PRECALCULUS
PACING SCHEDULE

PREREQUISITE CHAPTER

PRQ.1 "Real Number System"

Topics you must know / skills you must be able to show:
The different number sets (natural, integers, rationals, irrationals, and real numbers)
Interval notation and inequality notation
Assignments for PRQ.1:
Day 1: p. 9 Exercises # 21-53 odd

 

PRQ.2 "Properties of Real Numbers"

Topics you must know / skills you must be able to show:
How to evaluate an algebraic expression
Basic properties of algebra (distributive, commutative, associative, etc.)
How to work with exponents
Scientific notation
Assignments for PRQ.2:
Day 1: p. 18 Exercises # 1-18 all, 19-25 odd, 45-54 all,
Day 2: p. 19, #55 - 79 odd

 

PRQ.3 "Radicals and Rational Exponents"

Topics you must know / skills you must be able to show:
Properties of radicals; Simplifying radical expressions; Rationalizing denominators; Rational exponents
Assignments for PRQ.3:
Day 1: p. 24 Exercises # 29-51 odd, 59-75 odd

 

PRQ.4 "Polynomials and Special Products"

Topics you must know / skills you must be able to show:
Vocabulary: term, coefficient, degree (of a term, of a polynomial), monomial, binomial, polynomial, descending order, like terms, FOIL method
Skills: How to combine like terms; Use FOIL; Multiplying polynomials in vertical (stacked) form
Assignments for PRQ.4:
Day 1: p. 29 Exercises # 1-59 odd

 

PRQ.5 "Factoring Polynomials"

Topics you must know / skills you must be able to show:
Find (and factor out) a common monomial factor; Special products: difference of two squares & perfect square trinomial; Factoring trinomials with FOIL; Multiplying polynomials in vertical (stacked) form
Assignments for PRQ.5:
Day 1: p. 35 Exercises # 1-19 odd, 29-45 odd, 55-65 odd, 75, 77

 

PRQ.6 "Fractional Expressions"

Topics you must know / skills you must be able to show:
Find domain; Reducing rational expressions; Operations with rational expressions; Multiplying polynomials in vertical (stacked) form
Assignments for PRQ.6:
Day 1: p. 41 Exercises # 1-17 odd, 25-33 odd, 39, 41, 45-57 odd

 

PRQ.7 "Linear Equations and Inequalities"

Topics you must know / skills you must be able to show:
How to solve linear equations; How to solve linear inequalities
Assignments for PRQ.7:
Day 1: p. 48 Exercises # 7-12 all, 13-29 odd, 35-45 odd

 

PRQ.8 "Cartesian Coordinate System"

Topics you must know / skills you must be able to show:
Vocabulary: x-axis, y-axis, origin, quadrants, ordered pair, coordinates of a point
Use distance formula; Use midpoint formula
Assignments for PRQ.8:
Day 1: p. 55 Exercises # 9-21 odd

PREREQUISITE CHAPTER TEST

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Topic 1: Number, Algebra, and Functions

1.a Number Systems
Covered in Prerequisite Chapter

1.b Functions
Topics you must know / skills you must be able to show: (1) How to graph by point-plotting; (2) How to use a grapher and find an appropriate window; (3) Definition of function, domain, & range; (4) How to use function notation; (5) How to evaluate a function for given values
Assignments for § 1.2
Day 1: p. 75 Exercises # 3-12 all, 19-29 odd, 35-38 all, 39, 45
Day 2: Worksheet "What is my Domain?"

