Precalculus (Period Kranz) Assignments

Instructor

Term

Fall 2013

Department

Math

Description

Here is a Great Collection of Precalculus Videos from UC Irvine

Here are some great formulas to summarize the class

Here are Student Success Organizers You Can Use for Notes

Mr. Lange’s Planning Calendar

Here is a CoolMath Precalculus Review/Calculus Preview

August 2013 - Functions

Vocabulary: Function, Domain, range,
interval notation, increasing, decreasing, concave, maximum, minimum, transformation

Standards: Common Core Functions HSF-IF, HSF-BF

Functions: linear, quadratic, polynomial, rational, zeroes (roots), intercepts, composite function, transformation, translation

Worksheet: Unit 7- Graphs and Graphing Utilities.pdf

Common Core Standards

CCSS.Math.Content.HSF-IF.B.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.^★
CCSS.Math.Content.HSF-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.^★
CCSS.Math.Content.HSF-IF.B.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.^★

Mon	Tue	Wed	Thu	Fri
12 Pupil Free Day	13	14	15	16
19 Solving Equations/Algebraic Skills Review	20 Functions: Definition, Doman, Range: Around the Room, Interval Notation Korpi 1.1	21 Functions: Definition, Doman, Range: Around the Room, Interval Notation Korpi 1.1	22 Graphing Functions Lab Korpi 1.2, 1.3 Mixed Review 1.2 Agility, Functions, & Graphing (Notes, WS, WSe/KEY) 1.3 Coordinate Geometry, Equations, & Lines (Notes, WS, WSe)	23 Composite Function Algebra or 2.7 Mathematical models, Korpi 1.4 1.4 Complex Numbers, Modeling, & Calculators (Notes, WS, WSe)
26 - Odd, Even, Inc, Dec, Rate of Change (2.3) p 88 1-10, 11-27 odd HW Classwork from This Unit Plan KhanAcad Even and Odd Functions Increasing/Decreasing lLesson from Math is Fun	27 Family Album Family of Functions (2.5) Sample Assignment Example to Show Class	28 Piecewise Functions (2.5) Text #29-43 odds, 45,48,51,53 Math is Fun Notes: Piecewise Piecewise on a TI 84 Easy Piecewise Worksheet Patrick JMT Video 1 Video 2	29 - Transformation of Functions (2.6) - Desmos Example - Desmos Absolute Value Transformation HW 2.6 1-18 ALL Lesson on Blog includes Flashcards and links	30 – No School/Admissions Day

September 2013

Functions, Linear, Quadratic, Polynomial, Rational

Vocabulary and concepts: Linear, Quadratic, Factor, Completing the Square, Roots, Inverse\

Common Core Standards

CCSS.Math.Content.HSF-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
CCSS.Math.Content.HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
CCSS.Math.Content.HSF-IF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
CCSS.Math.Content.HSF-IF.C.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
CCSS.Math.Content.HSA-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
CCSS.Math.Content.HSA-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Mon	Tue	Wed	Thu	Fri
2 Labor Day Holiday	3 - Opportunity Day "SAT Practice Test"	4 2.4 Linear Functions and Models ] LINEAR FUNCTIONS – CHEAT SHEET Page 20 has good problems Half Your Age Plus Seven	5 - No School, Rosh Hashannah	6 -Functions Test"Ye Old Village" Page 153,4
9 - Test/Review Quadratics Summary notes	10 - Test/Review	11 -Graphing Quadratics Completing the Square/Quadratic Formula (3.1	12 - Quadratic Regession/Models (3.1) CALC Find the Equation of a Quadratic Given Three Points Real Life Quadratic Regression Problems Quad Reg on TI 84 Applet. Quadratic Regression Calculator	13 - Composite Functions (4.1/4.2) - out of sequence
16 - Polynomial Functions 3.2 Powerpoint Notes Purplemath Tutorials	17 - Synthetic Division Factoring 3rd, 4th, 5th Polynomials	18 - Synthetic Division Factoring 3rd, 4th, 5th Polynomials (3.6) The Zeroes of A Polynomial Function Rational Roots WS Video on Rational Root Theorem	19 - Polynomial Roots Cont Group Worksheet Exercises Team Polynomials Worksheet	20 - 3.5(a) Polynomial Inequalities Purplemath Notes More Notes and Practice Video Example
23 -Complex and Imaginary Roots (3.7) PowerPoint Review/Summary Kuta Worksheet	24 -Complex and Imaginary Roots Purplemath Notes Alternate Worksheet Alternate Worksheet TEST- Take home?	25 - Rational Graphs: Asymptotes (Text 3.3) Purplemath Tutorial Kuta Worksheet or MMM Unit 8 p 20-24 Khan Videos	26 - Rational Graphs (Text 3.4), end Behavior Possible Rational Functions Test	27 Rational Graphs (Inequalities) (3.5b) more on horizontal/oblique asymptotes Worksheet Sam Shah Rational Functions
30 - Inequalities w poly/rational (3.6)

