Precalculus (Period Kranz)
- Instructors
- Mr. Geoffrey Buck
- Mr. Salvador Hermosillo
- Mr. Jeremy Kranz
- Mr. Stephen Lange
- Department
- Math
Files
Course 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.★
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12 Pupil Free Day |
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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) |
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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) |
28 Piecewise Functions (2.5) Text #29-43 odds, 45,48,51,53 Math is Fun Notes: Piecewise |
29 - Transformation of Functions (2.6) - Desmos Absolute Value Transformation HW 2.6 1-18 ALL |
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.
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2 Labor Day Holiday |
3 - Opportunity Day "SAT Practice Test" |
4 2.4 Linear Functions and Models
LINEAR FUNCTIONS – CHEAT SHEET
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5 - No School, Rosh Hashannah |
6 -Functions Test"Ye Old Village" Page 153,4 |
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9 - Test/Review |
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
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13 - Composite Functions (4.1/4.2) - out of sequence |
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16 - Polynomial Functions 3.2
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17 - Synthetic Division Factoring 3rd, 4th, 5th Polynomials |
18 - Synthetic Division Factoring 3rd, 4th, 5th Polynomials (3.6) The Zeroes of A Polynomial Function |
19 - Polynomial Roots Cont Group Worksheet Exercises |
20 - 3.5(a) Polynomial Inequalities |
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23 -Complex and Imaginary Roots (3.7) |
24 -Complex and Imaginary Roots
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25 - Rational Graphs: Asymptotes (Text 3.3) MMM Unit 8 p 20-24 |
26 - Rational Graphs (Text 3.4), end Behavior |
27 Rational Graphs (Inequalities) (3.5b) |
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30 - Inequalities w poly/rational (3.6) |
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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.
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2 - Rational Applications |
3 - Partial Fraction Decmp 10.5 |
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7 - Inverse Functions (4.2) |
8 - Exponents/Graphing Exponential Equations (4.3) 4.1 Exponential and Logistic Functions (Notes, WS/KEY) WS Option Graphing Exponential- Kuta Exponential Transformations-- Desmos Demonstration
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9 - Solving Exponential Equations 4.1 Exponential and Logistic Functions (Notes, WS/KEY) Solving Exponential (without Logs) Worksheet |
10 - 4.4 Logarithmic Functions |
11 - Logaritmic Functions (4.4) |
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15 -Class does not meet |
16 -Textbook 4.6 Solving Log Equations 4.5 Exponential and Log Equations (Notes, WS/KEY) |
17 - Textbook 4.6 Logarithmic Equations Kuta |
18 - Min Day |
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21 - Application of Exponentials |
22 -Interest Rates Using Excel |
23 - Exponential Growth and Decay Text 4.8 |
24 - Applications of Exponentials |
25 Exponential/Logarithmic+ Appications Exam - |
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28 -Angles, Degrees-DMS. SOHCAHTOA, Calc Skills (Text 5.1) 5.1 Angles and Angle Measure (Notes, WS, WSe/KEY) |
29 - Radians and Conversion, Unit Circle Step 1 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 Linear Velocity/Angular Speed alternate ws |
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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
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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! |
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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 |
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11- Veteran's Day (NO SCHOOL) |
12 -6.1 Fundamental Identities (Notes/KEY, WS, WSe/KEY) Text 5.3 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 |
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18 - Basic Graphs of Sine, Cosine and Tangent (Text 5.4) 5.4 Sinusoids (Notes, WS, WSe/KEY) |
19 - Opportunity Day (Tutoring/Mixed Review) |
20- Transforming the Trig Graphs |
21 -Transforming the Trig Graphs |
22 - Intro Trig Application Project |
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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
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2- T Function Family Album 2 Assignment |
3 - Trig Graph Application/Projects |
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9 - Graphs of Other Trig Functions 5.6 The Other Trig Functions (Notes, WS, WSe/KEY) |
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16 Final Review |
17 Final Exams |
18 Final Exams |
19 Final Exams |
20 Final Exams- wrap Up |
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23 Winter Break |
24 Winter Break |
25 Winter Break |
26 Winter Break |
27 Winter Break |
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30 Winter Break |
31 Winter Break |
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January 2014
Analytical Trig
