Download AP Calculus AB Course Outline

PRECALCULUS – Mr. Andrew J. Byrum
Course Philosophy: Primary Objectives
 To help students truly understand the fundamental concepts of algebra,
trigonometry, and analytic geometry
 To foreshadow important ideas of calculus
 To show how functions can be used to model real-life problems
 To integrate technology through the use of graphics calculators
Teaching Strategies
Within the first few days of school, each student is issued a Texas
Instruments TI-83/TI-84 graphics calculator. Most students are not familiar
with using a graphing calculator, making it not only a challenge to teach the
course material, but also teaching the students how to use a graphics
calculator. The first week is designed to familiarize the students with the
particular nuances of using the TI-83/TI-84, with continual emphasis on the
fact that students should not rely heavily on the calculator. As content
progresses, more tidbits are revealed about the TI-83’s capabilities; and
each student is offered a manual should individualized exploration be
desired. The textbook used is Precalculus: Graphical, Numerical, Algebraic
6th edition by Demana, Waits, Foley, and Kennedy
Throughout the course, students collaborate together, usually informally, on
various classwork activities. The classroom seating structure is that of
tables, which make group work more conducive for cooperative learning.
Often, students do problems on the two marker boards located on the wall
at the head of the class; giving verbal explanations for their work. Marker
boards are employed so that students can visualize mathematics through
the use of color. Students are expected to use proper vocabulary and
terminology when giving verbal explanations to their fellow classmates, as
well as to the instructor. Technology is also available through the use of a
Texas Instruments TI-83/TI-84 graphics calculator that can be viewed via
an overhead projector.
1
Precalculus Course Outline with Common Core Standards
Chapter 1: Functions and Graphs (8 weeks)
A.
MODELING AND EQUATION SOLVING – 1.1 pp. 64 – 80






Numerical Models
Algebraic Models
Graphical Models
The Zero Factor Property
The Problem Solving Process
Graphics Calculator Failure and Hidden Behavior
Assignment: Textbook Section 1.1 pp. 76 – 79 # 1 – 10, 29 – 38
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 7a: Graph linear and quadratic functions and show intercepts,
maxima, and minima.
High School Conceptual Category: Algebra
Domain: Reasoning with equations and inequalities
Cluster: Solve equations and inequalities in one variable
Standard 4: Solve quadratic equations in one variable.
B.
FUNCTIONS AND THEIR PROPERTIES – 1.2 pp. 81 – 101









Function Definition and Notation
Domain and Range
Continuity and Types of discontinuity
Increasing and Decreasing Functions
Boundedness
Local and Absolute (Global) Extrema
Symmetry – Odd and Even Functions
Vertical and Horizontal Asymptotes
End Behavior
Assignment: Textbook Section 1.2 pp. 98 – 99 # 2 – 68 even
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Understand the concept of a function and use function notation
Standard 1: Understand that a function from one set (called the domain) to another set
(called the range) assigns to each element of the domain exactly one element of the
range. If f is a function and x is an element of its domain, the f(x) denotes the output of f
corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Standard 4: For a function that models a relationship between two quantities, interpret
key features of graphs and tables in terms of the quantities, and sketch graphs showing
key features given a verbal description of the relationship. Key features include:
intercepts; intervals where the function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end behavior; and periodicity.
2
C.
TWELVE BASIC FUNCTIONS – 1.3 pp. 101 - 112
 What Graphs Can Tell Us
 Twelve Basic Functions
 Analyzing Functions Graphically
Assignment: Textbook Section 1.3 pp. 80, 81 # 1 – 12, 19 – 24
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 7b: Graph square root, cube root, and piecewise-defined functions, including
step functions and absolute value functions.
D.
BUILDING FUNCTIONS FROM FUNCTIONS – 1.4 pp. 113 - 131




