Ontario Grade 12 University Math: MHF4U and MCV4U
A second teacher for Grade 12 university math: functions understood properly, then the calculus and vectors built on them, in step with your school course.
Syllabus updated October 2026
Questions? WhatsApp +91 91233 66161 or email connect@modernagecoders.com
Recordings are free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course.
Fees and enrolment
How to join Ontario Grade 12 University Math: Advanced Functions and Calculus and Vectors (MHF4U and MCV4U)
Choose how you want to pay, pick a plan and press Enrol. We then fix your class timing with you.
Rated 4.9 across 547 Google reviews.
How would you like to pay?
Pay once for 6 months and save 20%. Same live classes, same mentor, a lower price for every session.
Group Classes
6 months · 48 sessions
One payment for all 6 months
- Paying monthly
₹1,499 × 6 months = ₹8,994- You save
- ₹1,795 (20%)
- Per session
- ₹150
₹187
2 sessions a week · 15 to 20 students
Stop early? Every session you have not taken is refunded at ₹150. Refund policy
Enrol for 6 monthsMini Batch
6 months · 48 sessions
One payment for all 6 months
- Paying monthly
₹2,999 × 6 months = ₹17,994- You save
- ₹3,595 (20%)
- Per session
- ₹300
₹375
2 sessions a week · Up to 6 students
Stop early? Every session you have not taken is refunded at ₹300. Refund policy
Enrol for 6 monthsHow your 6-month price works
- Sessions
- 24 one-to-one sessions over 6 months, fully flexible timing
- Price per session
- ₹1,000 instead of
₹1,250 - Your 6-month fee
- ₹1,000 × 24 sessions = ₹24,000
- Paying monthly instead
₹4,999 × 6 months = ₹29,994- You save
- ₹5,994 (20%)
Everything in the monthly 1-on-1 plan is included: your own mentor, flexible timing, personal dashboard, class recordings, progress reports and parent-teacher meetings.
Stop early? Every session you have not taken is refunded at ₹1,000. Refund policy
Pay once for 6 months and save 25%. Same live classes, same mentor, a lower price for every session.
Group Classes
6 months · 48 sessions
One payment for all 6 months
- Paying monthly
$100 × 6 months = $600- You save
- $151 (25%)
- Per session
- $9.35
$12.50
2 sessions a week · 15 to 20 students
Stop early? Every session you have not taken is refunded at $9.35. Refund policy
Enrol for 6 monthsHow your 6-month price works
- Sessions
- 48 one-to-one sessions over 6 months, 2 sessions a week
- Price per session
- $14 instead of
$18.75 - Your 6-month fee
- $14 × 48 sessions = $672
- Paying monthly instead
$150 × 6 months = $900- You save
- $228 (25%)
Everything in the monthly 1-on-1 plan is included: your own mentor, flexible timing, personal dashboard, class recordings, progress reports and parent-teacher meetings.
Stop early? Every session you have not taken is refunded at $14. Refund policy
How enrolment works
Pick a plan
Group (15 to 20 students), Mini Batch (up to 6, India only) or 1-on-1 with your own mentor. Pay monthly, or for 6 months at once and save.
Press Enrol and pay
Fill in the student's name, email and phone, then pay securely: UPI, cards or net banking in India, or a debit or credit card from any other country.
Fix your class timing
After paying, WhatsApp or call +91 91233 66161 with the student's name and your preferred time. We confirm the batch or 1-on-1 slot and send the class link.
Start learning
Join your first live class at the time you chose. Your mentor takes it from there.
Want to see a class first? Book a Priority Demo: a live class of about 45 to 60 minutes with a mentor reserved for you. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off.
Pay monthly and cancel any time, or pay for 6 months at once and save. Stop a 6-month plan early and every session left is refunded.
International Students (Outside India)
Billed monthly in US dollars, the same price in every country. Contact us with any questions.
Questions before you enrol? Talk to our team.