October 2013:

Exponential and Logarithmic Functions

Trigonometry Basics

Vocabulary and concepts: exponent, base, power, logartihm, exponential growth, exponential decay, principal interest compounding

"degrees, minutes, seconds" <>decmal degrees, radian, unit circle, sine, cosine, tangent, secant, cosecant, cotangent, 30-60-90 triangle, 45-45-90 triangle, pythagorean theorem

Common Core Standards

CCSS.Math.Content.HSA-APR.D.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. (Partial Fractions)

CCSS.Math.Content.HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

CCSS.Math.Content.HSF-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
CCSS.Math.Content.HSF-TF.A.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.
CCSS.Math.Content.HSF-TF.A.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, cosine, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

Mon

Tue

Wed

Thu

Fri

1 - SAT Practice Test

2 - Rational Applications

Project

NumberSkill Videos on Partial Fractions

3 - Partial Fraction Decmp 10.5

Purplemath Tutorial

KhanAcademy Series

Partial Fractions MMM Unit 8 p 25-26

Math is Fun Lesson

4 - Test Poly and Rational Test Multiple Choice

7 - Inverse Functions (4.2)

Math Is Fun Tutorial

KhanAcademy Vids and Quiz

Desmos Demonstration

MMM Unit 7 Page 18-19

8 - Exponents/Graphing Exponential Equations (4.3)

4.1 Exponential and Logistic Functions (Notes, WS/KEY)

Purplemath Tutorial

WS Option Graphing Exponential- Kuta

Exponential Transformations-- Desmos Demonstration

9 - Solving Exponential Equations

4.1 Exponential and Logistic Functions (Notes, WS/KEY)

Solving Exponential (without Logs) Worksheet

WS option 2 =Solving Exponential- Kuta

PurpleMathTutorial

10 - 4.4 Logarithmic Functions

(4.4) Math is Fun- What is A Logarithm?

4.3 Logarithmic Functions (Notes, WS/KEY)

11 - Logaritmic Functions (4.4)

KUTA WORKSHEET - Exponential<>Logarithmic

KUTA Worksheet- Graphs

4.3 Logarithmic Functions (Notes, WS/KEY)

14Log Rules (4.5) 4.4 Properties of Logs (Notes, WS/KEY)

Kuta Worksheet- Properties

Kuta Worksheet- Change of Base

15 -Class does not meet

16 -Textbook 4.6 Solving Log Equations 4.5 Exponential and Log Equations (Notes, WS/KEY)

Solving Exponential Equations w/Logarithms Kuta WS

17 - Textbook 4.6 Logarithmic Equations Kuta

18 - Min Day

21 - Application of Exponentials

22 -Interest Rates

MMM Unit 9 p 6-9

Using Excel

23 - Exponential Growth and Decay

WS Option

Alt Worksheet CPM

Text 4.8

24 - Applications of Exponentials

25 Exponential/Logarithmic+ Appications Exam -

28 -Angles, Degrees-DMS. SOHCAHTOA, Calc Skills (Text 5.1)

5.1 Angles and Angle Measure (Notes, WS, WSe/KEY)

PurpleMath Tutorial

Dudefree Unit Circle Quiz

Degrees to Radians Leson

Interactive Unit Circle

29 -

MasterMathMetnor Unit 1

Radians and Conversion, Unit Circle Step 1

PurpleMathTutorial 2

RegentsPrep Help

Contimued Unit Circle Development and Practice

30 -Text 5.1 5.2 Applications of Angles (Notes, WS, WSe/KEY) Arc Length and Sector Area

Mini Test on Unit Circle- Draw a Unit Circle, Degrees and Radians with all multiples of 30 and 45 degrees

31 - Test on Text 5.1 (See Objectives)

Linear and Angular Velocity

Worksheet

Linear Velocity/Angular Speed alternate ws

November 2013

Trig Identiies
, Inverse Trig

Graphs of Trig Functions-

Vocabulary: sinusoid, amplitude, period, phase shift

Common Core Standards:

CCSS.Math.Content.HSF-TF.C.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

CCSS.Math.Content.HSF-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^★

CCSS.Math.Content.HSF-TF.A.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Biorhythm theory handout.doc

Mon	Tue	Wed	Thu	Fri
				1 - CoFunctions, Special Angles on the Unit Circle (Text 5.2) 5.3 Circular Trig Functions (Notes, WS, WSe/KEY) BLANK UNIT CIRCLE Cool Link HERE! Unit Circle Video: Patrick JMT
4 - 5.2 Continued Unit Circle Development	5 - Opportunity Day (Tutoring/Mixed Review)	6 - 5.3 Properties of the Trigonometric Functions 5.3 Circular Trig Functions (Notes, WS/KEY) BLANK UNIT CIRCLE Cool Link HERE!	7 Test	8 - 5.3 Properties of the Trigonometric Functions
11- Veteran's Day (NO SCHOOL)	12 -6.1 Fundamental Identities (Notes/KEY, WS, WSe/KEY) Text 5.3 PurpleMath Notes Inverse Trignometry 6.1, 6.2	13 -Inverse Trignometry 6.1, 6.2	14 Inverse Trignometry 6.1, 6.2 5.7 Inverse Trig Functions (Notes, WS, WSe/KEY)	15 Test
18 - Basic Graphs of Sine, Cosine and Tangent (Text 5.4) 5.4 Sinusoids (Notes, WS, WSe/KEY) Desmos Demo	19 - Opportunity Day (Tutoring/Mixed Review)	20- Transforming the Trig Graphs Mastermathmentor Unit 4- Graphs of Trig Functions.pdf	21 -Transforming the Trig Graphs Which Wave Lesson **	22 - Intro Trig Application Project
25 Fall Break	26 Fall Break	27 Fall Break	28 Fall Break	29 Fall Break

December 2013

CCSS.Math.Content.HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Trig Graphs sinusoid, amplitude, period, phase shift

Mon	Tue	Wed	Thu	Fri
2- T Function Family Album 2 Assignment	3 - Trig Graph Application/Projects	4 -	5 -	6 -
9 - Graphs of Other Trig Functions 5.6 The Other Trig Functions (Notes, WS, WSe/KEY)	10 -	11 -	12	13 -
16 Final Review	17 Final Exams	18 Final Exams	19 Final Exams	20 Final Exams- wrap Up
23 Winter Break	24 Winter Break	25 Winter Break	26 Winter Break	27 Winter Break
30 Winter Break	31 Winter Break

January 2014

Analytical Trig

Trig Identiities

Solving Trigonometric Equations

CCSS.Math.Content.HSF-TF.C.9 (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

CCSS.Math.Content.HSF-TF.B.7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.^★

Mon	Tue	Wed	Thu	Fri
		1 Winter Break	2 - Winter Break	3 - Winter Break
6 - Trig Identities (6.3, 6.4) 6.2 Trig Proofs!!! (Notes/KEY/V1/V2/V3/V4/V5, WS, WSe/KEY)	7 - Sum and Difference Identities 6.4 6.3 Composite Identities (Notes/KEY/V1/V2/V3, WS, WSe/KEY)	8 - Trig Identities 6.4 Other Identities (Notes/KEY/V1/V2/V3/V4, WS, WSe/KEY) Xtra Practice WS, WSe/KEY	9 - Trig Identities	10 -
13 -	14 - Solving Trig Equations (6.7, 6.8)	15 -Solving Trig Equations (6.7, 6.8)	16 - Solving Trig Equations (6.7, 6.8)	17 -
20 MLK Holiday	21 Solving Trig Equations	22 -Solving Trig Equations (6.7, 6.8)	23 - Mixed Application	24 - Test
27 -	28 -	29	30	31

February 2014

Trig application

Common Core Standards

CCSS.Math.Content.HSG-SRT.D.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.

