HS Pre-Calculus

SAT/ACT Sign up with Ms. Ware Room 105 3:15-5:00 Every Tuesday

Week 1 (Unit 6)
P.4 Equations of Lines
P.4 Graphing Lines
P.2 Equations of Circles pg. 18
P.2 Graphing Circles pg. 18
8.2 Ellipses Graphing Ellipses

Week 2 (Unit 6)
P.6 Complex (Imaginary) Numbers
P.5 Solving quadratic equations by factoring, The Quadratic Formula, and completing the square.
8.3 Hyperbolas Graphing Hyperbolas

Week 3 (Unit 6)

Week 4 (Unit 6)

FIRST EXAM: February 4, 2019

Week 5 (Review)
1.2 Function Behavior
4.1 Angles and Degree vs Radian Measure pg. 350-351
4.1 Degree/Radian Conversions pg. 353
Co-terminal Angles (pg. 370-371) and Reference Angles (Also, here is a video in radians https://www.youtube.com/watch?v=oXCRoGtR4Ho)
4.3 Meaning of "Unit Circle" pg. 377
4.2 Meaning of Angles in "Standard Position" and Drawing Such Angles pg. 360
Pythagorean Theorem Review and Solving for Missing Sides of Right Triangles
4.2 Trigonometric Ratios on Right Triangles pg. 360
4.2 Solving for Missing Sides of a Right Triangle Using Trig Ratios and an Angle (Read pg. 365 Example 5)

Week 5 (Unit 1)
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.)
4.3 "Unit Circle" Values Down to Pi/6 pg. 380
Special Right Triangles (Figures 4.9 and 4.10 on pages 361 and 362)
Trigonometry Applications (Word Problems, look at pg. 365 Example 6)
4.4 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)

Week 6 (Unit 1)
4.2 Finding trigonometric values if given the value of only one trig ratio (Read pg. 362 Example 3 and pg. 376 Example 7)
4.2 Cosecant, Secant, and Cotangent Relationships pg.360 (Also see the green box on pg. 445 and the "Cofunction Identities section on pg. 446")
4.5 The Graph of Tangent (Please refer to the handout for the graph and information on intercepts.)
4.5 The Behavior of Tangent pg. 396
4.4 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 (Read pg. 391 Example 7)

Week 7 (Unit 2)
Brief Discussion of "one-one" and the Horizontal Line Test
4.7 The inverse sine, inverse cosine, and inverse tangent functions (Arcsin, arccos, arctan)
4.7 The domain and range of the inverse trig functions
Meaning of "Principal Value" and How Calculators Report Solutions
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"
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)
1.5 Finding the Inverse of Functions (page 131 Example 7. Advanced: Example 4)
Restricting Domains to Make a Function Invertible (See in class handout)

Week 8 (Unit 3)
How Many Triangle are Possible? (A note on ambiguous cases. Very 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.)
Homework: pg. 484 #4, #8 and pg. 494 #2, #14

Week 9 (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 Formula

Week 10 (Unit 4)
What is an identity?
5.1 Fundamental Identities: 
        Basic Trigonometric Identities: Review of Reciprocal Identities and Tan(theta) = sin(utheta)/cos(theta) pg. 445 Green box
        Pythagorean Identities pg. 446 Green box
5.1 Simplifying expressions using identities pg. 448 Examples 3,4, 5, 6, and 7
Note: You have already done problems like Example 3 and Example 7 (The back of inverse graphs handout.) You used identities before you knew what they were!
5.2 Proving Trigonometric Identities (Basic) Video

Week 11 (Unit 4)
5.4 Multiple Angle Formulas (Double and Half Angles Formulas)
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.)

Week 12 (Unit 5 Matrices)
7.1 Solving Systems of Two Equations (Substitution and Graphing Methods 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)
7.1 Solving Systems of Two Equations (Elimination Method)
7.2 Transposing Matrices
7.2 Manipulating Data with Matrices (See Example 5 in the text for the class demonstration)

Week 13 (Unit 5 Matrices)
7.2 Zero Matrix and the Identity Matrix 
7.2 Finding the determinant of a 2X2 matrix (3X3 matrix)
7.2 Finding the Inverse of a Matrix

Week 14 (Unit 7 Vectors)
6.1Introduction to Vectors pg. 502-506

Week 15 (Unit 7 Vectors)
6.1 Finding Unit Vectors, and the standard unit vectors i and j pg. 506-507
6.1 Finding component forms of vectors given magnitudes and Direction Angles pg. 507-508
6.1 Finding direction angles
6.1 Drawing the resultant vector 1. Analytically 2. Parallelogram Law 3.Tail to Head

Week 16 (Unit 7 Vectors)
6.1 Drawing the resultant vector 1. Analytically 2. Parallelogram Law 3.Tail to Head
6.1 Bearings (Example 7) and word problems involving vectors
6.6 Introduction to Complex (Imaginary) Numbers (Worksheet)
6.4 Polar Coordinates vs. Rectangular Coordinates

Week 17 (Unit 7 Vectors)
P.6 Operations on Complex Numbers
Converting Between Polar and Rectangular Coordinates
6.2 Dot Products and Angles Between Vectors (Here is a short video) Classwork: page 467 of this document #1-8, 25-38, and 43-46

Week 18 (Unit 8 Probability)
Basic Probability Concepts Review
Expected Value (Video)

Week 19 Review
Review Day 1: Conic Sections

Additional Review
P.2 The Coordinate Plane
P.4 Finding solutions to linear systems of equations by graphing
Checking solutions to systems of equations
Finding solutions to linear systems by substitution
Finding solutions to general (non-linear) systems of equations algebraically
Finding solutions to systems of equations involving circles and lines algebraically

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