Ask about class timings, the right level for your child, what they need to know already, or payment. Parents and adult learners can reach us on WhatsApp, by email or by phone.
Our promise
The world's best learning experience, open to everyone.
- World-class instructorsEvery class is taught by an instructor who specialises in that exact field.
- No compromise on qualityEvery lesson, project and piece of feedback is held to the highest standard.
- Education for everyoneLearners aged 6 to 67, from first-time beginners to working professionals, in 25+ countries.
If you want the highest quality, Modern Age Coders is the right choice.
Book a Priority DemoHow long this course takes
This course runs 6 months (24 weeks) per plan, joinable any month and paced to your school course at 2 live classes/week + short practice sets between classes. The range allows for background and pace: a complete beginner uses the full span, and a student with prior knowledge finishes sooner. The syllabus below is planned to the shorter end, with margin kept for revision.
For personalised duration planning, call +91 91233 66161 and we'll map a schedule to your goals.
At a glance
- Who it is for
- Ontario students in Grade 12 (roughly ages 16 to 18) taking MHF4U, MCV4U or both at school. Age: Roughly 16 to 18 (Grade 12).
- Prerequisites
- Currently taking, or about to take, MHF4U, MCV4U or both at an Ontario school
- Format
- Live, interactive classes with a real teacher, never pre-recorded videos. Live classes run about one hour.
- Language
- English or Hindi, depending on the batch.
- Duration
- 6 months (24 weeks) per plan, joinable any month and paced to your school course
- Weekly commitment
- 2 live classes/week + short practice sets between classes
- Class size
- Group batches of 15 to 20 students, mini batches of up to 6, or 1-on-1.
- Certificate
- Certificate from Modern Age Coders, awarded on passing the final assessment (this is not an Ontario high school credit)
- Watch first
- Free recordings of real classes for ages 13 and up, free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course.
- Live demo
- Optional. Enrol directly on this page, or book a Priority Demo: a full live class of about 45 to 60 minutes with a mentor reserved for you.
- Questions
- WhatsApp +91 91233 66161 or email connect@modernagecoders.com.
How we teach
Deep understanding. Real projects. Expert guidance.
Learn coding, AI and maths through careful explanations, practical demonstrations, and hands-on problem-solving. Our instructors guide you from the foundations to advanced ideas, helping you understand what happens, why it happens, and how to build it yourself.
You will explore concepts step by step, write and improve code, investigate mistakes, ask questions, and apply your knowledge to meaningful projects. Lessons are designed around active participation, thoughtful feedback, and growing independence.
Expert-led live teaching, with practical participation built into every lesson.
- Students explain their thinking.
- Instructors demonstrate, then guide practice.
- Learners code, solve, or build during lessons.
- Questions and misconceptions get attention.
- Assignments receive useful feedback.
- Progress is checked before advancing.
Program Overview
MHF4U and MCV4U are Ontario's Grade 12 university-preparation math courses. In the ministry's course list, MHF4U is titled Advanced Functions and MCV4U is titled Calculus and Vectors, both issued in 2007. The ministry lists the MHF4U prerequisite as "Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation", and it says "The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U)". Both courses also appear in university admission requirements. The University of Waterloo's Computer Science page asks for "Six Grade 12 U and/or M courses including" Advanced Functions and Calculus and Vectors, and the University of Toronto lists MCV4U as a prerequisite for computer science on all three campuses, with MHF4U also listed at Mississauga and Scarborough.
This course runs alongside the student's own MHF4U or MCV4U class, and many students take both in the same year. We follow the order of the student's school course outline, so what is learned here is used in class the same week. What our course teaches for MHF4U students: polynomial and rational functions, trigonometric functions in radians with identities and equations, exponential and logarithmic functions, combining functions, and rates of change. What it teaches for MCV4U students: limits and the derivative, the derivative rules, curve sketching and optimization, then vectors, lines and planes. Every topic starts from meaning, with graphs and small examples, before the algebra. Tests and assignments stay the student's own work: we explain, question and review, and the student does the math.
