# HS Pre-Calculus

Our Current Warm - Ups can be found here: **SAT Practice** 2015 Set 1

SAT **Full Length Practice Exams**

**Direct Link to Practice 1 Answers**

**Week 1 (Unit 1)**

P.2 The Coordinate Plane

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)

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. 350-351

4.1 Degree/Radian Conversions pg. 353

4.2 Meaning of Angles in "Standard Position" and Drawing Such Angles pg. 360

4.3 "Unit Circle" Values Down to Pi/6 pg. 380. Students will practice filling in the degree and radian values on a unit circle

Co-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 **Handout**

**Week 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 Monday

**Week 4 (Unit 1)**

Academic Recovery Period Begins

1.2 Function Behavior

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)

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: A **guide**

Unit 1 Review

**Exam 1 TUESDAY September 3rd, 2019**

Academic Recovery Period Ends

**Week 5 (Unit 2)**

Brief Discussion of "one-one" and the Horizontal Line Test

Restricting Domains to Make a Function Invertible (See in class handout)

4.7 The domain and range of the inverse trig functions

1.5 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 Solutions

**Week 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, 2019**

**Week 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.)

**Homework: **pg. 484 #4, #8 and pg. 494 #2, #14

**Week 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 Formula

**Exam 3 FRIDAY September 27th, 2019**

**Week 9 (Unit 4)**

What 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 box

5.4 Multiple Angle Formulas (**Double** Angle Formulas)

**Week 10 (Unit 4)**

5.4 Multiple Angle Formulas (**Half** Angle Formulas)

**"Baby" Simplification Practice**

5.1 Simplifying expressions using identities pg. 448 Examples 3,4, 5, 6, and 7

5.2 Proving Trigonometric Identities (Basic) **Video**

5.2 **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.)

Fall Break October 10-14

**Exam 4 TUESDAY October 15th, 2019**

**Week 11 (Unit 5 Matrices - 2.5 weeks)**

P.4 Equations of Lines

P.4 Graphing Lines

P.4 Finding solutions to linear systems of equations by graphing

7.1 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 Matrix

**Weekend 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 **Matrix Multiplication** (**Class Worksheet**)

7.2 Transposing Matricesk

7.2 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 technology**

7.2 **Finding the Inverse** of a Matrix 2X2

**Finding 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 Examination**

**Exam 5 WEDNESDAY October 30, 2019**

**Week 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 algebraically

Finding solutions to systems of equations involving circles and lines algebraically

**Week 14 (Unit 6 Conics - 2 weeks)**

P.2 Equations of Circles pg. 18

P.2 Graphing Circles pg. 18

8.2 Ellipses **Graphing Ellipses**

Can you match the equation to the **graph of the ellipse**?

8.3 Hyperbolas **Graphing Hyperbolas**

**Week 15 (Unit 6 Conics)**

8.1 Parabolas **Finding the equation of parabolas using only the vertex and focus**

**Exam 5 FRIDAY November 15, 2019**

**Week 16 (Unit 7 Vectors - 2 weeks)**

6.1**Introduction to Vectors** pg. 502-506

6.1 Drawing the resultant vector 1. Analytically (Algebraically) 2. Parallelogram Law 3.Tail to Head

6.1 The standard unit vectors** i **and **j **and finding unit vectors (time permitting) 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 **Bearings** (Example 7) and **word problems** involving vectors

**THANKSGIVING HOLIDAY - Vectors Assignment due before class on December 2, 2019**

**Week 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 43-46

P.6 Complex (Imaginary) Numbers

P.6 **Operations** on Complex Numbers

6.6 Introduction to Complex (Imaginary) Numbers (**Worksheet**)

6.4 **Polar Coordinates** vs. Rectangular Coordinates

Converting Between Polar and Rectangular Coordinates

**Exam 7 MONDAY December 9, 2019**

**Week 18 (Unit 8 Probability - 1 week)**

Basic Probability Concepts Review

Simple Probability and

**compound events**Probability of

**compound independent events**and**mutually exclusive/inclusive events**(**Additional Video**)

**Conditional**Probability (**Video**)

**Counting Principal**, **Permutations, and Combination**s **Worksheet**

**Week 19 (Course Review & Finals Week)**

**Final Exam Study Guide** You may skip #19, 23, 24. On the diagnostic, you may skip 12

Review **Conic Sections**

Please consider taking AP Calculus