Ontario Grade 12 courses: what each one covers, what it leads to, and how to study it (MHF4U, MCV4U, MDM4U, SPH4U, SCH4U, SBI4U)

Ontario's Grade 12 university-preparation courses in math and science are MHF4U (Advanced Functions), MCV4U (Calculus and Vectors), MDM4U (Mathematics of Data Management), SPH4U (Physics), SCH4U (Chemistry) and SBI4U (Biology). Each is a one-credit course scheduled for at least 110 hours, organized in strands, with a Grade 11 prerequisite and a first-year course it leads into. The table below shows what each covers and how to study it, with a full guide per course.

The six codes, decoded

An Ontario course code has three parts. The first three letters name the subject and the course: MHF is Advanced Functions, SCH is Chemistry. The digit is the grade, so a 4 means Grade 12. The last letter is the destination the course prepares you for: U for university, C for college, M for either, O for open and E for workplace. SCH4U is therefore Grade 12 Chemistry, university preparation.

The official description of each course, its strands and its expectations lives on the Ministry of Education's curriculum site, under the Grades 11 and 12 mathematics and science documents. That text is Crown copyright, so this page does not reproduce it. What is here is our own one-line description of what each strand teaches, the course codes, and the idea lists from our course maps.

For admissions, U means one thing in one sentence: most university programs list specific 4U courses as prerequisites, and a program's own admission page is the only place that says which ones it wants.

The table

Six rows. The "ideas" column counts the concepts in our course map for that course, in the order a class usually meets them. The "leads to" column names the first-year course each one feeds, which is where the content goes next.

Code	Name	What it covers	Ideas in our map	Prerequisite	Leads to in first year	Our guide
MHF4U	Advanced Functions	Polynomial and rational functions; exponential and logarithmic functions; trigonometric functions in radians; characteristics of functions	26	MCR3U	Calculus I, Linear Algebra	MHF4U: map and study plan
MCV4U	Calculus and Vectors	Rates of change and limits; derivatives and their applications; vectors and the geometry of lines and planes	24	MHF4U, before or concurrently	Calculus I	MCV4U: map and study plan
MDM4U	Mathematics of Data Management	Counting and probability; probability distributions; data collection; statistical analysis	24	MCR3U or MCF3M	Statistics	Coming in this section
SPH4U	Physics	Dynamics; energy and momentum; gravitational, electric and magnetic fields; the wave nature of light; modern physics	25	SPH3U	Physics I	SPH4U: map and study plan
SCH4U	Chemistry	Organic chemistry; structure and properties of matter; energy changes and rates of reaction; equilibrium; electrochemistry	24	SCH3U	General Chemistry	SCH4U: map and study plan
SBI4U	Biology	Biochemistry; metabolic processes; molecular genetics; homeostasis; population dynamics	27	SBI3U	Biology I	SBI4U: map and study plan

The prerequisites in the table are the ones the Ministry's course descriptions set. Your school's course calendar is the final word for your own timetable, and some schools add their own recommendations on top. The full guides are listed at the foot of this page as they are published; the maths are the first two: the MHF4U map and the MCV4U map. Chapter 3 of the free playbook is the method for turning any one of these maps into a checklist you keep for the semester.

How the courses chain

Students in Grade 11 ask one practical question: which of these should I take together, and in what order. The dependencies answer it.

MHF4U then MCV4U is the one hard dependency. Calculus differentiates functions, so it assumes you can handle them: composition for the chain rule, the log laws for exponential and logarithmic derivatives, the identities for trigonometric derivatives, and the rate of change idea that becomes the derivative itself. The Ministry allows the two to run concurrently, and many students do that in a full-year timetable, but a student doing so has to keep the MHF4U ideas moving faster than the class reaches them.

SCH4U leans on MHF4U's logarithms. The pH, pOH and equilibrium calculations in the chemistry course are logarithm problems with units attached. A student who has not met the log laws will do them by button-pressing and be lost when a question changes shape.

SPH4U uses the derivative idea informally. Instantaneous velocity and acceleration are rates of change; the physics course states them with graphs and formulas rather than limits. A student in MCV4U at the same time sees the same idea from both sides, which helps both.

SBI4U is the least math-dependent of the six. It needs careful reading, diagrams and process, and its calculations stay at the Grade 10 level. It pairs with anything.

So the usual sequences are MHF4U first, or MHF4U and MCV4U together, with the sciences in whatever order the timetable allows.

