### HS Pre-Calculus

 Our Current Warm - Ups can be found here: SAT Practice 2015 Set 1Direct Link to Practice 1Direct Link to Practice 1 AnswersWeek 1 (Unit 1)P.2 The Coordinate PlanePythagorean Theorem Review and Solving for Missing Sides of Right Triangles4.2 Trigonometric Ratios on Right Triangles pg. 3604.2 Solving for Missing Sides of a Right Triangle Using Trig Ratios and an Angle (Read pg. 365 Example 5)4.2 Cosecant, Secant, and Cotangent Relationships pg.360 (Also see the green box on pg. 445 and the "Cofunction Identities section on pg. 446")4.2 Finding trigonometric values if given the value of only one trig ratio (Read pg. 362 Example 3 and pg. 376 Example 7)4.7 Brief overview of the inverse sine, inverse cosine, and inverse tangent functions (Arcsin, arccos, arctan)Week 2 (Unit 1)4.1 Angles and Degree vs Radian Measure pg. 350-3514.1 Degree/Radian Conversions pg. 3534.2 Meaning of Angles in "Standard Position" and Drawing Such Angles pg. 3604.3 "Unit Circle" Values Down to Pi/6 pg. 380. Students will practice filling in the degree and radian values on a unit circleCo-terminal Angles (pg. 370-371) and finding Reference Angles (Also, here is a video in radians)Trigonometry Applications (Word Problems, look at pg. 365 Example 6)Mid Level Word Problems HandoutWeek 3 (Unit 1)4.3 Meaning of "Unit Circle" pg. 377. Filling out the coordinates on a unit circle.Special Right Triangles (Figures 4.9 and 4.10 on pages 361 and 362)4.3 Applying Trigonometric Ratios to Angles in Standard Position (Extension of Trig Ratios to All Real Numbers) pg. 373 (Examine pg. 372 Figure 4.24)Using Reference Angles (Side Note: I don't love this video as memorizing the unit circle is fine as long as you know how the values were obtained, BUT, it does explain how reference angles are used.)All students are responsible for having the first three handouts completed by MondayWeek 4 (Unit 1)Academic Recovery Period Begins1.2 Function Behavior4.4 The Graphs of Sine and Cosine (Sinusoidal Functions. Please refer to the class handout rather than the textbook for these graphs and their intercepts.)4.4 The Behavior of Sine and Cosine (pg. 384 and 386)4.5 The Graph of Tangent (Please refer to the handout for the graph and information on intercepts.)4.5 The Behavior of Tangent pg. 3964.4 Identifying Amplitude, Phase Shift, Midline, and Vertical Shift in Sinusoidal Functions (pg. 386-390)4.4 Graphing Transformations on Sine and Cosine (pg. 386-390)4.4 Modeling Using Trigonometric Functions: A guideUnit 1 ReviewExam 1 TUESDAY September 3rd, 2019Academic Recovery Period EndsWeek 5 (Unit 2)Brief Discussion of "one-one" and the Horizontal Line TestRestricting Domains to Make a Function Invertible (See in class handout)4.7 The domain and range of the inverse trig functions1.5 Finding the Inverse of Functions (page 131 Example 7. Advanced: Example 4)4.7 Properties of the inverse sine, inverse cosine, and inverse tangent functions (Arcsin, arccos, arctan)Meaning of "Principal Value" and How Calculators Report SolutionsWeek 6 (Unit 2)4.8 Trigonometry Application Problems (Find Trig Review Packet Word Problem Solutions Here) 4.8 Angles of Depression and Angles of Elevation (Read page 425 and Example 1)5.1 Solving Trigonometric Equations (See Example 7 on pg. 450 only, for other examples, refer to "Solving Trig Equations Worksheet" Notes #1, #8, #9)Finding Solutions on [0,2pi) vs. Finding Solutions "Everywhere"Exam 2 THURSDAY September 12th, 2019Week 7 (Unit 3)How Many Triangle are Possible? (A note on ambiguous cases. Here is another short video.)5.5 Law of Sines (Main Goal: Set up two ratios and equate them. There should only be ONE unknown. Once this is accomplished, do the algebra!)5.6 Law of Cosines (As a note, try not to use rounded numbers on your way to a solution. This results in a loss of accuracy.)WorksheetHomework: pg. 484 #4, #8 and pg. 494 #2, #14Week 8 (Unit 3)5.6 Area of General Triangles (Generally, the area of a triangle equals half of the product of the lengths of any two sides and the sine of the angle between them. Area = (1/2)bc*sin(theta) where theta is the angle between sides b and c)5.6 Heron's FormulaPractice ExamExam 3 FRIDAY