MHF4U  Grade 12 Advanced Functions
Ontario Curriculum
Your Instructor
What's up everybody, my name is Patrick and welcome to my page for MHF4U Advanced Functions. Click the Enroll button above to access free content. Scroll down to find testimonials and videos for the course organized by chapter. If you have any questions, please text/call me directly at 6479614348 or email [email protected] If you're a student, I'll get back to you within a few hours.
"In my grade 12 school year, Patrick had tutored me in 4 of my class subjects. He provided me with YouTube videos of my class topics, crafted by himself in a way that was so easy for me to understand the concept I had difficulties in. With the help of Patrick, I was able to achieve a 97% in Data Management, 97% in Advance Functions, 96% in Calculus and Vectors, and a 92% in Accounting. Without his help, I truly believe that I would not be able to accomplish what I have achieved in my final high school year."
 Jacob Tran, Laurier and Waterloo University, BMath and BBA (double degree), Class of 2021
"After a lacklustre performance in Advanced Functions during the first semester of grade 12, I knew that I had to push even harder during semester two; in order to make up for my mediocre Functions mark. The problem was, math had always been my Achilles Heel throughout highschool, and I had two maths courses, Calculus and Data Management to be specific, during second semester. Luckily, I stumbled upon Allthingsmathematics, and with the help of Patrick I was able to effectively study and comprehend core math concepts which allowed me to excel in all forms of assessments. The one thing I love about Patrick’s videos is the clarity in which he presents core concepts and ideas. This reduces the friction in my learning, resulting in more effective studies. Furthermore, Patrick has always been quick to respond to emails and texts regarding school, math, or even life in general! This is something I hadn’t previously experienced with any tutor, paid or free. With the help of Patricks Calculus and Vectors videos, I was able to score a 95% in MCV4U1; which helped me immensely in gaining acceptance from top notch business schools in Ivey (Western) and the Smith School of Business (Queen’s)."
 Prajeya Parmar, Western University, Ivey Business Program (AEO), Class of 2023
"I came across allthingsmathamatics in grade 12 while watching youtube videos to better understand the MCV4U's material. I liked Patrick's teaching style and his method of approaching questions which I found beneficial. Patrick is a dedicated and trustworthy mentor; whenever I had questions regarding the course material or help solving problems he would regularly reply to my emails. Due to living in another city I wasn’t able to get one on one tutor sessione, however, through the content (videos on every topic in a unit and mock tests) on allthingsmathematics, I was able to succeed in my final high school year and achieve my goals."
 Jeel Patel, Schulich School of Business (York), BBA, Class of 2023
"I am currently a Junior transfer student at UC Berkeley’s Haas School of Business and I can confirm that the level of depth that Patrick enters for some of the topics in his finance courses, such as the Capital Structure and CAPM sections, are equivalent to what they’re teaching us here at Haas BUT, without a single grain of doubt, Patrick’s explanation of the topics he covered were much more coherent and concise compared to my finance professor, with all due respect. Our professor allowed us to make the final exam 70% of our grade and I was forced to take this option because I had done so poorly on my midterm (21/35, but looking back at it now, I would have done so much better had I come across patricks videos earlier). I put all my time an effort into studying for the final and thankfully, I came across Patrick and his finance videos before it was too late. Long story short, I went from a 21/35 on the midterm to 35/35 on the final exam. And because of the 70% policy, I managed to get a A+ in the class. My professor has been known to give out deadly finals (has a Ph.D in Finance from Wharton and in Physics) and has only had a handful of people get a perfect on his finals. I will recommend Patrick to anyone I come across who’s trying to learn finance."
 Aakash Patel, Haas School of Business, University of California Berkeley Kinesiology, B.S. Business Administration, Class of 2020
"Grade 11 was the year I began to see Patrick and it’s safe to say it was one of the best decisions I’ve made. In my grade 12 year he tutored me during first and second semester. Patrick made my dreams of obtaining an average above 90% in advanced functions as well as calculus and vectors a reality and I’m so grateful. He’s very patient and takes the time to make sure you thoroughly understand the concepts you’re learning, whether it’s with help from his videos, practice tests or him himself. He’s so supportive and dedicated to what he does and pushes you to do your best and succeed in not only whatever subject he’s tutoring you in, but anything you’re striving for."
 Ciera Kellesis, York University, Math and Statistics, Class of 2022
"When I started calculus and vectors in the second semester of grade 12, I knew that some extra help could be needed. Since calculus and vectors is much different than other math courses in high school, some of the new concepts can be difficult when learning them for the first time. I came across Patrick via online advertisement and decided to check out his website. His videos are thorough and became extremely helpful to me and allowed me to actually understand the mathematics rather than just memorizing how do do certain problems. With the help of Patrick, I passed calculus and vectors with a good mark and was able to achieve my highest average throughout my four years of highschool."
 Chase Jankovic, Laurier University, Honours Business Administration (BBA), Class of 2023
"Throughout the year, Patrick was truly dedicated to ensure that I understood all course concepts. I was able to earn a 94% in my Advanced Functions course as I scored a 97% on my final exam. As I transitioned into Second Semester, Patrick had started making his Calculus & Vectors students YouTube videos for each lesson in the course. This was very beneficial as I would be able to use these tools as a study guide for quizzes, tests, and my final exam. I was able to achieve a 90% overall mark in my Calculus & Vectors course. Without Patrick, none of my goals would have been achieved. Whether it’s about work, school, music, working out (the list goes on), Patrick and I still talk at least four times a week. I'm very fortunate to have met him not only as my tutor, but as my friend as well."
 Kyle Desouza, Western University, Kinesiology, Class of 2020
"Even before I met Patrick I have heard nothing but positive comments from my classmates that he had previously tutored concerning his work ethic, attention to detail, and being able to explain concepts. Patrick began tutoring me when I started Calculus & Vectors. I was happy to know that he was making YouTube videos concerning each lesson with additional example videos that vary in difficulty. If I ever missed a day at school I knew that Patrick's videos would help me understand the lesson on my own. When I was in the library and was done my homework, I asked Patrick for additional questions that I could do to better prepare myself for the unit test and he would never fail to challenge me. Without his help, I don't think I would be able to achieve my overall 90% in the course."
I started getting tutored by Patrick when I was in grade 11. With his help, I managed to raise my functions mark from 68% midterm to 90% final. He was very helpful and was able to answer all my questions easily. My study habits improved a lot as the library was a nice and quiet place to get work done. When I needed help outside of the library, he would send me videos to watch which were easy to follow and understand. I continued going to Patrick in grade 12 and with his help I achieved a final grade of 88% in Advanced Functions and 91% in Calculus and Vectors. Patrick’s tutoring allowed me to get into a University of my choice and I wouldn’t have been able to do it without him. Thank you!
"From grade 9 to 11, I never achieved above 80% in a math course. Knowing grade 12 was extremely important I sought out a math tutor and was recommended by many people to Patrick. Patrick was dedicated, patient, and extremely knowledgeable; answering any question I had. In grade 12 I took all 3 math courses (advanced functions, calculus, data management). He played an extremely important role in helping me get a 94% in data and a 90% in calc and advanced functions. Patrick also has videos and an abundance of extra practice questions assuring that you will be ready for any test or exam. Not only is Patrick a great tutor, he is also easy to talk to and made going to tutoring surprisingly enjoyable. He is one of the main reasons why I got into the extremely competitive BBA program at Laurier."
 Jatin Sehra, Laurier University, Honours Business Administration (BBA), Class of 2020
"I am very thankful for the support and help that Patrick has provided me for my final year of high school. Math was never my strong suit but with his patience and very informative videos, I was able to better understand and enhance my knowledge for advance functions, and for Calculus& Vectors. Achieving a final grade of 86% for Calculus & Vectors, and an 80% in Advance functions. Patrick is someone who connects very well with all of his students and will do his very best to help you succeed in all your courses. Best of luck to all of you!"
 Nerris White, University of Guelph, Biological Science/Microbiology, Class of 2020
"Exceptional detail in both videos and notes provided in the course that are easy to refer back to anytime. Well thought through material that relates perfectly to the high school math curriculum. In the in class sessions, I was the most productive in a great learning environment with Patrick always double checking to make sure I understood the concepts to the best of his ability. Through this course I achieved my goals in both Advanced Functions and Calculus of over 90% for both final grades."
 Matthew Toxidis, Laurier University, Honours Business Administration (BBA), Class of 2020
Course Curriculum

