Hlavní obsah
Math
Virginia Math
Algebra 1: Equations and Inequalities
Write a linear equation or inequality in one variable to represent a contextual situation.
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Solve multistep linear equations in one variable, including those in contextual situations, by applying the properties of real numbers and/or properties of equality.
Solve multistep linear inequalities in one variable algebraically and graph the solution set on a number line, including those in contextual situations, by applying the properties of real numbers and/or properties of inequality.
Rearrange a formula or literal equation to solve for a specified variable by applying the properties of equality.
Determine if a linear equation in one variable has one solution, no solution, or an infinite number of solutions.
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Verify possible solution(s) to multistep linear equations and inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of the answer(s). Explain the solution method and interpret solutions for problems given in context.
Create a system of two linear equations in two variables to represent a contextual situation.
- Systems of equations with elimination: apples and oranges
- Systems of equations with elimination: coffee and croissants
- Systems of equations with elimination: King's cupcakes
- Systems of equations with elimination: potato chips
- Systems of equations with elimination: TV & DVD
- Systems of equations with substitution: potato chips
- Systems of equations word problems (with zero and infinite solutions)
- Systems of inequalities word problems
Apply the properties of real numbers and/or properties of equality to solve a system of two linear equations in two variables, algebraically and graphically.
- Elimination method review (systems of linear equations)
- Equivalent systems of equations review
- Solutions to systems of equations: consistent vs. inconsistent
- Systems of equations with elimination
- Systems of equations with elimination (and manipulation)
- Systems of equations with elimination challenge
- Systems of equations with elimination: apples and oranges
- Systems of equations with elimination: coffee and croissants
- Systems of equations with elimination: King's cupcakes
- Systems of equations with elimination: potato chips
- Systems of equations with elimination: TV & DVD
- Systems of equations with elimination: x-4y=-18 & -x+3y=11
- Systems of equations with substitution: potato chips
- Systems of equations word problems (with zero and infinite solutions)
- Why can we subtract one equation from the other in a system of equations?
Determine whether a system of two linear equations has one solution, no solution, or an infinite number of solutions.
Create a linear inequality in two variables to represent a contextual situation.
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Represent the solution of a linear inequality in two variables graphically on a coordinate plane.
Create a system of two linear inequalities in two variables to represent a contextual situation.
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Represent the solution set of a system of two linear inequalities in two variables, graphically on a coordinate plane.
Verify possible solution(s) to a system of two linear equations, a linear inequality in two variable, or a system of two linear inequalities algebraically, graphically, and with technology to justify the reasonableness of the answer(s). Explain the solution method and interpret solutions for problems given in context.
Solve a quadratic equation in one variable over the set of real numbers with rational or irrational solutions, including those that can be used to solve contextual problems.
- Graphing quadratics in factored form
- Quadratic equations word problem: box dimensions
- Quadratic equations word problem: triangle dimensions
- Quadratic formula
- Quadratic formula review
- Quadratics by factoring
- Quadratics by factoring (intro)
- Solving quadratics by factoring
- Solving quadratics by factoring
- Solving quadratics by factoring review
- Solving quadratics by factoring: leading coefficient ≠ 1
- The quadratic formula
- Understanding the quadratic formula
- Worked example: quadratic formula (example 2)
- Worked example: quadratic formula (negative coefficients)
Determine and justify if a quadratic equation in one variable has no real solutions, one real solution, or two real solutions.
Verify possible solution(s) to a quadratic equation in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.