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Arkansas: HSA Math Standards

23 standards · 4 domains

HSA.APR

HSA.APR.A.1 Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication
HSA.APR.B.2 Know and apply the Factor and Remainder Theorems: 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).
HSA.APR.B.3 Identify zeros of polynomials when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.
HSA.APR.C.4 Prove polynomial identities and use them to describe numerical relationships. Note: Examples of Polynomial Identities may include but are not limited to the following: (a + b)^2 = a^2 + 2ab + b^2 (Algebra 1); a^2 – b^2 = (a – b)(a + b) (Algebra 1); (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples (Algebra 2).
HSA.APR.D.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) is the dividend, b(x) is the divisor, q(x) is the quotient, and r(x) is the remainder) 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.
HSA.APR.D.7 Add, subtract, multiply, and divide by nonzero rational expressions. Understand that rational expressions, like the integers, are closed under addition, subtraction, and multiplication.

HSA.CED

HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Note: Including but not limited to equations arising from: Linear functions, Quadratic functions, Simple rational functions, Exponential functions, Absolute value functions
HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.
HSA.CED.A.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.
HSA.CED.A.4 Rearrange literal equations using the properties of equality

HSA.REI

HSA.REI.A.1 Assuming that equations have a solution, construct a solution and justify the reasoning used.
HSA.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. For example: The area of a square equals 49 square inches. The length of the side is 7 inches. Although -7 is a solution to the equation, x2 = 49, -7 is an extraneous solution.
HSA.REI.B.4 Solve quadratic equations in one variable.
HSA.REI.C.5 Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.
HSA.REI.C.6 Solve systems of equations algebraically and graphically.
HSA.REI.C.7 Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically. For example: Find the points of intersection between y = -3x and y = x^2 + 2.
HSA.REI.C.8 (+) Represent a system of linear equations as a single matrix equation in a vector variable.
HSA.REI.C.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).
HSA.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); Find the solutions approximately by: Using technology to graph the functions; Making tables of values; Finding successive approximations. Include cases (but not limited to) where f(x) and/or g(x) are: Linear; Polynomial; Rational; Exponential (Introduction in Algebra 1, Mastery in Algebra 2); Logarithmic functions
HSA.REI.D.12 Solve linear inequalities and systems of linear inequalities in two variables by graphing.

HSA.SSE

HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
HSA.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example: See that (x + 3)(x + 3) is the same as (x + 3)^2 OR x^4 – y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2).
HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.