Maryland flagMaryland: Algebra Math Standards

35 standards · 4 domains

ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS

  • A.APR.A.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.
  • A.APR.B.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).
  • A.APR.B.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.
  • A.APR.B.3.a 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.
  • A.APR.C.4 Prove polynomial identities and use them to describe numerical relationships.
  • A.APR.C.5 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.
  • A.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), 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.
  • A.APR.D.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.

CREATING EQUATIONS

  • A.CED.A.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 and exponential functions.
  • A.CED.A.1.a Create equations and inequalities in one variable and use them to solve problems.
  • A.CED.A.1.b Create polynomial equations given roots.
  • A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A.CED.A.3 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.
  • A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

REASONING WITH EQUATIONS AND INEQUALITIES

  • A.REI.A.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.
  • A.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
  • A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • A.REI.B.4 Solve quadratic equations in one variable.
  • A.REI.C.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.
  • A.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • A.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
  • A.REI.C.7.a Solve systems of equations comprised of various combinations of all algebraic and transcendental functions in two variables.
  • A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
  • A.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, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
  • A.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

SEEING STRUCTURE IN EXPRESSIONS

  • A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
  • A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.
  • A.SSE.A.2.a Analyze the structure of the general form of a second degree equation, Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, to identify the conic section represented by the equation.
  • A.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • A.SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions.
  • A.SSE.B.3.d Choose and produce an equivalent form of a second degree equation, Ax^2 + Cy^2 + Dx + Ey + F = 0, to reveal and explain properties of the conic section represented by the equation.
  • A.SSE.B.3.e Translate between the standard and general form, Ax^2 + Cy^2 + Dx + Ey + F = 0, of a second degree equation.
  • A.SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
  • A.SSE.B.4.a Express the sums in a series using sigma notation.
  • A.SSE.B.5 Determine the sum, if it exists, of an infinite geometric series.