# Pre Calculus 12 Course Outline Table of Content:

## 1. Precalculus Course

Learn Precalculus in this full college course. These concepts are often used in programming.

This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her YouTube channel: youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw

⭐️ Lecture Notes ⭐️
🔗 Part 1 - Functions: lindagreen.web.unc.edu/files/2020/08/courseNotesM130_2019S_Part1_Functions.pdf
🔗 Part 2 - Trigonometry: lindagreen.web.unc.edu/files/2020/08/courseNotesM130_2019S_Part2_Trig.pdf
🔗 Part 3 - Conic Sections: lindagreen.web.unc.edu/files/2020/08/courseNotesM130_2019S_Part3_ConicSections.pdf
🔗 Part 4 - Parametric Equations, Polar Coordinates, and the Difference Quotient: lindagreen.web.unc.edu/files/2020/08/courseNotesM130_2019S_Part4_ParametricPolarDiffQuot.pdf

⭐️ Course Contents ⭐️
⌨️ (0:00:00) Functions
⌨️ (0:12:06) Increasing and Decreasing Functions
⌨️ (0:17:35) Maximums and minimums on graphs
⌨️ (0:26:38) Even and Odd Functions
⌨️ (0:36:12) Toolkit Functions
⌨️ (0:43:18) Transformations of Functions
⌨️ (0:55:48) Piecewise Functions
⌨️ (1:00:19) Inverse Functions
⌨️ (1:14:34) Angles and Their Measures
⌨️ (1:22:47) Arclength and Areas of Sectors
⌨️ (1:28:39) Linear and Radial Speed
⌨️ (1:33:02) Right Angle Trigonometry
⌨️ (1:40:38) Sine and Cosine of Special Angles
⌨️ (1:48:41) Unit Circle Definition of Sine and Cosine
⌨️ (1:54:11) Properties of Trig Functions
⌨️ (1:04:50) Graphs of Sine and Cosine
⌨️ (2:11:23) Graphs of Sinusoidal Functions
⌨️ (2:21:36) Graphs of Tan, Sec, Cot, Csc
⌨️ (2:30:29) Graphs of Transformations of Tan, Sec, Cot, Csc
⌨️ (2:39:02) Inverse Trig Functions
⌨️ (2:48:49) Solving Basic Trig Equations
⌨️ (2:55:49) Solving Trig Equations that Require a Calculator
⌨️ (3:05:44) Trig Identities
⌨️ (3:13:16) Pythagorean Identities
⌨️ (3:18:37) Angle Sum and Difference Formulas
⌨️ (3:26:33) Proof of the Angle Sum Formulas
⌨️ (3:31:09) Double Angle Formulas
⌨️ (3:38:39) Half Angle Formulas
⌨️ (3:44:50) Solving Right Triangles
⌨️ (3:51:24) Law of Cosines
⌨️ (4:01:24) Law of Cosines - old version
⌨️ (4:09:44) Law of Sines
⌨️ (4:17:34) Parabolas - Vertex, Focus, Directrix
⌨️ (4:29:24) Ellipses
⌨️ (4:40:33) Hyperbolas
⌨️ (4:54:23) Polar Coordinates
⌨️ (5:01:55) Parametric Equations
⌨️ (5:13:22) Difference Quotient

--

Read hundreds of articles on programming: freecodecamp.org/news

## 2. PreCalculus Full Course For Beginners

In mathematics education, #precalculus or college algebra is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.

