8.N.ME.08.01 Understand the meaning of a square root of a number and its connection to the square whose area is the number; understand the meaning of a cube root and its connection to the volume of a cube.
8.N.ME.08.03 Understand that in decimal form, rational numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the number line; know fraction forms of common repeating decimals, e.g., 0.1 repeating = 1/9; 0.3 repeating = 1/3.
8.N.ME.08.04 Understand that irrational numbers are those that cannot be expressed as the quotient of two integers, and cannot be represented by terminating or repeating decimals; approximate the position of familiar irrational numbers, e.g., square root of 2, square root of 3, pi, on the number line.
8 Understand the concept of non-linear functions using basic examples
8.A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships (y = k/x); cubics (y = ax3); roots (y = the square root of x); and exponentials (y = a to the x power, a > 0); using tables, graphs, and equations.
8.A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable.
8 Understand and represent quadratic functions
8.A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs, and vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function.
8.A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x-axis and the coordinates of the vertex; use words "parabola" and "roots"; include functions in vertex form and those with leading coefficient -1, e.g., y = x2 - 36, y = (x - 2)2 - 9; y = - x2; y = -(x - 3)2.
8 Recognize, represent, and apply common formulas
8.A.FO.08.07 Recognize and apply the common formulas:
8.A.FO.08.07.1 (a + b)2 = a2 + 2 ab + b2
8.A.FO.08.07.2 (a - b)2 = a2 - 2 ab + b2
8.A.FO.08.07.3 (a + b) (a - b) = a2 - b2; represent geometrically.
8 Understand solutions and solve equations, simultaneous equations, and linear inequalities
8.A.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true, e.g., determine whether a given value, or values from a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution).
8.A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions.
8.A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets.
8 Understand concepts of volume and surface area, and apply formulas
8.G.SR.08.06 Know the volume formulas for generalized cylinders ((area of base) x height), generalized cones and pyramids (1/3 (area of base) x height), and spheres (4/3 pi (radius)3) and apply them to solve problems.
8.G.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional solids including orthogonal views (top, front, and side), picture views (projective or isometric), and nets; use such two-dimensional representations to help solve problems.
8.D.PR.08.06 Understand the difference between independent and dependent events, and recognize common misconceptions involving probability, e.g., Alice rolls a 6 on a die three times in a row; she is just as likely to roll a 6 on the fourth roll as she was on any previous roll.