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MCSD Mathematics Curriculum

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Strand: 2.2 Standard: Computation and Estimation Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.2.11A	Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations.	Perform calculations involving polynomial, rational, trigonometric, exponential/logarithmic and any other previously learned functions or their inverses. Give exact answers to problems involving trigonometric functions of special angles. Evaluate inverse trigonometric functions with and without a calculator or by drawing a diagram. Evaluate expressions involving logarithms with and without a calculator.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11B	Use estimation to solve problems for which an exact answer is not needed.	Estimate answers to problems that contain any of the functions studied in this course without references (no calculators or notes). Use a calculator to find estimated answers to problems that involve any of the functions studied in this course.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11C	Construct and apply mathematical models to estimate values of related quantities.	Estimate values of related quantities by constructing and applying mathematical models including: polynomial functions rational functions trigonometric functions exponential/logarithmic functions arithmetic/geometric/other sequences or series other curves of best fit.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11D	Describe and explain the amount of error that may exist in a computation using estimates.	Identify and explain the amount of error that may exist in a computation using estimates when a real life answer is also known.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11E	Recognize that the degree of precision needed in calculating a number depends on how the results will be used and the instruments used to generate the measure.	Compare and contrast the solution(s) of an equation solved by graphing (hand and graphing calculator) the related function and solved using other techniques.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.2.11F	Demonstrate skills for using scientific and graphing calculators.	Using a calculator: graph the functions studied in this course evaluate expressions involving the six trigonometric functions (both degree and radian measures) and their inverses evaluate expressions involving logarithms and anti logarithms solve problems involving sequences and series find regression equations (exponential, power, and quadratic) solve problems involving various functions.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.3 Standard: Measurement and Estimation Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.3.11A	Select and use appropriate units in measurement situations.	Select and use appropriate units in all measurement situations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
			Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.3.11B	Compare and use angles in degrees and radians.	Convert between degree and radian measure. Find values for trigonometric ratios of angles measured in radians or degrees. Solve problems that involve angles measured in radians or degrees.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.4 Standard: Mathematical Reasoning and Connections Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.4.11A	Use direct proofs, indirect proofs, proof by contradiction or mathematical induction to validate conjectures.	Explain the reasoning for each step in a given direct proof. Summarize, in the students’ own words, the basic reasoning in an indirect proof. Use proof by contradiction to validate conjectures. Use mathematical induction to prove the validity of formulas.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.4.11B	Construct valid arguments from stated facts.	Construct valid arguments from stated facts (possible choices include law of cosines, law of sines, trigonometric identities, and area of triangles).	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.4.11C	Determine the validity of an argument.	Determine the validity of an argument (possible choices include law of sines, law of cosines, and trigonometric identities and area of triangles). Given a proof’s steps and reasons, determine if the steps and reasons are valid.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.4.11E	Demonstrate mathematical solutions to problems.	Demonstrate mathematical solutions to problems that involve applications of the content studied in this course. Solve problems by using linear programming procedures. Solve problems involving simple harmonic motion. Solve problems related to the motion of a projectile, its trajectory, and range. Solve problems using vectors and right triangle trigonometry. Solve linear velocity and angular velocity problems.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.5 Standard: Mathematical Problem Solving and Communication Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.5.11A	Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems.	Select, use, and display all of the mathematical procedures that are necessary to the solution of a problem situation and achieve the correct answer.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.5.11B	Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results.	Communicate all of the mathematical procedures concepts, conclusions, etc. necessary to the solution of a problem situation using correct and appropriate mathematical representations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.5.11C	Present mathematical procedures and results clearly, systematically, succinctly and correctly.	Present all of the procedures important to the solution of a problem in ways that are understandable.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.5.11D	Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid.	Explain how a problem was solved and why the chosen procedures were used.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.6 Standard: Statistics and Data Analysis Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.6.11C	Determine the regression equation of best fit (e.g. quadratic, exponential, periodic, and logarithmic).	Determine the regression equation of best fit for a problem situation and use it to make predictions about the situation.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.6.11D	Make predictions using interpolation, extrapolation, regression and estimation using technology to verify them.	Make predictions using interpolation, extrapolation, regression and estimation for any of the functions studied in this course and use a graphing calculator to verify them.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.6.11I	Describe the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed.	