Please read this plainly: Modern Age Coders teaches alongside school and does not grant Ontario high school credits. Families who need the credit take the course through their school or a ministry-inspected credit provider. What we add is understanding, practice and confidence, in live classes with a real teacher.
What Makes This Program Different
- Built around Ontario's MHF4U and MCV4U, following the student's own school course outline week by week
- Taught for students taking one course or both at once, with MHF4U ideas reviewed exactly where calculus needs them
- Meaning before algebra: graphs, tables and small examples come first, then the rules and the proofs
- Honest about credits: we teach alongside school and do not grant Ontario high school credits
- Tests and assignments stay the student's own work: we explain and review, we never do school work for them
- Exam review technique taught directly: full written solutions, communication marks and timed practice papers
Your Learning Journey
Career Progression
Detailed Course Curriculum
Explore the complete week-by-week breakdown of what you'll learn in this comprehensive program.
Topics Covered
- A starting conversation and short diagnostic: the school, the course outline, the next test and the Grade 11 ideas to refresh
- Function notation, domain and range, and reading a graph carefully
- Transformations of functions: shifts, stretches and reflections
- Inverse functions and what their graphs show
- Factoring review: common factors, trinomials and the difference of squares
- Setting up a clean notebook system for definitions, examples and mistakes
Projects You Build
- A one-page function toolkit summary, with a sketch of each parent function and its transformations
Practice & Assignments
Short daily sets that mix new work with one or two Grade 11 refresher questions
Topics Covered
- Degree, leading coefficient and end behaviour
- Zeros, their order, and how the graph behaves at each zero
- Sketching a polynomial from its factored form
- Finding an equation from a graph or from given zeros
- Even and odd functions and symmetry
- Finite differences and what they say about degree
Projects You Build
- A polynomial sketch set: ten polynomials sketched by hand from factored form, then checked with graphing technology
Practice & Assignments
For every sketch, write the end behaviour and the behaviour at each zero before drawing
Assessment
Month 1 check: a short written test on functions and polynomial graphs, reviewed with written feedback
Topics Covered
- Polynomial long division and synthetic division
- The remainder theorem and the factor theorem
- Factoring cubics and quartics, including sums and differences of cubes
- Solving polynomial equations exactly
- Solving polynomial inequalities with a sign chart and a graph
- Families of polynomials and word problems
Projects You Build
- A worked solutions file for factoring and inequalities, with every step justified in words
Practice & Assignments
Mixed equation and inequality sets, with answers checked by substitution or graph
Topics Covered
- Reciprocal functions and their graphs
- Vertical and horizontal asymptotes, and holes
- Sketching rational functions from their factored form
- Solving rational equations and checking for restricted values
- Solving rational inequalities with a sign chart
- Average rate of change on a rational graph
Projects You Build
- A rational function sketch set with asymptotes, intercepts and behaviour near each asymptote explained
Practice & Assignments
For every rational function, list restrictions and asymptotes first, then sketch
Assessment
Phase 1 assessment: a timed test on polynomial and rational functions in the style of a school unit test, marked with comments
Topics Covered
- Radian measure and converting between radians and degrees
- Special angles and the unit circle, without memorizing tables
- Graphs of sine, cosine and tangent in radians
- Amplitude, period, phase shift and vertical shift
- Modelling periodic situations with sinusoidal functions
- Reciprocal trigonometric functions and their graphs
Projects You Build
- A sinusoidal model of a real periodic situation, with the equation built from the data and explained
Practice & Assignments
Unit circle and transformation sets, each answer checked against a quick sketch
Topics Covered
- Proving identities: working one side, and writing each step clearly
- Compound angle formulas and double angle formulas
- Solving linear and quadratic trigonometric equations in radians
- Finding all solutions in a given interval
- Equivalent trigonometric expressions using related angles
- Common mistakes: dividing by a variable and losing solutions
Projects You Build
- An identity proof file: ten identities proved in full, with the strategy for each written first
