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AP Calc Summer Prep: A 20-Minute-a-Day Plan

Walk in ahead without taking a summer course.

You do not need a summer course to be ready for AP Calculus, and you should not spend July teaching yourself derivatives — your teacher will do that better in the fall. What actually predicts your calc grade is precalculus fluency: the algebra, functions, and trig that every calculus problem is built on. Twenty focused minutes a day of problems — not videos — is enough, because math is learned by reps.

The plan

Weeks 1–2 · Algebra fluency. Fractions, distribution, factoring (including special forms), exponents. Goal: zero hesitation. Sign errors and fraction slips are the #1 point-loser in calculus. Start with our precalculus review problems.

Weeks 3–4 · Functions and trig. Piecewise evaluation, composition (the chain rule's prerequisite), average rate of change, then the unit circle in radians until it's automatic. Drill functions and trig review.

Week 5 · Exponentials and logs. Log properties and solving exponential equations — see the logarithm problems.

Weeks 6+ · A head start on limits. The one calculus topic worth previewing, because it's really precalc in disguise: substitution, factoring, and reading one-sided behavior. Work the limits practice problems — if those feel comfortable, day one of AP Calc will feel like review.

How to practice: do problems until you miss, then drill that exact skill until you stop missing. The six checkpoints below — one per phase — tell you where your plan should start.

Checkpoint problems

Problem 1

Factor

16 x^{2} - 16

Problem 2

x f (x) - 5 - 3 - 4 - 5 - 2 5

Compare the average rate of change of

f

over the two intervals

Problem 3

For large

x

, which is eventually greater:

f (x) = 2^{x}

g (x) = x^{3}

Problem 4

x \to 4 lim \frac{x ^{2} - 2 x - 8}{x - 4}

Problem 5

x \to 0 lim \frac{tan ( 5 x )}{x}

Problem 6

f (x) = ⎩ ⎨ ⎧ \frac{18 - 2 x ^{2}}{x + 3} k x \neq = - 3 x = - 3

What value of

k

makes

f

continuous at

x = - 3

Want more than 6 problems?

These are fixed examples. Lodera is an adaptive question bank for AP Calculus AB and Precalculus that never runs out: miss a question and it serves you variations of the same skill until it sticks. Every problem is generated from a template and solved by a computer algebra system — exact answers, no AI-written solutions. 10 free questions a day, forever.

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