### A1: Algebra I

#### A1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

A1.1.2: Simplify square roots using factors.

#### A1.2: Students solve linear equations and inequalities in one variable. They solve word problems that involve linear equations, inequalities, or formulas.

A1.2.1: Solve linear equations.

A1.2.2: Solve equations and formulas for a specified variable.

A1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

A1.2.4: Solve linear inequalities using properties of order.

A1.2.5: Solve combined linear inequalities.

#### A1.3: Students sketch and interpret graphs representing given situations. They understand the concept of a function and analyze the graphs of functions.

A1.3.1: Sketch a reasonable graph for a given relationship.

A1.3.3: Understand the concept of a function, decide if a given relation is a function, and link equations to functions.

A1.3.4: Find the domain and range of a relation.

#### A1.4: Students graph linear equations and inequalities in two variables. They write equations of lines and find and use the slope and y-intercept of lines. They use linear equations to model real data.

A1.4.1: Graph a linear equation.

A1.4.2: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

A1.4.3: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept of the graph are related to the equation.

A1.4.4: Write the equation of a line given appropriate information.

A1.4.5: Write the equation of a line that models a data set and use the equation (or the graph of the equation) to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

A1.4.6: Graph a linear inequality in two variables.

#### A1.5: Students solve pairs of linear equations using graphs and using algebra. They solve pairs of linear inequalities using graphs. They solve word problems involving pairs of linear equations.

A1.5.1: Use a graph to estimate the solution of a pair of linear equations in two variables.

A1.5.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

A1.5.4: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

A1.5.5: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

A1.5.6: Use pairs of linear equations to solve word problems.

#### A1.6: Students add, subtract, multiply, and divide polynomials. They factor quadratics.

A1.6.2: Multiply and divide monomials.

A1.6.4: Multiply polynomials.

A1.6.5: Divide polynomials by monomials.

A1.6.6: Find a common monomial factor in a polynomial.

A1.6.7: Factor the difference of two squares and other quadratics.

A1.6.8: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.

#### A1.7: Students simplify algebraic ratios and solve algebraic proportions.

A1.7.1: Simplify algebraic ratios.

A1.7.2: Solve algebraic proportions.

#### A1.8: Students graph and solve quadratic and radical equations. They graph cubic equations.

A1.8.2: Solve quadratic equations by factoring.

A1.8.3: Solve quadratic equations in which a perfect square equals a constant.

A1.8.5: Derive the quadratic formula by completing the square.

A1.8.8: Solve equations that contain radical expressions.

### A2: Algebra II

#### A2.1: Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.

A2.1.1: Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.

A2.1.2: Use function notation. Add, subtract, multiply, and divide pairs of functions.

A2.1.4: Graph relations and functions with and without graphing technology.

A2.1.5: Find the zeros of a function.

A2.1.6: Solve an inequality by examining the graph.

A2.1.8: Interpret given situations as functions in graphs, formulas, and words.

#### A2.2: Students solve systems of linear equations and inequalities and use them to solve word problems. They model data with linear equations.

A2.2.1: Graph absolute value equations and inequalities.

A2.2.2: Use substitution, elimination, and matrices to solve systems of two or three linear equations in two or three variables.

A2.2.3: Use systems of linear equations and inequalities to solve word problems.

#### A2.3: Students solve quadratic equations, including the use of complex numbers. They interpret maximum and minimum values of quadratic functions. They solve equations that contain square roots.

A2.3.2: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

A2.3.3: Solve quadratic equations in the complex number system.

A2.3.4: Graph quadratic functions. Apply transformations to quadratic functions. Find and interpret the zeros and maximum or minimum value of quadratic functions.

A2.3.6: Solve equations that contain radical expressions.

A2.3.7: Solve pairs of equations, one quadratic and one linear, or both quadratic.

#### A2.4: Students write equations of conic sections and draw their graphs.

A2.4.1: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

A2.4.2: Graph conic sections.

#### A2.5: Students use the binomial theorem, divide and factor polynomials, and solve polynomial equations.

A2.5.2: Divide polynomials by others of lower degree.

A2.5.3: Factor polynomials completely and solve polynomial equations by factoring.

A2.5.7: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.

#### A2.6: Students use negative and fractional exponents. They simplify algebraic fractions and solve equations involving algebraic fractions. They solve problems of direct, inverse, and joint variation.

A2.6.2: Add, subtract, multiply, divide, and simplify algebraic fractions.

