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.
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
|
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
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 |
|
Back to Top
|
|
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 |
|
Back to Top
|
|
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 |
|
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 |
Back
to Top
|
|
|
|
|
Mathematics curriculum e-mail
contact:
|
Boise
School District
8169 W. Victory Rd., Boise, ID 83709 |
| |
© Independent School
District of Boise City
All rights reserved |
|