Course Description
Open to: Grade 12 One Year Course
Prerequisite: Geometry,Algebra 2 and/or Instructor Approval
Content: Students will study advanced topics in trigonometry such as identities,
circular functions and other special formulas. Emphasis will be on functions
and relations. 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: Precalculus: Mathematics for Calculus 4th
Edition: 2002
Publisher: Brooks/Cole
ISBN: 0-534-43421-5
Mathematics Curriculum
Map
Course overview, activities, vocabulary, supplemental materials in pdf format.
Copyright
Resources
Course Scope for Semester 1
| Unit 1 |
Fundamentals |
4 Weeks |
| Unit 2 |
Functions |
4 Weeks |
| Unit 3 |
Polynomial and Rational Functions |
3 Weeks |
| Unit 4 |
Exponential and Logarithmic Functions |
2 Weeks |
| Unit
5 |
Trigonometric Functions of Real Numbers |
1.5 Weeks |
| Unit 6 |
Trigonometric Functions of Angles |
2 Weeks |
Course Scope for Semester 2
| Unit 7 |
Analytic Trigonometry |
4 Weeks |
| Unit 8 |
Systems of Equations and Inequalities |
3 Weeks |
| Unit 9 |
Topics in Analytic Geometry |
4 Weeks |
| Unit 10 |
Sequences and Series |
2.5 Weeks |
| Unit 11 |
Counting and Probability |
2 Weeks |
| Unit 12 |
Limits: A Preview of Calculus |
optional |
Assessment
Correlation acronyms key
Mathematics Curriculum Matrix K-12 pdf or Word
document
|
Unit
1 |
Fundamentals |
Semester 1, 4 weeks |
|
Instructional Objective
0831.01 Review the basic ideas from algebra
and coordinate geometry that will be needed
throughout the course. |
Standard Reference
|
|
No. |
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify properties of real numbers. |
text |
EOC |
|
02 |
Use algebraic, exponential and radical properties. |
text |
EOC |
|
03 |
Solve quadratics. |
text |
EOC |
|
04 |
Solve equations and inequalities. |
text |
EOC |
|
05 |
Use distance and midpoint formula. |
text |
EOC |
|
06 |
Identify and describe the graph and equation
of a circle. |
text |
EOC |
|
07 |
Write and graph linear equations. |
text |
EOC |
|
Instructional Objective
0831.02 Apply the general properties of functions
to linear rational functions. |
Standard Reference
|
|
No. |
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify the domain and range of functions. |
text |
EOC |
|
02 |
Perform operations with functions. |
text |
EOC |
|
03 |
Find the compositions of functions. |
text |
EOC |
|
04 |
Graph linear equations and inequalities. |
text |
EOC |
|
05 |
Identify graphs of simple polynomial functions
and absolute value functions. |
text |
EOC |
|
06 |
Find the transformation and inverses of functions. |
text |
EOC |
|
07 |
Find minimum or maximum value of a function |
text |
EOC |
|
Back to Top |
|
Unit
3 |
Polynomial and Rational
Functions |
Semester 1, 3 weeks |
|
Instructional Objective
0831.03 Define and analyze functional relationships |
Standard Reference
|
|
No. |
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Graph rational functions and inverse functions. |
text |
EOC |
|
02 |
Determine horizontal, vertical and slant asymptotes. |
text |
EOC |
|
03 |
Find the critical points of the graph of a polynomial
function. |
text |
EOC |
|
04 |
Determine roots of polynomial equations. |
text |
EOC |
|
05 |
Apply the fundamental theorem of algebra. |
text |
EOC |
|
06 |
Solve and graph quadratic equations and inequalities. |
text |
EOC |
|
07 |
Analyze the discriminant of a quadratic equation. |
text |
EOC |
|
08 |
Find the factors of polynomials. |
text |
EOC |
|
09 |
Graph and determine all rational roots of a
polynomial equation. |
text |
EOC |
|
10 |
Determine the number of positive and negative
real zeros of a polynomial function. |
text |
EOC |
|
Back to Top |
|
Unit
4 |
Exponential and Logarithmic
Functions |
Semester 1, 2 weeks |
|
Instructional Objective
0831.04 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. |
text |
EOC, AB |
|
02 |
Use the properties of logarithms to simplify
logarithmic expressions. |
text |
EOC, AB |
|
03 |
Solve logarithmic and exponential equations
and inequalities. |
text |
EOC, AB |
|
Back to Top |
|
Unit
5 |
Trigonometric Functions
