Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

Writing Expressions In Different Forms To Demonstrate How The Quantities Are Related

Adding And/or Subtracting Rational Algebraic Expressions

Knowing That Rational Algebraic Expressions Are Closed Under The Operations Of Addition, Subtraction, Multiplication And Division

Multiplying Two Or More Rational Algebraic Expressions

Rewriting Rational Algebraic Expressions By Cancelling Out Common Non-zero Factors

Writing A(x)/b(x) In The Form Of Q(x) + R(x)/b(x), With The Degree Of R(x) Less Than The Degree Of B(x) Using Either Inspection Or Technology

Applying Properties Of Operations To Simplify Algebraic Expressions Involving Exponents And/or Radicals

Solving Multi-step Problems Involving Absolute Value Linear Equations In One Variable

Graphing Multi-variable Equations

Solving Linear Equation Systems (exact & Approximate)

Solving Pairs Of Linear Equations In Two Variables

Understanding And Solving Linear Equations In Three Variables

Understanding Pairs Of Linear Equations In Two Variables

Solving Linear Equations And Inequalities

Solving Multi-step Problems Using Linear Equations In One Variable

Inverse Matrix To Solve Equations

Matrix Representation Of Linear Equations

Explaining And Justifying Each Step In Solving A Non-linear Equation

Solving Exponential Equations In One Variable (including Unlike Bases)

Solving Logarithmic Equations In One Variable

Solving Radical Equations In One Variable (including Extraneous Solutions)

Solving Rational Equations In One Variable (including Extraneous Solutions)

Framing Non-linear Equations In One Variable

Representing Constraints By Linear Or Non-linear Equations In One Variable

Completing The Square & Deriving Quadratic Formula

Solving Quadratic Equations

Recognising When A Quadratic Equation Has Complex Solutions Using The Discriminant

Writing A Quadratic Equation In The Standard Form (ax^2 + Bx + C = 0)

Representing Solutions Of Linear Inequalities In One Variable On A Number Line

Solving/interpreting Linear Inequalities In One Variable

Framing/writing Linear Inequalities In Two Variables

Graphing Linear Inequalities

Representing Solutions Of Linear Inequalities In Two Variables On A Graph

Solutions In Equation Modeling

Solving/interpreting Linear Inequalities In Two Variables

Solving Quadratic Inequalities In One Variable (algebraically Or Graphically)

Factorising Polynomials By Finding The Gcf Or Gcd Or Hcf

Factorising Polynomials By Grouping

Factorising Polynomials That Are Of The Form Or Reducible To The Form Ax^2 + Bx + C

Using Algebraic Identities To Factorise Polynomials And/or Solve Mathematical Problems

Quadratic Equations

Adding Two Or More Polynomials

Subtracting Polynomials

Writing A(x)/b(x) In The Form Of Q(x) + R(x)/b(x), With The Degree Of R(x) Less Than The Degree Of B(x) Using Inspection/technology/long Division

Writing A(x)/b(x) In The Form Of Q(x) + R(x)/b(x), With The Degree Of R(x) Less Than The Degree Of B(x) Using The Long Division Algorithm

Multiplying Two Or More Monomials

Multiplying Two Or More Polynomials

Using Algebraic Identities To Solve Mathematical Problems

Identifying Zeroes Of Polynomials (degree > 2) When Suitable Factorisations Are Available

Stating And Applying The Factor Theorem In Reasoning With Polynomials

Stating And Applying The Remainder Theorem In Reasoning With Polynomials

Using Zeroes Of Polynomials To Sketch Their Graphs And/or Write The Polynomials

Determining The Coefficients Of The Binomial Expansion By Pascal’s Triangle

Stating The Binomial Theorem (n Is A Positive Integer) For The Expansion Of (x + Y)^n

Stating/using The Binomial Theorem (n Is A Positive Integer) For The Expansion Of (x + Y)^n

Using The Binomial Theorem To Solve Problems

Solving Problems Involving Nth Roots

Evaluating Expressions Involving Cube Roots Of Positive/negative Numbers

Evaluating Expressions Involving Nth Roots

Evaluating Expressions Involving Square Roots Of Positive Numbers

Evaluating Nth Roots

Using The Cube Root Symbol For Solutions To Equations Of The Form X^3 = P

Using The Nth Root Symbol For Solutions To Equations Of The Form X^n = P

Using The Square Root Symbol For Solutions To Equations Of The Form X^2 = P

Identifying And Writing Rules For A Sequence When Given Some Terms Of The Sequence (including Arithmetic And Geometric Sequences)

Writing Terms Of A Sequence Recursively (including Arithmetic And Geometric Sequences)

Writing Terms Of A Sequence When Given The General Formula (including Arithmetic And Geometric Sequences)

Using Arithmetic Sequences To Model Situations

Using Geometric Sequences To Model Situations

Applying The Formula For The Sum Of A Finite Arithmetic Series To Solve Problems

Applying The Formula For The Sum Of A Finite Geometric Series To Solve Problems

Applying The Formula For The Sum Of An Infinite Geometric Series To Solve Problems

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Arithmetic & Geometric Sequences: Recursive & Explicit

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

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

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

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

Interpreting Exponential 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

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

Graphing Exponential, Logarithmic & Trigonometric Functions

Applying The Laws Of Logarithms To Simplify/evaluate Expressions

Graphing The Sine And Cosine Functions (including Transformations)

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

Calculating Areas Of Irregular Polygons

Understanding That An Angle That Turns Through 'n' One-degree Angles Has An Angle Measure Of 'n' Degrees

