## MAT-HS.A-APR
## Domain DescriptionAn expression is a record of a computation with numbers, symbols that represent numbers, arithmetic operations, exponentiation, and, at more advanced levels, the operation of evaluating a function. Conventions about the use of parentheses and the order of operations assure that each expression is unambiguous. Creating an expression that describes a computation involving a general quantity requires the ability to express the computation in general terms, abstracting from specific instances. Reading an expression with comprehension involves analysis of its underlying structure. This may suggest a different but equivalent way of writing the expression that exhibits some different aspect of its meaning. For example, Algebraic manipulations are governed by the properties of operations and exponents, and the conventions of algebraic notation. At times, an expression is the result of applying operations to simpler expressions. For example, A spreadsheet or a computer algebra system (CAS) can be used to experiment with algebraic expressions, perform complicated algebraic manipulations, and understand how algebraic manipulations behave. ## Standards in this Domain- MAT-HS.A-APR.01 - 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.
- MAT-HS.A-APR.02 - 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*).
- MAT-HS.A-APR.03 - 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.
- MAT-HS.A-APR.04 - Prove polynomial identities and use them to describe numerical relationships.
*For example, the polynomial identity (x*^{2}+ y^{2})^{2}= (x^{2}- y^{2})^{2}+ (2xy)^{2}can be used to generate Pythagorean triples.
- MAT-HS.A-APR.05 - Know and apply the Binomial Theorem for the expansion of (
*x*+*y*)^{n}in powers of*x*and*y*for a positive integer*n*, where*x*and*y*are any numbers, with coefficients determined for example by Pascal's Triangle.
- MAT-HS.A-APR.06 - 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.
- MAT-HS.A-APR.07 - 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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## MAT-HS.A-APR.01
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## Proficiency Scale
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## MAT-HS.A-APR.02
## Student Learning Targets:
## Alg II Solve Polynomial Equations Proficiency Scale
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## MAT-HS.A-APR.03
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## MAT-HS.A-APR.04
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## MAT-HS.A-APR.05
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## Proficiency Scale
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## MAT-HS.A-APR.06
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## MAT-HS.A-APR.07
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## MAT-HS.A-CED
## Domain DescriptionAn equation is a statement of equality between two expressions, often viewed as a question asking for which values of the variables the expressions on either side are in fact equal. These values are the solutions to the equation. An identity, in contrast, is true for all values of the variables; identities are often developed by rewriting an expression in an equivalent form. The solutions of an equation in one variable form a set of numbers; the solutions of an equation in two variables form a set of ordered pairs of numbers, which can be plotted in the coordinate plane. Two or more equations and/or inequalities form a system. A solution for such a system must satisfy every equation and inequality in the system. An equation can often be solved by successively deducing from it one or more simpler equations. For example, one can add the same constant to both sides without changing the solutions, but squaring both sides might lead to extraneous solutions. Strategic competence in solving includes looking ahead for productive manipulations and anticipating the nature and number of solutions. Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of The same solution techniques used to solve equations can be used to rearrange formulas. For example, the formula for the area of a trapezoid, Connections to Functions and Modeling. Expressions can define functions, and equivalent expressions define the same function. Asking when two functions have the same value for the same input leads to an equation; graphing the two functions allows for finding approximate solutions of the equation. Converting a verbal description to an equation, inequality, or system of these is an essential skill in modeling. ## Standards in this Domain- MAT-HS.A-CED.01 - 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*.
- MAT-HS.A-CED.02 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- MAT-HS.A-CED.03 - 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*.
- MAT-HS.A-CED.04 - 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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## MAT-HS.A-CED.01
This standard is divided into parts. Click on these links to see specific proficiency scales.
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