Approximate the graph of a normal curve using a version of the graph of the natural number and use the graph to answer questions about the situation.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.8 Standard: Algebra and Functions Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.8.11A	Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically.	Analyze a given set of data for the existence of a pattern of any of the functions studied in this course and represent the pattern algebraically and graphically.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11B	Give examples of patterns that occur in data from other disciplines.	Give examples of any of the functions studied in this course that occur in real-world situations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11C	Use patterns, sequences and series to solve routine and non-routine problems.	Use patterns, sequences and series to solve routine and non-routine problems involving any of the functions studied in this course.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11D	Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations.	Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11D1	Select and use a strategy to solve a non-linear equation or inequality, explain the solution and check the solution for accuracy.	Solve quadratic equations. Solve rational equations and inequalities. Solve radical equations and inequalities. Solve trigonometric equations. Solve exponential or logarithmic equations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11E	Use equations to represent curves and functions (e.g. circles, ellipses, parabolas, hyperbolas, polynomial functions, rational functions, trigonometric functions, exponential and logarithmic functions).	Use equations to represent curves and functions studied in this course.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11G	Create, analyze and explain systems of equations, systems of inequalities and matrices.	Create systems of equations (including non-linear systems), inequalities, and matrices. Find solutions to systems of equations (including non-linear systems), inequalities, and matrices. Explain how a solution was found for a system.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11H	Select and use an appropriate strategy to solve systems of equations and inequalities.	Determine an appropriate strategy to solve a system of equations and inequalities and then solve the system. Use linear programming procedures to solve problems.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11J	Demonstrate the connections between algebraic equations and inequalities and the geometry of relations in the coordinate plane.	Given an algebraic equation or inequality, draw the graph on the coordinate plane. Determine the algebraic equation or inequality from its graph on the coordinate plane.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11K	Select, justify and apply an appropriate technique to graph a function in two variables, including slope-intercept, x- and y- intercepts, graphing by transformations and the use of a graphing calculator.	Select, justify and apply an appropriate technique to graph a function in two variables, including slope-intercept, x- and y- intercepts, graphing by transformations and the use of a graphing calculator. Note: All functions studied in this course should be used.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11L	Write the equation of a function when given enough information to find its equation.	Write the equation of a function when given enough information to find its equation.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11M	Given a set of data points, write an equation for a line of best fit.	Given a set of data points, write an equation for a line of best fit.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11N	Solve polynomial, rational, trigonometric, and exponential equations both symbolically and graphically.	Solve polynomial, rational, trigonometric, and exponential equations both symbolically and graphically.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11O	Determine the domain and range of a relation, given a graph or set of ordered pairs and possible asymptotes for the function.	Determine the domain and range of all the relations and functions studied in this course, given a graph or set of ordered pairs. Determine horizontal, vertical, and slant asymptotes. Find possible holes in graphs of rational functions.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11Q	Represent functional relationships in tables, charts and graphs.	Represent all functional relationships studied in this course in tables, charts and graphs. Find inverses for all studied relations and graph them. Determine roots of polynomial equations to help graph. Apply the Fundamental Theorem of Algebra to help graph. Use the discriminant to describe the roots of quadratic equations	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11R	Create and interpret functional models.	Create and interpret functional models for the various functions studied in this course.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11S	Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic)	Use transformations to "parent" functions to determine properties and relationships of functions. Identify graphs of the following: simple polynomial functions absolute value functions step functions rational functions trigonometric functions exponential and logarithmic functions inverses for relations and functions.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.8.11T	Analyze and categorize functions by their characteristics.	Given a graph of a function, identify it using algebraic equations to describe the function. Given an algebraic equation for a function, determine the type of function the equation represents. Identify an odd function and an even function. Determine continuity or discontinuity of functions. Identify the end behavior of graphs. Find the factors of polynomials using the remainder and factor theorems. Identify all possible rational roots of a polynomial equation by using the rational root theorem. Determine the number of positive and negative real zeros a polynomial function has. Approximate the real zeros of a polynomial function.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.9 Standard: Geometry Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.9.11E	Solve problems involving inscribed and circumscribed polygons.	Find the apothem of a regular polygon. Solve problems involving inscribed and circumscribed polygons.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.9.11F	Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles.	Use the unit circle to define a radian. Find the length of an arc, given the measure of the central angle. Find the area of a sector. Use the unit circle to define the six trigonometric functions. Find the area of a circular segment. Use circles and their properties and characteristics to solve problems.