## Pre-Calculus 30 Course Description:

PreCalculus 30 covers probability, trigonometry, logarithms, algebra and a great deal of graphing. Use of graphing technology (calculator or computer) is strongly recommended.

The course is a preparation for taking Calculus 30 and is intended for students who want to challenge themselves to the highest level of math possible in high school. It is a very challenging course that is a good preparation for university courses and technology based SIAST courses. Content in this pathway was chosen to meet the needs of students interested in pursuing careers in science-related areas.

Textbook used:

**Pre-Calculus 12**

McGraw – Hill Ryerson

copyright 2012

_{Purchase here}

**Chapter 1 – Transformations **(Feb 2 – 11, 2022)

Marbleslides on Desmos Classroom:

Homework:

1.1 p.12 #1, 2ab, 3ab, 4b, 5ab, 6, 7, 8, 9, 11

1.2 p.28 #1, 2, 3, 5, 6, 7, 11, 14, 15

1.3 p.38 #1, 2, 3, 4, 6bd, 7, 9, 10

1.4 p.51 #1, 2, 3, 4, 5ac, 6, 10, 11, 13bd

Review Asn’t: Practice Test p.58

- PC 30 1.1 Vertical and Horizontal Translations Lesson (2019)
- PC 30 1.1 Graph Animation (Reflections) in Desmos
- PC 30 1.2 Reflections of functions #1of2
- PC 30 1.2 Stretches of functions #2of2
- PC 30 1.2 Identifying horizontal and vertical stretches
- PC 30 1.3 – Combined Transformations Lesson 2022
- PC 30 1.3 Combining transformations to GRAPH a new function 2017 (#1of2)
- PC 30 1.3 Equations of Transformations 2017 (Part 2of2)
- PC 30 Function Transformation AWESOME DESMOS Demonstration!
- PC 30 1.4 Completing the Square
- PC 30 1.4 Inverse of a Relation

**Chapter 2 – Radical Functions** (Feb 12 – 28, 2022)

Homework:

2.1#1ab,2ab,3,4ab,5,6,10

2.2#1-3,5,6,8,11,pick one from #12-15,16 (extra class time for this asn’t given)

Quiz 2.1-2.2

2.3#1-3,7,9,16

Quiz 2.3

Review p.99 #1a,2a,3a,4b,6,7a,8a,9,10a,11,12,14,15,16a

- PC 30 2.1 Radical Functions and Transformations (2020)
- PC 30 2.2 Square Root functions of Non Linear graphs (2020)
- PC 30 2.2 Square Root function Animation
- PC 30 2.3 Solving Radical Equations
- PC 30 Ch 2 REVIEW VIDEO

**Chapter 3 – Polynomial Functions **(Mar 1 – 15)

3.1 #1-3,4ace,5,6,12

3.2 #1ac,2ac,3ac,4ace,5ace,6ace,8ac,10

3.3 #1,2ace,3ace,4a,5ace,6ace,7a, pick one from #8-16

3.4 #1ab,2a,3-5,7,9ab,15

Review #1-5,8c,11c,13,14

- PC 30 3.1 Polynomial function Characteristics
- PC 30 3.2 Remainder theorem Full Lesson 2020
- PC 30 3.2 Synthetic Division 2022
- PC 30 3.2 Synthetic Division Example
- PC 30 3.2 Remainder Theorem
- PC 30 3.3 Factor Theorem 2020
- PC 30 3.4 Equations and Graphs of Polynomial functions (#1of2)
- PC 30 3.4 Equations and Graphs of Polynomial Functions Examples (#2of2)
- PC 30 3.4 Sketching a polynomial function Example
- PC 30 3.4 #1,2 solving polynomial equations homework
- PC 30 3.4 #3, 7 Polynomial Equation from graph homework ques
- PC 30 3.4 #4a,b homework characteristics of graph
- PC 30 3.4 #4d homework question – x-intercepts, intervals, multiplicity
- PC 30 3.4 #5 homework question – matching graphs and equations of polynomials
- PC 30 3.4 #7homework question

- PC 30 Ch 3 Review Video

**Chapter 4 – Radian Measure and Trigonometric Functions **(Mar 16 – 30)

4.1#1-9(ac), 13, pick one from #14-27

4.2#2-5(ace)

