Kansas: Algebra Math Standards
38 standards · 4 domains
ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS
- A.APR.1 (9/10) Add, subtract, and multiply polynomials.
- A.APR.2 (11) Factor higher degree polynomials; identifying that some polynomials are prime.
- A.APR.3 (11) Know and apply the Remainder Theorem: For a polynomial p(x) and a number c, the remainder on division by (x - c) is p(c), so p(c) = 0 if and only if (x - c) is a factor of p(x).
- A.APR.4 (9/10/11) Generate polynomial identities from a pattern. For example, difference of squares, perfect square trinomials, (emphasize sum and difference of cubes in grade 11).
- A.APR.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. The Binomial Theorem can be proven by mathematical induction or by a combinatorial argument.
- A.APR.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.7 (+) Add, subtract, multiply, and divide rational expressions.
CREATING EQUATIONS
- A.CED.1 (all) Apply and extend previous understanding to create equations and inequalities in one variable and use them to solve problems.
- A.CED.2 (all) Apply and extend previous understanding to create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- A.CED.3 (all) 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.
- A.CED.4 (all) 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.
REASONING WITH EQUATIONS AND INEQUALITIES
- A.REI.1 (all) 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.2 (all) Apply and extend previous understanding to solve equations, inequalities, and compound inequalities in one variable, including literal equations and inequalities.
- A.REI.3 Solve equations in one variable and give examples showing how extraneous solutions may arise.
- A.REI.3a (9/10/11) Solve rational, absolute value and square root equations. (9/10) Limited to simple equations such as, 2√x−3 + 8 = 16, x+3/2x-1 = 5, x ≠ 1/2.
- A.REI.3b (+) Solve exponential and logarithmic equations.
- A.REI.4 (11) Solve radical and rational exponent equations and inequalities in one variable, and give examples showing how extraneous solutions may arise.
- A.REI.5 Solve quadratic equations and inequalities.
- A.REI.5a (9/10) Solve quadratic equations by inspection (e.g. for x^2 = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives no real solutions.
- A.REI.5b (11) Solve quadratic equations with complex solutions written in the form a +/- bi for real numbers a and b.
- A.REI.5c (11) Use the method of completing the square to transform and solve any quadratic equation in x into an equation of the form (x - p)^2 that has the same solutions.
- A.REI.5d (+) Solve quadratic inequalities and identify the domain.
- A.REI.6 (9/10) Analyze and solve pairs of simultaneous linear equations.
- A.REI.6a (9/10) Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
- A.REI.6b (9/10) Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
- A.REI.6c (9/10) Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
- A.REI.7 (+) Represent a system of linear equations as a single matrix equation and solve (incorporating technology) for matrices of dimension 33 or greater.
- A.REI.8 (all) 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.9 (9/10/11) Solve an equation f(x) = g(x) by graphing y = f(x) and y = g(x) and finding the x-value of the intersection point. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. For (9/10) focus on linear, quadratic, and absolute value.
- A.REI.10 (9/10) 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.1 (all) Interpret expressions that represent a quantity in terms of its context.
- A.SSE.1a (all) Interpret parts of an expression, such as terms, factors, and coefficients.
- A.SSE.1b (all) Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and (1+r)^n.
- A.SSE.2 (all) Use the structure of an expression to identify ways to rewrite it.
- A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- A.SSE.3a (9/10) Factor a quadratic expression to reveal the zeros of the function it defines.
- A.SSE.3b (11) Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- A.SSE.3c (11) Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)12^t ≈ 1.012^12^t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.