⌨️ (0:00:00) The real number system
⌨️ (0:08:24) Order of operations
⌨️ (0:16:31) Interval notation
⌨️ (0:24:19) Union and intersection
⌨️ (0:30:36) Absolute value
⌨️ (0:38:16) Absolute value inequalities
⌨️ (0:55:06) Fraction multiplication
⌨️ (1:02:16) Fraction devision
⌨️ (1:10:46) Exponents
⌨️ (1:34:40) Lines
⌨️ (1:43:44) Expanding
⌨️ (1:52:00) Pascal's review
⌨️ (1:59:14) Polynomial terminology
⌨️ (2:08:22) Factors and roots
⌨️ (2:28:54) Factoring formulas
⌨️ (2:37:30) Factoring by grouping
⌨️ (2:43:52) Polynomial inequalities
⌨️ (2:52:57) Rational expressions
⌨️ (3:00:12) Functions - introduction
⌨️ (3:04:05) Functions - Definition
⌨️ (3:10:08) Functions - examples
⌨️ (3:19:05) Functions - notation
⌨️ (3:27:21) Functions - Domain
⌨️ (3:34:43) Functions - Graph basics
⌨️ (3:44:33) Functions - arithmetic
⌨️ (3:53:00) Functions - composition
⌨️ (4:03:40) Fucntions - inverses
⌨️ (4:17:32) Functions - Exponential definition
⌨️ (4:27:25) Functions - Exponential properties
⌨️ (4:35:55) Functions - logarithm definition
⌨️ (4:44:00) Functions - logarithm properties
⌨️ (4:53:21) Functions - logarithm change of base
⌨️ (4:59:31) Functions - logarithm examples
⌨️ (5:09:29) Graphs polynomials
⌨️ (5:20:14) Graph rational
⌨️ (5:39:32) Graphs - common expamples
⌨️ (5:50:36) Graphs - transformations
⌨️ (5:58:37) Graphs of trigonometry function
⌨️ (6:08:20) Trigonometry - Triangles
⌨️ (6:16:04) Trigonometry - unit circle
⌨️ (6:34:10) Trigonometry - Special angles
⌨️ (6:43:56) Trigonometry - The six functions
⌨️ (6:51:19) Trigonometry - Basic identities
⌨️ (6:57:15) Trigonometry - Derived identities

## 3. PreCalculus Lesson 1

This video is a review of the exponent laws and the rules for simplifying rationals in preparation for a course in calculus.

## 4. How to Make it Through Calculus (Neil deGrasse Tyson)

Neil deGrasse Tyson talks about his personal struggles taking calculus and what it took for him to ultimately become successful at it.

## 5. MCV4U Grade 12 Calculus & Vectors - Course outline - Course description - Ontario Virtual School OVS

Ontario Virtual School
ontariovirtualschool.ca/
Grade 12 Calculus & Vectors - MCV4U Course outline
ontariovirtualschool.ca/courses/mcv4u/

## 6. Why People FAIL Calculus (Fix These 3 Things to Pass)

Calculus is one of the biggest struggles for many college students. I'm talking today about my three biggest reason as to why students fail calculus. I hope this video helps you out and gets you on the road to passing your calculus class!
#calculus #calculus #brithemathguy

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Prove It Like A Mathematician! (Intro To Math Proofs)
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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

## 8. Grade 12 Math Courses in Ontario

Confused about which grade 12 math course to take? 1, 2, or all 3 of them? Calculus and Vectors vs. Data Management?
Here's a quick overview of each course, what's easy about them vs. what makes them difficult, and why your university plan may help you decide in which course to enroll.
Whatever route you choose, we've got the materials and the expert tutors to help you understand these complex topics in simple ways!!!

Send us more questions at [email protected]

## 9. Precalculus Final Exam Review

This precalculus final exam review covers topics on logarithms, graphing functions, domain and range, arithmic sequences, geometric series, asymptotes, and more.

Get The Full Video on Patreon:
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Precalculus Final Exam Review Part 1 - Questions 1-30:

Precalculus Final Exam Review Part 2 - Questions 31-54:

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## 10. Calculus 1 - Full College Course

Learn Calculus 1 in this full college course.

This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her YouTube channel: youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw

This course combines two courses taught by Dr. Green. She teaches both Calculus 1 and a Calculus 1 Corequisite course, designed to be taken at the same time. In this video, the lectures from the Corquisite course, which review important Algebra and Trigonometry concepts, have been interspersed with the Calculus 1 lectures at the places suggested by Dr. Green.