Practice & Assignments
One identity proof and two equations every day, with every solution in the interval listed
Assessment
Month 3 check: a written test on trigonometric functions, identities and equations, reviewed with written feedback
Topics Covered
- Exponential functions and their graphs, growth and decay
- The logarithm as the inverse of an exponential function
- Laws of logarithms and when each one applies
- Solving exponential and logarithmic equations, and checking for extraneous roots
- Changing the base of a logarithm
- Applications: compound interest, half-life, sound and pH scales
Projects You Build
- An applications pack: four real situations modelled with exponential or logarithmic functions and solved in full
Practice & Assignments
Mixed log law and equation sets, with each step named
Topics Covered
- Sums, differences, products and quotients of functions, and their graphs
- Composition of functions and its domain
- Average rate of change over an interval
- Estimating instantaneous rate of change, the bridge to calculus
- Choosing a function family to model a situation
- MHF4U exam review: full solutions, communication and timed practice
Projects You Build
- A personal MHF4U review pack: one-page summaries for each unit, a mistakes list and a reviewed timed paper
Practice & Assignments
Trace the meaning of a rate of change on a graph before calculating it
Assessment
Phase 2 assessment: a mixed MHF4U-style review paper, marked with written comments
Topics Covered
- From average rate of change to instantaneous rate of change
- Limits, explained with tables and graphs before algebra
- The derivative from first principles
- The power, constant multiple, sum and difference rules
- The product, quotient and chain rules
- The derivative as a slope and as a rate, in words and in units
Projects You Build
- Three derivatives worked from first principles, then confirmed with the rules, with a short written explanation
Practice & Assignments
Daily derivative sets, each with one question asking what the derivative means in context
Topics Covered
- Increasing and decreasing intervals, and local maxima and minima
- Concavity and points of inflection from the second derivative
- Sketching a curve from its derivatives
- Optimization problems: setting up the function, the domain and the check
- Derivatives of exponential and sinusoidal functions
- Rates of change in motion: position, velocity and acceleration
Projects You Build
- An optimization pack: four real problems set up and solved in full, each with a domain check
Practice & Assignments
For every optimization problem, write the function and its domain before differentiating
Assessment
Month 5 check: a written test on derivatives and their applications, reviewed with written feedback
Topics Covered
- Geometric vectors: magnitude, direction, addition and scalar multiples
- Cartesian vectors in two and three dimensions
- The dot product, angles between vectors and projections
- The cross product and what it measures
- Applications: force, velocity and work
- Drawing a clear diagram for every vector problem
Projects You Build
- A vector applications set with a labelled diagram and a full written solution for each problem
Practice & Assignments
Short vector sets mixing geometric and Cartesian forms
Topics Covered
- Equations of lines in two and three dimensions: vector, parametric and symmetric forms
- Equations of planes and their normal vectors
- Intersections of lines and planes, and what each case looks like
- Making a one-page summary for each unit of the school course
- Full written solutions: showing reasoning so communication marks are earned
- Timed review papers in the style of school exams, with careful review afterwards
Projects You Build
- A personal MCV4U review pack: unit summaries, a mistakes list and two reviewed timed papers
Practice & Assignments
A timed mixed review each week, with every mistake written up and fixed
Assessment
Final assessment: a timed review paper plus a short live walk-through of two of the student's own solutions
Projects You'll Build
Build a professional portfolio with A file of worked solutions, sketch sets, proofs and review packs, all the student's own work real-world projects.
Weekly Learning Structure
Certification & Recognition
Technologies & Skills You'll Master
Comprehensive coverage of the entire modern web development stack.
Support & Resources
Career Outcomes & Opportunities
Transform your career with industry-ready skills and job placement support.
Prerequisites
Who Is This Course For?
Career Paths After Completion
Course Guarantees
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What families say
Straight from the parents and students who learn with us. Rated 4.9 across 547 Google reviews.