PreviewREVIEW  relations, domain and range (video)

PreviewREVIEW  functions and vertical line test (video)

Previewfinding domain and range from table of values or coordinates

Startfinding domain and range from mapping diagram

Startfinding domain and range from a graph

Startfinding domain and range from algebraic expressions part 1

Startfinding domain and range from algebraic expressions part 2

Startrelations and functions example 1

StartFinding Domain and Range from Complex Graph Example 1 (video)

StartFinding Domain and Range from Complex Graph Example 2 (video)

StartFinding Domain from Complex Functions Example 1 (video)

StartFinding Domain from Complex Functions Example 2 (video)

StartFinding Domain from Complex Functions Example 3 (video)

StartFinding Domain from Complex Functions Example 4 (video)

StartREVIEW  Absolute Value Function Overview (video)

Startabsolute value inequalities part 1 (video)

Startabsolute value inequalities part 2 (video)

StartAdvanced Absolute Value Function 1 (video)

StartAdvanced Absolute Value Function 2 (video)

StartAdvanced Absolute Value Function 3 (video)

StartAdvanced Absolute Value Function 4 (video)

Previewintervals of increase and decrease (6:01)

Previewsymmetry (6:07)

Startsymmetry example (video) (8:14)

StartAdvanced Symmetry Example 1 (video)

StartAdvanced Symmetry Example 2 (video)

StartAdvanced Symmetry Example 3 (video)

StartAdvanced Symmetry Example 4 (video)

StartAdvanced Symmetry Example 5 (video)

StartAdvanced Symmetry Example 6 (video)

StartAdvanced Symmetry Example 7 (video)

Startcontinuity and discontinuity (3:22)

Startend behaviours (4:44)

Startcharacteristics of parent functions (video) (11:59)

Startcharacteristics of sin(x) (video) (11:50)

Startquiz (pdf)

Startquiz solutions (pdf and video) (11:57)