Pre-Calculus 11 tutoring

If your child is in Pre-Calculus 11 right now

Pre-Calculus 11 has a reputation among parents for a reason. It is very often the first course where a student who has always been "fine at math" starts coming home frustrated. Homework takes twice as long as it used to. Test marks slip in a way that feels sudden. Nothing about the student has changed — the demands of the course have.

The shift is that grade 11 math stops rewarding memorised recipes. Questions combine two or three ideas at once, they are phrased less predictably, and the algebra underneath them has to be automatic so the student's attention is free for the actual thinking. If any part of that algebra is still effortful, the whole course feels overwhelming even when the student understands the new concepts perfectly well.

What the course covers

In plain terms, this is the year students move from working with straight lines to working with curves, and from single-step algebra to multi-step algebra. The mathematics involved is stable and worth knowing regardless of curriculum wording: quadratic relationships and the shapes they describe, roots and radicals, expressions written as fractions with variables in them, systems of equations, sequences and series, absolute value and reciprocal relationships, and the beginnings of trigonometry beyond right triangles.

Much of the year is spent on quadratics in one form or another — factoring them, completing the square, graphing them, and solving real situations that turn out to be quadratic underneath. Students also learn to be careful in a new way: to check whether an answer is actually allowed, since radicals and rational expressions both have values that break them.

Where students commonly get stuck

Factoring is the first place things break. Students learn one factoring pattern at a time and cope, then meet a mixed exercise set and cannot tell which pattern a question wants. We teach recognition explicitly, so choosing the method stops being guesswork.

Completing the square is the second. It is the step where a lot of students decide the course is arbitrary, because the procedure looks like it comes from nowhere. Once a student sees the geometric idea behind it, it becomes one procedure instead of six memorised lines.

Rational expressions are the third, and they are almost always an old problem wearing a new costume — a student who is shaky on fractions with numbers will struggle with fractions containing variables. Non-permissible values, restrictions on radicals, and extraneous solutions are all versions of the same habit: checking whether an answer is legal. Finally, word problems that turn into quadratics catch out students who can solve the equation perfectly but cannot build it from a paragraph.

How sessions are structured for this course

We start by finding out which of those sticking points is actually the problem, because "struggling in Pre-Calculus 11" almost never means all of them. A short diagnostic on factoring and fraction work usually reveals it within one session.

From there, sessions run on two tracks at once. One track repairs the underlying algebra so the student stops losing marks to mechanics. The other keeps them current with whatever their class is doing this week, so they are not falling further behind while we backfill. Before unit tests we shift into targeted review: mixed problem sets, timed practice, and the specific question types that student tends to lose marks on.

Students meet us in person across Metro Vancouver or online over Zoom with an interactive whiteboard, which suits this course well — most of the work is written out step by step, and both people can write.

Related pages

This course sits inside our broader math tutoring. Other math courses we support:

• Pre-Calculus 12 tutoring
• Foundations of Math and Pre-Calculus 10 tutoring