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Algebra

Algebraic Expressions

Interpreting And Manipulating Expressions

Interpreting Expressions

Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Rewriting Expressions Using Structure

Writing, Reading, And Evaluating Algebraic Expressions

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

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

Rational Expressions

Operations On Rational Algebraic Expressions

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

Operations With Rational Expressions

Simplifying Rational Expressions

Simplifying Expressions

Simplifying Algebraic Expressions

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

Equations

Linear Equations

Absolute Value Equations

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

Solving Absolute Value Equations With Extraneous Solutions

Solving Equations Where Absolute Value Expressions Are On One Side Of The The Equation

Multi-variable Linear Equations

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

Solving A System Of Linear Equations In Three Variables Algebraically

Solving Real-world Problems Involving Multi-step Linear Equations In Three Variables

Understanding Pairs Of Linear Equations In Two Variables

Writing A Linear Equation In Two Variables In The Standard Form (ax + By + C = 0)

One-variable Linear Equations

Solving Linear Equations And Inequalities

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

Solving Absolute Value Equations With Extraneous Solutions

Solving Equations Where Absolute Value Expressions Are On One Side Of The The Equation

Solving Multi-step Problems Using Linear Equations In One Variable

Solving Linear Equations In One Variable, Where Coefficients Are Represented By Letters

Solving Linear Equations And Inequalities

Three-variable Linear Equations

Understanding And Solving Linear Equations In Three Variables

Solving A System Of Linear Equations In Three Variables Algebraically

Solving Real-world Problems Involving Multi-step Linear Equations In Three Variables

Two-variable Linear Equations

Graphing Multi-variable Equations

Solving Linear Equation Systems (exact & Approximate)

Solving Pairs Of Linear Equations In Two Variables

Solving Systems Of Linear Equations Using Elimination, Substitution, And Graphing

Solving Systems With No Solution Or Infinitely Many Solutions

Using The Inverse Of A Matrix To Solve Systems Of Linear Equations

Understanding Pairs Of Linear Equations In Two Variables

Writing A Linear Equation In Two Variables In The Standard Form (ax + By + C = 0)

Matrix Equations

Solving Equations With Matrices

Inverse Matrix To Solve Equations

Matrix Representation Of Linear Equations

Non-linear Equations

Other Non-linear Equations

Framing Non-linear Equations

Solving Multi-step Problems Using Non-linear Equations In One Variable

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)

Solving Radical Equations

Steps In Solving Non-linear Equations

Understanding Multi-step Problems Involving Non-linear Equations In One Variable

Framing Non-linear Equations In One Variable

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

Quadratic Equations

Completing The Square & Deriving Quadratic Formula

Solving Multi-step Problems Using Quadratic Equations In One Variable

Solving Quadratic Equations

Understanding Quadratic Equations In One Variable

Recognising When A Quadratic Equation Has Complex Solutions Using The Discriminant

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

Systems With Non-linear Equations

Inequalities

Linear Inequalities

One-variable Linear Inequalities

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

Representing Solutions Of Absolute Value Inequalities On Number Lines

Solving/interpreting Linear Inequalities In One Variable

Solving And/or Interpreting Absolute Value Inequalities

Two-variable Linear Inequalities

Framing/writing Linear Inequalities In Two Variables

Framing Linear Inequalities In Two Variables

Graphing Linear Inequalities

Representing Solutions Of Linear Inequalities In Two Variables On A Graph

Graphing The Solution Set To A System Of Linear Inequalities In Two Variables As The Intersection Of The Half-planes

Representing Solutions Of Inequalities Of The Form Px + Qy ≤ R Or Px + Qy < R On Graphs

Representing Solutions Of Inequalities On Graphs

Representing Solutions Of Linear Inequalities In Two Variables On Graphs

Solutions In Equation Modeling

Solving/interpreting Linear Inequalities In Two Variables

Solving Real-world Problems Involving Multi-step Linear Inequalities In Two Variables

Non-linear Inequalities

One-variable Non-linear Inequalities

Solving Multi-step Problems Using Non-linear Inequalities In One Variable

Solving Quadratic Inequalities In One Variable (algebraically Or Graphically)

Polynomials

Advanced Polynomial Operations

Applying The Remainder Theorem

Dividing 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

Factorising Polynomials

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

Graphing Polynomial Zeros

Using Polynomial Identities

Basic Polynomial Operations

Adding And Subtracting Polynomials

Adding Two Or More Polynomials

Subtracting Polynomials

Adding, Subtracting And Multiplying Polynomials

Multiplying Polynomials

Multiplying Two Or More Monomials

Multiplying Two Or More Polynomials

Factoring Polynomials

Factorising Polynomials

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

Polynomial Applications

Applying Algebraic Identities To Solve Problems

Using Algebraic Identities To Solve Mathematical Problems

Applying Binomial Theorem

Understanding And Applying The Binomial Theorem

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

Using The Binomial Theorem To Solve Problems

Understanding Zeroes And Factors Of Polynomials

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

Roots And Radicals

Applying Roots

Solving Problems Involving Nth Roots

Evaluating 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 Symbols For Solutions To Equations

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

Understanding Roots

Applying Roots

Solving Problems Involving Nth Roots

Evaluating 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 Symbols For Solutions To Equations

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

Sequences And Series

Sequences

Identifying And Writing Sequences

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)

Understanding And Applying Sequences

Using Arithmetic Sequences To Model Situations

Using Geometric Sequences To Model Situations

Series

Sum Of Finite Geometric Series Formula

Understanding And Applying Arithmetic Series

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

Understanding And Applying Geometric Series

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

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11th Grade Factoring Polynomials Passages

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Simplifying Equations - Factorization Techniques - Mathematical Manipulation

11th Grade

Math

Develop proficiency in simplifying, factorizing, and manipulating equations relevant to engineering. Learn techniques to isolate variables and rearrange formulas, enhancing problem-solving skills and mathematical reasoning.

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1. 2021 survey of 800+ teachers conducted by Wayground

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

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