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Math

Algebra

Functions

Advanced Functions

Advanced Function Analysis

Applying And Analysing Functions

Graphing Functions

Functions With Special Properties

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Understanding Sequences As Recursive Functions

Sequence Functions

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Equation Of A Line

Graphing The Equation Of A Straight Line

Graphing A Horizontal Line And/or Vertical Line

Graphing An Equation Of A Straight Line Represented In Different Forms

Identifying Axes Intercepts When A Line Is Represented Graphically

Writing The Equation Of A Straight Line

Writing An Equation Of A Straight Line Using A Slope And A General Point

Writing An Equation Of A Straight Line Using Two Points

Writing An Equation Of A Straight Line When The Line Is Represented Graphically

Exponential And Logarithmic Functions

Applications

Applying And Analysing Exponential And Logarithmic Functions

Applying The Laws Of Exponents To Interpret Expressions For Exponential Functions

Expressing The Solution Of Exponential Models (ab^(ct) = D) Where The Base Is B As Logarithms Using Technology

Observing That A Quantity Increasing As An Exponential Function Eventually Exceeds A Quantity Increasing As A Polynomial Function

Solving Real-world Problems Involving Exponential And/or Logarithmic Functions (including Modelling)

Understanding And Using The Inverse Relationship Between Exponential And Logarithmic Functions To Solve Problems

Comparing Function Types

Comparing Exponential & Polynomial Growth

Identifying Linear Vs Exponential Models

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

Exponential Functions

Graphing Exponential And Logarithmic Functions

Graphing Exponential Functions (including Growth/decay), Showing Intercepts And End Behavior

Performing Multiple Transformations On Different Exponential/logarithmic Functions (including Writing The Final Function)

Rewriting Exponential Functions To Reveal Properties

Interpreting Exponential Functions

Understanding Exponential And Logarithmic Functions

Identifying And Evaluating Exponential Functions

Proving That Exponential Functions Grow Or Decay By Equal Factors Over Equal Intervals

Recognising Situations And Solving Problems In Which A Quantity Grows Or Decays By A Constant Percent Rate

Writing And Interpreting Exponential Functions

Constructing An Exponential Function (including Geometric Sequences) From A Description

Constructing An Exponential Function (including Geometric Sequences) From A Graph

Constructing An Exponential Function (including Geometric Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters In An Exponential Function In Terms Of A Context

Function Relationships

Constructing Linear & Exponential Functions

Interpreting Parameters In Linear/exponential Functions

Understanding Inverse Of Exponents & Logarithms

Logarithmic Functions

Evaluating Logarithms In Exponential Models

Graphing Symbolic Functions

Graphing Exponential, Logarithmic & Trigonometric Functions

Graphing Logarithmic Functions, Showing Intercepts And End Behavior

Understanding Exponential And Logarithmic Functions

Applying The Laws Of Logarithms To Simplify/evaluate Expressions

Function Concepts

Analyzing Functions

Calculate & Interpret Function's Average Rate Of Change

Comparing Functions In Different Formats

Interpreting And Sketching Graphs Of Functions

Writing And Interpreting Functions

Function Analysis

Function Basics

Evaluating And Interpreting Functions

Relating Function's Domain To Its Graph

Understanding Functions, Domains, And Ranges

Understanding Functions

Function Fundamentals

Evaluating And Interpreting Functions

Relating Function's Domain To Its Graph

Understanding Functions, Domains, And Ranges

Understanding Functions

Function Operations

Function Writing For Quantity Relationship

Combining Standard Functions With Arithmetic

Deriving Expressions & Processes From Context

Function Composition

Writing And Interpreting Functions

Function Transformations

Graph Transformation & Identification With K Value

Identify The Effect On The Graph Of Replacing F(x) By F(x) + K, K F(x), F(kx), And F(x + K)

Inverse Functions

Inverse Functions Finding

Creating Invertible Functions By Domain Restriction

Reading Inverse Function Values From Graphs/tables

Solving Equations & Writing Inverse Functions

Verifying Inverse Functions By Composition

Understanding Functions

Evaluating And Interpreting Functions

Relating Function's Domain To Its Graph

Understanding Functions, Domains, And Ranges

Understanding Functions

Functions (general)