A2.6.4: Solve equations involving algebraic fractions.

A2.6.5: Solve word problems involving fractional equations.

A2.6.6: Solve problems of direct, inverse, and joint variation.

#### A2.7: Students graph exponential functions and relate them to logarithms. They solve logarithmic and exponential equations and inequalities. They solve word problems using exponential functions.

A2.7.1: Graph exponential functions.

A2.7.4: Solve logarithmic and exponential equations and inequalities.

A2.7.8: Solve word problems involving applications of exponential functions to growth and decay.

#### A2.8: Students define and use arithmetic and geometric sequences and series.

A2.8.1: Define arithmetic and geometric sequences and series.

A2.8.2: Find specified terms of arithmetic and geometric sequences.

A2.8.4: Solve word problems involving applications of sequences and series.

#### A2.9: Students use fundamental counting principles to compute combinations, permutations, and probabilities.

A2.9.1: Understand and apply counting principles to compute combinations and permutations.

A2.9.2: Use the basic counting principle, combinations, and permutations to compute probabilities.

#### C.1: Students understand the concept of limit, find limits of functions at points and at infinity, decide if a function is continuous, and use continuity theorems.

C.1.1: Understand the concept of limit and estimate limits from graphs and tables of values.

C.1.4: Find limits of rational functions that are undefined at a point.

C.1.11: Find the types of discontinuities of a function.

#### C.3: Students find slopes and tangents, maximum and minimum points, and points of inflection. They solve optimization problems and find rates of change.

C.3.10: Find average and instantaneous rates of change. Understand the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed, and acceleration.

C.3.11: Find the velocity and acceleration of a particle moving in a straight line.

#### C.4: Students define integrals using Riemann Sums, use the Fundamental Theorem of Calculus to find integrals, and use basic properties of integrals. They integrate by substitution and find approximate integrals.

C.4.2: Calculate the values of Riemann Sums over equal subdivisions using left, right, and midpoint evaluation points.

C.4.3: Interpret a definite integral as a limit of Riemann Sums.

C.4.8: Understand and use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values.

#### C.5: Students find velocity functions and position functions from their derivatives, solve separable differential equations, and use definite integrals to find areas and volumes.

C.5.1: Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions, and applications to motion along a line.

C.5.7: Apply integration to model and solve problems in physics, biology, economics, etc., using the integral as a rate of change to give accumulated change and using the method of setting up an approximating Riemann Sum and representing its limit as a definite integral.

### DM: Discrete Mathematics

#### DM.1: Students use counting techniques.

DM.1.1: Use networks, traceable paths, tree diagrams, Venn diagrams, and other pictorial representations to find the number of outcomes in a problem situation.

DM.1.3: Use combinatorial reasoning to solve problems.

#### DM.2: Students use matrices.

DM.2.1: Use matrices to organize and store data.

#### DM.3: Students use recursive techniques.

DM.3.1: Use recursive thinking to solve problems.

DM.3.2: Use finite differences to solve problems.

### G: Geometry

#### G.1: Students find lengths and midpoints of line segments. They describe and use parallel and perpendicular lines. They find slopes and equations of lines.

G.1.1: Find the lengths and midpoints of line segments in one- or two-dimensional coordinate systems.

G.1.2: Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass, explaining and justifying the process used.

G.1.3: Understand and use the relationships between special pairs of angles formed by parallel lines and transversals.

G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

#### G.2: Students identify and describe polygons and measure interior and exterior angles. They use congruence, similarity, symmetry, tessellations, and transformations. They find measures of sides, perimeters, and areas.

G.2.2: Find measures of interior and exterior angles of polygons, justifying the method used.

G.2.3: Use properties of congruent and similar polygons to solve problems.

G.2.4: Apply transformations (slides, flips, turns, expansions, and contractions) to polygons in order to determine congruence, similarity, symmetry, and tessellations. Know that images formed by slides, flips and turns are congruent to the original shape.

G.2.5: Find and use measures of sides, perimeters, and areas of polygons, and relate these measures to each other using formulas.

G.2.6: Use coordinate geometry to prove properties of polygons such as regularity, congruence, and similarity.

#### G.3: Students identify and describe simple quadrilaterals. They use congruence and similarity. They find measures of sides, perimeters, and areas.

G.3.1: Describe, classify, and understand relationships among the quadrilaterals square, rectangle, rhombus, parallelogram, trapezoid, and kite.

G.3.2: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.