§ 1.3 Linear Functions and their Graphs
Topics you must know / skills you must be able to show: (1) Definition of a linear function; (2) Formulas: slope, point-slope form of a linear equation, slope-intercept form, general/standard form, vertical lines, horizontal lines; (3) How to find the equation of a line given two points or a point and the slope; (4) Relationship between parallel / perpendicular lines
Assignments for § 1.3
Day 1: p. 91 Exercises # 9-17 odd, 23-29 odd
Day 2: p. 91 # 31-41 odd, 61-64 all, 76

Piecewise Defined Functions
Topics you must know / skills you must be able to show: (1) How to plot points to sketch piecewise defined function
HW: Supplemental packet (worksheet)

TEST

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Topic 2: Equation Solving

2.a Solving Equations Graphically
Topics you must know / skills you must be able to show: Connection between a solution, a root of , a zero of a function, and an x-intercept of a graph; How to find intercepts with the graphing calculator; How to find the intersection points of graphs with the graphing calculator
HANDOUT: Finding Intercepts
Assignments for § 2.1
Day 1: p. 142 Exercises # 9-25 odd, 39, 41

2.b Solving Quadratic Equations Algebraically
Topics you must know / skills you must be able to show: Standard form of a quadratic equation; Attributes of quadratic functions (vertex form, line of symmetry); How to complete the square to solve a QE; How to use the quadratic formula (from memory); How to solve QEs by factoring; How to use the discriminant to predict the number of solutions; How to find the equation of a parabolic function given the vertex and a point on the graph; Find Intercepts (see notes)
Assignments for § 2.2
Day 1: p. 155 Exercises # 1-7 odd, 11, 13, 17-23 odd
Day 2: p. 156 # 33-69 odd
Day 3: Supplemental Worksheet - Attributes of Quadratic Functions

2.c Solving Absolute Value and Radical Equations and Inequalities
Topics you must know / skills you must be able to show: How to solve absolute value equations and inequalities; How to solve radical equations and inequalities and to check for extraneous solutions
Assignments for § 2.3
Day 1: p. 167 Exercises # 1-13 odd
Day 2: p. 168 # 29-45 odd

MID-CHAPTER 2 TEST - SECTIONS 2.1-2.3

2.d Operations on Functions: Combinations and Compositions
Topics you must know / skills you must be able to show: How to combine (by addition, subtraction, multiplication, and division) functions and to simplify the combinations; How to create a function composition; How to recognize a function composition and to decompose them into individual functions; How to find the domain of a function composition / combination
HANDOUT: Functions and the Calculus - A Sneak Preview
Assignments for § 2.4
Day 1: p. 179 Exercises # 1-9 odd, 15-35 odd, 39

2.e Transformations of Graphs
Topics you must know / skills you must be able to show: How to recognize and describe rigid transformations in the form of vertical / horizontal translations; How to recognize and describe reflections over lines of symmetry; How to recognize and describe vertical / horizontal stretches or shrinks
Assignments for § 2.6
Day 1: p. 197 Exercises # 1-15 odd, 25-37 odd
Day 2: p. 198 # 47-61 odd

2.f Inverses of Functions
Topics you must know / skills you must be able to show: How to graph an inverse of a relation given a table of ordered pairs; The relationship between a function and its inverse; How to find, by algebraic means, the inverse of simple functions
Assignments for § 2.7
Day 1: p. 204 Exercises # 1-7 odd, 17-23 odd

END-OF-CHAPTER 2 TEST - SECTIONS 2.1-2.7

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Topic 3: Polynomial Functions

3.a Quadratic Functions
Topics you must know / skills you must be able to show: Write a polynomial in standard form; Identify the degree of a polynomial; Use standard form / vertex form of quadratic functions; Find line of symmetry & vertex of a quadratic function
Assignments for § 3.1
Day 1: p. 220 Exercises # 1-5 odd, 51-55 odd, 61, 65, 72, 73
QUIZ on Section 3.1

3.b Polynomials Functions of Higher Degree
Topics you must know / skills you must be able to show: ; How to recognize the basic shape of a graph from the leading term (i.e. end behavior); Find zeros by factoring; Find zeros by graphing and approximating; How to create a polynomial that will have specific zeros
Assignments for § 3.2
Day 1: p. 233 Exercises # 1-5 odd, 13-27 odd
Day 2: p. 233 Exercises # 35-40 all, 45-53 odd, 54, & 55