Analyzing Functions

Analyzing & Sketching Graphs Of Functions

Comparing Properties Of Functions

Comparing Properties Of Two Functions That Are Represented Either Algebraically, Graphically, In Tables And/or Using Verbal Statements

Identifying Whether A Given Relation Is A Function

Writing And Interpreting Functions

Calculating/estimating And Interpreting The Average Rate Of Change (including Using The Initial Value Of The Function)

Understanding Functions

Graphing Functions

Graphing A Function Using Ordered Pairs (including Relating A Domain Of A Function To Its Graph)

Understanding Functions & Their Graphs

Understanding Functions

Classifying Equations/functions As Showing Direct Variation, Inverse Variation Or Neither

Understanding That A Function Is A Mapping From One Set Of Inputs (called The Domain) To Another Set Of Outputs (called The Range)

Functions (linear)

Linear Function Concepts

Interpreting Linear & Non-linear Functions

Modeling & Interpreting Linear Functions

Understanding Linear Functions

Distinguishing Between Linear And Non-linear Functions

Working With Linear Functions

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Description/equation

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Graph

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Linear Functions

Graphing Linear Functions

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

Understanding Linear Functions

Recognising Situations In Which One Quantity Changes At A Constant Rate With Respect To Another Quantity

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Description/equation

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Graph

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters Of A Linear Function In Terms Of A Context

Quadratic Functions

Applying And Analysing Quadratic Functions

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation/completing Square To Find/show Zeroes, Extreme Values And Symmetry On Graphs Of Quadratic Functions

Graphing Symbolic Quadratic Functions

Graphing Linear & Quadratic Functions

Graphing Quadratic Functions

Graphing Quadratic Functions (including Showing Intercepts, Maxima Or Minima)

Transformations On Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Interpreting Quadratic Graphs Via Factoring

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Specific Functions

Advanced Functions

Graphing Complex Functions

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Graphing Functions

Graphing Various Function Types

Identifying Effects Of Transformations On Graphs

Identifying Function Families

Identifying/finding Turning Points

Recursive Functions

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Understanding Sequences As Recursive Functions

Exponential And Logarithmic Functions

Applications Of Exponential And Logarithmic Functions

Applying And Analysing Exponential And Logarithmic Functions

Applying The Laws Of Exponents To Interpret Expressions For Exponential Functions

Comparing Exponential And Polynomial Growth Rates

Expressing Solutions Of Exponential Models Using Logarithms

Solving Real-world Problems With Exponential/logarithmic Functions

Using The Inverse Relationship Between Exponential And Logarithmic Functions

Understanding Exponential And Logarithmic Functions

Applying The Laws Of Logarithms

Identifying And Evaluating Exponential Functions

Proving Properties Of Exponential Growth/decay

Recognising Situations Involving Constant Percent Rates

Writing And Interpreting Exponential Functions

Constructing Exponential Functions From Various Representations

Interpreting Parameters In Exponential Contexts

Exponential Models

Comparing Exponential & Polynomial Growth

Constructing Linear & Exponential Functions

Identifying Linear Vs Exponential Models

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

Interpreting Parameters In Linear/exponential Functions

Rewriting Exponential Functions To Reveal Properties

Interpreting Exponential Functions

Logarithmic Functions

Evaluating Logarithms In Exponential Models

Graphing Exponential And Logarithmic Functions

Graphing Exponential Functions (including Growth/decay)

Graphing Logarithmic Functions

Performing Multiple Transformations On Functions

Understanding Inverse Of Exponents & Logarithms

Linear Functions

Graphing Linear Functions

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

Understanding Linear Functions

Recognising Situations In Which One Quantity Changes At A Constant Rate With Respect To Another Quantity

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function From Different Representations

Interpreting The Parameters Of A Linear Function In Terms Of A Context

Quadratic Functions

Expressions In Equivalent Forms

Quadratic Equations

Factoring Quadratics

Max/min Of Quadratic Functions

Transforming Exponential Functions

Graphing And Analyzing Quadratics

Graphing Symbolic Quadratic Functions

Graphing Linear & Quadratic Functions

Graphing Quadratic Functions

Graphing Quadratic Functions (including Showing Intercepts, Maxima Or Minima)

