Course Description
Open to: Grade 9-11 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 |
Linear and Quadratic Functions |
1 Week |
| Unit 2 |
Vector Operations |
2 Weeks |
| Unit 3 |
Polynomial and Rational Functions |
2 Weeks |
| Unit 4 |
Language of Functions |
3 Weeks |
| Unit
5 |
Exponents and Logarithms |
2 Weeks |
| Unit 6 |
Analytic Geometry |
1 Week |
| Unit 7 |
Trigonometric Functions |
2 Weeks |
| Unit 8 |
Trigonometric Equations and Applications |
2 Weeks |
Course Scope for Semester 2
| Unit 9 |
Triangle Trigonometry |
2 Weeks |
| Unit 10 |
Trigonometric Addition Formulas |
2 Weeks |
| Unit 11 |
Polar Coordinates and Complex Numbers |
2 Weeks |
| Unit 12 |
Matrices |
2 Weeks |
| Unit 13 |
Combinatorics and Probability |
4 Weeks |
| Unit 14 |
Sequences and Series |
3 Weeks |
| Unit 15 |
Rational Functions and Continuity |
1 Week |
Assessment
Correlation acronyms key
Mathematics Curriculum Matrix K-12 pdf or Word
document
|
Unit
1 |
Linear and Quadratic
Functions |
Semester 1, 1 week |
|
Unit
2 |
Vector Operations |
Semester 1, 2 weeks |
|
Instructional Objective
0832.01 Apply the general properties of functions
to families of functions. |
Standard Reference
PC.3.4.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify the domain and range of functions. |
Text |
TMA, EOC |
|
02 |
Perform operations with functions. |
Text |
TMA, EOC |
|
03 |
Construct appropriate linear and quadratic models
to solve applications problems. |
Text |
TMA, EOC |
|
04 |
Perform vector operations geometrically and
algebraically. |
Text |
TMA, EOC |
|
05 |
Using parametric equations to describe motion. |
Text |
TMA, EOC |
|
06 |
Predict vector relationships |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
3 |
Polynomial Functions
and Inequalities |
Semester 1, 2 weeks |
|
Instructional Objective
0832.02 Demonstrate understanding of graphic
representations of functions. |
Standard Reference
PC.3.2.6; PC.1.3.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Sketch and analyze graphs of simple polynomial
functions and their extrema. |
Text |
TMA, EOC |
|
02 |
Graph rational functions and inverse functions. |
Text |
TMA, EOC |
|
03 |
Determine horizontal, vertical and slant asymptotes. |
Text |
TMA, EOC |
|
04 |
Perform operations with complex numbers and
plot complex numbers in the complex plane. |
Text |
T/O, TMA, EOC |
|
05 |
Find the critical points of the graph of a polynomial
function. |
Text |
TMA |
|
06 |
Determine roots of polynomial equations. |
Text |
TMA, EOC |
|
07 |
Apply the fundamental theorem of algebra. |
Text |
TMA, EOC |
|
08 |
Solve radical and rational equations and inequalities. |
Text |
TMA, EOC |
|
09 |
Graph and determine all rational roots of a
polynomial equation. |
Text |
TMA, EOC |
|
10 |
Find the factors of polynomials. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
4 |
Language of Functions |
Semester 1, 3 weeks |
|
Instructional Objective
0832.04 Combine functions in a variety of
ways and explore the relationships between
the graph and an algebraic rule. |
Standard Reference
PC.3.1.2; 3.1.3 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify the domain, range, and zeros of a function
and graph the function. |
Text |
TMA, EOC |
|
02 |
Perform operations on functions and determine
the domain of the resulting functions. |
Text |
TMA, EOC |
|
03 |
Reflect graphs and use symmetry to sketch graphs. |
Text |
TMA, EOC |
|
04 |
Determine in periodicity and amplitude from
graphs, stretch and shrink both vertically and
horizontally and translate graphs. |
Text |
TMA, EOC |
|
05 |
Find the inverse of a function if the inverse
exits. |
Text |
TMA, EOC |
|
06 |
Graph functions of two variables in a two-dimensional
coordinate system and read such graphs. |
Text |
TMA, EOC |
|
07 |
Form a function of one variable from a verbal
description and determine the minimum or maximum
value of the function. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
5 |
Exponents and Logarithms |
Semester 1, 2 weeks |
|
Instructional Objective
0832.05 Apply the general properties of logarithmic
and exponential functions to solve problems. |
Standard Reference
PC.3.2.3; 3.2.4 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Analyze exponential and logarithmic functions
and their graphs. |
Text |
TMA |
|
02 |
Use the properties of logarithms to simplify
logarithmic expressions. |
Text |
TMA, EOC |
|
03 |
Solve logarithmic and exponential equations
and inequalities. |
Text |
TMA, EOC |
|
04 |
Use Gaussian models and logistic models to solve
real-life problems. |
Text |
TMA |
|
05 |
Fit exponential and logarithmic models to sets
of data. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
6 |
Analytic Geometry |
Semester 1, 1 week |
|
Instructional Objective
0832.06 Demonstrate understanding of conic
sections. |
Standard Reference
PC.3.2.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify and describe the graphs and equations
of the conic sections. |
Text |
TMA, EOC |
|
02 |
Determine the graph of a conic section. |
Text |
TMA, EOC |
|
03 |
Determine the equation of a conic section from
a graph or geometric description. |
Text |
TMA |
|
04 |
Use discriminants to classify conics. |
Text |
TMA, EOC |
|
05 |
Write systems of quadratic equations. |
Text |
TMA, EOC |
|
06 |
Write equations of conics in polar form. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
7 |
Trigonometric Functions |
Semester 1, 2 weeks |
|
Instructional Objective
0832.07 Apply the general properties of trigonometric
functions to solve equations and problems. |
Standard Reference
PC.4.4.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Analyze trigonometric functions. |
Text |
TMA |
|
02 |
Determine trigonometric function values and
their reciprocal functions. |
Text |
TMA, EOC |
|
03 |
Find trigonometric values for angles from the
unit circle. |
Text |
TMA, EOC |
|
04 |
Apply trigonometric ratios to solve triangles. |
Text |
TMA, EOC |
|
05 |
Evaluate the composition of trigonometric functions. |
Text |
TMA, EOC |
|
06 |
Identify the graph of trigonometric functions
and determine their period, amplitude, and phase
shift. |
Text |
TMA, EOC |
|
07 |
Graph trigonometric functions and their inverses |
Text |
TMA, EOC |
|
08 |
Write equations of trigonometric functions and
their inverses. |
Text |
TMA |
|
Back to Top |
|
Unit
8 |
Trigonometric Equations
and Applications |
Semester 1, 2 weeks |
|
Instructional Objective
0832.08 Solve simple trigonometric equations
and apply them to problems from analytic geometry.
