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217 items
MAFS.912.A-APR.1.1
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
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Content Complexity: Level 1: Recall

Belongs to: Perform arithmetic operations on...

Remarks/Examples:

Algebra 1 - Fluency Recommendations

Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in algebra, as well as in their symbolic work with functions. Manipulation can be more mindful when it is fluent.

MAFS.912.A-APR.2.2
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x).
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Content Complexity: Level 1: Recall

Belongs to: Understand the relationship between zeros...

MAFS.912.A-APR.2.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
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Content Complexity: Level 1: Recall

Belongs to: Understand the relationship between zeros...

MAFS.912.A-APR.3.4
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x + y) = (x y) + (2xy) can be used to generate Pythagorean triples.
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Content Complexity: Level 1: Recall

MAFS.912.A-APR.3.5
Know and apply the Binomial Theorem for the expansion of (x in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascals Triangle.
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Content Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-APR.4.6
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form 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, for the more complicated examples, a computer algebra system.
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Content Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-APR.4.7
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
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Content Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.912.A-CED.1.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.
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Content Complexity: Level 2: Basic Application of Skills & Concepts

Belongs to: Create equations that describe numbers or...

MAFS.912.A-CED.1.2
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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Content Complexity: Level 2: Basic Application of Skills & Concepts

Belongs to: Create equations that describe numbers or...

MAFS.912.A-CED.1.3
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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
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Content Complexity: Level 3: Strategic Thinking & Complex Reasoning

Belongs to: Create equations that describe numbers or...

MAFS.912.A-CED.1.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohms law V = IR to highlight resistance R.
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Content Complexity: Level 1: Recall

Belongs to: Create equations that describe numbers or...

MAFS.912.A-REI.1.1
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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Content Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-REI.1.2

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

Content Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.912.A-REI.2.3

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

Content Complexity: Level 2: Basic Application of Skills & Concepts

Belongs to: Solve equations and inequalities in one...

MAFS.912.A-REI.2.4
Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) = q that has the same solutions. Derive the quadratic formula from this form.Solve quadratic equations by inspection (e.g., for x = 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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Content Complexity: Level 2: Basic Application of Skills & Concepts

Belongs to: Solve equations and inequalities in one...

MAFS.912.A-REI.3.5
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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Content Complexity: Level 3: Strategic Thinking & Complex Reasoning

Belongs to: Solve systems of equations. (Algebra 1 -...

MAFS.912.A-REI.3.6
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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Content Complexity: Level 1: Recall

Belongs to: Solve systems of equations. (Algebra 1 -...

MAFS.912.A-REI.3.7
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 x + y = 3.
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Content Complexity: Level 2: Basic Application of Skills & Concepts

Belongs to: Solve systems of equations. (Algebra 1 -...

MAFS.912.A-REI.3.8

Represent a system of linear equations as a single matrix equation in a vector variable.

Content Complexity: Level 1: Recall

Belongs to: Solve systems of equations. (Algebra 1 -...

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MAFS.912.A-REI.3.9
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).
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Content Complexity: Level 2: Basic Application of Skills & Concepts