G.3.3: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas.

G.3.4: Use coordinate geometry to prove properties of quadrilaterals such as regularity, congruence, and similarity.

#### G.4: Students identify and describe types of triangles. They identify and draw altitudes, medians, and angle bisectors. They use congruence and similarity. They find measures of sides, perimeters, and areas. They apply inequality theorems.

G.4.1: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.

G.4.3: Construct triangles congruent to given triangles.

G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

G.4.5: Prove and apply theorems involving segments divided proportionally.

G.4.6: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

G.4.7: Find and use measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.

G.4.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and hinge theorem.

G.4.9: Use coordinate geometry to prove properties of triangles such as regularity, congruence, and similarity.

#### G.5: Students prove the Pythagorean Theorem and use it to solve problems. They define and apply the trigonometric relations sine, cosine, and tangent.

G.5.1: Prove and use the Pythagorean Theorem.

G.5.2: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

G.5.4: Define and use the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) in terms of angles of right triangles.

G.5.5: Know and use the relationship sin²x + cos²x = 1.

G.5.6: Solve word problems involving right triangles.

#### G.6: Students define ideas related to circles: e.g., radius, tangent. They find measures of angles, lengths, and areas. They prove theorems about circles. They find equations of circles.

G.6.2: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent.

G.6.3: Prove theorems related to circles.

G.6.5: Define, find, and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

G.6.6: Define and identify congruent and concentric circles.

G.6.7: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems.

G.6.8: Find the equation of a circle in the coordinate plane in terms of its center and radius.

#### G.7: Students describe and make polyhedra and other solids. They describe relationships and symmetries, and use congruence and similarity.

G.7.2: Describe the polyhedron that can be made from a given net (or pattern). Describe the net for a given polyhedron.

G.7.4: Describe symmetries of geometric solids.

G.7.5: Describe sets of points on spheres: chords, tangents, and great circles.

G.7.6: Identify and know properties of congruent and similar solids.

G.7.7: Find and use measures of sides, volumes of solids, and surface areas of solids, and relate these measures to each other using formulas.

### PC: Pre-Calculus/Trigonometry

#### PC.1: Students use polynomial, rational, and algebraic functions to write functions and draw graphs to solve word problems, to find composite and inverse functions, and to analyze functions and graphs. They analyze and graph circles, ellipses, parabolas, and hyperbolas.

PC.1.1: Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators.

PC.1.2: Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators.

PC.1.3: Model and solve word problems using functions and equations.

PC.1.5: Describe the symmetry of the graph of a function.

PC.1.7: Apply transformations to functions.

PC.1.10: Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).

#### PC.2: Students solve word problems involving logarithmic and exponential functions. They draw and analyze graphs and find inverse functions.

PC.2.1: Solve word problems involving applications of logarithmic and exponential functions.

PC.2.2: Find the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.

PC.2.3: Draw and analyze graphs of logarithmic and exponential functions.

PC.2.4: Define, find, and check inverse functions of logarithmic and exponential functions.

#### PC.3: Students define trigonometric functions using right triangles. They solve word problems and apply the laws of sines and cosines.

PC.3.1: Solve word problems involving right and oblique triangles.

PC.3.3: Find the area of a triangle given two sides and the angle between them.

#### PC.4: Students define trigonometric functions using the unit circle and use degrees and radians. They draw and analyze graphs, find inverse functions, and solve word problems.

PC.4.1: Define sine and cosine using the unit circle.

PC.4.3: Learn exact sine, cosine, and tangent values for 0, pi/2, pi/3, pi/4, pi/6, and multiples of pi. Use those values to find other trigonometric values.

PC.4.4: Solve word problems involving applications of trigonometric functions.

PC.4.5: Define and graph trigonometric functions (i.e., sine, cosine, tangent, cosecant, secant, cotangent).

PC.4.6: Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions.

PC.4.7: Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.

PC.4.9: Find values of trigonometric and inverse trigonometric functions.

PC.4.10: Know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.

PC.4.11: Make connections between right triangle ratios, trigonometric functions, and circular functions.

#### PC.5: Students prove trigonometric identities, solve trigonometric equations, and solve word problems.

PC.5.1: Know the basic trigonometric identity cos²x + sin²x = 1 and prove that it is equivalent to the Pythagorean Theorem.

PC.5.2: Use basic trigonometric identities to verify other identities and simplify expressions.

PC.5.3: Understand and use the addition formulas for sines, cosines, and tangents.