CCSS.Math.Content.HSG-SRT.D.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.

CCSS.Math.Content.HSG-SRT.D.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).

Mon	Tue	Wed	Thu	Fri
3 - Trig Application Text (7.1) 5.8 Problem Solving with Trigonometry (Notes, WS, WSe/KEY)	4 - 7.2 Law of Sines 6.5 The Law of Sines (Notes/KEY/V1/V2/V3/V4, WS, WSe/KEY)	5 -	6 - 7.3 Law of Cosines	7 -
10 - Heron's Formula and Area by Sines (7.4)	11 -	12	13	14 -
17- PRESIDENT's DAY, No School	18 -	19 -	20 -	21
24 - A	25 -	26	27	28

March 2014

Mon	Tue	Wed	Thu	Fri
3 - Vectors 7.4 Vectors (Notes, WS, WSe)	4 -	5 -	6 -	7 -
10 - Vectors	11 -	12 -	13	14 -
17 - Parametrics 9.7 7.3 Plane Curves and Parametric Equations (Notes, WS, WSe)	18	19 -	20 -	21 -
24 - Polars 7.1 Polar Coordinates (Notes, WS, WSe)	25 -	26 -	27 7.2 Graphs of Polar Equations (Notes, WS, WSe)	28 -
31 - NO School Chavez

April 2014

Mon	Tue	Wed	Thu	Fri
	1 - Polars	2 - Polar Graphs	3 -	4 -
7- Systems and Matrices	8 -	9 -	10 -	11 -
14-Spring Break	15 Spring Break	16 Spring Break	17 Spring Break	18 Spring Break
21 - Systems and Matrices	22 - A	23 -	24 -	25 -
28 -	29 -	30 -

May 2014

Mon	Tue	Wed	Thu	Fri
			1 -	2
5-	6 -	7 -	8 -	9 -
12 - Seq and Series	13 -	14 - A	15 - B	16 -
19 - Seq and Series	20 -	21 -	22 - A	23 -
26 Memorial Day Holiday	27 - Probability	28 - Probability	29 -Probability	30 -Probability

June 2014

Mon

Tue

Wed

Thu

Fri

2 - Final Exams

3 - Final Exams

4 - Final Exams

5 -Final Exams

6- Final Exams

Week 1 13-Aug UNIT 0 Precalculus Review/Preview

Are you ready for precalculus? KEY

Week 2 20-Aug UNIT 0 Algebra Revisited

August 19 - Solving Linear and Quadratic Equations Review

August 20/21- Bring Book

Family of Functions UNIT PLAN

Additional Unit Plan with Good Common Core Lessons

Round the Room Activity on Funcitons/Graph Analysis

Key Concepts: Domain, Range, Interval Notation, Zeroes, Asymptotes, Increasing/Decreasing, Concave Up/Concave Down

Video Enrichment: Vi Hart, Connecting the Dots

Students will need to solve linear and quadratic equations and inequalities.
Include Review of Factoring and the quadratic formula

Include fraction and decimal operation/review

Include application problems

Graphing functions-- include persistence in making tables of values and in finding roots of quadratics to graph.

TEXTBOOK: Appendices

Week 3 27-Aug UNIT 1 Functions and Their Graphs

Domain, Range, Input, Output, Function, Relation

Graphing Skills with Functions

Operations on Functions

Transformations

Chapter 1 and 2

Week 4 3-Sep FUNCTIONS AND THEIR GRAPHS

Chapter 2

Week 5 10-Sep FUNCTIONS AND THEIR GRAPHS

Inverses, Rate of change (avg vs instantaneous)

Week 6 17-Sep UNIT 2 POLYNOMIAL AND RATIONAL FUNCTIONS

Polynomial Graphs: Roots and Zeroes, Remainder and Factor Theorem

Factoring higher order polynomials, synthetic division,

Week 7 24-Sep UNIT 2 POLYNOMIAL AND RATIONAL FUNCTIONS

Polynomials: Complex Zeroes

Rational Graphs: Holes, Asymptotes, End Behavior

Week 8 1-Oct UNIT 2 POLYNOMIAL AND RATIONAL FUNCTIONS

Complex Conjugates, Square Root of a Negative???