⭐️ Prerequisites ⭐️

⭐️ Lecture Notes ⭐️
🔗 Calculus 1 Corequisite Notes: lindagreen.web.unc.edu/files/2020/08/courseNotes_math231L_2020Fall.pdf
🔗 Calculus 1 Notes: lindagreen.web.unc.edu/files/2019/12/courseNotes_m231_2018_S.pdf

⭐️ Course Contents ⭐️
(0:00:00) [Corequisite] Rational Expressions
(0:09:40) [Corequisite] Difference Quotient
(0:18:20) Graphs and Limits
(0:25:51) When Limits Fail to Exist
(0:31:28) Limit Laws
(0:37:07) The Squeeze Theorem
(0:42:55) Limits using Algebraic Tricks
(0:56:04) When the Limit of the Denominator is 0
(1:08:40) [Corequisite] Lines: Graphs and Equations
(1:17:09) [Corequisite] Rational Functions and Graphs
(1:30:35) Limits at Infinity and Graphs
(1:37:31) Limits at Infinity and Algebraic Tricks
(1:45:34) Continuity at a Point
(1:53:21) Continuity on Intervals
(1:59:43) Intermediate Value Theorem
(2:03:37) [Corequisite] Right Angle Trigonometry
(2:11:13) [Corequisite] Sine and Cosine of Special Angles
(2:19:16) [Corequisite] Unit Circle Definition of Sine and Cosine
(2:24:46) [Corequisite] Properties of Trig Functions
(2:35:25) [Corequisite] Graphs of Sine and Cosine
(2:41:57) [Corequisite] Graphs of Sinusoidal Functions
(2:52:10) [Corequisite] Graphs of Tan, Sec, Cot, Csc
(3:01:03) [Corequisite] Solving Basic Trig Equations
(3:08:14) Derivatives and Tangent Lines
(3:22:55) Computing Derivatives from the Definition
(3:34:02) Interpreting Derivatives
(3:42:33) Derivatives as Functions and Graphs of Derivatives
(3:56:25) Proof that Differentiable Functions are Continuous
(4:01:09) Power Rule and Other Rules for Derivatives
(4:07:42) [Corequisite] Trig Identities
(4:15:14) [Corequisite] Pythagorean Identities
(4:20:35) [Corequisite] Angle Sum and Difference Formulas
(4:28:31) [Corequisite] Double Angle Formulas
(4:36:01) Higher Order Derivatives and Notation
(4:39:22) Derivative of e^x
(4:46:52) Proof of the Power Rule and Other Derivative Rules
(4:56:31) Product Rule and Quotient Rule
(5:02:09) Proof of Product Rule and Quotient Rule
(5:10:40) Special Trigonometric Limits
(5:17:31) [Corequisite] Composition of Functions
(5:29:54) [Corequisite] Solving Rational Equations
(5:40:02) Derivatives of Trig Functions
(5:46:23) Proof of Trigonometric Limits and Derivatives
(5:54:38) Rectilinear Motion
(6:11:41) Marginal Cost
(6:16:51) [Corequisite] Logarithms: Introduction
(6:25:32) [Corequisite] Log Functions and Their Graphs
(6:36:17) [Corequisite] Combining Logs and Exponents
(6:40:55) [Corequisite] Log Rules
(6:49:27) The Chain Rule
(6:58:44) More Chain Rule Examples and Justification
(7:07:43) Justification of the Chain Rule
(7:10:00) Implicit Differentiation
(7:20:28) Derivatives of Exponential Functions
(7:25:38) Derivatives of Log Functions
(7:29:38) Logarithmic Differentiation
(7:37:08) [Corequisite] Inverse Functions
(7:51:22) Inverse Trig Functions
(8:00:56) Derivatives of Inverse Trigonometric Functions
(8:12:11) Related Rates - Distances
(8:17:55) Related Rates - Volume and Flow
(8:22:21) Related Rates - Angle and Rotation
(8:28:20) [Corequisite] Solving Right Triangles
(8:34:54) Maximums and Minimums
(8:46:18) First Derivative Test and Second Derivative Test
(8:51:37) Extreme Value Examples
(9:01:33) Mean Value Theorem
(9:09:09) Proof of Mean Value Theorem
(0:14:59) [Corequisite] Solving Right Triangles
(9:25:20) Derivatives and the Shape of the Graph
(9:33:31) Linear Approximation
(9:48:28) The Differential
(9:59:11) L'Hospital's Rule
(10:06:27) L'Hospital's Rule on Other Indeterminate Forms
(10:16:13) Newtons Method
(10:27:45) Antiderivatives
(10:33:24) Finding Antiderivatives Using Initial Conditions
(10:41:59) Any Two Antiderivatives Differ by a Constant
(10:45:19) Summation Notation
(10:49:12) Approximating Area
(11:04:22) The Fundamental Theorem of Calculus, Part 1
(11:15:02) The Fundamental Theorem of Calculus, Part 2
(11:22:17) Proof of the Fundamental Theorem of Calculus
(11:29:18) The Substitution Method
(11:38:07) Why U-Substitution Works
(11:40:23) Average Value of a Function
(11:47:57) Proof of the Mean Value Theorem for Integrals