Transformations On Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Interpreting Quadratic Graphs Via Factoring

Working With Quadratic Functions

Applying And Analysing Quadratic Functions

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation/completing Square To Find/show Zeroes, Extreme Values And Symmetry On Graphs Of Quadratic Functions

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Trigonometric Functions

Applications Of Trigonometric Functions

Applying And Analysing Trigonometric Functions

Applying The Unit Circle To Explain Symmetry And Periodicity

Applying Trigonometric Identities And Formulas

Evaluating And Interpreting Trigonometric Equation Solutions

Solving Real-world Problems With Trigonometric Functions

Using Inverse Functions To Solve Trigonometric Equations

Understanding Trigonometric Functions

Extension Of Trig Functions Via Unit Circle

Understanding Radian Measure Of An Angle

Understanding Trigonometric Functions

Understanding And Using The Unit Circle To Extend Trigonometric Functions To All Real Numbers

Unit Circle: Symmetry & Periodicity In Trig Functions

Using Special Triangles & Unit Circle In Trigonometry

Working With Trigonometric Functions

Graphing Trigonometric Functions

Graphing The Sine And Cosine Functions (including Transformations)

Modeling Periodic Phenomena With Trig Functions

Proving & Applying Trig Addition/subtraction

Proving & Using Pythagorean Trigonometric Identity

Solving Trigonometric Equations With Inverse Functions

Understanding Inverse Of Restricted Trigonometric Functions

Trigonometric Functions

Graphing Trig Functions

Graphing Trigonometric Functions

Graphing The Sine And Cosine Functions (including Transformations)

Solving Trig Equations

Evaluating And Interpreting The Solutions To Trigonometric Equations In Real-world Contexts Using Technology

Solving Real-world Problems Involving Trigonometric Functions (including Frequencies And Modelling)

Using Inverse Functions To Solve Trigonometric Equations

Using Inverse Functions To Solve Trigonometric Equations Using Technology And/or Intrepret The Solutions

Trigonometric Applications

Modeling Periodic Phenomena With Trig Functions

Solving Trigonometric Equations With Inverse Functions

Understanding Inverse Of Restricted Trigonometric Functions

Trigonometric Basics

Extension Of Trig Functions Via Unit Circle

Understanding Radian Measure Of An Angle

Unit Circle: Symmetry & Periodicity In Trig Functions

Using Special Triangles & Unit Circle In Trigonometry

Trigonometric Identities

Applying And Analysing Trigonometric Functions

Proving & Applying Trig Addition/subtraction

Proving & Using Pythagorean Trigonometric Identity

Understanding Trig Functions

Understanding Trigonometric Functions

Understanding And Using The Unit Circle To Extend Trigonometric Functions To All Real Numbers (both Degrees And Radians)

Types Of Functions

Advanced Functions

Applying And Analysing Functions

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Graphing Functions

Understanding Sequences As Recursive Functions

Exponential And Logarithmic Functions

Function Sequence Relationships

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Linear Functions

Graphing Linear Functions

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

Understanding Linear Functions

Recognising Situations In Which One Quantity Changes At A Constant Rate With Respect To Another Quantity

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Description/equation

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Graph

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters Of A Linear Function In Terms Of A Context

Quadratic Functions

Applying And Analysing Quadratic Functions

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation/completing Square To Find/show Zeroes, Extreme Values And Symmetry On Graphs Of Quadratic Functions

Graphing Symbolic Quadratic Functions

Graphing Linear & Quadratic Functions

Graphing Quadratic Functions

Graphing Quadratic Functions (including Showing Intercepts, Maxima Or Minima)

Transformations On Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Interpreting Quadratic Graphs Via Factoring

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Trigonometric Functions

Geometry

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Measurement And Data

Number System

Ratios And Proportional Relationships

Statistics And Probability

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Linear System Solutions - Problem Solving Applications - Algebra

9th Grade - 12th Grade

Math

Study the application of solving linear systems in real-world scenarios to enhance algebraic problem-solving proficiency. Develop the ability to efficiently determine unique and infinite solutions through mastery of key techniques.

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1. 2021 survey of 800+ teachers conducted by Wayground

2. Journal of Education and e-Learning Research (Source)

3. International Online Journal of Education and Teaching (Source)

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