PC.5.4: Understand and use the half-angle and double-angle formulas for sines, cosines, and tangents.

#### PC.6: Students define polar coordinates and complex numbers and understand their connection with trigonometric functions.

PC.6.1: Define polar coordinates and relate polar coordinates to Cartesian coordinates.

PC.6.2: Represent equations given in rectangular coordinates in terms of polar coordinates.

PC.6.3: Graph equations in the polar coordinate plane.

PC.6.4: Define complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form.

#### PC.7: Students define and use arithmetic and geometric sequences and series, understand the concept of a limit, and solve word problems.

PC.7.3: Prove and use the sum formulas for arithmetic series and for finite and infinite geometric series.

PC.7.4: Use recursion to describe a sequence.

PC.7.6: Solve word problems involving applications of sequences and series.

#### PC.8: Students model data with linear and nonlinear functions.

PC.8.1: Find linear models using the median fit and least squares regression methods. Decide which model gives a better fit.

PC.8.2: Calculate and interpret the correlation coefficient. Use the correlation coefficient and residuals to evaluate a “best-fit” line.

PC.8.3: Find a quadratic, exponential, logarithmic, power, or sinusoidal function to model a data set and explain the parameters of the model.

### PS: Probability and Statistics

#### PS.1: Students gather and display data and use measures of central tendency and variability.

PS.1.1: Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency polygons, cumulative distribution functions, pie charts, scatter plots, stem-and-leaf plots, and box-and-whisker plots. Draw these by hand or use a computer spreadsheet program.

PS. 1.2: Compute and use mean, median, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation.

#### PS.2: Students solve problems involving the use of probability and probability distributions.

PS.2.1: Understand the counting principle, permutations, and combinations, and use them to solve problems.

PS.2.3: Understand and use the multiplication rule to calculate probabilities for independent and dependent events.

PS.2.6: Use discrete random variables and probability distributions, including the binomial and geometric distributions.

PS.2.7: Compute and interpret the mean and variance of a probability distribution.

PS.2.10: Use other continuous random variables and probability distributions to solve problems.

#### PS.3: Students use confidence intervals and hypothesis tests, fit curves to data, and calculate correlation coefficients.

PS.3.2: Understand hypothesis tests of means and differences between means and use them to reach conclusions.

PS.3.4: Calculate and interpret the correlation coefficient of a set of data.

### IM1: Integrated Mathematics I

#### IM1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

IM1.1.1: Compare real number expressions.

IM1.1.2: Simplify square roots using factors.

#### IM1.2: Students solve linear equations and inequalities in one variable. They write equations of lines and find and use the slope and y-intercept of lines. Students solve pairs of linear equations using graphs and algebra. Students add, subtract, multiply, and divide polynomials and solve word problems using exponential functions.

IM1.2.1: Solve linear equations.

IM1.2.2: Solve equations and formulas for a specific variable.

IM1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

IM1.2.4: Solve linear inequalities using properties of order.

IM1.2.6: Sketch a reasonable graph for a given relationship.

IM1.2.8: Understand the concept of a function, decide if a given relation is a function and link equations to functions.

IM1.2.9: Find the domain and range of a relation.

IM1.2.10: Graph a linear equation.

IM1.2.11: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

IM1.2.12: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept are related to the equation.

IM1.2.13: Write the equation of a line given appropriate information.

IM1.2.14: Write the equation of a line that models a given situation and use (or the graph of the line) to make predictions. Describe the slope of the line in terms of the given situation, recognizing that the slope is the rate of change.

IM1.2.15: Use the graph to estimate the solution of a pair of linear equations in two variables.

IM1.2.17: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

IM1.2.18: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

IM1.2.19: Use pairs of linear equations to solve word problems.

IM1.2.21: Multiple and divide monomials.

IM1.2.22: Find powers and roots of monomials (only when the answer has an integer exponent).

IM1.2.23: Multiply polynomials.

IM1.2.24: Divide polynomials by monomials.

IM1.2.25: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.

IM1.2.30: Graph exponential functions.

IM1.2.31: Solve word problems involving applications of exponential functions to growth and decay.

#### IM1.3: Students identify and describe polygons, including finding measures of sides, perimeters, and areas. They use congruence, similarity, symmetry, tessellations, and transformations. Students understand the Pythagorean Theorem and use it to solve problems. They describe relationships and symmetries in geometric solids.