Combining Functions Algebraically
Composition of Functions
Relations and Implicitly Defined Functions
Inverse Relations and Inverse Functions
Assignment: Textbook Section 1.4 pp. 127 – 129 # 1 – 20, 39 – 56
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Understand the concept of a function and use function notation
Standard 2: Use function notation, evaluate functions for inputs in their domains, and
interpret statements that use function notation in terms of a context.
High School Conceptual Category: Functions
Domain: Building Functions
Cluster: Build a Function that models a relationship between two quantities
Standard 1: Write a function that describes a relationship between two quantities. A)
Determine an explicit expression, a recursive process, or steps for calculation from a
context. B) Combine standard function types using arithmetic operations. C) Compose
functions.
High School Conceptual Category: Functions
Domain: Building Functions
Cluster: Build new functions from existing functions
Standard 4: Find inverse functions. A) Solve an equation of the form f(x) = c for a
simple function f that has an inverse and write an expression for the inverse. B) Verify
by composition that one function is the inverse of another. C) Read values of an inverse
function from a graph or table, given that the function has an inverse. D) Produce an
invertible function from a non-invertible function by restricting the domain.
E.
GRAPHICAL TRANSFORMATIONS – 1.5 pp. 131 - 142




Transformations
Vertical and Horizontal Translations
Reflections Across Axes
Vertical and Horizontal Stretches and Compressions (Shrinks)
Assignment: Textbook Section 1.5 pp. 139 – 150 # 1 – 16, 25 – 28, 47 – 54
3
High School Conceptual Category: Functions
Domain: Building Functions
Cluster: Build new functions from existing functions
Standard 3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and
f(x + k) for specific values of k (both positive and negative); find the value of k given the
graphs. Experiment with cases and illustrate an explanation of the effects on the graph
using technology.
F.
MODELING WITH FUNCTIONS – 1.6 pp. 142 - 155




Functions from Formulas
Functions from Graphs
Functions from Verbal Descriptions
Functions from Data
Assignment: Textbook Section 1.6 pp. 152 – 153 # 2 – 32 even
High School Conceptual Category: Functions
Domain: Linear and Exponential Models
Cluster: Interpret expressions for functions in terms of the situation they model
Standard 5: Interpret the parameters in a linear or exponential function in terms of a
context.
Test: Chapter 1 – Multiple Choice
G.
PACESETTER – THE MILE RUN
High School Conceptual Category: Functions
Domain: Linear and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems
Standard 1: Distinguish between situations that can be modeled with linear functions
and with exponential functions.
Standard 1a: Prove that linear functions grow by equal differences over equal intervals,
and that exponential functions grow by equal factors over equal intervals.
Standard 5: Interpret the parameters in a linear function in terms of a context.
H.
PACESETTER – SHIPS IN THE FOG
High School Conceptual Category: Functions
Domain: Linear and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems
Standard 1: Distinguish between situations that can be modeled with linear functions
and with exponential functions.
Standard 1b: Recognize situations in which one quantity changes a constant rate per
unit interval relative to another.
Standard 5: Interpret the parameters in a linear function in terms of a context.
4
Chapter 2: Polynomial, Power, and Rational Functions (8 weeks)
A.
LINEAR AND QUADRATIC FUNCTIONS AND MODELING – 2.1
pp. 162 – 180





