Helping with AP Calculus when you don't remember calculus

Your job is not to teach it

What makes a student good at calculus is rarely knowing more formulas. It is choosing a method without being told which one, carrying it through, and explaining why the answer is right. You can check all three without following a line of the algebra.

So the useful role is closer to a coach than a teacher. You ask, your teen answers, and you listen for whether the answer is clear. If you find yourself working through a solution together, step back: the thinking you are doing is the thinking your teen needs to do.

Questions you can ask without knowing the answers

1. “How did you know which method to use?” In the textbook, the method is the title of the section. On a test it is not, and choosing it is half the work.
2. “What does this answer mean?” Much of calculus is about rates of change. When an answer is a rate, ask what is changing, whether it is going up or down, and in what units. A student who understands can say it in one sentence.
3. “How would you convince a marker?” The College Board lists “justifying reasoning and solutions” among the course's skills. On the free-response questions, the reason written in words earns marks of its own.
4. “Was this one with or without a calculator?” On the AP exam, the parts where no calculator is allowed carry more than two thirds of the score. Homework done entirely on a calculator does not prepare for them.
5. “Can you do one without looking at the example?” Pick a question at random, close the notes, and see whether your teen can start.
6. “Explain it to me in two minutes.” You will not follow every step, and you do not need to. Listen for whether the explanation goes somewhere in order, or goes round in circles.
7. “What is the next test on, and which part feels shaky?” The answer tells you where the coming week's practice should go.

Real practice, or rereading?

Rereading feels like studying, which is why it is so easy to mistake for it. From across the room the two look the same, so here is how to tell them apart.

Looks like work, tests nothing

• Reading the notes again, or highlighting them.
• Watching a solution video and nodding along.
• Copying a worked example with the numbers changed.
• Checking the answer after every line.
• Doing only the questions from the section just taught.

Real practice

• A question tried with the notes closed, written out in full, and only then checked.
• Questions mixed from several units, so the method has to be chosen rather than read off the chapter heading.
• Some of it timed, and some of it without a calculator.
• Mistakes redone a few days later, not just read over.
• Questions in the exam's own style. The College Board publishes the free-response questions from the past three exams, with scoring guidelines and sample student answers. The scoring guidelines show where the marks actually go.

The free AP Calculus AB worksheets are one set per unit, with questions on every topic in it, printable and with no sign-up. Hand one over with the notes put away, and the first few questions will tell you how the unit really went.

A week that works

• Short and often. Several half-hour sittings through the week do more than one long evening before the test.
• Old with new. A few questions from an earlier unit in every sitting, so nothing is learned once and dropped.
• One closed-book set before each test, done in one go, then marked.

When it is time to bring someone in

Signs that the gap is bigger than homework time can close:

• The same kind of mistake keeps coming back after it was corrected.
• Homework takes far longer than it used to, or gets copied from the solutions.
• Test marks sit well below homework marks, unit after unit.
• The trouble is in the algebra or trigonometry underneath. Calculus leans on the algebra, functions and trigonometry of Secondary 4 and 5 all at once, and a shaky prerequisite often sounds like “I don't get calculus”.
• Your teen has stopped asking questions in class.

Timing matters. Each AP unit builds on the ones before it, so a gap found in the fall is far easier to close than the same gap found in April, with the exam on Monday, May 10, 2027.

If you bring me in, we start with a written diagnostic: a short paper that separates the prerequisites that are genuinely solid from the ones that only look solid, so the sessions go to the real gap. Practice between sessions, if you want it, is set on the exact topic and marked before we next meet. After every session, a written recap goes to whoever booked it: what was covered, what your teen handled unaided, what has been assigned and what comes next. You can follow the progress without following the calculus. Sessions are in person in Montreal or on Zoom.

Free AP Calculus AB worksheets for closed-book practice

• AP Calculus AB Unit 1: Limits and Continuity worksheet
• AP Calculus AB Unit 2: Definition of the Derivative and the Basic Rules worksheet
• AP Calculus AB Unit 4: Rates of Change and Related Rates worksheet