3.c Polynomial Division
Topics you must know / skills you must be able to show: Polynomial long division and synthetic division; Connection between zero remainder after division and the divisor being a factor
Assignments for § 3.3
Day 1: p. 246 Exercises # 1-7 odd, 15-19 odd, 31, 33, 43, 45

QUIZ on Sections 3.2-3.3

3.d Real Zeros of Polynomial Functions
Topics you must know / skills you must be able to show: Use the rational zeros test to find linear factors of polynomials
Assignments for § 3.4
Day 1: p. 260 Exercises # 31-47 odd

3.e Complex Numbers
Topics you must know / skills you must be able to show: Definition of the imaginary unit, pattern of the powers of i; Standard form of a complex number; Operations with complex numbers (add, subtract, multiply, divide), including use of complex conjugates; Complex solutions to quadratic equations
Assignments for § 3.5
Day 1: p. 268 Exercises # 1-27 odd
Day 2: p. 268 # 37-49 odd, 55-58 all

3.f Fundamental Theorem of Algebra
Topics you must know / skills you must be able to show: Fundamental Theorem of Algebra; Linear factorization theorem; How to find linear factors
Assignments for § 3.6
Day 1: p. 276 Exercises #9-20 all, 21-31 odd

CHAPTER 3 TEST - SECTIONS 3.1-3.6

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Topic 4: Exponential and Logarithmic Functions

Project: Exponential Growth and Interest on Investments
Pacing = 3 days.

4.a Exponential Functions
Topics you must know / skills you must be able to show: Characteristics of exponential function graphs; End behavior of exponential function graphs; Difference between power functions and exponential functions; Difference between exponential growth and decay.
HANDOUT: Notes - Exponential Growth and Decay with the Graphing Calculator (Part I)
Assignments for § 4.1
Day 1: p. 294 Exercises # 1-24 odd
Day 2: p. 294 Exercises # 25-45 odd
Day 3: p. 295 Exercises # 49-54 all, 57, 58
Day 4: QUIZ - § 4.1

4.b Logarithmic Functions
Topics you must know / skills you must be able to show: Inverse relationship between logarithmic and exponential functions; The number e, defined as the number the expression (1 + 1/x)x approaches as x approaches infinity; Logarithms of base 10 and base e; Ability to solve equations with exponents and logarithms; Graph logarithmic functions.
Assignments for § 4.2
Day 1: p. 306 Exercises # 1-30 all
Day 2: p. 307 Exercises # 31-49 odd

4.3 Properties of Logarithmic Functions; Equation Solving
Topics you must know / skills you must be able to show: How to use the Change of Base Formula to evaluate and graph logs; How to use the Product, Quotient, and Power rules to aid in solving equations.
Assignments for § 4.3
Day 1: p. 316 Exercises # 1-23 odd
Day 2: p. 317 Exercises # 25-61 odd

4.4 More Equation Solving and Applications
Topics you must know / skills you must be able to show: How to solve various exponential and logarithmic equations; How to use the logistic growth function to model population growth; Solve problems involving logistic growth models .
Assignments for § 4.4
Day 1: p. 327 Exercises # 1-19 odd
Day 2: p. 327 Exercises # 27-45 odd
Day 3: p. 327 Exercises # 47, 48, & 49
Day 4: Worksheet packet on Exponential Growth and Decay - Part II
Day 5: QUIZ: § 4.3-4.4

4.5 Interest and Annuities
Topics you must know / skills you must be able to show: Formula for the value of an investment with compound interest rate growth; Solving various application problems involving compound interest.
Assignments for § 4.4
Day 1: p. 340 Exercises # 1-8 all, 9-15 odd,
Day 2: p. 340 Exercises # 17, 18, 19, 24, 28, 29, 30, 36