Polynomial Functions
Linear Functions and Their Graphs
Average Rate of Change
Linear Correlation and Modeling
Quadratic Functions and Their Graphs
Assignment: Textbook Section 2.1 pp. 175 – 176 # 1 – 18, 24 – 44 even, 45 – 48
High School Conceptual Category: Algebra
Domain: Reasoning with Equations and Inequalities
Cluster: Solve equations and inequalities in one variable
Standard 4b: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square
roots, completing the square, the quadratic formula and factoring, as appropriate to the
initial form of the equation. Recognize when the quadratic formula gives complex
solutions and write them in a ± bi for real numbers a and b.
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Interpret functions that arise in applications in terms of the context
Standard 6: Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval. Estimate the rate of change from a
graph.
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 7a: Graph linear and quadratic functions and show intercepts,
maxima, and minima.
Standard 8a: Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret these
in terms of a context.
B.
POWER FUNCTIONS WITH MODELING – 2.2 pp. 181 – 192
 Power Functions and Variation
 Graphs of Power Functions
 Modeling with Power Functions
Assignment: Textbook Section 2.2 pp. 189 – 190 # 1 – 22, 29 – 34
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 9: Compare properties of two functions each represented in a different way
(algebraically, graphically, and numerically in tables, or by verbal descriptions).
5
C.
POLYNOMIAL FUNCTIONS OF HIGHER DEGREE WITH
MODELING – 2.3 pp. 193 – 206
 Graphs of Polynomial Functions
 End Behavior of Polynomial Functions
 Zeros of Polynomial Functions
 Intermediate Value Theorem
Assignment: Textbook Section 2.3 pp. 203, 204 # 9 – 12, 17 – 24, 29 – 38, 43 – 52
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Interpret functions that arise in applications in terms of the context
Standard 5: Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes.
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 7c: Graph polynomial functions, identifying zeros when suitable factorizations
are available, and showing end behavior.
D.
REAL ZEROS OF POLYNOMIAL FUNCTIONS – 2.4 pp. 207 – 220
 Long Division and the Division Algorithm
 Remainder and Factor Theorems
 Synthetic Division
 Rational Zeros Theorem
Assignment: Textbook Section 2.4 pp. 216 – 218 # 1 – 12, 27 – 30, 49 – 56
High School Conceptual Category: Algebra
Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Rewrite rational expressions
Standard 6: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the
form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of
r(x) less than the degree of b(x), using inspection, long division, or, for the more
complicated examples, a computer algebra system.
Standard 7: Understand that rational expressions form a system analogous to the
rational numbers, closed under addition, subtraction, multiplication, and division by a
nonzero rational expression; add, subtract, multiply, and divide rational expressions.
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 7: Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more complicated cases.
Standard 8: Write a function defined by an expression in different, but equivalent forms
to reveal and explain different properties of the function.
6
E.
COMPLEX NUMBERS – 2.5 pp. 221 – 228
 Complex Numbers
 Operations with Complex Numbers
 Complex Conjugates and Division
 Complex Solutions of Quadratic Equations
 The Complex Number Plane
Assignment: Textbook Section 2.5 pp. 227 # 1 – 40
High School Conceptual Category: Number and Quantity
Domain: The Complex Number System
Cluster: Perform arithmetic operations with complex numbers
Standard 1: Know there is a complex number “ i ” such that i2 = -1, and every complex
number has the form a + bi where a and b are real numbers.
Standard 2: Use the relation i2 = -1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers.
Standard 3: Find the conjugate of a complex number; use conjugates to find moduli
and quotients of complex numbers.
Standard 4: Represent complex numbers on the complex plane in rectangular and
polar form (including real and imaginary numbers), and explain why the rectangular and
polar forms of a given complex number represent the same number.
F.
COMPLEX ZEROS AND THE FUNDAMENTAL THEOREM OF
ALGEBRA – 2.6 pp. 229 – 236
 Two Major Theorems
 Complex Conjugate Zeros
 Factoring with Real Number Coefficients
Assignment: Textbook Section 2.6 pp. 234, 235 # 2 – 32 even
High School Conceptual Category: Number and Quantity
Domain: The Complex Number System
Cluster: Use complex numbers in polynomial identities and equations
Standard 7: Solve quadratic equations with real coefficients that have complex
solutions.
Standard 8: Extend polynomial identities to complex numbers.
Standard 9: Know the Fundamental Theorem of Algebra; show it is true for quadratic
polynomials.
G.
GRAPHS OF RATIONAL FUNCTIONS – 2.7 pp. 237 – 248
 Rational Functions
 Limits and Asymptotes
 Analyzing Graphs of Rational Functions
Assignment: Textbook Section 2.7 pp. 246, 247 # 11 – 18, 20 – 30 even, 31 – 44
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 7d: Graph rational functions, identifying zeros and asymptotes when suitable
factorizations are available, and showing end behavior.
7
H.
SOLVING EQUATIONS IN ONE VARIABLE – 2.8 pp. 249 – 257
 Solving Rational Equations
 Extraneous Solutions
Assignment: Textbook Section 2.8 pp. 254, 255 # 2 – 30 even
High School Conceptual Category: Algebra
Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the
reasoning
Standard 2: Solve simple rational and radical equations in one variable, and give
examples showing how extraneous solutions may arise.
I.
SOLVING INEQUALITIES IN ONE VARIABLE – 2.9 pp. 258 – 268
 Polynomial Inequalities
 Rational Inequalities
 Other Inequalities
Assignment: Textbook Section 2.9 pp. 265, 266 # 1 – 6, 13 – 20, 34 – 44 even
High School Conceptual Category: Algebra
Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the
reasoning
Standard 2: Solve simple rational and radical equations in one variable, and give
examples showing how extraneous solutions may arise.
Test: Chapter 2 – Multiple Choice
Chapter 3: Exponential, Logistic, and Logarithmic Functions
(8 weeks)
A.
EXPONENTIAL AND LOGISTIC FUNCTIONS – 3.1 pp. 276 – 289