IM1.3.2: Apply transformations (slides, flips, turns, expansions, and contractions) to polygons to determine congruence, similarity, symmetry, and tessellations. Know that images formed by slides, flips, and turns are congruent to the original shape.

IM1.3.3: Find and use measures of sides, perimeter, and areas of polygons, and relate these measures to each other using formulas.

IM1.3.4: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.

IM1.3.5: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas.

IM1.3.6: Prove and use the Pythagorean Theorem.

IM1.3.8: Describe symmetries of geometric solids.

#### IM1.4: Students find measures of the center and variability of a set of data, as well as construct and analyze data displays and plot least square regression lines.

IM1.4.1: Construct a line plot.

IM1.4.2: Find measures of central tendency for a set of data.

IM1.4.4: Construct a histogram using a graphing calculator.

IM1.4.6: Find a linear transformation.

IM1.4.7: Construct a stem-and-leaf plot using a graphing calculator.

IM1.4.12: Construct a scatterplot from a set of data.

IM1.4.15: Compare sets of data using scatterplots and the line y = x, and interpret these comparisons for real-world data.

IM1.4.16: Recognize patterns in tables and graphs that are modeled by linear equations.

#### IM1.5: Students use simulations, find probabilities, and use the Law of Large Numbers.

IM1.5.1: Design and use simulations in order to estimate answers related to probability.

IM1.5.2: Use empirical (experimental) and theoretical probabilities.

IM1.5.3: Understand independent events.

IM1.5.4: Use the Law of Large Numbers to understand situations involving chance.

IM1.5.5: Understand the concept of a probability distribution. Understand how an approximate probability can be constructed using simulation involving chance.

#### IM1.6: Students construct graphs, explore algorithms, and use recursion equations and matrices.

IM1.6.5: Use a recursion function to describe an exponential function.

### IM2: Integrated Mathematics II

#### IM2.1: Students graph linear inequalities in two variables and quadratics. They model data with linear equations.

IM2.1.1: Graph a linear inequality in two variables.

IM2.1.2: Interpret given situations as functions in graphs, formulas, and words.

IM2.1.4: Graph quadratic functions. Show and explain the effects on the graph of changing a coefficient in a quadratic function. Find and interpret the zeros and maximum or minimum value of quadratic functions.

#### IM2.2: Students identify and describe types of triangles. They define and apply the trigonometric relations. Students apply theorems to triangles and circles.

IM2.2.2: Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass, explaining and justifying the process used.

IM2.2.3: Find the measures of interior and exterior angles of polygons, justifying the method used.

IM2.2.4: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

IM2.2.5: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.

IM2.2.6: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

IM2.2.7: Find measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.

IM2.2.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and the hinge theorem.

IM2.2.9: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

IM2.2.11: Define and apply the trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) defined by angles of right triangles.

IM2.2.12: Know and use the relationship sin²x + cos²x = 1.

IM2.2.13: Solve word problems involving right triangles.

IM2.2.15: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent.

IM2.2.16: Prove theorems related to circles.

IM2.2.18: Define, find, and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

IM2.2.20: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems.

IM2.2.21: Describe sets of points on spheres: chords, tangents, and great circles.

#### IM2.3: Students interpret scatterplots and analyze correlation.

IM2.3.1: Describe the association between two variables by interpreting a scatterplot.

IM2.3.2: Interpret correlation coefficients.

IM2.3.4: Understand that a correlation between two variables does not necessarily imply one directly causes the other.

IM2.3.5: Understand the effects of outliers on correlation coefficients, on the least squares regression line, and on the interpretations of correlation coefficients and regression lines in real-life contexts.

#### IM2.4: Students construct probability distributions, understand fundamental probability concepts, and use counting principles.

IM2.4.1: Construct a probability distribution by simulation and use it to understand and analyze the probabilistic situation.

IM2.4.2: Explore the geometric, or waiting-time, distribution.

IM2.4.3: Understand fundamental concepts of probability (i.e., independent events, multiplication rule, expected value).

IM2.4.4: Understand and apply counting principles to compute combinations and permutations.

IM2.4.5: Use the basic counting principle, combinations, and permutations to compute probabilities.

#### IM2.6: Students apply trigonometric ratios to right triangles.

IM2.6.1: Explore properties and applications of the sine, cosine, and tangent ratios for the lengths of sides of right triangles.