Explore changes in trigonometric curves and
develop models to real-world phenomena. |
Standard Reference
PC.3.2.2; 4.3.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve simple trigonometric equations and apply
them. |
Text |
TMA, EOC |
|
02 |
Find equations of different sine and cosine
curves and apply these equations. |
Text |
TMA, EOC |
|
03 |
Use trigonometric functions to model periodic
behavior. |
Text |
TMA, EOC |
|
04 |
Simplify trigonometric expressions and prove
trigonometric identities. |
Text |
TMA, EOC |
|
05 |
Use trigonometric identities to solve more difficult
trigonometric equations. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
9 |
Triangle Trigonometry |
Semester 2, 2 weeks |
|
Unit
10 |
Trigonometric Addition
Formulas |
Semester 2, 2 weeks |
|
Instructional Objective
0832.09 Use the basic identities and formulas
of trigonometry to transform expressions and
find the trigonometric function values of angles. |
Standard Reference
PC.4.4.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Verify and use the trigonometric identities. |
Text |
TMA, EOC |
|
02 |
Find numerical values of trigonometric functions. |
Text |
TMA, EOC |
|
03 |
Use the sum and difference identities. |
Text |
TMA, EOC |
|
04 |
Use the double- and half-angle identities. |
Text |
TMA, EOC |
|
05 |
Use power-reducing, product-to-sum, and sum-to-product
formulas. |
Text |
TMA, EOC |
|
06 |
Solve trigonometric equations. |
Text |
TMA, EOC |
|
07 |
Use Law of Sines and Law of Cosines to solve
problems. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
11 |
Polar Coordinates and
Complex Numbers |
Semester 2, 2 weeks |
|
Instructional Objective
0832.10 Use trigonometric functions to solve
problems involving polar relations. |
Standard Reference
PC.4.2.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Analyze circular functions. |
Text |
TMA, EOC |
|
02 |
Analyze parametric and polar relations. |
Text |
TMA, EOC |
|
03 |
Perform operations with complex numbers in polar
and rectangular form. |
Text |
TMA, EOC |
|
04 |
Convert back and forth between polar and rectangular
form. |
Text |
TMA, EOC |
|
Instructional Objective
0832.11 Demonstrate understanding of the uses
of matrices. |
Standard Reference
PC.3.2.9 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Perform basic operations on matrices. |
Text |
TMA, EOC |
|
02 |
Establish inverse matrices to solve linear systems. |
Text |
TMA |
|
03 |
Use matrices to create networks and understand
the predictive power of matrices. |
Text |
TMA, EOC |
|
04 |
Perfom graphical transformations using vectors
and matrices.. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
13 |
Combinatorics and Probability |
Semester 2, 4 weeks |
|
Instructional Objective
0832.11 Demonstrate understanding of the prediction,
probability, and counting items based on data. |
Standard Reference
PC.5.1.1; 5.2.5-6 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Determine sample spaces and probabilities of
events. |
Text |
TMA, EOC |
|
02 |
Identify and determine independent and dependent
probabilities. |
Text |
TMA |
|
03 |
Compute combinations and permutations. |
Text |
TMA, EOC |
|
04 |
Write binomial expansions. |
Text |
TMA, EOC |
|
Back to Top |
|
Unit
14 |
Sequences and Series |
Semester
2, 3 weeks |
|
Unit
15 |
Rational Functions
and Continuity |
Semester 2, 1 week |
|
Instructional Objective
0832.12 Analyze sequences and series and find
the sums of arithmetic and geometric series,
both finite and infinite. |
Standard Reference
PC.5.2.1-4 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Find the nth term, arithmetic means and sum
of an arithmetic sequence. |
Text |
TMA, EOC |
|
02 |
Find the nth term, geometric means and sum of
a geometric sequence. |
Text |
TMA, EOC |
|
03 |
Analyze properties of infinite sequences and
series. |
Text |
TMA, EOC |
|
04 |
Determine the convergence or divergence of a
sequence or series. |
Text |
TMA, EOC |
|
05 |
Use sigma notation. |
Text |
TMA, EOC |
|
06 |
Use mathematical induction to prove summation
formulae. |
Text |
TMA, EOC |
Back to Top
|
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