Boise Schools Curriculum

Accelerated Math Analysis

District Course #0832

Course Description

Open to: Grade 11 One Year Course
Prerequisite: Geometry and Algebra 2 or Instructor Approval
Content: Students will study advanced topics in trigonometry such as identities, circular functions and other special formulas. Emphasis will be on topics in limits as well as problem solving throughout the year. Linear, quadratic, slope, polynomial, exponential, and logarithmic functions will be included. Pre-calculus concepts, including many ideas on permutations, combinations, and probability will be introduced. Recommended for students entering college mathematics, science or engineering programs.

Adopted Materials

Title: Advanced Mathematics; Precalculus with Discrete mathematics and Data Analysis
Edition: 2003
Publisher: McDougal Little Inc.
ISBN: 0-618-25037-9

Mathematics Curriculum Map
Course overview, activities, vocabulary, supplemental materials in pdf format.

Copyright Resources

Course Scope for Semester 1

Unit 1	Review of Prerequisite Skills	1 Week
Unit 2	Relations and Functions	2 Weeks
Unit 3	Polynomial and Rational Functions	3 Weeks
Unit 4	Exponential and Logarithmic Functions	2 Weeks
Unit 5	Trigonometric Functions	3 Weeks
Unit 6	Analytic Trigonometry	3 Weeks
Unit 7	Vectors and Parametric Equations	1.5 Weeks

Course Scope for Semester 2

Unit 8	Systems of Equations and Inequalities	3 Weeks
Unit 9	Polar Coordinates and Complex Numbers	2 Weeks
Unit 10	Conics	2 Weeks
Unit 11	Sequences and Series	1.5 Weeks
Unit 12	Combinatorics and Probability	1.5 Weeks
Unit 13	Limits	3 Weeks

Assessment Correlation acronyms key
Mathematics Curriculum Matrix K-12 pdf or Word document

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Unit 1

Review of Prerequisite Skills

Semester 1, 1 week

Instructional Objective 0832.01 Review of mathematical skills acquired in previous courses.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Plot points in the coordinate plane and use the Distance and Midpoint Formulas.	CH P, text		TMA
02	Sketch graphs of equations by point-plotting and using a graphing utility.	CH P, text		TMA
03	Find and use the slope of a line to write and graph linear equations	CH P, text		TMA
04	Solve equations: linear, quadratic, and polynomial and those involving radicals, fractions, and absolute values.	CH P, text		TMA
05	Solve linear, rational, and polynomial inequalities and those involving absolute values.	CH P, text		TMA

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Unit 2	Relations and Functions	Semester 1, 2 weeks

Instructional Objective 0832.02 Apply the general properties of functions to families of functions.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Identify the domain and range of functions.	CH 1, text		TMA, EOC
02	Perform operations with functions.	CH 1, text		TMA, EOC
03	Find the compositions of functions.	CH 1, text		TMA, EOC
04	Graph equations and inequalities.	CH 1, text		TMA, EOC
05	Find inverses of functions algebraically and graphically.	CH 1, text		TMA, EOC
06	Identify and graph shifts, reflections, and non-rigid transformations of functions.	CH 1, text		TMA, EOC

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Unit 3	Polynomial and Rational Functions	Semester 1, 3 weeks

Instructional Objective 0832.03 Demonstrate understanding of graphic representations of functions.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Sketch and analyze graphs of simple polynomial functions and their extrema.	CH 2, text		TMA, EOC
02	Graph rational functions and inverse functions.	CH 2, text		TMA, EOC
03	Determine horizontal, vertical and slant asymptotes.	CH 2, text		TMA, EOC
04	Perform operations with complex numbers and plot complex numbers in the complex plane.	CH 2, text		T/O TMA, EOC
05	Find the critical points of the graph of a polynomial function.	CH 2, text		TMA
06	Determine roots of polynomial equations.	CH 2, text		TMA, EOC
07	Apply the fundamental theorem of algebra.	CH 2, text		TMA, EOC
08	Solve radical and rational equations and inequalities.	CH 2, text		TMA, EOC
09	Graph and determine all rational roots of a polynomial equation.	CH 2, text		TMA, EOC
10	Find the factors of polynomials.	CH 2, text		TMA, EOC

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Unit 4	Exponential and Logarithmic Functions	Semester 1, 2 weeks

Instructional Objective 0832.04 Apply the general properties of logarithmic and exponential functions to solve problems.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Analyze exponential and logarithmic functions and their graphs.	CH 3, text		TMA AB
02	Use the properties of logarithms to simplify logarithmic expressions.	CH 3, text		TMA AB, EOC
03	Solve logarithmic and exponential equations and inequalities.	CH 3, text		TMA AB, EOC
04	Use Gaussian models and logistic models to solve real-life problems.	CH 3, text		TMA
05	Fit exponential and logarithmic models to sets of data.	CH 3, text		TMA, EOC

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Unit 5	Trigonometric Functions	Semester 1, 3 weeks

Instructional Objective 0832.05 Apply the general properties of trigonometric functions to solve equations and problems.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Analyze trigonometric functions.	CH 4, text		AB TMA
02	Determine trigonometric function values and their reciprocal functions.	CH 4, text		AB TMA, EOC
03	Find trigonometric values for angles from the unit circle.	CH 4, text		AB TMA, EOC
04	Apply trigonometric ratios to solve triangles.	CH 4, text		AB TMA, EOC
05	Evaluate the composition of trigonometric functions.	CH 4, text		TMA, EOC
06	Identify the graph of trigonometric functions and determine their period, amplitude, and phase shift.	CH 4, text		TMA, EOC
07	Graph trigonometric functions and their inverses	CH 4, text		TMA, EOC
08	Write equations of trigonometric functions and their inverses.	CH 4, text		TMA