## 11. Precalculus Syllabus

-- Created using Powtoon -- Free sign up at powtoon.com/youtube/ -- Create animated videos and animated presentations for free. PowToon is a free tool that allows you to develop cool animated clips and animated presentations for your website, office meeting, sales pitch, nonprofit fundraiser, product launch, video resume, or anything else you could use an animated explainer video. PowToon's animation templates help you create animated presentations and animated explainer videos from scratch. Anyone can produce awesome animations quickly with PowToon, without the cost or hassle other professional animation services require.

Sample lesson from BJU Press video course for Precalculus. Mr. Matesevac encourages his students to master challenging concepts as they progress through this college prep course. Students will cover the foundations of calculus as well as its practical, real-world applications. Segments give students a visual walkthrough of difficult problems. To learn more about this course and its components, visit bjupresshomeschool.com/product/433011

## 13. The Map of Mathematics

The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.

#mathematics #DomainOfScience

If you would like to buy a poster of this map, they are available here:
North America: store.dftba.com/products/map-of-mathematics-poster
Everywhere else: redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u

I have also made a version available for educational use which you can find here: flickr.com/photos/[email protected]/32264483720/in/dateposted-public/

To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!

1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).

2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.

3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.

4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: youtu.be/O4ndIDcDSGc

5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.

Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. patreon.com/domainofscience

Here are links to some of the sources I used in this video.

Summary of mathematics: en.wikipedia.org/wiki/Mathematics
Earliest human counting: mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: en.wikipedia.org/wiki/0#History livescience.com/27853-who-invented-zero.html
First use of negative numbers: quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: rossroessler.tripod.com/ en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof

Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.

Frontiers of Space: nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Intergalactic Activity Book: nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: minilabstudios.com/apps/professor-astro-cats-solar-system/

Find me on twitter, instagram, and my website:
dominicwalliman.com
instagram.com/dominicwalliman

## 14. PreCalculus Full Course For Beginners

In mathematics education, #precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework. In this precalculus course following topics have been discussed in a very comprehensive way.

⭐️ Table of Content ⭐️
0:00 Functions
11:53 Increasing and Decreasing Functions
17:22 Maximums and minimums on graphs
26:25 Even and Odd Functions
35:39 Toolkit Functions
43:05 Transformations of Functions
55:34 Piecewise Functions
1:00:06 Inverse Functions
1:14:20 Angles and Their Measures
1:22:23 Arclength and Areas of Sectors
1:32:49 Right Angle Trigonometry
1:40:24 Sine and Cosine of Special Angles
1:48:28 Unit Circle Definition of Sine and Cosine
1:53:58 Properties of Trig Functions
2:4:36 Graphs of Sine and Cosine
2:11:09 Graphs of Sinusoidal Functions
2:21:22 Graphs of Tan, Sec, Cot, Csc
2:30:15 Inverse Trig Functions
2:39:49 Pythagorean Identities
2:45:09 Angle Sum and Difference Formulas
2:53:06 Proof of the Angle Sum Formulas
2:57:41 Double Angle Formulas
3:05:11 Half Angle Formulas
3:11:23 Solving Right Triangles
3:17:57 Law of Cosines
3:27:57 Law of Cosines - old version
3:36:16 Law of Sines
3:44:06 Parabolas - Vertex, Focus, Directrix
3:55:56 Ellipses
4:7:05 Hyperbolas
4:20:55 Polar Coordinates
4:28:27 Parametric Equations
4:39:54 Difference Quotient

⭐️ Credit ⭐️
Author: Prof. Linda Green