Calculus practice problems from your own lectures
Upload your calculus lectures and StudyPDF writes new practice problems from them, in your course's own notation: limits, derivatives, integrals and series.
- Math stays intact in the viewer, the PDF and Anki
- Blank worksheet with the answer key on its own page
- Timed practice exam, graded when you submit
Where does most of a cell's ATP come from?
- AGlycolysis
- BThe electron transport chain
- CThe Calvin cycle
On this page
Problems that match your calculus course
StudyPDF makes calculus practice problems from your own lectures. You upload your slides or notes, pick a lecture or a topic such as limits, derivatives, integrals or series, and get new problems in the notation your instructor uses, each with an explanation and the page it came from.
Search for calculus practice problems and you get university problem lists, textbook PDFs and Paul's Online Notes. They are good, they are free, and they are fixed: someone else's order, someone else's notation, and once you have solved them there are no more. Keep using them. StudyPDF adds the one thing a public list cannot, which is problems from the course you are actually sitting.
What a set looks like
Say you upload your Calculus I notes and scope a quiz to the lecture on the chain rule: 10 problems, medium difficulty. Each item is tagged with the concept it tests and cites the page it came from. Here are two items to show the shape. The exact problems depend on your material.
Problem 3, short answer
- Problem
- Differentiate f(x) = x^2 sin(3x), then find f'(0).
- Model answer
- f'(x) = 2x sin(3x) + 3x^2 cos(3x), so f'(0) = 0.
- Concept
- Product rule and chain rule
- Source
- Lecture 6, page 4
Problem 7, multiple choice
- Problem
- The limit of sin(5x) / (3x) as x approaches 0 is
- Options
- A) 0, B) 1, C) 5/3, D) it does not exist
- Correct
- C
- Why
- Sin(5x) / (3x) = (5/3) * sin(5x) / (5x), and sin(u) / u tends to 1 as u tends to 0.
A set mixes types. Multiple choice and true or false suit concepts, short answer suits the work-it-out problems, and you grade those yourself against the model answer. Fill-in-the-blank and matching work well for rules and definitions.
Print a worksheet or sit a timed exam
For paper practice, export the set as a PDF. The problems come blank and the answer key sits on its own page, so you can work with a pen and check afterwards. A Word export is there if you want to rewrite a problem.
Formulas stay formulas. Math written in LaTeX shows as proper math in the viewer, in the PDF and in an Anki deck, not as raw dollar signs. That matters for flashcards on rules like the quotient rule or the standard integrals, which export to Anki with the math intact.
For exam conditions, make a practice exam from the same scope. It is split into sections, you can set a timer, you get no feedback until you submit, and then a graded report shows the result per section. Calculus exams reward speed on the routine problems, so time yourself on limits and derivatives before you try the hard ones.
Let your mistakes pick the next set
After a set, the results break down by concept, weakest first. You do not just see 7 out of 10. You see that the chain rule and integration by parts cost you the points, and the next set can start from exactly those concepts.
If a model answer does not make sense, open Bo next to the problem and ask why. Bo sees the problem on screen and what you answered, so a bare "why?" is enough, and the explanation comes from your own lecture pages, not from the open internet.
What this does not do
The problems are generated, and generated math can be wrong. Check the answer key against your lecture or a solution you trust before you rely on it. Short answers are self-graded against a model answer, so you compare your steps with it rather than getting a verdict.
The problems are only as rich as your material. Slides with two worked examples per topic give simpler sets than full lecture notes or a textbook chapter.
They are not official AP or exam questions, and StudyPDF is not affiliated with any exam body. And a set is no replacement for a book of a thousand drill problems if sheer volume is what you need. Use one next to your course sets.
How to make calculus practice problems
Four steps from your lecture notes to a set you can solve or print.
- 1
Upload your calculus material
Add lecture slides, your own notes, a scan of handwritten notes, or a problem set from class. Free takes up to 3 files per upload and 300 pages per file.
- 2
Choose what to practice
Press New material and pick Quiz. Scope it to one lecture, a topic such as related rates, or your weakest concepts, then set the number of problems and the difficulty.
- 3
Solve and check
Work through the problems. Each one comes with an explanation and the page of your material it is based on.
- 4
Print it or sit it as an exam
Export a blank worksheet with the answer key, or turn the same scope into a timed practice exam that is graded only when you submit.
What you get
Practice that follows your course, not a fixed problem list you finish and then run out of.
- New problems every time, not one fixed set
- Scoped to one lecture, one topic or your weak concepts
- An explanation and the source page for every problem
- Free to start, no credit card
Quiz yourself on your own material.
Upload one lecture or chapter and answer your first questions.
Questions and answers
Where can I find calculus practice problems with answers?
Free lists exist, such as Paul's Online Notes and university problem pages, and they are worth using. If you want problems that follow your own course, upload your lectures to StudyPDF and make a set with a model answer for each problem and an answer key you can print.
Can I get calculus practice problems as a PDF with an answer key?
Yes. Export a set as a PDF worksheet: the problems come blank and the answer key sits on its own page. A Word export is also available if you want to edit the problems.
What is the easiest calculus problem?
A common first one is the derivative of x^2, which is 2x by the power rule, or a limit you can solve by substituting the number. In StudyPDF you can set the difficulty low to start there, then raise it to multi-step problems such as related rates or integration by parts.
4 more questions
What is the hardest question in calculus?
There is no single one. The hard problems are usually the ones that combine several techniques, like an optimization problem that needs implicit differentiation, or a series that needs more than one convergence test. Set the difficulty high and scope the set to the topic you struggle with to get that kind of problem from your own material.
Are the answers always correct?
No tool is perfect, and generated math can contain mistakes. Every problem cites the page of your material it is based on, so you can check it, and you should compare the answer key with your lecture or a solution you trust. Short answers are self-graded against a model answer.
Are these AP Calculus or official exam questions?
No. StudyPDF is not affiliated with the College Board or any exam body and does not use official questions. It writes new problems from the material you upload. For AP-style practice from a fixed bank, the site also has an AP Calculus AB practice test.
Is it free?
StudyPDF is free to start, no credit card, and Free gives you about 4 materials a week. Free takes up to 3 files per upload and 300 pages per file. You only upgrade if you need more weekly credits during exam season.