of Real Numbers |
Semester 1, 1.5 weeks |
|
Instructional Objective
0831.05 Apply the general properties of trigonometric
functions to construct and analyze graphs. |
Standard Reference
|
|
No. |
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify the graph of trigonometric functions
and determine their period, amplitude and phase
shift. |
text |
EOC, AB |
|
02 |
Graph trigonometric functions and their inverses. |
text |
EOC, AB |
|
03 |
Write equations of trigonometric functions and
their inverses |
text |
EOC, AB |
|
04 |
Find trigonometric values for angles from the
unit circle. |
text |
AB, EOC |
|
Back to Top |
|
Unit
6 |
Trigonometric Functions
of Angles |
Semester 1, 2 weeks |
|
Instructional Objective
0831.06 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. |
text |
AB, EOC |
|
02 |
Determine trigonometric function values and
their reciprocal functions. |
text |
AB, EOC |
|
03 |
Find trigonometric values for angles from the
unit circle. |
text |
AB, EOC |
|
04 |
Apply trigonometric laws to solve triangles. |
text |
AB, EOC |
|
Back to Top |
|
Unit
7 |
Analytic Trigonometry |
Semester 2, 4 weeks |
|
Instructional Objective
0831.07 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. |
text |
EOC, AB |
|
02 |
Find numerical values of trigonometric functions |
text |
EOC, AB |
|
03 |
Use the sum and difference identities |
text |
EOC, AB |
|
04 |
Use the double- and half-angle identities |
text |
EOC, AB |
|
05 |
Solve trigonometric equations |
text |
EOC, AB |
|
06 |
Demonstrate the properties of vectors in planes
and space. |
text |
EOC, AB |
|
07 |
Determine the sum, difference, dot and cross
product of 2 vectors. |
text |
EOC, AB |
|
Back to Top |
|
Unit
8 |
Systems of Equations
and Inequalities |
Semester 2, 3 weeks |
|
Instructional Objective
0831.08 Apply discrete math to the manipulation
of matrices and algorithms. |
Standard Reference
|
|
No. |
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Perform operations on matrices. |
text |
EOC |
|
02 |
Solve systems of equations algebraically and
using matrices. |
text |
EOC, AB |
|
03 |
Use linear programming to solve problems. |
text |
TMA |
|
Back to Top |
|
Unit
9 |
Topics in Analytic
Geometry |
Semester 2, 4 weeks |
|
Instructional Objective
0831.09 Demonstrate understanding of conic
sections and use trigonometric functions to
solve problems involving polar relations. |
Standard Reference
|
|
No. |
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Analyze circular functions. |
text |
EOC, AB |
|
02 |
Analyze parametric and polar relations. |
text |
EOC, AB |
|
03 |
Perform operations with complex numbers in polar
and rectangular form. |
text |
EOC, AB |
|
04 |
Identify and describe the graphs and equations
of the conic sections. |
text |
EOC, AB |
|
05 |
Determine the graph of a conic section. |
text |
AB, TMA |
|
06 |
Determine the equation of a conic section from
a graph or geometric description. |
text |
EOC, AB |
|
Back to Top |
|
Unit
10 |
Sequences and Series |
Semester 2, 2.5 weeks |
|
Instructional Objective
0831.10 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. |
text |
AB, EOC |
|
02 |
Find the nth term, geometric means and sum of
a geometric sequence. |
text |
AB, EOC |
|
03 |
Analyze properties of infinite sequences and
series. |
text |
AB, TMA |
|
04 |
Use sigma notation. |
text |
AB, EOC |
|
05 |
Solve annuities and installment problems |
text |
TMA |
|
06 |
Use Binomial Theorem to expand binomials |
text |
EOC |
|
Back to Top |
|
Unit
11 |
Counting and Probability |
Semester 2, 2 weeks |
|
Instructional Objective
0831.11 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. |
text |
AB, EOC |
|
02 |
Identify and determine independent and dependent
probabilities. |
text |
AB, TMA |
|
03 |
Compute combinations and permutations. |
text |
EOC, AB |
|
04 |
Apply the binomial probability theorem. |
text |
AB, TMA |
|
Back to Top |
|
Unit
12 |
Limits: A Preview of
Calculus |
Semester 2, optional |
Back to Top
|
|
|
|
|
Mathematics curriculum e-mail
contact:
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