Exponential Functions and Their Graphs
The Natural Base “ e “
Logistic Functions and Their Graphs
Population Models
Assignment: Textbook Section 3.1 pp. 286 – 288 # 1 – 14, 41 – 44, 52, 54, 56
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 7e: Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and amplitude.
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Interpret expressions for functions in terms of the situation they model
Standard 5: Interpret the parameters in a linear or exponential function in terms of a
context.
8
B.
EXPONENTIAL AND LOGISTIC MODELING – 3.2 pp. 290 – 299




Constant Percentage Rate and Exponential Functions
Exponential Growth and Decay Models
Using Regression to Model Population
Other Logistic Models
Assignment: Textbook Section 3.2 pp. 296, 297 # 2 – 32 even
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Analyze functions using different representations
Standard 8b: Use the properties of exponents to interpret expressions for exponential
functions. For example, identify percent rate of change in functions such as y = (1.02)5,
y = (0.97)5, y = (1.01)12t, y = (1.2) t/10, and classify them as representing exponential
growth or decay.
C.
PACESETTER – POPULATION GROWTH
High School Conceptual Category: Functions
Domain: Linear and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems
Standard 1: Distinguish between situations that can be modeled with linear functions
and with exponential functions.
Standard 1c: Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.
High School Conceptual Category: Functions
Domain: Interpreting Functions
Cluster: Interpret expressions for functions in terms of the situation they model
Standard 5: Interpret the parameters in a linear or exponential function in terms of a
context.
D.
LOGARITHMIC FUNCTIONS & GRAPHS – 3.3 pp. 300 – 309




