Mathematics - Pre-Calculus
District Course #0831
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
Course Scope for Semester 1
Unit 1
Unit 2
Unit 3
Unit 4
Fundamentals
Functions
Polynomial and Rational Functions
Exponential and Logarithmic Functions
4 Weeks
4 Weeks
3 Weeks
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
Unit 8
Unit 9
Unit 10
Unit 11
Analytic Trigonometry
Systems of Equations and Inequalities
Topics in Analytic Geometry
Sequences and Series
Counting and Probability
Unit 12
Limits: A Preview of Calculus
Unit 1
4 Weeks
3 Weeks
4 Weeks
2.5 Weeks
2 Weeks
Optional
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.
No.
Performance Objective
Standard Reference
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
Unit 2
Write and graph linear equations.
text
Functions
Semester 1, 4 weeks
Instructional Objective
0831.02 Apply the general properties of functions to linear rational
functions.
No.
Performance Objective
EOC
Standard Reference
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
Unit 3
Polynomial and Rational Functions
Semester 1, 3 weeks
Instructional Objective
0831.03 Define and analyze functional relationships
No.
Performance Objective
Standard Reference
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
Unit 4
Systems of Equations and Inequalities
Instructional Objective
0831.08 Apply discrete math to the manipulation of matrices and
algorithms.
Semester 1, 2 weeks
Standard Reference
No.
Performance Objective
Resource Reference
Assessment
Correlation
01
Perform operations on matrices.
text
EOC, AB
02
Solve systems of equations algebraically and using
matrices.
text
EOC, AB
03
Use linear programming to solve problems.
text
EOC, AB
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.
No.
Performance Objective
Standard Reference
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
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.
No.
Performance Objective
Standard Reference
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
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.
No.
Performance Objective
Standard Reference
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
Unit 8
Exponential and Logarithmic Functions
Semester 2, 3 weeks
Instructional Objective
0831.04 Apply the general properties of logarithmic and exponential
functions to solve problems.
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
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.
No.
Performance Objective
Standard Reference
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
Unit 10
Sequences and Series
Instructional Objective
Semester 2, 2.5 weeks
Standard Reference
0831.10 Analyze sequences and series and find the sums of arithmetic
and geometric series.
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
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.
No.
Performance Objective
01
Standard Reference
Resource Reference
Assessment
Correlation
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
Unit 12
Limits: A Preview of Calculus
Semester 2, optional