Mn Dept of Education Standards used:

Benchmark

1.1.2.1 Use number lines to model and solve addition and subtraction problems.

1.2.2.2 Determine if equations involving addition and subtraction are true.

1.2.2.3 Use number sense and models of addition and subtraction such as number lines to identify missing numbers in equations.

4.2.2.2 Use multiplication, division and unknowns to represent a given problem situation using a number sentence.

6.1.1.5 Factor whole numbers, express a whole number as a  product of prime factors with exponents.

6.3.2.1 Solve problems using the relationships between the angles formed by intersecting lines.

6.3.2.2 Determine missing angle measures in a triangle using the triangle sum theorem.

8.1.1.1 Classify real numbers as rational or irrational.

8.2.1.2 Use linear functions to represent relationships.

8.2.1.3 Understand that a function is linear if it can be written in slope-intercept form or it's graph is a straight line.

8.2.3.1 Evaluate algebraic expressions that contain radicals.

8.2.3.2 Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra.

8.2.4.2 Solve multi-step equations in one variable.

8.2.4.3 Express linear equations in slope-intercept and point slope form and convert between these two forms.

8.3.1.1 Use the Pythagorean Theorem to solve problems involving right triangles.

8.3.1.2 Determine the distance between two points on a coordinate plane.

9.2.1.1 Understand the definition of a function.  Use functional notation and evaluate a function at a given point in its domain.

9.2.1.3 Find the domain of a function defined symbolically, graphically or in real world context.

9.2.1.4 Obtain information and draw conclusions from graphs of functions and other relations.

9.2.1.5 Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in general, vertex or intercept (factored form).

9.2.1.6 Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.

9.2.1.9 Determine how translations affect the symbolic and graphical forms of a function.

9.2.2.2 Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.

9.2.2.3 Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representation. Know how to use graphing technology to graph these functions.

9.2.2.4 Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively.

9.2.3.2 Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.

9.2.3.4 Add, subtract, multiply, divide and simplify algebraic fractions.

9.2.3.5 Check whether a given complex number is a solution of a quadratic equation by substituting it for the variable and evaluating the expression, using arithmetic with complex numbers.

9.2.4.1 Represent relationships in various contexts using quadratic equations and inequalities.  Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist.  Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.

9.2.4.2 Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically.  Know how to use calculators, graphing utilities or other technology to solve these equations.

9.2.4.3 Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers.  In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.

9.2.4.4 Represent relationships in various contexts using systems of linear inequalities; solve them graphically.  Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines.

9.2.4.5 Solve linear programming problems in two variables using graphical methods.

9.2.4.6 Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically.

9.2.4.8 Assess the reasonableness of a solution in its given context and compare the solution to appropriate graphical or numerical estimates, interpret a solution in the original context.

9.3.2.4 Write two column proofs.

9.3.3.1 Know and apply properties of parallel lines including properties of angles formed by a transversal.

9.3.3.2 Know and apply properties of angles, including exterior, interior, supplementary and complementary angles to solve problems and justify results.

9.3.3.4 Apply the Pythagorean Theorem.

9.3.3.6 Know and apply properties of congruent and similar figures to solve problems and logically justify results.

9.3.3.8 Know and apply properties of a circle to solve problems and logically justify results.

9.3.4.1 Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.

9.3.4.2 Apply the trigonometric ratios sine, cosine, and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios.

9.3.4.3 Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.

9.3.4.5 Know the equation for the graph of a circle with radius r, and center (h,k), and justify this equation using the Pythagorean Theorem and properties of translations.

9.4.3.1 Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

9.4.3.8 Apply probability concepts to real-world situations to make informed decisions.