“Mivaan enjoys the class. He understands the concepts and completes his tasks with excitement. He started taking interest in coding… truly amazing class.”
“I absolutely love it here! I made new friends and learned important valuable coding skills while having the fun of my life. It's not just coding here, it's outings, bonding and most importantly preparing you for your future. Definitely five stars.”
“What stands out most is how excited my son is before every class. He looks forward to learning, problem-solving, and sharing what he's built. I've noticed a big boost in his confidence!”
“Modern Age Coders has been a game-changer for me! I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I'm now the topper in my class and can confidently write complex programs with ease.”
“Modern Age Coder have wonderful teachers who teach in a clear, easy and practical way. The teacher boosts students' confidence, keeps them updated with technology, and inspires them to learn without hesitation.”
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“Very good classes. Don't worry about coding. They teach the best, especially Shivam sir.”
“Very good classes. Makes learning very easy and interactive.”
Hear it from our students
Real parents and students in their own words, on our public YouTube channel.
Straight answers about Ontario Grade 12 University Math: Advanced Functions and Calculus and Vectors (MHF4U and MCV4U)
- Who should take this course?
- Ontario students in Grade 12 (roughly ages 16 to 18) taking MHF4U, MCV4U or both at school. Age: Roughly 16 to 18 (Grade 12). It suits grade 12 students in mhf4u who want functions to make sense, not just to pass; students in mcv4u meeting derivatives, optimization and three-dimensional vectors; students taking mhf4u and mcv4u in the same year who want the two courses to fit together.
- What will they learn and build?
- MHF4U and MCV4U are Ontario's Grade 12 university-preparation math courses. In the ministry's course list, MHF4U is titled Advanced Functions and MCV4U is titled Calculus and Vectors, both issued in 2007.
- How deeply are topics covered?
- The course runs 6 months (24 weeks) per plan, joinable any month and paced to your school course at 2 live classes/week + short practice sets between classes, across 3 phases listed week by week in the syllabus below.
- Who teaches it?
- Modern Age Coders mentors, who teach the live classes themselves. You can watch them at work in the free class recordings before you decide.
- How do practice, feedback and assessment work?
- Classwork in every session and homework after every class. Doubt support between classes over WhatsApp, so you are never left stuck. A certificate from Modern Age Coders that you earn by passing the final assessment, with a free retest after revision if needed. It is not an Ontario high school credit.
- What does it cost?
- Three monthly plans: a group batch, a mini batch and 1-on-1. Prices are shown in your currency in the plans section. Monthly billing, cancel any time.
- When can classes take place?
- Live classes are scheduled around your week. Group batches meet at a fixed weekly slot; 1-on-1 students choose their own. International students are scheduled in their own timezone. Ask on WhatsApp for the current slots.
- Can I watch the teaching before deciding?
- Yes. Full recordings of real 13 and up classes are free to watch, free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course. Some classes are in English and some in Hindi; everyone follows at their own pace. Watch a class end to end, like you are in it. Sessions are interactive and each moment builds on the last.
- Can I enroll without a live demo?
- Yes. Choose a plan on this page and enrol directly; a demo is not required. If you would like to see a full class with a mentor first, book a Priority Demo.
- How do I reach you with a question?
- WhatsApp +91 91233 66161, email connect@modernagecoders.com, or call +91 91233 66161. Tell us the student's age and what they have learned so far, and we will point you to the right plan and batch.
Common Questions About Ontario Grade 12 University Math: Advanced Functions and Calculus and Vectors (MHF4U and MCV4U)
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Read ArticleReady to start Ontario Grade 12 University Math: Advanced Functions and Calculus and Vectors (MHF4U and MCV4U)?
Book a Priority Demo to see a full live class with a mentor reserved for you, today or tomorrow. Or choose a plan and enrol now.
Questions? WhatsApp +91 91233 66161 or email connect@modernagecoders.com