#### M3.1: Solving problems

M3.1.A: Select and justify functions and equations to model and solve problems.

M3.1.B: Solve problems that can be represented by systems of equations and inequalities.

M3.1.D: Solve problems that can be represented by exponential and logarithmic functions and equations.

M3.1.E: Solve problems that can be represented by inverse variations of the forms f(x) = a/x + b, f(x) = a/xÂ² + b, and f(x) = a/(bx+c).

#### M3.2: Transformations and functions

M3.2.A: Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x.

M3.2.B: Determine and apply properties of transformations.

M3.2.D: Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.

M3.2.E: Construct new functions using the transformations f(x - h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).

#### M3.3: Functions and modeling

M3.3.A: Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

M3.3.B: Graph an exponential function of the form f(x) = ab to the x power and its inverse logarithmic function.

M3.3.C: Solve exponential and logarithmic equations.

M3.3.D: Plot points, sketch, and describe the graphs of functions of the form f (x) = a times the square root of x - c + d, and solve related equations.

M3.3.E: Plot points, sketch, and describe the graphs of functions of the form f(x) = a/x² + b and f(x) = a/(bx + c), and solve related equations.

M3.3.F: Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.

#### M3.4: Quantifying variability

M3.4.A: Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets.

M3.4.B: Calculate and interpret margin of error and confidence intervals for population proportions.

#### M3.5: Three-dimensional geometry

M3.5.A: Describe the intersections of lines in the plane and in space, of lines and planes, and of planes in space.

M3.5.B: Describe prisms, pyramids, parallelepipeds, tetrahedra, and regular polyhedra in terms of their faces, edges, vertices, and properties.

M3.5.D: Apply formulas for surface area and volume of three-dimensional figures to solve problems.

#### M3.6: Algebraic properties

M3.6.A: Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved.

M3.6.C: Add, subtract, multiply, and divide polynomials.

M3.6.D: Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions.