### G: Geometry

#### G.1: Compute and determine the reasonableness of a result in mathematical and real-world situations with and without technology.

G.1.a: Apply problem-solving skills to solve and verify the solutions for unknown measures in similar polygons.

G.1.c: Solve real-world or application problems that involve square roots and the Pythagorean Theorem.

#### G.2: Understand relations, functions, and patterns. Analyze change using various geometric properties.

G.2.a: Represent data from geometric and real-world contexts with expressions, formulas, tables, charts, graphs, relations, and functions.

G.2.b: Recognize and write the equation of a circle in standard form (x-h)_ + (y-k)_ = r_ and identify the center and radius.

G.2.c: Use slope to analyze and write equations for parallel and perpendicular lines.

G.2.d: Apply the Midpoint and Distance Formulas to solve application problems involving the coordinate plane.

G.2.e: Determine the effects of rigid (translations, rotations, and reflections) and nonrigid (dilations) motions and compositions when performed on objects on the coordinate plane.

#### G.3: Investigate, apply, and prove properties and theorems from postulates and definitions related to angles, lines, circles, polygons, and two- and three-dimensional figures. Explore applications of patterns and transformational geometry.

G.3.a: Use inductive reasoning to make conjectures and deductive reasoning to make valid conclusions.

G.3.b: Develop and evaluate mathematical arguments and proofs to include paragraph, two-column, and flow chart forms.

G.3.c: Identify, classify, and apply angle relationships formed by parallel lines cut by transversals.

G.3.d: Use the properties of altitudes, medians, angle bisectors, and perpendicular bisectors of triangles to solve problems.

G.3.e: Classify triangles and apply postulates and theorems to test for triangle inequality, congruence, and similarity.

G.3.g: Describe and draw cross-sections of prisms, cylinders, pyramids, and cones.

G.3.h: Graph a vector and determine the magnitude and direction of a given vector.

G.3.i: Given the pre-image or image, find figures obtained by applying reflections, translations, rotations, and dilations; describe and justify the method used.

#### G.4: Select and apply various strategies, tools, and formulas to calculate length, surface area, volume, and angle measurements.

G.4.b: Solve real-world applications and mathematical problems to find missing measurements in right triangles by applying special right triangle relationships, geometric means, or trigonometric functions.

G.4.c: Solve real-world and mathematical problems involving the lateral area, surface area and volume of three-dimensional figures, including prisms, cylinders, cones, pyramids, and spheres.

G.4.e: Apply the relationships of sine, cosine, and tangent to problems involving right triangles.

#### G.5: Represent, analyze, and make inferences based on data with and without the use of technology.

G.5.a: Apply multiple strategies and representations, including area models, to solve probability problems.

### AII: Algebra 2

#### AII.1: Understand relationships among numbers and compute fluently. Verify with technology.

AII.1.a: Diagram the relationship among the subsets of the complex number system.

AII.1.b: Compute with rational and radical expressions and complex numbers, expressing in simplest form.

AII.1.e: Solve applications and problems in mathematical settings involving arithmetic and geometric sequences and series.

AII.1.h: Solve application problems involving exponential functions related to growth and decay.

#### AII.2: Use algebraic concepts to identify patterns, use multiple representations of relations and functions, and apply operations to expressions, equations, and inequalities.

AII.2.a: Solve compound and absolute value inequalities, graphing and writing solutions in interval notation.

AII.2.b: Solve systems of absolute value and quadratic equations using a variety of solution methods including graphing.

AII.2.c: Given constraints, find the maximum and minimum value(s) of a system of linear inequalities and explain your reasoning.

AII.2.d: Given the solution(s) to a quadratic equation, find a quadratic equation to fit the solution(s) and explain or justify the solution process.

AII.2.e: Use the discriminant to classify and predict the types of solutions of quadratic equations and justify the classification.

AII.2.f: Factor sums and differences of cubes and factor polynomials by grouping.

AII.2.l: Interpret the zeros and maximum or minimum value(s) of quadratic functions.

#### AII.3: Use coordinate geometry to specify locations, describe relationships, and apply transformations to analyze algebraic relationships.

AII.3.a: Determine and justify whether the inverse of a relation or a function exists.

AII.3.b: Classify functions based on sketches of their graphs.

AII.3.c: Sketch and describe transformations of quadratic and absolute value functions.

AII.3.d: Represent complex numbers and the sum of complex numbers in a complex coordinate plane.

AII.3.e: Identify and sketch the essential graphs of the four conic sections: circle, parabola, ellipse, and hyperbola.

#### AII.4: Understand measurable attributes of objects and apply appropriate techniques and formulas to determine measurements.

AII.4.b: Describe the level of accuracy of measurements in real-world situations by using absolute value inequalities.

#### AII.5: Use technology to represent, analyze, and make inferences based on data.

AII.5.a: Through the use of technology, use scatter plots and linear and quadratic regression analysis to determine an appropriate function to model real-life data.