CHAPTER 4 TEST - SECTIONS 4.1-4.5

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Topic 5: Rational Functions

5.a Rational Functions and Asymptotes
Topics you must know / skills you must be able to show: Introduction to Rational functions using inverse variations, Finding vertical and horizontal asymptotes

5.b Graphing Rational Functions
Topics you must know / skills you must be able to show: End behavior; Finding slant asymptotes

5.c Rational Equations and Inequalities
Topics you must know / skills you must be able to show: Solving rational equations; extraneous solutions; solving rational inequalities

5.d Partial Fractions
Topics you must know / skills you must be able to show: Intro to partial fractions with denominators that can be factored into linear factors

Homework and pacing for Rational Functions:
Day 1: Worksheet # 1-Inverse Variation [Addressing Topic 5a]
Day 2: Worksheet # 2-Graphing a Rational Function [Topic 5b]
Day 3: Worksheet # 3-Equation Solving [Topic 5c]
QUIZ - Worksheets 1-3 [Brief quiz - 15-20 minutes]
Day 4: Worksheet # 4-Simplifying Rationals [Topic 5c]
Day 5: Worksheet # 5-More Simplifying Rationals (with additional graphing) [Topics 5b&c]
Day 6: Worksheet # 6-Adding & Subtracting Rational Expressions [Topic 5c]
Day 7: Worksheet # 7-More Equation Solving [Topic 5c]
Day 8: QUIZ - Worksheets 4-7
Day 9: Worksheet # 8-Asymptotes and End Behavior [Topic 5b]
Day 10: Worksheet # 9-Partial Fractions [Topic 5b]
Day 11: TEST on all topics covered in worksheets.

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Topic 6: Trigonometric Functions

6.a Exponential Functions
Topics you must know / skills you must be able to show: Coterminal angles; compliments / supplements; Degree & radian measure; arc length formula; angles and navigation
HANDOUTS: § 6.1 Radians and Arc Length
Assignments for § 6.1:
Day 1: § 6.1, p. 399 # 1-32 all
Day 2: § 6.1, p. 399 # 33-59 odd, 66 & Compass Direction and Trigonometry Worksheet # 1
Day 3: QUIZ - § 6.1 Angles and their Measures

6.b Trigonometric Functions of Acute Angles
Topics you must know / skills you must be able to show:
Right angle trigonometry; Fundamental Identities (Reciprocal, Quotient, Pythagorean); applications
HANDOUTS: Fundamental Trigonometric Identities, Given a fixed angle…, Special Angle Ratios
Assignments for § 6.2:
Day 1: § 6.2 Worksheet: Geometry Review - Special Angles and Trigonometry; and
§ 6.2, p. 411 # 1-8 all
Day 2: § 6.2, p. 411 # 9-23 odd
Day 3: § 6.2, p. 412 # 25-43 odd
Day 4: § 6.2, Worksheet: Find an Acute Angle q for the Given Trig Ratios
Day 5: § 6.2 Worksheet: Using Sin-Cos-Tan to find Missing Sides; § 6.2, p. 412 # 71, 73, 81, 85, & 86
QUIZ: Unit Circle # 1 - No Calculator allowed [Brief quiz … approx. 20 minutes]

6.c Extending Trigonometric Functions
Topics you must know / skills you must be able to show:
Unit circle and trig ratios using special reference angles
Assignments for § 6.3:
Day 1: § 6.3, p. 424 # 3-12 (by 3s), 17-27 odd
Day 2: § 6.3, p. 425 # 35-41, 49-55 odd
Day 3: § 6.3, p. 425 # 57-67 odd
Day 4: QUIZ: Unit Circle # 2 - No Calculator allowed [Brief quiz … approx. 20 minutes]