Inverses of Exponential Functions
Common Logarithms – Base 10
Natural Logarithms – Base e
Graphs of Logarithmic Functions
Assignment: Textbook Section 3.3 pp. 308, 309 # 1 – 40, 60 – 62
High School Conceptual Category: Functions
Domain: Building Functions
Cluster: Build new functions from existing functions
Standard 5: Understand the inverse relationship between exponents and logarithms
and use this relationship to solve problems involving logarithms and exponents.
High School Conceptual Category: Functions
Domain: Linear and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems
Standard 4: For exponential models, express as a logarithm the solution to abct = d
where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm
using technology.
9
E.
PROPERTIES OF LOGARITHMIC FUNCTIONS – 3.4 pp. 310 – 319
 Properties of Logarithms
 Change of Base
 Graphs of Logarithmic Functions with Base b
Assignment: Textbook Section 3.4 pp. 317 # 1 – 32, 43 – 46
High School Conceptual Category: Algebra
Domain: Seeing the structure of expressions
Cluster: Write expressions in equivalent forms to solve problems
Standard 3: Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
High School Conceptual Category: Functions
Domain: Building Functions
Cluster: Build new functions from existing functions
Standard 5: Understand the inverse relationship between exponents and logarithms
and use this relationship to solve problems involving logarithms and exponents.
F.
EQUATION SOLVING AND MODELING – 3.5 pp. 320 – 333
 Solving Exponential Equations
 Solving Logarithmic Equations
Assignment: Textbook Section 3.5 pp. 331 # 2 – 18 even, 19 – 24, 26 – 38 even
High School Conceptual Category: Algebra
Domain: Seeing the structure of expressions
Cluster: Write expressions in equivalent forms to solve problems
Standard 3: Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
High School Conceptual Category: Functions
Domain: Building Functions
Cluster: Build new functions from existing functions
Standard 5: Understand the inverse relationship between exponents and logarithms
and use this relationship to solve problems involving logarithms and exponents.
G.
PACESETTER – A POWERFUL FUNCTION
High School Conceptual Category: Functions
Domain: Linear and Exponential Models
Cluster: Construct and compare linear and exponential models and solve problems
Standard 4: For exponential models, express as a logarithm the solution to abct = d
where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm
using technology.
Test: Chapter 3A – Multiple Choice
10
H.
MATHEMATICS OF FINANCE – 3.6 pp. 334 – 345





Interest Compounded Annually
Interest Compounded k Times per year
Interest Compounded Continuously
Annuities – Future Value
Loans and Mortgages – Present Value
Assignment: Textbook Section 3.6 pp. 342, 343 # 1 – 20, 22 – 30 E, 48 – 56 E
High School Conceptual Category: Algebra
Domain: Seeing the structure of expressions
Cluster: Write expressions in equivalent forms to solve problems
Standard 3c: Use the properties of exponents to transform expressions for exponential
functions. For example the expression1.15t can be written as (1.15 1/12)12t ≈ 1.01212t to
reveal the approximate equivalent monthly interest rate if the annual rate is 15%
Standard 4: Derive the formula for the sum of a finite geometric series (when the
common ratio is not 1), and use the formula to solve problems. For example, calculate
mortgage payments.
I.
PACESETTER – PENNSYLVANIA LOTTERY
High School Conceptual Category: Algebra
Domain: Seeing the structure of expressions
Cluster: Write expressions in equivalent forms to solve problems
Standard 3c: Use the properties of exponents to transform expressions for exponential
functions. For example the expression1.15t can be written as (1.15 1/12)12t ≈ 1.01212t to
reveal the approximate equivalent monthly interest rate if the annual rate is 15%
Standard 4: Derive the formula for the sum of a finite geometric series (when the
common ratio is not 1), and use the formula to solve problems. For example, calculate
mortgage payments.
Test: Chapter 3B – Multiple Choice
Chapter 4: Trigonometric Functions (8 weeks)
A.
ANGLES AND THEIR MEASURES – 4.1 pp. 352 – 361




The Problem of Angular Measure
Degrees and Radians
Circular Arc Length
Angular and Linear Motion
Assignment: Textbook Section 4.1 pp. 358 – 360 # 2 – 38 even, 39, 40, 45, 47, 54
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Extend the domain of trigonometric functions using the unit circle
Standard 1: Understand radian measure of an angle as the length of the arc on the unit
circle subtended by the angle.
11
B.
TRIGONOMETRIC FUNCTIONS: ACUTE ’S – 4.2 pp. 362 – 371





Right Triangle Trigonometry
Two Famous Triangles
Evaluating Trigonometric Functions with a Calculator
Common Calculator Errors When Evaluating Trigonometric Functions
Applications of Right Triangle Trigonometry
Assignment: Textbook Section 4.2 pp. 368 – 370 # 1 – 8, 10 – 58 E, 62, 66, 74
High School Conceptual Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles
Standard 6: Understand that by similarity, side ratios in right triangles are properties of
the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Standard 8: Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
C.
TRIGONOMETRY: CIRCULAR FUNCTIONS – 4.3 pp. 372 – 385




