Mathematics Curriculum
  Precalculus
 

Precalculus includes all the topics of Trigonometry and a thorough treatment of functions through the study of polynomials, rational functions, logarithmic, exponential, and inverse functions.  Topics include continuity, maximum and minimum points, an intuitive approach to limits, and rates of change.  A transformational approach to graphing is used with families of related graphs.  Numerical, graphical, and algebraic solutions are considered for all problems as applicable.  Emphasis will be placed on problem solving techniques.  Graphing utilities, especially graphing calculators, are integral to the course.

Last Updated: 08/17/12 10:28 AM
 
 
MTH.PC
Standard 1
  CONNECT CIRCULAR FUNCTION WITH TRIG FUNCTION DEFINITIONS
 

Benchmark 1.a
Connect Circular Function with Trig Function Definitions
 
Indicator 1.a.1
Define the six triangular trigonometric functions of an angle
 
Indicator 1.a.2
Define the six circular trigonometric functions of an angle
 
Indicator 1.a.3
Make the connection between the trig function and unit circle
 
Indicator 1.a.4
Recognize and draw an angle in standard position
 
Indicator 1.a.5
Determine a triangle from a point on the terminal side of an angle
 
Indicator 1.a.6
Find angles that are coterminal with a given angle.
 
MTH.PC
Standard 2
  FIND THE VALUES OF TRIGONOMETRIC FUNCTIONS
 

Benchmark 2.a
Given Value of One Trig Function, Find Values of Others
 
Indicator 2.a.1
Find all related trig function values, given the value of one
 
Indicator 2.a.2
Label the special angles and quadrantal angles on the unit circle
 
Indicator 2.a.3
Use circular function definitions and unit circle to solve problems
 
Indicator 2.a.4
Make connections between unit circle and coordinate geometry
 
Indicator 2.a.5
Make connections between unit circle & cosine/sine values
 
Indicator 2.a.6
Make connections between unit circle & special right triangles
 
MTH.PC
Standard 3
  FIND EXACT TRIG VALUES OF SPECIAL ANGLES IN DEGREES AND RADIANS
 

Benchmark 3.a
Find Trig Values of Special Angles Without A Calculator
 
Indicator 3.a.1
Find trig function values of special angles in degrees and radians
 
Indicator 3.a.2
Apply the properties of the unit circle without using a calculator
 
Indicator 3.a.3
Convert from radians to degrees and from degrees to radians
 
Indicator 3.a.4
(Optional) Find the arc length, linear speed, and angular velocity
 
MTH.PC
Standard 4
  APPROXIMATE VALUES OF TRIG FUNCTIONS AND INVERSE TRIG FUNCTIONS
 

Benchmark 4.a
Use A Calculator To Approximate Trig Values and Inverse Trig Values
 
Indicator 4.a.1
Use a calculator to approximate trig values in degrees and radians
 
Indicator 4.a.2
Define inverse trigonometric functions
 
Indicator 4.a.3
Use inverse trig functions to find angle measures
 
MTH.PC
Standard 5
  VERIFY BASIC TRIGONOMETRIC IDENTITIES
 

Benchmark 5.a
Verify Basic Trig Identities Using Substitution
 
Indicator 5.a.1
Verify trig identities using reciprocal and Pythagorean identities
 
Indicator 5.a.2
Verify trig identities using sum and difference identities
 
Indicator 5.a.3
Verify trig identities using double-angle identities
 
Indicator 5.a.4
Verify trig identities using half-angle identities
 
Indicator 5.a.5
Verify trig identities using quotient identities
 
MTH.PC
Standard 6
  FIND DOMAIN, RANGE, AMPLITUDE, PERIOD AND GRAPH TRIG FUNCTIONS
 

Benchmark 6.a
Determine The Domain And Range Of Trig Functions
 
Indicator 6.a.1
State the domain and range of trig functions
 

Benchmark 6.b
Determine Amplitude, Period, Phase Shift, Vertical Shift, & Asymptoles
 
Indicator 6.b.1
Determine amplitude, period, phase shift, vertical shift, & asymptotes
 
Indicator 6.b.2
Describe the effects of changing parameters in a trig equation
 
Indicator 6.b.3
Write equations of trig functions
 
Indicator 6.b.4
Determine and graph trig functions from real-world situations
 

Benchmark 6.c
Sketch The Graph Of A Trig Function Using Transformations
 
Indicator 6.c.1
Sketch the graph of a trig function for at least two periods or cycle
 
Indicator 6.c.2
Sketch the graph of the parent functions, relating to the unit circle
 
MTH.PC
Standard 7
  IDENTIFY THE DOMAIN, RANGE, AND GRAPHS OF INVERSE TRIG FUNCTIONS
 

Benchmark 7.a
Identify The Domain, Range, And Graphs Of Inverse Trig Functions
 
Indicator 7.a.1
Find the domain and range of inverse trig functions
 
Indicator 7.a.2
Find the values of inverse trig functions
 
Indicator 7.a.3
Identify the graphs of inverse trig functions
 
Indicator 7.a.4
Evaluate expressions of composite trig and inverse trig functions
 