Drawing And Understanding Skew Lines And Planes

Drawing And Identifying Parallel And/or Perpendicular Lines

Using The Angle Bisector Theorem To Solve Problems

Using The Perpendicular Bisector Theorem To Solve Problems

Naming Points, Line Segments, Rays, Lines And Planes

Knowing Precise Definitions Of Line Segments, Perpendicular Lines And Parallel Lines

Use Congruency Criteria To Solve Problems

Use Similarity Criteria To Solve Problems

Establishing The Conditions Necessary For Two Triangles To Be Congruent

Reasoning How Two Figures Are Congruent Using Transformations

Describing A Sequence Of Transformations To Demonstrate Similarity Between Two Figures

Establishing The Conditions Necessary For Two Triangles To Be Similar

Identifying Similar Figures

Using The Circumcenter Of A Triangle To Solve Geometric Problems

Using The Incenter Of A Triangle To Solve Geometric Problems

Describing An Informal Argument For The Formula For The Circumference Of A Circle

Applying Properties Of Special Parallelograms (square, Rectangle And Rhombus) To Solve Geometric Problems

Applying Properties Related To Angles And/or Sides And/or Diagonals In A Parallelogram To Solve Geometric Problems

Proving And Using The Properties Of Angles For A Quadrilateral

Applying Properties Based On The Relationship Between Side Lengths And Angle Measures To Solve Geometric Problems

Applying Properties Related To Altitudes To Solve Geometric Problems

Applying Properties Related To Medians To Solve Geometric Problems

Applying The Triangle Midsegment Theorem (intercept Theorem Or Basic Proportionality Theorem) To Solve Geometric Problems

Applying Concepts Of Density Based On Volume In Modeling Situations

Using Geometric Shapes (including Their Measures And Properties) To Describe Real-life Objects

Applying Geometry In Design Problem Solving

Describing Objects Using Geometric Shapes

Identifying 2d Cross-sections & 3d Rotations

Reasoning With Three-dimensional Shapes And Their Attributes

Deriving And Using The Formula For The Area Of A Triangle In Terms Of Sides And The Sine Ratio

Using The Law Of Sines And/or Cosines In Triangles To Solve Problems

Solving Problems Involving Trigonometric Ratios In Right Triangles

Defining The Six Fundamental Ratios For Acute Angles

Explaining And Using The Relationship Between The Sine And Cosine Of Complementary Angles

Applying Conjugates To Find Quotients

Finding The Conjugate Of A Complex Number

Finding The Square Root Of A Negative Number

Knowing The Existence Of A Complex Number I And That I^2 = –1

Understanding That Every Complex Number Has The Form Of A + Bi Where A And B Are Real Numbers

Using Different Properties (commutative, Associative) To Add And/or Subtract Complex Numbers

Calculating The Distance Between Complex Numbers

Extending Algebraic Polynomial Identities To Complex Numbers

Finding The Midpoint Of A Segment Connecting Two Complex Numbers

Knowing The Fundamental Theorem Of Algebra

Solving Problems Involving A Mix Of Addition, Subtraction, Multiplication And/or Division Of Complex Numbers

Using I^2 = –1 And Different Properties (commutative, Associative, Distributive) To Multiply Complex Numbers (including Cases Where Addition/subtraction Are Involved)

Finding The Modulus And/or Argument Of A Complex Number

Representing Complex Numbers In The Polar Form

Representing Complex Numbers In The Rectangular Form

Understanding Why The Rectangular And Polar Forms Of A Complex Number Represent The Same Number

Solving Problems Involving A Mix Of Addition, Subtraction And/or Multiplication Of Matrices

Finding The Inverse Of A Matrix (if It Exists)

Representing And Manipulating Data Through Matrices

Adding And/or Subtracting Matrices Of Appropriate Dimensions

Multiplying A Vector (column Matrix) By A Matrix To Produce Another Vector

Multiplying Matrices By Scalars

Multiplying Two Matrices Of Appropriate Dimensions

Understanding That Matrix Multiplication Is Associative And Distributive

Understanding That Matrix Multiplication Is Associative And Distributive But Not Commutative

Understanding The Role Of The Identity Matrix In Matrix Multiplication

Understanding And Applying Laws Of Exponents (product Law, Quotient Law And Power Law) To Numerical Expressions For Exponents >0.

Understanding And Using Zero And Negative Exponents, Applying Law Of Exponents To Numerical Expressions Where Exponent Is Zero Or Negative.

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

Understanding That The Definition Of Rational Exponents Follows From Extending Understanding Of Integer Exponents

Defining Quantities For Descriptive Modeling

Interpreting Units & Scales In Problem Solving

Selecting Accuracy Level For Quantity Reporting

Assessing Function Fit Via Residual Analysis

Fit & Use Functions To Solve Data Problems

Fit Linear Function For Scatter Plot

Distinguishing Between Qualitative And Quantitative Data

Investigating And Describing Patterns Such As Clustering And Outliers

Representing Data Using Box-and-whisker Plots

Representing Data Using Dot Plots

Representing Data Using Histograms

Choosing And Interpreting The Scale In Graphs And Data Displays

Developing A Margin Of Error Through The Use Of Simulation Models

Explaining How Randomisation Relates To Sample Surveys, Experiments And Observational Studies

Recognising The Purposes Of And Differences Among Sample Surveys, Experiments And Observational Studies

Understanding Representative Samples And The Idea That Examining A Sample Can Lead To Useful Information About The Population

Using Data From A Sample Survey To Estimate A Population Mean Or Proportion

Recognising A Statistical Question