AP Calculus AB Tutoring in Montreal

What AP Calculus AB covers

The College Board designs the course as “the equivalent of a first semester college calculus course devoted to topics in differential and integral calculus,” taught over a full year. Its eight units, with the share of the exam each one carries:

• Unit 1, Limits and Continuity: 10–15%
• Unit 2, Differentiation: Definition and Fundamental Properties: 10–15%
• Unit 3, Differentiation: Composite, Implicit, and Inverse Functions: 5–10%
• Unit 4, Contextual Applications of Differentiation: 10–15%
• Unit 5, Analytical Applications of Differentiation: 15–20%
• Unit 6, Integration and Accumulation of Change: 15–20%
• Unit 7, Differential Equations: 5–10%
• Unit 8, Applications of Integration: 10–15%

Across all eight, the course builds four practices: carrying out procedures, connecting representations, justifying a conclusion, and writing it in correct notation. On the exam a function may arrive as an equation, a graph, a table or a sentence, and at least two of the free-response questions are set in a real-world context.

The exam: Monday, May 10, 2027

The AP Calculus AB exam lasts 3 hours 10 minutes. It is a hybrid digital exam: multiple-choice questions are answered in the College Board's Bluebook testing app, and free-response questions are read there and answered by hand in a paper booklet.

• Section I, multiple choice: 42 questions in 1 hour 40 minutes, 50% of the score. Part A is 29 questions in 62 minutes with no calculator. Part B is 13 questions in 38 minutes, with a graphing calculator required for some of them.
• Section II, free response: 6 questions in 1 hour 30 minutes, 50% of the score. Part A is 2 questions in 30 minutes with a graphing calculator required. Part B is 4 questions in 60 minutes with no calculator.

Two things follow. The two no-calculator parts carry about two thirds of the score, so the algebra and the derivatives have to be quick by hand. And the multiple-choice section changes in May 2027: it used to be 45 questions in 1 hour 45 minutes, so a timed practice paper from an earlier year runs to a different count and a different clock.

Where the points go

The College Board's Course and Exam Description is frank about what costs students points, and its warnings make a good list of what to practise:

• Showing the structure. Estimating a derivative from a table needs the difference quotient written out; a product needs the product rule written out before the values go in. A correct number without that structure can lose the point.
• Checking hypotheses. Before the Intermediate Value Theorem, the Mean Value Theorem or L'Hospital's rule, the conditions have to be shown to hold, for example that both limits are 0 before L'Hospital's rule is applied.
• Naming the function. A justification has to say $f$, $f^{\prime }$ or $f^{″}$, never “it”, and must not read a feature of the graph of $f^{\prime }$ as if it belonged to $f$. “Increasing because it's going up” is the CED's own example of insufficient evidence.
• The chain rule. The CED calls it the target of many questions and a step in many more, and names missing it, in something like ${\sin }^{2}x$ or $e^{x^2}$, as a common error. It comes back in reverse in Unit 6, as substitution.
• Calculator answers. The setup, such as the integral with its limits and its differential, has to be on the page, and decimals are typically given to three places.

How sessions prepare for it

I'm Marius. We start with a short written diagnostic on what the course takes for granted. The College Board expects the equivalent of four years of secondary mathematics first; for a Quebec student that is Secondary 5 math in the TS or SN option, plus two things it handles differently or not at all: rational functions beyond $\frac{ax+b}{cx+d}$, with their holes and asymptotes, and interval notation, since Quebec writes $]-2,5]$ where AP writes $(-2,5]$. The diagnostic separates what is genuinely solid from what only looks solid, so sessions aim at the real gap.

After that, sessions follow the unit your class is on and the material it is actually testing. If you want work between sessions, you get a practice set written for exactly the topic we covered, and I mark it before we next meet, reading each error for what caused it. A short written recap goes to whoever books after every session: what we covered, what was handled unaided, what has been assigned and what comes next. Behind it sits a standing record with a dated route through the course and a short list of recurring slips to catch. Before the exam, we work through past-exam-style problems until the method is second nature. Practice problems, summaries and formula sheets are included in the session rate.

I sat a two-year diploma programme that ends in external exams, with higher-level mathematics, so preparing for an external exam is something I have done myself, not only taught. I meet students in person downtown and at public libraries such as the Grande Bibliothèque, or online on Zoom with a shared digital whiteboard. Sessions are booked and paid one at a time.

AP Calculus AB and CEGEP Calculus I and II

Units 1 to 5 line up almost one for one with CEGEP Calculus I, which the ministry's Science program defines as differential calculus. Units 6 to 8 (antiderivatives, the definite integral, differential equations, area and volume) are CEGEP Calculus II, integral calculus. Calculus II then goes further than AB: integration by parts, trigonometric substitution, improper integrals and infinite series are all in the CEGEP course, and none of them is in AB. A student who took AB and goes on to CEGEP Science meets those there for the first time; the CEGEP calculus tutoring page covers that course.

When families usually get in touch

Usually at one of four points: the first weeks, when limits and the definition of the derivative replace the algebra the student was good at; after a first unit test or report card that comes back lower than expected; the turn to integration in Unit 6; and the months before May, while there is still time to practise all eight units against the exam's own format. Starting earlier lets the spring go to exam practice rather than to repairs.

There is a free worksheet for each of the eight units below, written to the College Board's framework topic by topic, and trying one is a quick way to see which unit needs attention first.

Free practice worksheets

Every practice sheet is free to print, with no sign-up.

• AP Calculus AB worksheets: 8 sets

For parents

• Helping with AP Calculus when you don't remember calculus
• Should my teen take AP Calculus in high school? Questions to ask

Topics explained, with a self-check

• From the graph of f′ to the graph of f: what each feature means
• Left, right, midpoint, trapezoid: which sums over- or underestimate
• Removable, jump or infinite: telling discontinuities apart
• The Mean Value Theorem in one picture, and the two conditions it needs

Common questions

Tutoring at other levels

• High school math tutoring in Montreal
• Secondary 4 and 5 math tutoring in Montreal
• CEGEP Science calculus and linear algebra tutoring in Montreal
• University math and science courses