Common Core for High School - Algebra (lessons, worksheets, solutions, examples, games) (2024)

HSA-CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

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  Modeling with one-variable equations and inequalities

  Create Equations & Inequalities

  Words to Algebra Games

HSA-CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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  Linear Equations

  Quadratic Equations

  Rational Functions

  Exponential Functions

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  Graph Linear Equations

  Solve Quadratic Equations

  Modeling with two-variable equations and graphs

  Equation of Line Games

HSA-CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

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  Represent Constraints

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  Modeling constraints with two-variable inequalities

  Systems of Equations Word Problems

HSA-CED.A.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

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  Rearrange Formulas

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  Manipulate formulas

  Solving equations in terms of a variable

  See Also

  8.EE.C.8 Worksheets - Common Core MathSolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math

  Rearrange Formulas

HSA-REI.A.1

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

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  1-Step Equations

  2-Step Equations

  Multi-Step Equations

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  Understand process for solving linear equations

  Understand process for solving quadratic equations

  Algebra Worksheets

  Equations with variables on both sides

  Algebra Games

HSA-REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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  Rational Equations

  Radical Equations

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  Extraneous solutions to rational equations

  Rational equations 1

  Rational equations 2

  Extraneous solutions to radical equations

  Radical Equations

HSA-REI.A.2

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

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  Linear Inequalities

  Compound Inequalities

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  Multi-step linear inequalities

  Compound inequalities

HSA-REI.B.4

Solve quadratic equations in one variable.

HSA-REI.B.4a

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x -p)² = q that has the same solutions. Derive the quadratic formula from this form.

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  Complete the Square and Quadratic Formula

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  Completing the square 1

  Completing the square 2

HSA-REI.B.4b

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

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  Solve Quadratic Equations

  Quadratic Formula

  Derive Quadratic Formula

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  Solve quadratics by taking the square root

  Solve quadratics by factoring

  Solve quadratics by factoring 2

  Using the quadratic formula

  Quadratic formula with complex solutions

  Types of solutions to quadratic equations

HSA-REI.C.5

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.

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  Understand Systems of Equations

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  Graphically understand systems of equations

HSA-REI.C.6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

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  Solve Systems of Equations

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  Systems of Equations Worksheets

  Systems of equations

  Graphing systems of equations

  Systems of equations word problems

HSA-REI.C.7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x² + y² = 3.

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  Systems of Linear and Quadratic Equations

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  Systems of nonlinear equations

HSA-REI.C.8

HSA-REI.C.9

(+) 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 (using technology for matrices of dimension 3 נ3 or greater).

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  Writing systems of equations as matrix equations

  Solving matrix equations

  Matrix Equations

HSA-REI.D.10

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 (which could be a line).

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  Graphs of Equations

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  Interpret graphs of linear and nonlinear functions

  Graphs of Equations

HSA-REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y =f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

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  Intersection of Graphs

  Successive Approximation (Newton's Method)

  Graphs of Exponential Functions

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  Intersecting functions

  Points of Intersection

HSA-REI.D.12

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

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  Graph linear inequalities

  Graph & solve linear inequalities

  Graph systems of inequalities

  Graph & solve systems of inequalities