October 16, 2026

What's the Hardest Unit in Advanced Functions?

Short answer: Exponential and Logarithmic Functions. Of all the MHF4U answers students have handed in on Martian Lab, that unit has the lowest share marked right, 39%. Trigonometric Ratios (50%) and Rational Functions (58%) come next. Both polynomial units sit around 72%. These are early numbers from a small group of students, so treat them as a strong hint rather than the final word.

The numbers

Every marked answer to an MHF4U question on Martian Lab up to October 16, 2026, by unit. Trigonometric Functions and Combining Functions have no marked answers yet, so they are not ranked.

Unit	Marked answers	Right	Students
Exponential & Logarithmic Functions	18	39%	1
Trigonometric Ratios	20	50%	1
Rational Functions	26	58%	1
Polynomial Functions	90	72%	3
Polynomial Equations	102	73%	3

The polynomial units have the most answers by far, because they come first and that is where most students start practising. The three units at the top each come from one student, so one good night could move them. We will update this post as more answers come in.

1. Exponential & Logarithmic Functions

Logs are new notation for an idea you already know: a logarithm is just an exponent. The trouble is that the log laws look like algebra you can do on autopilot, and they are not. Most mistakes here are small rule slips, not big misunderstandings. Restrictions are the classic one. Try this question from the free test:

The restriction on

\log_2(x+2) + \log_2(x-2)

Show answer

x > 2

x \in \mathbb{R}

Each log needs its own argument to be positive, so both conditions have to hold at once. Combining the logs first and then checking only the product is how people end up with the wrong answer.

2. Trigonometric Ratios

This is where radians take over. The ideas are the MCR3U ones, but every angle is now a fraction of π, and the special angles, co-terminal angles and related angles all have to be fast. If you are still converting in your head one step at a time, the test runs out before you do.

Convert

680^{\circ}

into radians as an exact value (keep as an improper fraction).

Show answer

\dfrac{34\pi}{9}

3. Rational Functions

Rational functions ask you to read a lot off one equation: domain, zeros, holes, vertical and horizontal asymptotes. Each step is short. Mixing them up is easy, especially telling a hole from an asymptote when a factor cancels.

What is the horizontal asymptote of

f(x) = \dfrac{6-2x}{6x-3}

Show answer

y = \dfrac{-1}{3}

What about polynomials?

Polynomial Functions and Polynomial Equationsscore best, but they are not easy, they are just practised the most. They are also the base for everything after them: factoring, sketching from factored form and the factor theorem come back in rational functions and again in combining functions. Weak polynomial skills tend to show up later as a "hard" rational functions test.

How to study the hard units

Do one unit test cold, before you review, so you know which questions actually cost you marks.
For logs, write the law you are using next to each line. Slips get caught when the rule is on the page.
For radians, drill the special angles until you can write them without thinking, then do mixed questions.
For rational functions, run the same checklist on every function: domain, zeros, holes, asymptotes.
Redo every question you got wrong a few days later, without looking at the answer first.

Try the free MHF4U tests

Martian Lab has lessons and 115 practice tests for MHF4U, and the first test in every unit is free. No credit card required. There is also a free sample test on the MHF4U page.

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