QUIZ: § 6.2-3 Trigonometric Functions

6.d Graphs of Trigonometric Functions
Topics you must know / skills you must be able to show:
Graphs of Sine and Cosine; transformations; sinusoids; amplitude; period; phase shift; describing natural periodic phenomena using sinusoids
HANDOUT: Properties of Trig Functions
Assignments for § 6.4:
Day 1: § 6.4 Worksheet #1-Graphing Sine & Cosine
Day 2: § 6.4 Worksheet #2-Graphing Sine & Cosine
Day 3: § 6.4 Worksheet #3-Graphing Sine & Cosine
Day 4: § 6.4 Worksheet #4-Graphing Sine & Cosine; Tides & Sinusoids - Worksheet

6.e Graphs of Other Trigonometric Functions
Topics you must know / skills you must be able to show:
Graphs of tangent, cotangent, secant, and cosecant functions.
Assignments for § 6.5:
Day 1: § 6.5 Worksheet: In-Class Practice; and § 6.5, p. 448 # 5-11 odd, 13-16 all
Day 2: § 6.5, p. 448 # 17, 21, 25, 39-43 odd
Day 3: QUIZ: § 6.4-6.5

TEST: "Mid-Chapter 6" § 6.1-6.5

6.f Advanced Trigonometric Functions
Topics you must know / skills you must be able to show:
Sums that are / are not sinusoids; Combining trig and algebraic functions
Assignments for § 6.6:
Day 1: § 6.6, p. 456 # 7-11 odd, 23-26 all
Day 2: § 6.6, p. 456 # 34-42 EVEN (with WinPlot software)

6.g Inverse Trigonometric Functions
Topics you must know / skills you must be able to show:
Inverse relations; evaluating inverse sine, cosine and tangent functions; composing trig and inverse trig functions
Assignments for § 6.7:
Day 1: § 6.7, p. 465 # 1-22 all
Day 2: § 6.7, p. 466 # 23-30 all

6.h Applications of Trigonometric Functions
Topics you must know / skills you must be able to show:
Indirect measurements
Assignments for § 6.8:
Day 1: § 6.8, p. 473 # 1, 3, 5, 6, & 8 [Note ALL work must be shown for these problems.]

TEST: Chapter 6: § 6.1-6.8

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Topic 7: Analytic Trigonometry

7.a The Use of Fundamental Identities
Topics you must know / skills you must be able to show:
Fundamental Identities; Simplifying and factoring expressions [Identities need not be memorized - a "fact sheet" will be supplied for all quizzes, tests, and for the final exam.]
HANDOUT: Are sin x^2 and sin^2 x different?
Day 1 & 2: § 7.1, p. 487 # 1-8 all, 15 & 16

7.b Confirming Trigonometric Identities
Topics you must know / skills you must be able to show:
Confirming identities by combining / separating terms, using factors, simplifying fractions, and converting to sines and cosines only.
Day 1 & 2: § 7.2, p. 493 # 7 - 14 all, & 30
QUIZ: § 7.1-7.2

7.c Solving Trigonometric Equations
Topics you must know / skills you must be able to show:
Solving equations involving special angles precisely and finding approximate solutions
HANDOUT: § 7.3 Solving Trig Equations - Supplement
Day 1: § 7.3, p. 502 # 1, 3, 9, 14, 15, 16
Day 2: § 7.3, p. 502 # 19 - 22 all, 33, 35

7.d Solving Triangles using the Law of Sines
Topics you must know / skills you must be able to show:
Solving triangles using the Law of Sines; determining the number of triangles and the ambiguous case.
HANDOUT: Law of Sines - Two Possible Triangles
Day 1 & 2: § 8.1, p. 531 # 1-11 odd,
Day 3: § 8.1, p. 531 # 13 - 19 odd , & 37 (a)

7.f Solving Triangles using the Law of Cosines
Topics you must know / skills you must be able to show:
Solving triangles using the Law of Cosines
Day 1 & 2: § 8.2, p. 541 # 1-11 odd

QUIZ: § 8.1-8.2

TEST: "Analytic Trigonometry" § 7.1, 2, 3, 5, § 8.1-8.2

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