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High School Maths  Algebra  Common Core
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High School Maths  Number and Quantity  Common Core (High School Maths)
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Table of Contents
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Seeing Structure in Expressions
Interpret the structure of expressions
Interpret expressions that represent a quantity in terms of its context
Use the structure of an expression to identify ways to rewrite it
Write expressions in equivalent forms to solve problems
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression
Derive the formula for the sum of a finite geometric series
Arithmetic with Polynomials and Rational Functions
Perform arithmetic operations on polynomials
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication
Understand the relationship between zeros and factors of polynomials
Know and apply the Remainder Theorem
Identify zeros of polynomials when suitable factorizations are available
Use polynomial identities to solve problems
Prove polynomial identities and use them to describe numerical relationships
Know and apply the Binomial Theorem for the expansion
Rewrite rational functions
Understand that rational expressions form a system analogous to the rational numbers
Creating Equations
Create equations that describe numbers or relationships
Create equations and inequalities in one variable and use them to solve problems
Create equations in two or more variables to represent relationships between quantities
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities
Rearrange formulas to highlight a quantity of interest
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
Explain each step in solving a simple equation as following from the equality of numbers
Solve simple rational and radical equations in one variable
Solve equations and inequalities in one variable
Solve linear equations and inequalities in one variable
Solve quadratic equations in one variable
Solve systems of equations
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions
Solve systems of linear equations exactly and approximately
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically
Represent a system of linear equations as a single matrix equation in a vector variable
Find the inverse of a matrix if it exists and use it to solve systems of linear equations
Represent and solve equations and inequalities graphically
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve
Explain why the xcoordinates of the points where the graphs of the equations y = fx and y = gx intersect are the solutions of the equation
Graph the solutions to a linear inequality in two variables as a halfplane
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