MAT-12 Standards
Completion requirements
ALL
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MAT-12.AR.01
MAT-12.AR.01 Rearrange multi-variable formulas to highlight a quantity of interest.Progressions
Decompose Numbers and/or Expressions
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MAT-12.AR.02
MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.Progressions
Factor Pairs/Multiples
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MAT-12.AR.03
MAT-12.AR.03 Interpret expressions that represent a quantity in context.Progressions
Equations/Expressions
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MAT-12.AR.04
MAT-12.AR.04 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Progressions
Factor Pairs/Multiples
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MAT-12.AR.05
MAT-12.AR.05 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.Progressions
Adding and Subtracting Fractions
Multiplying and Dividing Fractions
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MAT-12.AR.06
MAT-12.AR.06 Rewrite simple rational expressions indifferent forms. Write a(x)/b(x) in the form of q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or technology for the more complicated examples.Progressions
Decompose Numbers and/or Expressions
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MAT-12.AR.07
MAT-12.AR.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic equations and simple rational and exponential equations.Progressions
Exponents
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MAT-12.AR.08
MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.Progressions
Exponents
Unit Size and Scale
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MAT-12.AR.09
MAT-12.AR.09 Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non- viable options in a modeling context.Progressions
Compare Numbers and/or Expressions
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MAT-12.AR.10
MAT-12.AR.10 Derive the quadratic formula from the form 0 = ax² + bx + c.Progressions
Quadratic Equations
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MAT-12.AR.11
MAT-12.AR.11 Solve quadratic equations with real coefficients that have solutions of the form a + bi and a - bi.Progressions
Complex Numbers
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MAT-12.AR.12
MAT-12.AR.12 Solve simple rational and radical equations in one variable and identify extraneous solutions.Progressions
Linear Equations
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MAT-12.AR.13
MAT-12.AR.13 Add, subtract, and multiply polynomials beyond quadratics. Understand that polynomials form a system comparable to integers, namely, they are closed under the operations of addition, subtraction, and multiplication.Progressions
Addition and Subtraction
Multiplication and Division
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MAT-12.AR.14
MAT-12.AR.14 Identify zeros of polynomial equations when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.Progressions
Quadratic Equations
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MAT-12.AR.15
MAT-12.AR.15 Apply the Factor and Remainder Theorems to determine efficiently whether a linear expression is a factor of a polynomial equation. Apply the Remainder Theorem in context.Progressions
Linear Equations
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MAT-12.AR.16
MAT-12.AR.16 Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) are the x- value(s) that result in the y-values of f(x) and g(x)being the same.Progressions
Linear Equations
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MAT-12.AR.17
MAT-12.AR.17 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.Progressions
Linear Equations
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MAT-12.AR.18
MAT-12.AR.18 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 × 3 or greater).Progressions
Linear Equations
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MAT-12.AR.19
MAT-12.AR.19 Solve a system of equations in three or more variables with matrices (using technology).Progressions
Linear Equations
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MAT-12.AR.20
MAT-12.AR.20 Apply the Binomial Theorem for the expansion of (ax + by)ⁿ in powers of x and y for a positive integer n and integers a and b.Progressions
Decompose Numbers and/or Expressions
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MAT-12.AR.F.01
MAT-12.AR.F.01 Write a function that describes a relationship between two quantities.
Progressions
Functional Relationships
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MAT-12.AR.F.02
MAT-12.AR.F.02 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.Progressions
Unit Rate
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MAT-12.AR.F.03
MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
Progressions
Exponents
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