MathsQ&A by dot point

Solve absolute-value equations and inequalities in one variable, splitting into two cases and representing solution sets symbolically and on a number line (A.EI.3).

Rearrange formulas and literal equations to solve for a specified variable, treating the other letters as constants and using inverse operations (A.EI.1).

Solve multi-step linear equations in one variable, including equations with the variable on both sides and with rational-number coefficients, and classify an equation as having one solution, no solution, or infinitely many solutions (A.EI.1).

Solve multi-step linear inequalities in one variable, represent the solution set on a number line and in interval notation, and interpret solutions in context, flipping the inequality when multiplying or dividing by a negative (A.EI.2).

Solve systems of two linear equations in two variables by graphing, substitution, and elimination, and interpret one solution, no solution, or infinitely many solutions in context (A.EI.4).

Graph systems of linear inequalities in two variables, identify the overlapping solution region, and determine whether a given point is a solution (A.EI.5).

Compare and contrast linear, quadratic, and exponential functions using tables, graphs, and equations, and determine which family best models a situation (A.F.2).

Identify and interpret exponential functions of the form f(x) = ab^x from tables, graphs, equations, and contexts, including the initial value and the constant growth or decay factor (A.F.2).

Model and interpret exponential growth and decay using the form y = a(1 + r)^t for growth and y = a(1 - r)^t for decay, and evaluate to solve real-world problems (A.F.2).

Distinguish arithmetic from geometric sequences and use the explicit nth-term formulas to find terms and relate sequences to linear and exponential functions (A.F.2).

Determine whether two algebraic expressions are equivalent, and use equivalent forms (expanded, factored, or simplified) to reveal structure and interpret meaning (A.EO.6).

Simplify expressions involving integer exponents using the laws of exponents, and represent and operate with very large or very small numbers in scientific notation (A.EO.2).

Factor polynomial expressions in one variable: a greatest common monomial factor, trinomials of the form ax^2 + bx + c, perfect-square trinomials, and the difference of two squares (A.EO.5).

Add, subtract, and multiply polynomial expressions in one variable, including multiplying binomials and applying special products (A.EO.4).

Apply the order of operations and the properties of real numbers (commutative, associative, distributive, identity, and inverse) to simplify and evaluate numerical and algebraic expressions in one variable (A.EO.1).

Simplify square-root and cube-root radical expressions involving numerical and monomial radicands, and convert between radical notation and rational-exponent notation (A.EO.3).

Determine and represent the domain and range of a function from a graph, table, set of ordered pairs, or context, distinguishing discrete from continuous and reasonable domains in real situations (A.F.2).

Determine whether a relation is a function from a table, graph, mapping, or equation, and use and evaluate function notation f(x) (A.F.1).

Calculate and interpret the slope of a linear function as a rate of change from a graph, table, equation, or two points, and identify the meaning of slope and intercepts in context (A.F.3).

Graph and analyze quadratic functions, identifying the vertex, axis of symmetry, intercepts, and direction of opening, and connecting standard, vertex, and factored forms (A.F.5).

Write equations of linear functions in slope-intercept and point-slope form given a graph, a slope and a point, or two points, and apply the slope relationships for parallel and perpendicular lines (A.F.4).

Identify and interpret key features of a function graph, including x- and y-intercepts, zeros, maximum or minimum values, and intervals where the function increases or decreases (A.F.1).

Solve quadratic equations by completing the square, and use completing the square to rewrite a quadratic in vertex form (A.EI.6).

Solve quadratic equations using the quadratic formula, and use the discriminant to determine the number and nature of the real solutions (A.EI.6).

Solve quadratic equations in one variable by factoring and applying the zero product property, and interpret the solutions as the zeros of the related function (A.EI.6).

Solve quadratic equations of the form x^2 = k or a(x - h)^2 = k by taking square roots, including the plus-or-minus sign, and recognize when there is no real solution (A.EI.6).