AII.5.b: Solve simple combinations.

AII.5.d: Identify the difference between permutations and combinations and use them to solve real-world problems.

### AA: Advanced Algebra

#### AA.1: Understand and perform computations with different representations of numbers.

AA.1.e: Solve application problems involving e and exponential functions related to growth and decay.

#### AA.2: Use algebraic concepts to identify patterns and use multiple representations of relations and functions. Apply operations to expressions and equations.

AA.2.a: Find the sum, difference, product, and quotient of functions, noting any restrictions on the domain.

AA.2.c: Describe patterns found in Pascal's Triangle and explain the relationship to the Binomial Theorem.

AA.2.d: Write and graph the equations of conic sections.

AA.2.e: Solve linear-quadratic and quadratic-quadratic systems of equations and inequalities.

#### AA.3: Recognize, analyze, and graph conic sections.

AA.3.a: Describe and explain the conic sections resulting from cutting a cone.

AA.3.b: Explain and perform the geometric constructions of conic sections.

#### AA.4: Apply simple probability and curve fitting to data.

AA.4.a: Use technology and regression analysis to determine appropriate quadratic and cubic functions modeling real-life data.

### T: Trigonometry

#### T.1: Represent and compare numbers in various forms and perform operations.

T.1.a: Perform conversions across measurement systems including degree to radian measurements of angles, radian measurements to degree measurements of angles, polar to rectangular coordinates, rectangular to polar coordinates, rectangular to trigonometric forms of complex numbers, and trigonometric to rectangular forms of complex numbers.

T.1.b: Determine the product and quotient of complex numbers in trigonometric form.

T.1.c: Apply De Moivre's theorem to determine the nth roots of a complex number given in polar form.

T.1.d: Explain the addition formulas for sine and cosine and use them to prove (or simplify) other trigonometric functions.

#### T.2: Investigate basic concepts of vectors and operations with vectors.

T.2.a: Recognize and draw different notations for vectors to represent a quantity.

T.2.b: Analyze properties of vectors and the effects of these properties on operations with vectors.

#### T.3: Compare and produce equivalent forms of trigonometric expressions and solve trigonometric equations.

T.3.a: Determine the domain and range of trigonometric functions.

T.3.b: Identify and apply trigonometric identities.

T.3.c: Verify identities analytically and with technology.

T.3.d: Solve trigonometric equations in real-world situations or mathematical settings.

#### T.4: Use geometric modeling to analyze trigonometric relationships.

T.4.a: Use the unit circle to solve real-world applications and problems in mathematical settings.

T.4.b: Apply the six trigonometric functions in relation to a right triangle to solve real-world applications and problems in mathematical settings.

T.4.c: Find exact values of trigonometric functions of special angles in the unit circle.

T.4.d: Recognize, sketch, and interpret graphs of the six trigonometric functions and include restrictions on their domain.

T.4.e: Model and apply right triangle formulas, Law of Sines, and Law of Cosines to problem-solving situations.

T.4.f: Use the graph of polar coordinates and associated equations to model real-world applications and mathematical situations.

#### T.5: Select and apply formulas to determine length and area.

T.5.a: Find arc length and sector area of a circle.

T.5.b: Using graphs of functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C), interpret A, B, C in terms of amplitude, frequency, period, and phase shift.

T.5.c: Given one angle and the measures of two adjacent sides, determine the area of a triangle and explain the process used.

### PC: Pre-Calculus

#### PC.1: Explore and illustrate the characteristics and operations connecting sequences and series.

PC.1.a: Express sequences and series using recursive and explicit formulas.

PC.1.b: Evaluate and apply formulas for arithmetic and geometric sequences and series.

PC.1.d: Evaluate and apply infinite geometric series.

#### PC.2: Analyze, manipulate, and solve equations and inequalities.

PC.2.a: Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).

PC.2.b: Determine horizontal, vertical, and slant asymptotes and holes of rational functions and explain how each was found.

PC.2.c: Determine the domain and range of functions, including piece-wise functions.

PC.2.d: Determine the end behavior of polynomial functions.

PC.2.f: Solve exponential and logarithmic equations to include real-world applications.

PC.2.h: Find the zeros of polynomial functions by synthetic division and the Factor Theorem.

PC.2.i: Graph and solve quadratic inequalities.

PC.2.j: Decompose a rational function into partial fractions.

#### PC.3: Recognize, sketch, and transform graphs of functions.

PC.3.a: Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer).

PC.3.b: Explain the effects of changing the parameters in transformations of functions.

PC.3.c: Predict the shapes of graphs of exponential, logarithmic, rational, and piece-wise functions, and verify the prediction with and without technology.

PC.3.d: Relate symmetry of the behavior of even and odd functions.

#### PC.4: Adapt curves to data.

PC.4.a: Use regression methods available through technology to determine appropriate exponential and logarithmic functions that model real-life data.