4.3#1,3,6,8,9,14

4.4#1,2,4ace,5ace,7,14,15,16,18

Practice Test – all questions

- PC 30 4.1 Radian Measure Introduction
- PC 30 4.2 UNIT CIRCLE Lesson 2022
- PC 30 4.3 Trigonometric Ratios and the Unit Circle
- PC 30 4.4 Intro to Solving Trigonometric Equations
- PC 30 4.4 Solving Trig Equations Tip
- Ch 4 Review Questions
- Trigonometry BASIC REVIEW video

Unit Circle

**Chapter 5 – Trigonometric Equations **(Mar 31 – Apr 11)

5.1#1,2,4,5,6,10,11,14

5.2 Part 1 #1ace,2ace,4,5,6

5.2 Part 2 #14,15,16

5.3#1a, 2ace, 3,10, 11, 12,

5.4#1,2,3,4,9,15,16,17,19,20

Review Asn’t – practice test All questions

Marbleslides – Sine / Cosine Transformations Activity

Sine/ Cosine/ Tangent Interactive Graph page

- PC 30 5.1 Sine and Cosine graphs as they relate to the Unit Circle
- PC 30 5.2 graphing sine and cosine using transformations (#1)
- PC 30 5.2 Graphing Sine and Cosine #2 of 3
- PC 30 5.2 Determining Equation given graph (video #3)
- PC 30 5.2 Sinusoidal Equations from a Graph Example
- PC 30 5.3 The Tangent function
- PC 30 5.3 #11 – PreCalculus 30 determine equation from word problem
- PC-30-Sinusoidal-Regression-5.3-example-and-steps – see download below

- PC 30 5.4 Equations and Graphs of Trig functions and Applications
- PC 30 5.4 Sinusoidal Regression (using Ti-83 graphing calculator)
- Pre-Calculus 30 (PC 30) Graphing Secant Example
- PC 30 Ch. 5 Review – Trigonometric Functions and Graphs -BEST Pre-Calculus 30 Math REVIEW

**Chapter 6 – Trigonometric Identities** (Apr 5 – May 3 —* Easter Break Apr 7-16)*

6.1 #1-5,7,12

6.1 (Part 2) #6,8,9,11,15(optional)

6.2#1,2ac,4ac,5ac,8ace,9,11ac,16,20ac

6.3#1ac,2ac,3ac,6,7, 11

Review p. 322 #1a, 3a, 5a, 7a, 8a, 15a

Proving Identities worksheet Questions TBA in class

Link to Interactive Mathematics that contains notes, formulas, and practice questions for this chapter and lots of other math concepts studied in this course. I encourage you to explore this website.

- PC 30 6.1 Trigonometric Identities (2021 Lesson) (Pythagorean, Reciprocal, and Quotient)
- PC 30 6.1 Trigonometric Identities (2017 Lesson)
- PC 30 6.2 Sum, Difference, Double Angle Identities (2021 Lesson)
- PC 30 6.3 Proving Trigonometric Identities (FULL Lesson 2021)
- PC 30 6.3 Proving identities Intro (Lesson 2017)
- PC 30 Proving Identities Asn’t Question#1
- PC 30 Proving Identities Asn’t Question#5
- PC 30 Proving Identities Asn’t Question#12
- PC 30 Proving Identities Asn’t Question#13
- PC 30 Proving Identities Asn’t Question#17
- PC 30 Proving Identities Asn’t Question#19
- PC 30 Proving Identities Asn’t Question #21
- PC 30 Proving Identities Asn’t Question #22
- PC 30 Proving Identities (Level 1 Asn’t Questions #2,11,15)
- PC 30 Proving Identities (Level 2 Asn’t Questions #18,27)
- PC 30 Proving Identities (Level 3 Asn’t Questions #24,25 )
- PC 30 Proving Identities Asn’t #31
- PC 30 Proving Identities Asn’t #35
- PC 30 Proving Identities Asn’t #37
- PC 30 Proving Identities Asn’t #40
- PC 30 Proving Identities Asn’t #43
- PC 30 Proving Identites Asn’t #46
- PC 30 Proving Identities Asn’t #47
- PC 30 Proving Identities Asn’t #51