Indicator 7.a.5
Graph inverse trig functions using transformations
 
MTH.PC
Standard 8
  SOLVE TRIG EQUATIONS AND INEQUALITIES
 

Benchmark 8.a
Solve Trig Equations With Infinite Solutions and Restricted Domains
 
Indicator 8.a.1
Solve trig equations over a restricted domain
 
Indicator 8.a.2
Solve trig equations with infinite solutions
 
Indicator 8.a.3
Verify algebraic solutions and check reasonableness
 
MTH.PC
Standard 9
  SOLVE PRACTICAL PROBLEMS USING THE LAW OF SINES AND COSINES
 

Benchmark 9.a
Use The Pythagorean Theorem, The Law Of Sines, And The Law Of Cosines
 
Indicator 9.a.1
Create a real-world problem involving triangles
 
Indicator 9.a.2
Solve a real-world problem involving triangles
 
Indicator 9.a.3
Solve problems using Law of Sines, Cosines, and Pythagorean Theorem
 
Indicator 9.a.4
Identify a solution technique that could be used with a given problem
 
Indicator 9.a.5
Prove + and - formulas for sine/cosine/tangent & use to solve problem
 
Indicator 9.a.6
Find the area of triangles using Heron's formula and the sine formula
 
MTH.PC
Standard 10
  IDENTIFY CHARACTERISTICS AND GRAPH POLYNOMIAL AND RATIONAL FUNCTIONS
 

Benchmark 10.a
Identify Characteristics And Graph Polynomial And Rational Functions
 
Indicator 10.a.1
Identify a polynomial function, given an equation or graph
 
Indicator 10.a.2
Identify a rational function, given an equation or graph
 
Indicator 10.a.3
Identify characteristics of a function given its graph
 
Indicator 10.a.4
Sketch the graph of a polynomial function
 
Indicator 10.a.5
Sketch the graph of a rational function
 
Indicator 10.a.6
Use a graphing utility to investigate characteristics of a function
 
Indicator 10.a.7
Identify chars. of polynomial/rational functions given equation
 
Indicator 10.a.8
Find the intersection points of two or more functions
 
Indicator 10.a.9
Determine whether a function is even, odd, or neither
 
Indicator 10.a.10
Solve polynomial or rational equations and inequalities
 
Indicator 10.a.11
Decompose a rational expression into partial fractions
 
MTH.PC
Standard 11
  FIND COMPOSITIONS AND INVERSES OF FUNCTIONS
 

Benchmark 11.a
Find The Composition Of Functions And The Inverse Of A Function
 
Indicator 11.a.1
Find the composition of two or more functions
 
Indicator 11.a.2
Find the inverse of a function, if it exists
 
Indicator 11.a.3
Find the domain and range of the composition of functions
 
Indicator 11.a.4
Find the domain and range of the inverse of a function
 
Indicator 11.a.5
Model problems using composition of functions
 
MTH.PC
Standard 12
  INVESTIGATE AND DESCRIBE THE CONTINUITY OF FUNCTIONS
 

Benchmark 12.a
Describe The Continuity Of Functions From A Graph
 
Indicator 12.a.1
Identify absolute value, step, and piece-wise functions
 
Indicator 12.a.2
Describe the continuity of a function
 
Indicator 12.a.3
Investigate the continuity of various functions
 
Indicator 12.a.4
Use transformations to sketch the graphs of various functions
 
Indicator 12.a.5
Verify graphs of functions using a graphing utility
 
Indicator 12.a.6
Graph absolute value, piece-wise-defined and step functions
 
Indicator 12.a.7
Use transformations to sketch piece-wise-defined functions
 
MTH.PC
Standard 13
  FIND THE LIMIT OF FUNCTIONS GRAPHICALLY, NUMERICALLY AND ALGEBRAICALLY
 

Benchmark 13.a
Find The Limit Of A Function, If It Exists
 
Indicator 13.a.1
Find limits of algebraic functions
 
Indicator 13.a.2
Find a limit algebraically and verify graphically
 
Indicator 13.a.3
Find a limit numerically and verify graphically
 
Indicator 13.a.4
Use limit notation when describing end behavior of a function
 
Indicator 13.a.5
Use the formal definition of continuity to solve problems
 
Indicator 13.a.6
Recognize a limit doesn't exist when evaluating a 1 or 2 sided limit
 
