A Composite Function
• Limits Of Trigonometric Functions
• Evaluate A Limit Using The Dividing Out Technique
• Evaluate A Limit Using The Rationalizing Technique
• Evaluate A Limit Using The Squeeze Theorem
• Determine Continuity At A Point And On An Open Interval
• One-Sided Limits
• Greatest Integer Function
• Continuity On A Closed Interval
• Charles’s Law And Absolute Zero
• Determine Infinite Limits From The Left
• Determine Infinite Limits From The Right
• Use Vertical Asymptotes To Help In Determining Limits
• Properties Of Continuity