**Chapter 7 – Exponential Functions and Equations** (May 4 – 10)

7.1#1-8

7.2#1,2,3,4,9

7.3#1-7(a,b only), 8, 11

Review p.366 #1-12

- PC 30 7.1 – Exponential Functions (y=c^x) Introduction (2023 Lesson)
- PC 30 7.2 Transformations of Exponential Functions (2019)
- PC 30 7.3 Solving Exponential Equations (2019)
- PC 30 7.3 Solving Exponential Equations
- PC 30 7.3 Solving Exponential Equations Algebraically and Graphically EXAMPLE
- PC 30 Exponential Equation Transformation (Ch 7 Review #5c)
- Ch 7 Review – Exponential Functions

**Chapter 8 – Logarithms **(May 11 – 20)

8.1 #1-4, 12,14,19

8.2 #1,3,4,6,8,13

8.3#1-3,7,8,10,15

8.4#1,2,4,5,7,8, pick 3 from #11-22

Ch 8 Review p. 416 #1-15,18,19

- PC 30 8.1 Logarithms #1of2
- PC 30 8.1 Logarithms #2of2
- PC 30 8.2 Transformations of Logarithm graphs (2018)
- PC 30 8.2 Logarithm Transformations (2019)
- PC 30 8.3 Laws of Logarithms
- PC 30 8.4 Logarithmic and Exponential Equations
- PC 30 8.4 Solving Logarithmic equations graphically and algebraically EXAMPLE 1
- PC 30 8.4 Solving Logarithmic equations graphically and algebraically EXAMPLE 2
- PC 30 8.4 – Solving Exponential Equations EXAMPLE
- PC 30 Ch 8 Logarithms Practice Test REVIEW
- Ch 8 Review – Logarithms
- PC Ch 7/8 Cumulative review questions
- PC 30 Ch 7/8 Cum. Rev. #16, 18 – Solving Logarithmic and Exponential Equations
- PC 30 Ch 7/8 Cum. Rev. #15 word problem solving Logarithmic equations

**Chapter 9 – Rational Functions** (May 21 – Jun 1)

9.1 part 1 #1,3,4,14,18

9.1 part 2 #5,6,7,8,13

9.2 #1,2ac,3,4ac,5,6,11

9.3 #1-4,7,13

Practice Test p.470 #1-16

- PC 30 9.1 Rational Functions (2017)
- PC 30 9.1 Transformations of Rational Functions (Desmos graphing example)
- PC 30 9.2 Analyzing Rational Functions (Full Lesson 2019)
- PC 30 9.2 Analyzing Rational Functions (review lesson)
- PC 30 9.3 Solving Rational Equations Graphically and Algebraically (Lesson 2021)
- PC 30 9.3 #1of2 Solving Rational Equations (2016)
- PC 30 9.3 #2of2 Solving Rational Equations (2016)
- PC 30 9.3 Oblique (Slant) Asymptotes
- Ch 9 Review Rational Functions

**Chapter 10 – Composite Functions **(Jun 2 – 8)

10.1 #1-4,6,7,12 (optional – pick one from 13-22)

10.2 #1-3,4a,5a,6ac,7ac, pick one from 11-17

10.3 #1-10,13,15,18,pick one “extend” question

Review p.510 #1,3-9,11,15

- PC 30 10.1 #1of2 Sum and Difference of functions
- PC 30 10.1 #2of2 Sum and Difference of functions
- PC 30 10.1 Sum and Difference of Functions DESMOS demo
- PC 30 10.2-10.3 Product, Quotient, and Composite Functions 2019
- PC 30 10.2 #1of2 Product Quotient Functions
- PC 30 10.2 #2of2 Product Quotient Functions
- PC 30 10.3 #1of2 Composite Functions
- PC 30 10.3 #2of2 Composite Functions
- Review – Function Operations / Composite Functions (Pre-Calculus 30)

**Chapter 11 – Permutations, Combinations, and Binomial Theorem** (Jun 9-15)

11.1 #1-5,7,10,11

11.2 #1-6,10,14,18

11.3 #1b,2b,3b,4b,5b,6b,7bd,12,17b,18

Review Asn’t; Practice Test p. 548

- PC 30 11.1 Permutations and Fundamental Counting Principle
- PC 30 11.2 Combinations
- Permutations and Combinations -what’s the difference?
- PC 30 11.3 Binomial Theorem 2017
- PC 30 11.3 Binomial Theorem Examples

##### Heading to Calculus!!

Sometime before your first Calculus class, it would be a great idea to refresh yourself on some important PreCalculus skills found on the Calculus 30 page. Maybe near the end of summer when all this math knowledge has flown out of your brain!! See you in Calculus!