MTH.PC
Standard 14
  IDENTIFY CHARACTERISTICS AND GRAPH EXPONENTIAL AND LOG FUNCTIONS
 

Benchmark 14.a
Identify Characteristics And Graph Exponential And Log Functions
 
Indicator 14.a.1
Identify exponential functions
 
Indicator 14.a.2
Identify logarithmic functions
 
Indicator 14.a.3
Define Euler's constant, e
 
Indicator 14.a.4
Write log equations in exponential form and vice versa
 
Indicator 14.a.5
Identify common and natural logarithms
 
Indicator 14.a.6
Solve exponential equations & use of law exponents
 
Indicator 14.a.7
Solve logarithmic equations
 
Indicator 14.a.8
Model real-world problems using exponential and logarithmic functions
 
Indicator 14.a.9
Graph exponential/logarithmic functions & identify key characteristics
 
MTH.PC
Standard 15
  EXPAND BINOMIALS USING THE BINOMIAL THEOREM AND PASCAL'S TRIANGLE
 

Benchmark 15.a
Expand Binomials Using The Binomial Theorem And Pascal's Triangle
 
Indicator 15.a.1
Expand binomials having positive integral exponents
 
Indicator 15.a.2
Use the binomial theorem, combinations, and Pascal's triangle
 
MTH.PC
Standard 16
  SOLVE PROBLEMS INVOLVING SEQUENCES AND SERIES
 

Benchmark 16.a
Solve Problems Involving Arithmetic and Geometric Sequences and Series
 
Indicator 16.a.1
Use and interpret notation of sequences and series
 
Indicator 16.a.2
Find the nth term of a sequence
 
Indicator 16.a.3
Find the sum of a series
 
Indicator 16.a.4
Model and solve problems using sequences and series
 
Indicator 16.a.5
Distinquish between a convergent and divergent series
 
Indicator 16.a.6
Discuss convergent series in relation to the concept of a limit
 
MTH.PC
Standard 17
  PROVE FORMULAS AND STATEMENTS USING MATHEMATICAL INDUCTION
 

Benchmark 17.a
Prove Formulas And Statements Using Induction
 
Indicator 17.a.1
Compare inductive and deductive reasoning
 
Indicator 17.a.2
Prove formulas/statements, using mathematical induction
 
MTH.PC
Standard 18
  IDENTIFY CHARACTERISTICS AND GRAPH POLAR EQUATIONS
 

Benchmark 18.a
Identify Characteristics And Graph Polar Equations
 
Indicator 18.a.1
Recognize the type of polar graph, given an equation or graph
 
Indicator 18.a.2
Determine the effects of changing parameters in polar equations
 
Indicator 18.a.3
Convert complex numbers between rectangular & polar form
 
Indicator 18.a.4
Find the intersection points of two or more polar graphs
 
Indicator 18.a.5
Identify and plot polar coordinates
 
Indicator 18.a.6
Find equivalent polar coordinates
 
Indicator 18.a.7
Convert coordinates between rectangular form and polar form
 
Indicator 18.a.8
(Optional) Apply DeMoivre's theorem
 
Indicator 18.a.9
(Optional) Identify rectangular graphs from polar graphs & vice versa
 
Indicator 18.a.10
(Optional) Graph polar equations by hand
 
MTH.PC
Standard 19
  MODEL AND SOLVE PROBLEMS PARAMETRICALLY
 

Benchmark 19.a
Model And Solve Problems Parametrically
 
Indicator 19.a.1
Graph parametric equations
 
Indicator 19.a.2
Model motion using parametric equations
 
Indicator 19.a.3
Solve parametric equations
 
Indicator 19.a.4
Compare solution methods
 
Indicator 19.a.5
Eliminate parameters and sketch curves defined by parametrics
 
MTH.PC
Standard 20
  PERFORM OPERATIONS ON VECTORS AND SOLVE PRACTICAL PROBLEMS
 

Benchmark 20.a
Perform Operations on Vectors and Solve Real-World Problems
 
Indicator 20.a.1
Use vector notation
 
Indicator 20.a.2
Perform operations on vectors
 
Indicator 20.a.3
Graph vectors and resultant vectors
 
Indicator 20.a.4
(Optional) Express complex numbers in vector notation
 
Indicator 20.a.5
Define unit vector and find unit vectors
 
Indicator 20.a.6
Perform vector addition, scalar multiplication and find dot products
 
Indicator 20.a.7
Find vector components
 
Indicator 20.a.8
Find the norm of a vector
 
Indicator 20.a.9
(Optional) Use vectors in geometric proofs
 
Indicator 20.a.10
(Optional) Perform operations with vectors in space
 
MTH.PC
Standard 21
  INVESTIGATE FUNDAMENTAL PRINCIPLES OF DIFFERENTIAL CALCULUS
 

Benchmark 21.a
Investigate Principles Of Calculus
 
Indicator 21.a.1
Investigate derivative definition graphically and algebraically
 
Indicator 21.a.2
Find derivatives using the definition and apply to problems
 
Indicator 21.a.3
Find derivatives using the power, product, quotient and chain rules
 
Indicator 21.a.4
Determine the differentiability of functions
 
Indicator 21.a.5
(Optional) Find second derivatives and apply to problems


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