### IM3: Integrated Mathematics III

#### IM3.1: Students solve inequalities, quadratic equations, and systems of equations. They graph polynomial, rational, algebraic, and piece-wise defined functions. They graph and write the equations of conic sections and compute with and factor polynomials and algebraic fractions. They solve problems involving exponential and logarithmic expressions, as well as define and use arithmetic and geometric sequences and series.

IM3.1.1: Solve combined linear inequalities.

IM3.1.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

IM3.1.3: Find a common monomial factor in a polynomial.

IM3.1.4: Factor the difference of two squares and other quadratics.

IM3.1.5: Simplify algebraic ratios.

IM3.1.6: Solve algebraic proportions.

IM3.1.7: Solve quadratic equations by factoring.

IM3.1.8: Solve quadratic equations in which a perfect square equals a constant.

IM3.1.10: Derive the quadratic formula by completing the square.

IM3.1.12: Recognize and graph various types of functions, including polynomials, rational, and algebraic functions.

IM3.1.13: Use function notation. Add, subtract, multiply, and divide pairs of functions.

IM3.1.16: Find the zeros of a function.

IM3.1.17: Solve an inequality by examining the graph.

IM3.1.19: Graph absolute value equations and inequalities.

IM3.1.20: Use substitution, elimination, and matrices to solve systems of two or three equations in two or three variables.

IM3.1.21: Use system of equations and inequalities to solve word problems.

IM3.1.23: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

IM3.1.24: Solve quadratic equations in the complex number system.

IM3.1.27: Solve pairs of equations, one quadratic and one linear, or both quadratic.

IM3.1.28: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

IM3.1.29: Graph conic sections.

IM3.1.31: Divide polynomials by others of lower degree.

IM3.1.32: Factor polynomials completely and solve polynomial equations by factoring.

IM3.1.36: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of the graph, and the factors of a polynomial expression.

IM3.1.38: Add, subtract, multiply, divide, and simplify algebraic fractions.

IM3.1.40: Solve equations involving algebraic fractions.

IM3.1.41: Solve word problems involving fractional equations.

IM3.1.42: Solve problems of direct, inverse, and joint variation.

IM3.1.49: Solve word problems involving applications of exponential functions to growth and decay.

IM3.1.50: Define arithmetic and geometric sequences and series.

IM3.1.51: Find specified terms of arithmetic and geometric sequences.

IM3.1.53: Solve word problems involving applications of sequences and series.

#### IM3.2: Students describe and use parallel and perpendicular lines. They use coordinate geometry and prove that triangles are congruent or similar. They find the equation of a circle in the coordinate plane and describe and use properties of solids.

IM3.2.1: Understand and use the relationships between special pairs of angles formed by parallel lines and transversals.

IM3.2.2: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

IM3.2.3: Use properties of congruent and similar polygons to solve problems.

IM3.2.4: Use coordinate geometry to prove properties of polygons such as regularity, congruence, and similarity.

IM3.2.5: Describe, classify, and understand relationships among quadrilaterals square, rectangles, rhombus, parallelogram, trapezoid, and kite.

IM3.2.6: Use coordinate geometry to prove properties of quadrilaterals such as regularity, congruence, and similarity.

IM3.2.7: Construct triangles congruent to given triangles.

IM3.2.9: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

IM3.2.10: Use coordinate geometry to prove properties of triangles such as regularity, congruence, and similarity.

IM3.2.11: Find the equation of a circle in the coordinate plane in terms of its center and radius.

IM3.2.13: Describe the polyhedron that can be made from a given net (or pattern). Describe the net for a given polygon.

IM3.2.14: Identify and know properties of congruent and similar solids.

IM3.2.15: Find and use measures of sides, volumes of solids, and surface areas of solids. Relate these measures to each other using formulas.

#### IM3.3: Students design and interpret surveys, use sampling distributions, and understand standard deviation.

IM3.3.1: Understand and apply basic ideas related to the design and interpretation of surveys, such as background information, random sampling, and bias.

IM3.3.2: Construct simulated sampling distributions of sample proportions and use sampling distributions to identify which proportions are likely to be found in a sample of a given size.

#### IM3.6: Students use the Law of Sines and the Law of Cosines to solve problems. They analyze families of trigonometric functions.

IM3.6.1: Find the measures of sides and angles in triangles using the Law of Sines.

IM3.6.2: Find the measures of sides and angles in triangles using the Law of Cosines.

IM3.6.3: Compare and contrast families of trigonometric functions.

Correlation last revised: 12/3/2009

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.