PC.4.b: Use regression methods available through technology to determine appropriate cubic functions that model real-life data.

### DM: Discrete Math

#### DM.2: Use algebraic methods to represent simple and complex relationships among statements. Use models to represent patterns and operations.

DM.2.a: Define sentence (proposition), and use logic to determine if the sentence is true or false.

DM.2.c: Define a conditional statement using truth tables.

DM.2.e: Define a sequence recursively and explicitly.

DM.2.f: Find the explicit formula for a recursively-defined sequence using iteration.

DM.2.g: Use mathematical induction to verify explicit formulas for arithmetic, geometric, and other sequences and/or series.

#### DM.3: Use geometric models to describe and analyze mathematical relationships, establish the validity of conjectures, and determine solutions to real applications.

DM.3.a: Construct a logic circuit from a Boolean expression to determine output.

DM.3.b: Construct a Boolean expression given a logic circuit.

DM.3.c: Construct a logic circuit and Boolean expression given an input/output table.

#### DM.4: Investigate and explain strategies for solving simple games.

DM.4.c: Create and use simulations for probability models.

### C: Calculus

#### C.2: Demonstrate basic knowledge of functions, including their behavior and characteristics.

C.2.a: Predict and explain the characteristics and behavior of functions and their graphs (domain, range, increasing/decreasing intervals, intercepts, symmetry, and end behavior).

C.2.b: Investigate, describe, and determine asymptotic behavior using tables, graphs, and analytical methods.

C.2.c: Determine and justify the continuity and discontinuity of functions.

#### C.8: Adapt integration methods to model situations to problems.

C.8.a: Apply integration to solve problems of area.

#### C.9: Apply appropriate techniques, tools, and formulas to determine values for the definite integral.

C.9.a: Interpret the concept of definite integral as a limit of Riemann sums over equal subdivisions.

### S: Statistics

#### S.1: Explore phenomena using probability and simulation. Compute appropriate statistical and probabilistic measures.

S.1.a: Describe the comparison of center and spread within groups and between or across group variation.

S.1.b: Interpret and apply the concept of the Law of Large Numbers.

S.1.c: Apply the counting principles, including permutations and combinations.

S.1.d: Construct and interpret sample spaces, events, and tree diagrams.

S.1.e: Identify types of events, including mutually exclusive, independent, and complements.

S.1.f: Calculate geometric probability using two-dimensional models, and explain the processes used.

S.1.g: Create simulations and experiments that correlate to theoretical probability.

S.1.h: Use Markov Chains to calculate probability by constructing matrix models.

S.1.i: Apply the concept of a random variable to generate and interpret probability distributions.

#### S.2: Analyze one and two variable data using algebraic concepts and methods.

S.2.a: Analyze and describe outliers and shape of the data including linearity and correlation across graphs and data sets.

S.2.b: Calculate mean, median, mode, standard deviation, z-scores, t-scores, quartiles, and ranges, and explain their applications.

S.2.d: Use algebraic concepts and methods to determine mathematical models of best fit.

#### S.3: Design an appropriate form of displaying data collected, whether in tabular or graphic form.

S.3.a: Organize data using graphs that are appropriate to the data set, including frequency distributions, stacked line and bar graphs, stem-and-leaf plots, scatter plot, frequency polygon, and histograms.

S.3.b: Determine and justify the graph type that best represents a given set of data.

#### S.4: Collect, read, interpret, and analyze data as it relates to the real world.

S.4.a: Make inferences and predictions from charts, tables, and graphs that summarize data.

S.4.b: Determine the most appropriate measure to describe a data set, including mean, median, mode, standard deviation, and variance.

S.4.d: Explain and defend regression models using correlation coefficients and residuals.

#### S.5: Design a study by clarifying a question and deciding upon a method of data collection and analysis.

S.5.c: Analyze sources of bias and sampling error(s) in studies.

S.5.d: Compare and contrast sampling methods, including simple random sampling, stratified random sampling, and cluster sampling with regard to benefits and trade-offs.

### SMT: Survey of Mathematical Topics

#### SMT.2: Identify and apply the practices that affect employer and employee decision-making.

SMT.2.a: Identify and apply appropriate algebraic formulas to personal finance situations.

SMT.2.b: Apply linear programming to business decisions.

### IE: Introduction to Engineering

#### IE.1: Compute unit conversions and illustrate graphical interpretations.

IE.1.b: Convert decimal to binary numbers and binary to decimal numbers.

#### IE.2: Apply algebraic equations and functions to engineering situations.

IE.2.a: Write mass and energy balance equations to solve for some unknown value.

IE.2.b: Find voltage, current, resistance, and solve power in series, parallel, and complex electric circuit theory problems using simultaneous equations generated from Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law (i.e., 3 equations and 3 unknowns).

IE.2.c: Graph a "Line of Best Fit" from given lab data and determine the degree of linearity (R_ value), slope of the line, and equation of the line.

Correlation last revised: 3/26/2010

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