Fundamental Theorem of Algebra

Week 9 8-Oct UNIT 3 Exponential and Logarithmic Functions

Solve Exponential Equations

Week 10 15-Oct UNIT 3 Exponential and Logarithmic Functions

Solve logarithmic problems

Applied Exponential and Logartithmic

Week 11 22-Oct UNIT 4 Trigonometry

Six basic trig functions

Degrees/DMS

Special Right Triangles

Solving Right Triangles

Indirect Measurement

Week 12 29-Oct UNIT 4 TRIGONOMETRY

Degrees, Radians, Rotations

Negative Angles and Angles Greater than 180

Coterminal Angles

Arc Length

Coordinate Trig

Week 13 5-Nov UNIT 4 TRIGONOMETRY

Unit Circle Measurements/Memorization

Textbook: 5.1, 5.2

Week 14 12-Nov UNIT 5 TRIGONOMETRIC GRAPHS

Graph the basic trig functions

Graph the cofunctions

State domain and range

Include Unit Circle Values

Symmetry

Week 15 19-Nov UNIT 5 TRIGONOMETRIC GRAPHS

More Transformations of Trig Graphs

Period and Amplitude

Week 16 26-Nov UNIT 5 TRIGONOMETRIC GRAPHS

Identities from Graphs ie sin x = cos(x-90)

Week 17 3-Dec UNIT 6 SOLVING TRIG EQUATIONS

Inverse Trig

Graphical solutions

Stating complete solutions sets

Domain and Range

Week 18 10-Dec UNIT 6 SOLVING TRIG EQUATIONS
Use identities and other techniques

Inverse Trig Packet-

FINAL EXAMS/WINTER BREAK

Week 19 7-Jan UNIT 7 Trig Identities

Identities from Graphs

Proving Identities

Pythagorean Identities

Week 20 14-Jan UNIT 7 Trig Identities

Additiona nd Subtraction Identities for Sine , Cosine and Tangent

Cofunction Identities

Week 21 21-Jan UNIT 7 Trig Identities

Double Angle Identities

Higher power Identities

Half Angle Identities

Product to Sum Identities

Week 22 28-Jan UNIT 8 Trig Applications

Law of Sines

Law of Cosines

Heron and other Area Formula

Week 23 4-Feb UNIT 8 Trig Applications

More Trig Area

Binomial Theorem,. Binomial Expansion:?

Week 24 11-Feb Unit 8 Trig Application

Graphing complex numbers in the comple x plane

Absolute value of a complex number: modulus, argument

complex number in polar form

polar multiplication and division

Demoivres Theorem

Week 25 18-Feb Unit 8 Trig Application

Vectors

Vector Peroperties

Dot Product

Vector Arithmetic

Week 26 25-Feb Unit 9 Analytic Geometry

Graphs of conics, hyperbolas and ellipses

Week 27 11-Mar Unit 9 Analytic Geometry

Translating Conics

Parabolas

Week 28 11-Mar Unit 9 Analytic Geometry

Polar Coordinate System

Polar to Rectangular Conversion

gtaphs of cardioids, lemniscakates, etc

Eccentricity og ellipse, etc

General Polar Equation of a Conic Section

Week 29 18-Mar Unit 10 Systems of Equations

Solving sytems of equations

Matrices

Week 30 25-Mar Unit 10 Systems of Equations\

Matrix Operations

Consistent and inconsistent systems

Inverse Matrices

Week 31 1-Apr Unit 10 Systems of Equations

Applications of Systems

Solving Non Linear Systms + Graphically

Week 32 8-Apr Unit 10 Systems of Equations

Multiply matrices

solve systems using inverse matrices

Week 33 15-Apr Unit 10 Systems of Equations

Week 34   22-Apr
Week 35   29-Apr
Week 36   6-May
Week 37   13-May
Week 38   20-May
Week 39   27-May
Week 40   3-Jun
Week 41   10-Jun
Week 42   17-Jun

Here is a Unit Guide

Detailed Weekly Plannig Guide

Another Unit Plan Model

Another Precalc Guide from Santa Fe Public Schools

Georgia's Curriculum Guide

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