How to study any of them: the three moves that fit every course

Across the review of ten study techniques by Dunlosky and colleagues (2013), two came out with the strongest evidence for every subject and every kind of student: testing yourself and spacing your sessions. The third move is the subject's own.

Answer first. Close the notes, attempt the problem or write the definition, then open and mark. Testing yourself is the method, including the honest marking rules; it holds for a derivative and for a diagram of a cell alike.

Space it. Every idea comes back on at least two separate days before it is tested. The spacing schedule shows how to run that on paper, and the course guides below give a week-by-week version per course.

Add the subject's layer. For the two maths, every question is a problem: the method is worked examples, redone cold, with an error log, as how to study math sets out. For the three sciences, diagrams, processes and the words of the course carry the marks, and how to study biology, chemistry and physics has that version.

For readers outside Ontario

If you landed here from the United States, the nearest equivalences are these. MHF4U is roughly a precalculus course, or Algebra 2 with trigonometry: the function families, logarithms and trig in radians, and no calculus. The precalculus guide lists the twelve ideas a calculus course assumes, and every one of them is in the MHF4U map. MCV4U is a first calculus course without integrals, plus a unit on vectors; the derivative half overlaps AP Calculus AB. SCH4U and SPH4U overlap the AP sciences in content and sit a step below them in depth. None of this is a claim about credit: a university decides what it accepts, and these are content overlaps, not equivalences.

Worked example: one idea from each of the two maths

So the table has a face, here is one problem from each of the two math courses, with the answer derived.

MHF4U, idea 21 (solving trigonometric equations). Solve 2cos²x − 1 = 0 on [0, 2π]. Add 1 and divide by 2: cos²x = 1/2, so cos x = ±√2/2. Cosine is +√2/2 at x = π/4 and 7π/4, and −√2/2 at 3π/4 and 5π/4. Four solutions: π/4, 3π/4, 5π/4, 7π/4. The common wrong line keeps only the two where cosine is positive, which is forgetting the ± when taking the square root.

MCV4U, idea 20 (the dot product and the angle between vectors). Find the angle between u = (1, 2, 2) and v = (2, 1, −2). The dot product is 1·2 + 2·1 + 2·(−2) = 2 + 2 − 4 = 0. A zero dot product between two non-zero vectors means they are perpendicular, so the angle is 90°, with no magnitudes needed. The common wrong line computes |u| and |v| first and divides before noticing the numerator is zero.

Both answers are checkable by substitution, which is the point of a worked example: you can tell on your own whether you have it.

The course guides

Each guide in this section follows the same shape: the course's ideas in the order they are taught, what each unlocks, the ideas that carry the rest, a worked problem per strand with its common wrong line, a week-by-week plan and an exam-week triage.

• MHF4U Advanced Functions: the 26 ideas, and the three everything leans on: polynomial division, the log laws and the trig identities.
• MCV4U Calculus and Vectors: the 24 ideas from the limit to planes in space, and the chain-rule and related-rates traps.
• SPH4U Physics: the 25 ideas across strands B to F, and deriving a formula before memorizing it in the kinematics and energy chains.
• SCH4U Chemistry: the 24 ideas, the calculation chapters as procedures and the naming chapters as vocabulary.
• Molecular geometry and bond angles: electron geometry, molecular geometry and the lone-pair effect for every shape, with a self-test.
• Precalculus and Algebra 2: the twelve ideas calculus assumes, for the US reader, with a self-test.
• First-year calculus: what changes after high school, and the 26 ideas in order with a week-by-week plan.
• SBI4U Biology: the 27 ideas, vocabulary against mechanism, and the diagrams to redraw from memory.

The six, on one screen

1. MHF4U: polynomials and rationals, exponentials and logs, trig in radians, characteristics of functions.
2. MCV4U: limits and rates of change, derivatives and applications, vectors through lines and planes.
3. MDM4U: counting and probability, distributions, data collection, statistical analysis.
4. SPH4U: dynamics, energy and momentum, fields, the wave nature of light, modern physics.
5. SCH4U: organic chemistry, structure and properties, energy and rates, equilibrium, electrochemistry.
6. SBI4U: biochemistry, metabolism, molecular genetics, homeostasis, population dynamics.

Where YSR Studies does the bookkeeping

Each of the six courses is a pack in YSR Studies: its ideas in the order they are taught, a course map marking each one Learned, Shaky or Not shown yet, and practice whose answers are checked on the maths with the worked steps from the course's answer key shown after your attempt, with five free hours every month.