Trigonometric Functions of any Angle
Trigonometric Functions of Real Numbers
Periodic Functions
The 16 – Point Unit Circle
Assignment: Textbook Section 4.3 pp. 383 # 2 – 48 even
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Extend the domain of trigonometric functions using the unit circle
Standard 2: Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit circle.
Standard 3: Use special triangles to determine geometrically the values of sine, cosine,
tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine,
cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is
any real number.
D.
PACESETTER – DAYLIGHT HOURS
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Model periodic phenomena with trigonometric functions
Standard 5: Choose trigonometric functions to model periodic phenomena with
specified amplitude, frequency, and midline.
Test: Trigonometry Test 1
12
E.
GRAPHS OF SINE & COSINE: SINUSOIDS – 4.4 pp. 386 – 397
 The Basic Waves Revisited
 Sinusoids and Transformations
 Modeling Periodic Behavior with Sinusoids
Assignment: Textbook Section 4.4 pp. 394, 395 # 2 – 16 even, 29 – 34, 57 – 60
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Model periodic phenomena with trigonometric functions
Standard 4: Use the unit circle to explain symmetry (odd and even) and periodicity of
trigonometric functions.
Standard 5: Choose trigonometric functions to model periodic phenomena with
specified amplitude, frequency, and midline.
F.
GRAPHS OF TAN, COT, SEC & CSC – 4.5 pp. 398 – 406




The Tangent Function
The Cotangent Function
The Secant Function
The Cosecant Function
Assignment: Textbook Section 4.5 pp. 403 # 1 – 20
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Model periodic phenomena with trigonometric functions
Standard 5: Choose trigonometric functions to model periodic phenomena with
specified amplitude, frequency, and midline.
G.
GRAPHS OF COMPOSITE TRIG FUNCTIONS – 4.6 pp. 407 – 415
 Combining Trigonometric and Algebraic Functions
 Sums and Differences of Sinusoids
 Damped Oscillation
Assignment: Textbook Section 4.6 pp. 413, 414 # 2 – 42 even
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Model periodic phenomena with trigonometric functions
Standard 5: Choose trigonometric functions to model periodic phenomena with
specified amplitude, frequency, and midline.
H.
SUPPLEMENTAL – THE SINE FUNCTION pp. 68 – 78






Activity 34 – The Sine Function: Amplitude
Activity 35 – The Sine Function: Vertical Shift
Activity 36 – The Sine Function: Period
Activity 37 – The Sine Function: Phase Shift
Activity 38 – The General Sine Function: A sin [B(x – C)] + D
Activity 39 – Periodic Problems
Test: Trigonometry Test 2 – Multiple Choice
13
I.
INVERSE TRIGONOMETRIC FUNCTIONS – 4.7 pp. 416 – 425




Inverse Sine Function
Inverse Cosine and Tangent Functions
Composing Trigonometric and Inverse Trigonometric Functions
Applications of Inverse Trigonometric Functions
Assignment: Textbook Section 4.7 pp. 423 # 1 – 32
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Model periodic phenomena with trigonometric functions
Standard 6: Understand that restricting a trigonometric function to a domain on which it
is always increasing or always decreasing allows its inverse to be constructed.
Standard 7: Use inverse functions to solve trigonometric equations that arise in
modeling contexts; evaluate the solutions using technology, and interpret them in terms
of context.
J.
SOLVING PROBLEMS WITH TRIGONOMETRY – 4.8 pp. 426 – 437
 More Right Triangle Problems
 Simple Harmonic Motion
Assignment: Textbook Section 4.8 pp. 432 – 434 # 1 – 10, 16, 20
High School Conceptual Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles
Standard 8: Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Test: Trigonometry Test 3 – Multiple Choice
Chapter 5: Analytic Trigonometry (4 weeks)
A.
FUNDAMENTAL IDENTITIES – 5.1 pp. 444 – 453