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Unit 6	Analytic Trigonometry	Semester 1, 3 weeks

Instructional Objective 0832.06 Use the basic identities and formulas of trigonometry to transform expressions and find the trigonometric function values of angles.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Verify and use the trigonometric identities.	CH 5, text		TMA AB, EOC
02	Find numerical values of trigonometric functions.	CH 5, text		TMA AB, EOC
03	Use the sum and difference identities.	CH 5, text		TMA AB, EOC
04	Use the double- and half-angle identities.	CH 5, text		TMA AB, EOC
05	Use power-reducing, product-to-sum, and sum-to-product formulas.	CH 5, text		TMA AB EOC
06	Solve trigonometric equations.	CH 5, text		TMA, EOC
07	Use Law of Sines and Law of Cosines to solve problems.	CH 6, text		TMA, EOC

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Unit 7	Vectors and Parametric Equations	Semester 1, 1.5 weeks

Instructional Objective 0832.07 Analyze vector and parametric relations.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Demonstrate the properties of vectors in planes and space.	CH 6 and 11, text		TMA AB, EOC
02	Determine the sum, difference, dot and cross product of 2 vectors.	CH 6 and 11, text		TMA AB, EOC
03	Solve problems using vectors and right triangle trigonometry.	CH 6 and CH 11, text		TMA, EOC
04	Demonstrate the properties of lines in planes and space through the use of parametric equations.	CH 10 and CH 11, text		TMA, EOC
05	Define, graph and perform operations on parametric equations.	CH 10, text		TMA, EOC
06	Rewrite sets of parametric equations as rectangular equations	CH 10, text		TMA, EOC

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Unit 8	Systems of Equations and Inequalities	Semester 2, 3 weeks

Instructional Objective 0832.08 Apply discrete math to the manipulation of matrices and algorithms.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Perform operations on matrices.	CH 8, text		TMA, EOC
02	Solve systems of equations algebraically and using matrices.	CH 7, text CH 8, text		TMA AB, EOC
03	Use linear programming to solve problems.	CH 7, text		TMA

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Unit 9	Polar Coordinates and Complex Numbers	Semester 2, 2 weeks

Instructional Objective 0832.09 Use trigonometric functions to solve problems involving polar relations.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Analyze circular functions.	CH 10, text		TMA AB, EOC
02	Analyze parametric and polar relations.	CH 10, text		TMA AB, EOC
03	Perform operations with complex numbers in polar and rectangular form.	CH 10, text		TMA AB, EOC
04	Convert back and forth between polar and rectangular form.	CH 10, text		TMA, EOC

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Unit 10	Conics	Semester 2, 2 weeks

Instructional Objective 0832.10 Demonstrate understanding of conic sections.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Identify and describe the graphs and equations of the conic sections.	CH 10, text		TMA AB, EOC
02	Determine the graph of a conic section.	CH 10, text		TMA AB, EOC
03	Determine the equation of a conic section from a graph or geometric description.	CH 10, text		TMA AB
04	Use discriminants to classify conics.	CH 10, text		TMA, EOC
05	Write systems of quadratic equations.	CH 10, text		TMA, EOC
06	Write equations of conics in polar form.	CH 10, text		TMA, EOC

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Unit 11	Sequences and Series	Semester 2, 1.5 weeks

Instructional Objective 0832.11 Analyze sequences and series and find the sums of arithmetic and geometric series.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Find the nth term, arithmetic means and sum of an arithmetic sequence.	CH 9, text		AB TMA, EOC
02	Find the nth term, geometric means and sum of a geometric sequence.	CH 9, text		AB TMA, EOC
03	Analyze properties of infinite sequences and series.	CH 9, text		AB TMA, EOC
04	Determine the convergence or divergence of a sequence or series.	CH 9, text		AB TMA, EOC
05	Use sigma notation.	CH 9, text		AB TMA, EOC
06	Use mathematical induction to prove summation formulae.	CH 9, text		TMA, EOC

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Unit 12	Combinatorics and Probability	Semester 2, 1.5 weeks

Instructional Objective 0832.12 Demonstrate understanding of the prediction, probability, and counting items based on data.			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Determine sample spaces and probabilities of events.	CH 9, text		AB TMA, EOC
02	Identify and determine independent and dependent probabilities.	CH 9, text		TMA AB
03	Compute combinations and permutations.	CH 9, text		TMA AB, EOC
04	Write binomial expansions.	CH 9, text		TMA AB, EOC

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Unit 13	Limits	Semester 2, 3 weeks

Instructional Objective 0832.13 Evaluate limits and use them in relation to the tangent line problem and the area problem in Calculus			Standard Reference
No.	Performance Objective	Resource Reference		Assessment Correlation
01	Estimate limits and use properties and operations of limits.	CH 12, text		TMA, EOC
02	Find limits by direct substitution and by using dividing and rationalizing techniques.	CH 12, text		TMA, EOC
03	Approximate slopes of tangent lines, use the limit definition of slope, and use derivatives to find slopes of graphs.	CH 12, text		TMA, EOC
04	Evaluate limits at infinity and find limits of sequences.	CH 12, text		TMA, EOC

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Boise School District
8169 W. Victory Rd., Boise, ID 83709