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.9.11G	Solve problems using analytic geometry.	Prove geometric theorems involving parallel and perpendicular lines analytically. Solve problems using analytic geometry.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.9.11H	Construct a geometric figure and its image using various transformations.	Use the parent graph of a function to construct the graph of a new function by applying knowledge of various transformations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.9.11I	Model situations geometrically to formulate and solve problems.	Model situations geometrically to formulate and solve problems.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.9.11J	Analyze figures in terms of the kinds of symmetries they have.	Identify symmetrical graphs. Use symmetry to complete a graph.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.10 Standard: Trigonometry Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.10.11A1	Use graphing calculators to display periodic and circular functions; describe properties of the graphs.	Graph periodic and circular functions. Determine the amplitude, period, phase shift, and the vertical shift for all circular and periodic functions. Graph inverses of trigonometric functions using principal values.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.10.11A2	Graph periodic and circular functions by hand; describe properties of the graphs.	Graph periodic and circular functions. Determine the amplitude, period, phase shift, and the vertical shift for all circular and periodic functions. Graph inverses of trigonometric functions using principal values.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.10.11B	Identify, create and solve practical problems involving triangles using the trigonometric functions, the Pythagorean Theorem and the Law of Sines/Cosines.	Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. Determine whether a triangle has zero, one, or two solutions. Identify, create and solve practical problems involving triangles using Law of Sines or Law of Cosines. Find the area of triangles using various formulas.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.10.11B1	Analyze, evaluate, and identify characteristics of angles with respect to trigonometric concepts.	Find angles that are coterminal with a given angle. Find the reference angle for a given sum. Find the values of the six trigonometric functions of an angle in standard position given a point on its terminal side. Find numerical values of trigonometric functions. Use sum and difference identities for sine, cosine, and tangent. 1Use the double- and half-angle identities for the sine, cosine, and tangent functions.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.10.11C	Develop and apply trigonometric concepts to vectors and parametric equations.	Find equal, opposite, and parallel vectors. Add and subtract vectors geometrically. Find ordered pairs that represent vectors. Determine whether two vectors are perpendicular. Write vector and parametric equations of lines. Graph parametric equations. Model the motion of a projectile using parametric equations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: 2.11 Standard: Concepts of Calculus Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
2.11.11A	Determine maximum and minimum values of a function over a specified interval by using derivative concepts.	Determine the derivative of a polynomial function using the limit form. Find the derivative of a polynomial function using the power rule and other properties. Find the slope and the equation of a line tangent to the graph of a function at a given point. Find the critical points of the graph of a polynomial function and determine if each is a minimum, maximum, or point of inflection. Use the maximum and minimum values of a periodic function to help graph it.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.11.11B	Interpret maximum and minimum values in problem situations.	Solve problem situations that involve maximum or minimum value interpretations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.11.11C	Graph and interpret exponential and logarithmic functions including rates of growth/decay.	Use properties of exponents to simplify expressions. Evaluate and simplify expressions containing rational exponents. Evaluate expressions with irrational exponents. Graph exponential and logarithmic functions and inequalities with and without a graphing calculator. Graph the exponential function that contains the natural number as a base. Use the natural logarithm when the natural number is involved in the problem. Solve equations involving logarithms without the use of a calculator by applying the properties of logarithms. Find common logarithms and antilogarithms of numbers. Solve exponential and logarithmic equations and inequalities. Solve equations using natural logarithms. Find answers to growth/decay problem situations.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response
2.11.11D	Work with series and sequence problems which include determining sums of finite sequences of numbers and infinite geometric series.	Find the nth term and arithmetic means of an arithmetic sequence. Find the sum of n terms of an arithmetic series. Find the nth term and geometric means of a geometric sequence. Find the sum of n terms of a geometric series. Find the sum of an infinite geometric series. Use sigma notation. Use the binomial theorem to expand binomials. Evaluate an exponential function with the natural number as the base by using the exponential series. Use Euler’s formula to write the exponential form of a complex number. Evaluate the logarithms of negative numbers.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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Strand: None Standard: Polar Coordinates and Complex Numbers Course: Precalculus
	Course Objectives	Performance Indicators	Assessment Options
12.11A	Develop and apply polar coordinate and complex number concepts.	Graph polar coordinates and simple polar equations. Graph polar equations. Convert between polar coordinates and rectangular coordinates. Write the polar form of a linear equation. Graph the polar form of a linear equation. Add, subtract, multiply, and divide complex numbers in rectangular form. Change complex numbers between polar form and rectangular form. Find the product and quotient of complex numbers in polar form. Find powers and roots of complex numbers in polar form using DeMoivre’s theorem.	Observation Evaluate written work Performance assessments Tests, quizzes Problem solving journal/activity Evaluate oral response

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