Basic Trigonometric Identities
Pythagorean Identities
Cofunction Identities
Odd-Even Identities
Simplifying Trigonometric Expressions
Solving Trigonometric Equations
Assignment: Textbook Section 5.1 pp. 451, 452 # 9 – 16, 27 – 32, 51 – 56
High School Conceptual Category: Functions
Domain: Trigonometric Functions
Cluster: Prove and apply trigonometric identities
Standard 8: Prove the Pythagorean identity and use it to calculate trigonometric ratios.
sin2 (θ) + cos2 (θ) = 1
Standard 9: Prove the addition and subtraction formulas for sine, cosine, and tangent
and use them to solve problems.
14
B.
THE LAW OF SINES – 5.5 pp. 478 – 486




Deriving the Law of Sines
Solving Triangles (AAS, ASA)
The Ambiguous Case (SSA)
Applications
Assignment: Textbook Section 5.5 pp. 484, 485 # 2 – 22 even, 40, 44
High School Conceptual Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Cluster: Apply trigonometry to general triangles
Standard 10: Prove the Laws of Sines and Cosines and use them to solve problems.
Standard 11: Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems,
resultant forces).
C.
THE LAW OF COSINES – 5.6 pp. 487 – 496
 Deriving the Law of Cosines
 Solving Triangles (SAS, SSS)
 Triangle Area and Heron’s Formula
Assignment: Textbook Section 5.6 pp. 494, 495 # 2 – 20 even, 30 – 34
High School Conceptual Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Cluster: Apply trigonometry to general triangles
Standard 9: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing
an auxiliary line from a vertex perpendicular to the opposite side.
Standard 10: Prove the Laws of Sines and Cosines and use them to solve problems.
Standard 11: Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems,
resultant forces).
Test: Trigonometry Test 4 – Multiple Choice
Student Evaluation
Quarterly grades are computed using attendance, classwork activities, homework, quiz results,
and test results. Grades are determined by dividing the points a student achieves by the points
assigned during the grading period in order to compute the percentage attained.
GRADING SCALE:
FINAL GRADES FOR THE COURSE:
A
B
C
D
F
1st 9 weeks = 2/9 of final grade.
2nd 9 weeks = 2/9 of final grade.
3rd 9 weeks = 2/9 of final grade.
4th 9 weeks = 2/9 of final grade.
Final Exam = 1/9 of final grade.
=
=
=
=
=
90. 0 % and up
80 .0 % to 89. 9 %
70. 0 % to 79. 9 %
60. 0 % to 69. 9 %
0. 0 % to 59. 9 %
15
Resource Materials
Primary Resource:
Demana, Franklin D., Bert K. Waits, Gregory D. Foley and Daniel Kennedy.
Precalculus – Graphical, Numerical, Algebraic. 6th edition. Boston, Massachusetts:
Pearson – Addison Wesley, 2004.
Secondary Resources:
Academic Content Standards k-12 Mathematics. Ohio Department of Education. Center
for Curriculum and Assessment. Office of Curriculum and Instuction
Bentley, Wayne J. Precalculus. Grand Rapids, Michigan 49544: Instructional Fair - TS
Denison, 1997.
Lund, Charles and Edwin Andersen. Graphing Calculator Activities: Exploring Topics in
Algebra 1 & Algebra 2. Menlo Park, California, 1998.
Pacesetter Mathematics: Precalculus Through Modeling 1998 – 1999. The College Board,
Educational Testing Service, 1996.
Pacesetter Mathematics: Precalculus Through Modeling 1998 – 1999. Volume 1 Teacher’s
Edition. The College Board, Educational Testing Service, 1996.
Pacesetter Mathematics: Precalculus Through Modeling 1998 – 1999. Volume 2 Teacher’s
Edition. The College Board, Educational Testing Service, 1996.
16