Math
- Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate.
- Recognize linear, quadratic, exponential and other common functions in real world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.
- Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.
- Represent real world and mathematical situations using equations and inequalities involving linear, quadratic, exponential and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.
- Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.
- Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.
- Know and apply properties of geometric figures to solve real world and mathematical problems and to logically justify results in geometry.
- Solve real-world and mathematical geometric problems using algebraic methods.
- Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships.
- Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions.
- Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.
Minnesota Math
Algebra: Represent real world and mathematical situations using equations and inequalities involving linear, quadratic, exponential and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.
Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.
- Completing the square
- Completing the square review
- Discriminant review
- Equations & inequalities word problems
- Graphing quadratics review
- Graphing quadratics: standard form
- Number of solutions of quadratic equations
- Proof of the quadratic formula
- Quadratic equations word problem: box dimensions
- Quadratic equations word problem: triangle dimensions
- Quadratic formula
- Quadratic formula proof review
- Quadratic formula review
- Quadratic inequality word problem
- Quadratic word problem: ball
- Quadratic word problems (standard form)
- Quadratics by factoring
- Quadratics by factoring (intro)
- Quadratics by taking square roots
- Quadratics by taking square roots (intro)
- Quadratics by taking square roots: strategy
- Quadratics by taking square roots: with steps
- Quadratics by taking square roots: with steps
- Solve by completing the square: Integer solutions
- Solve by completing the square: Non-integer solutions
- Solve equations by completing the square
- Solve quadratic equations: complex solutions
- Solving quadratic equations: complex roots
- Solving quadratics by completing the square
- Solving quadratics by completing the square: no solution
- Solving quadratics by factoring
- Solving quadratics by factoring
- Solving quadratics by factoring review
- Solving quadratics by factoring: leading coefficient ≠ 1
- Solving quadratics by taking square roots
- Solving quadratics by taking square roots
- Solving quadratics by taking square roots examples
- Solving quadratics by taking square roots: strategy
- Solving simple quadratics review
- Strategy in solving quadratic equations
- Strategy in solving quadratics
- The quadratic formula
- Understanding the quadratic formula
- Using the quadratic formula: number of solutions
- Worked example: completing the square (leading coefficient ≠ 1)
- Worked example: quadratic formula (example 2)
- Worked example: quadratic formula (negative coefficients)
- Worked example: Solving equations by completing the square
Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations.
- Analyzing graphs of exponential functions
- Analyzing graphs of exponential functions: negative initial value
- Analyzing tables of exponential functions
- Connecting exponential graphs with contexts
- Construct exponential models
- Constructing exponential models
- Constructing exponential models: half life
- Constructing exponential models: percent change
- Exponential decay intro
- Exponential equation with rational answer
- Exponential equation word problem
- Exponential expressions word problems (algebraic)
- Exponential expressions word problems (algebraic)
- Exponential expressions word problems (numerical)
- Exponential expressions word problems (numerical)
- Exponential function graph
- Exponential functions from tables & graphs
- Exponential growth vs. decay
- Graphing exponential growth & decay
- Graphs of exponential growth
- Interpret exponential expressions word problems
- Interpreting exponential expression word problem
- Intro to exponential functions
- Linear vs. exponential growth: from data
- Linear vs. exponential growth: from data
- Linear vs. exponential growth: from data (example 2)
- Modeling with basic exponential functions word problem
- Solve exponential equations using exponent properties
- Solve exponential equations using exponent properties (advanced)
- Solving exponential equations using exponent properties
- Solving exponential equations using exponent properties (advanced)
- Writing exponential functions
- Writing exponential functions from graphs
- Writing exponential functions from tables
- Writing functions with exponential decay
- Writing functions with exponential decay
Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.
- Classify complex numbers
- Classifying complex numbers
- i as the principal root of -1
- Intro to complex numbers
- Intro to complex numbers
- Intro to the imaginary numbers
- Parts of complex numbers
- Plot numbers on the complex plane
- Plotting numbers on the complex plane
- Powers of complex numbers
- Quadratic formula
- Quadratic formula review
- Simplify roots of negative numbers
- Simplifying roots of negative numbers
- Solve quadratic equations: complex solutions
- Solving quadratic equations: complex roots
- The complex plane
- The quadratic formula
- Understanding the quadratic formula
- Visualizing complex number powers
- Worked example: quadratic formula (example 2)
- Worked example: quadratic formula (negative coefficients)
Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines.
- Comparing linear rates word problems
- Graphing systems of inequalities
- Graphs of systems of inequalities word problem
- Intro to graphing systems of inequalities
- Modeling with systems of inequalities
- Systems of inequalities graphs
- Systems of inequalities word problems
- Writing systems of inequalities word problem
Solve linear programming problems in two variables using graphical methods.
Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically.
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Solve equations that contain radical expressions. Recognize that extraneous solutions may arise when using symbolic methods.
- Extraneous solutions
- Extraneous solutions of equations
- Extraneous solutions of radical equations
- Extraneous solutions of radical equations
- Extraneous solutions of radical equations (example 2)
- Intro to solving square-root equations
- Intro to square-root equations & extraneous solutions
- Solving cube-root equations
- Solving square-root equations
- Solving square-root equations: no solution
- Solving square-root equations: one solution
- Solving square-root equations: two solutions
- Square-root equations
- Square-root equations intro
Assess the reasonableness of a solution in its given context and compare the solution to appropriate graphical or numerical estimates; interpret a solution in the original context.
- Interpret a quadratic graph
- Interpret a quadratic graph
- Interpret parabolas in context
- Interpreting a parabola in context
- Relating linear contexts to graph features
- Solutions of inequalities: algebraic
- Solutions of inequalities: graphical
- Solutions of systems of inequalities
- Solving systems of inequalities word problem
- Systems of inequalities word problems
- Testing solutions to inequalities
- Testing solutions to systems of inequalities