An excellent Unit Plan from Georgia
Trig Identities
Solving Trigonometric Equations
- 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.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.★
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1 Winter Break |
2 - Winter Break |
3 - Winter Break |
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6 - Winter Break |
7 - Winter Break |
8 - Winter Break |
9 - Winter Break |
10 - Winter Break |
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13 - Text 6.3 Trig Identities (6.3, 6.4) 6.2 Trig Proofs!!! (Notes/KEY/V1/V2/V3/V4/V5, WS, WSe/KEY)
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14 - Class does not meet |
15 -Text Sum and Difference Identities 6.4 6.3 Composite Identities (Notes/KEY/V1/V2/V3, WS, WSe/KEY) |
16 - Text 6.5 Trig Identities 6.4 Other Identities (Notes/KEY/V1/V2/V3/V4, WS, WSe/KEY) Xtra Practice WS, WSe/KEY |
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20 MLK Holiday |
21 Solving Trig Equations |
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24 - Test |
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27 - Solving Trig Equations Application |
28 -Solving Trig Equations Prescott AZ Daylight problem |
29 Solving Trig Equations |
30Mixed Application |
31 Test |
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).
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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) |
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6 - 7.3 Law of Cosines |
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10 - Heron's Formula and Area by Sines (7.4) |
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17- PRESIDENT's DAY, No School |
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24 - Vectors Day 1 Intro to Vectors |
25 -Vectors Day 2 Converting Between Rectangular and Polar |
26 Vectors Day 3 Scalar Multiplication |
27 Vecotrs Day 4 Vector Addition |
28 Vectors Day 5 Vecotr Subtraction |
March 2014 Vectors, Complex Numbers, Polar, Parametric
Represent and model with vector quantities.
- CCSS.Math.Content.HSN-VM.A.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
- CCSS.Math.Content.HSN-VM.A.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
- CCSS.Math.Content.HSN-VM.A.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
Perform operations on vectors.
- CCSS.Math.Content.HSN-VM.B.4 (+) Add and subtract vectors.
- CCSS.Math.Content.HSN-VM.B.4a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
- CCSS.Math.Content.HSN-VM.B.4b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
- CCSS.Math.Content.HSN-VM.B.4c Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
- CCSS.Math.Content.HSN-VM.B.5 (+) Multiply a vector by a scalar.
- CCSS.Math.Content.HSN-VM.B.5a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
- CCSS.Math.Content.HSN-VM.B.5b Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
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3 - Vectors 7.4 Vectors (Notes, WS, WSe) Day 6 Vector Equations of a Line |
4 -Day 7 Dot Product |
5 - Day 8 Angles Between Vectors Vector Applications |
6 -Day 9 3 Dimensional Space |
7 - Day 10 Vectors Lines and Planes |
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17 - Trig Form of Complex Numbers Mastermathmentor Unit 11 |
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19 - Midterm |
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24 - Parametrics 9.7 7.3 Plane Curves and Parametric Equations (Notes, WS, WSe) |
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31 - NO School Chavez |
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April 2014 Sysyems and Matrices
Unit Plan Comes From Better Lesson
N.VM.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
N.VM.7 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
N.VM.8 (+) Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.9 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
N.VM.10 (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
N.VM.11 (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
N.VM.12 (+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
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1 - Systems and Matrices |
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7- Systems and Matrices |
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14-Spring Break |
15 Spring Break |
16 Spring Break |
17 Spring Break |
18 Spring Break |
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21 - Systems and Matrices |
22 - A |
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May 2014
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12 - Seq and Series |
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15 - B |
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19 - Seq and Series |
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22 - A |
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26 Memorial Day Holiday |
27 - Probability |
28 - Probability |
29 -Probability |
30 -Probability |
June 2014
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2 - Final Exams |
3 - Final Exams |
4 - Final Exams |
5 -Final Exams |
6- Final Exams |
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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
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
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