September 27th, 2019Week 9 (Unit 4)Formula SheetWhat is an identity?5.1 Fundamental Identities:         Basic Trigonometric Identities: Review of Reciprocal Identities and Tan(theta) = sin(theta)/cos(theta) pg. 445 Green box        Pythagorean Identities pg. 446 Green box5.4 Multiple Angle Formulas (Double Angle Formulas)Week 10 (Unit 4)5.4 Multiple Angle Formulas (Half Angle Formulas)"Baby" Simplification Practice5.1 Simplifying expressions using identities pg. 448 Examples 3,4, 5, 6, and 75.2 Proving Trigonometric Identities (Basic) Video5.2 Proving Trigonometric Identities (Advanced)5.1 Solving and Simplifying Trigonometric Equations Revisited (We have more tools now! This is just Example 1 from this YouTuber, but there are more Examples on the side.)Unit 4 Practice ExaminationFall Break October 10-14Exam 4 TUESDAY October 15th, 2019Week 11 (Unit 5 Matrices - 2.5 weeks)P.4 Equations of LinesP.4 Graphing LinesP.4 Finding solutions to linear systems of equations by graphing7.1 Solving Systems of Two Equations (Substitution Method Review) 7.1 Solving Systems of Two Equations (Elimination Method Review)7.2 Introduction to Matrices (Converting Equations to Matrices, Square Matrices, Row & Column Vectors, Element (i,j) of a Matrix, Dimensions, Compatible Matrices)7.2 Matrix Algebra (Addition, Subtraction, Multiplication by a Scalar)7.2 Zero Matrix and the Identity MatrixWeekend Homework: Do the first 3 assignments on Matrices in Ck-12. Afterward, please read the Matrix Multiplication section (pg. 582-583) of 7.2 in your textbook. Of course, it is good practice to read the complete chapter as I teach. :) But I am only assigning 582-583 as required reading.Week 12 (Unit 5 Matrices)7.2 Transposing Matricesk7.2 Manipulating Data with Matrices (See Example 5 in the text for the class demonstration)7.2 Finding the determinant of a 2X2 matrix (3X3 matrix)Finding determinants with technology7.2 Finding the Inverse of a Matrix 2X2Finding the Inverse of a 3X3 with technology (Ti-84 Calculators)7.3 Solving a System Using Inverse Matrices Notes (pg. 600 Example 7)Week 13 (Unit 5 Matrices)Representing and Manipulating Data with Matrices (Advanced)Review and Practice ExaminationExam 5 WEDNESDAY October 30, 2019Week 13 Review Content (Time Permitting)Methods of factoring (Factoring, Quadratic Formula, Completing the Square, Taking Square Roots)Finding solutions to general (non-linear) systems of equations algebraicallyFinding solutions to systems of equations involving circles and lines algebraicallyWeek 14 (Unit 6 Conics - 2 weeks)P.2 Equations of Circles pg. 18P.2 Graphing Circles pg. 188.2 Ellipses Graphing EllipsesCan you match the equation to the graph of the ellipse?8.3 Hyperbolas Graphing HyperbolasWeek 15 (Unit 6 Conics)Practice ExamExam 5 FRIDAY November 15, 2019Week 16 (Unit 7 Vectors - 2 weeks)6.1Introduction to Vectors pg. 502-5066.1 Drawing the resultant vector 1. Analytically (Algebraically) 2. Parallelogram Law 3.Tail to Head6.1 The standard unit vectors i and j and finding unit vectors (time permitting) pg. 506-5076.1 Finding component forms of vectors given magnitudes and Direction Angles pg. 507-5086.1 Finding direction angles6.1 Bearings (Example 7) and word problems involving vectorsTHANKSGIVING HOLIDAY - Vectors Assignment due before class on December 2, 2019Week 17 (Unit 7 Vectors)6.2 Dot Products and Angles Between Vectors (Here is a short video) Classwork: page 467 of this document #1-8, 25-38, and 43-46P.6 Complex (Imaginary) NumbersP.6 Operations on Complex Numbers6.6 Introduction to Complex (Imaginary) Numbers (Worksheet)6.4 Polar Coordinates vs. Rectangular CoordinatesConverting Between Polar and Rectangular CoordinatesPRACTICE EXAMExam 7 MONDAY December 9, 2019Week 18 (Unit 8 Probability - 1 week)Basic Probability Concepts ReviewSimple Probability Simple Probability and compound eventsProbability of compound independent events and mutually exclusive/inclusive events (Additional Video)Conditional Probability (Video)Expected Value (Video)Week 19 (Course Review & Finals Week)Final Exam Study Guide You may skip #19, 23, 24. On the diagnostic, you may skip 12Review Conic SectionsPlease consider taking AP Calculus