Find free calculus practice check-ins, worked lessons and calculators for limits, derivatives and integrals. Start with the topic you are studying, review your reasoning, then use the matching lesson to work through a mistake. The check-ins open on this page; they are short skill checks, not full-length exams or a downloadable worksheet collection.
Calculus Online Center
Free Calculus Practice and Lessons
Build your understanding of limits, derivatives and integrals with free short practice check-ins, worked lessons and calculators. Choose a topic below, then review the steps behind a mistake. These skill checks are independent study resources, not full-length AP exams.
See the idea first
Look at the picture before the formula. Strong math starts when the symbols match something you can see.
Free calculus practice: choose a short skill check.
No need to read everything at once. Start with a small check-in, notice the part that feels shaky, and study that one skill with focus.
Listen to the limit
Try substitution first, then decide whether the expression needs simplifying or one-sided thinking.
Check continuity gently
Look for the value, the limit, and whether they agree. That three-part check catches most mistakes.
Differentiate with a reason
Choose the rule because of the structure you see: power, product, quotient, trig, logarithmic, or implicit.
Use derivatives in context
Connect slope, tangent lines, curve behavior, optimization, and related rates to the story in the problem.
Make integrals meaningful
Think of antiderivatives, area, accumulation, and total change as connected versions of the same idea.
Review advanced topics calmly
Practice convergence tests and series ideas by asking what the terms are doing over the long run.
Pick the lesson you need today
Use this as your study map. The order moves from foundations to mixed problem solving, but you can also jump straight to the skill that is blocking you right now.
59 guided lessons and tools
Limits and continuity
Derivatives and tangent lines
- Derivative Calculator
- Rules of Differentiation
- Power Rule of Differentiation
- Product Rule of Differentiation
- Quotient Rule
- Derivative of a Trigonometric Function
- Trigonometric Reciprocals
- Derivative of Logarithmic Functions
- Derivative of Radicals
- Implicit Differentiation
- Second Derivatives
- Tangent Line Calculator
Applications of derivatives
Integrals and accumulation
- Integral Calculator
- Definite Integral
- Properties of Definite Integrals
- Rules of Integral
- Power Rule of Integration
- Integral of Radicals
- Integration by Parts
- Partial Fractions Technique
- Trigonometric Integrals
- Exponential and Logarithmic Integrals
- Improper Integrals
- Fundamental Theorem of Calculus
- Arc Length Using Integration
- Cumulative Growth
Series, polar topics, and advanced review
Formulas with meaning
Do not rush this section. Read one formula, say what it measures in plain English, then work one example where that formula actually helps.
lim f(x) is the value f(x) approaches as x gets close to a pointCompare what f(x) approaches from the left and right. A two-sided limit needs both sides to approach the same value; f(a) itself may be different.
f'(x)=lim[h->0] (f(x+h)-f(x))/hThe difference quotient measures average change over a small interval. Its limit, when it exists, gives the tangent slope and instantaneous rate at x.
d/dx x^n = n x^(n-1)Multiply by the exponent, then reduce the exponent by one. For x³, the derivative is 3x². Check the domain when powers are negative or fractional.
(fg)'=f'g+fg'Differentiate each factor once while leaving the other unchanged, then add. Multiplying the two derivatives does not give the product derivative.
(f/g)'=(f'g-fg')/g^2Keep the numerator order f′g − fg′, and square the denominator. This rule applies where g is not zero and both derivatives exist.
Integral from a to b of f(x) dx = F(b)-F(a) when F'=fFor continuous f on [a,b], evaluate an antiderivative at the upper endpoint and subtract its value at the lower endpoint. A definite integral measures signed accumulation.
Helpful tools when you get stuck
Use these after you try a problem on your own. They are best for checking steps, seeing a pattern again, or building a longer review plan.
Limit Calculator
Use this to compare your limit method with the steps, especially when direct substitution is not enough.
Derivative Calculator
Differentiate first on your own, then compare the rule choice and simplification with the guided steps.
Integral Calculator
Check antiderivatives, definite integrals, and area-style problems after you write the meaning in words.
Ultimate Calculus Course
Open this when you want a broader worksheet-and-review path after practicing the focused skills here.
Common mistakes we can fix early
Treating every limit like plug-and-chug
Try substitution first, but if it gives 0/0 or another indeterminate form, that is a signal to simplify, not a final answer.
Missing the chain rule idea
When one function sits inside another, differentiate the outside and multiply by the inside derivative. Mark the inside function before you start.
Mixing derivative and integral meaning
A derivative is instant rate of change. An integral is accumulation across an interval. Naming the meaning prevents many wrong setups.
Leaving answers without context
For applications, name the units: slope, velocity, area, total change, or accumulated amount. That turns a number into an answer.
A practical study plan
If time is short, do not try to read every lesson in one sitting. Use a check-in first, then spend your energy on the weakest skill.
Match the review to your course. For a first calculus course, begin with limits, differentiation and integration, then follow your instructor’s syllabus. AP students can check the official AP Calculus AB outline or AP Calculus BC outline: BC includes additional work with parametric and polar functions, sequences and series. The short checks here support topic review; use official AP materials for exam-format practice.
Limits
Limits, continuity, and the meaning of approaching a value before you ever touch a derivative rule.
Derivative rules
Derivative rules, tangent lines, and curve behavior, with a sentence explaining why each rule applies.
Applications: optimization
Applications: optimization, related rates, motion, and graph analysis with units written beside every answer.
Integrals
Integrals, area, accumulation, and the Fundamental Theorem, always tied back to total change.
Mixed review
Review the topics on your course syllabus and revisit errors without looking at the solution. Add series, polar or parametric work only when your course includes it.
Need a book alongside the free lessons?
Use a book when you want a longer sequence of explanations and written practice. Our comparison of five calculus books separates beginner explanations, worked-problem practice and AP preparation, so you can choose for the task you need help with.
For an Effortless Math digital option, preview the current Calculus for Beginners PDF before purchasing. Its approved preview shows functions and limits/continuity in the contents. Check the current edition, format, price and delivery details on the product page; paperback listings in the comparison are separate purchase paths and may be different editions.
Questions students usually ask
What is the best order to study calculus?
Study limits, derivatives, applications and integrals in the order your course uses. Add series or other advanced topics when they appear on your syllabus. Review algebra and functions when those steps are the source of an error.
Why do calculus problems feel so different from algebra?
Calculus asks what happens as a value changes. Keep asking whether the problem is about approaching, changing instantly, or accumulating.
How should I practice before a test?
Do one mixed set each day: one limit, two derivative-rule problems, one application, one integral, and one explanation written in words.
Keep the next study session focused.
Choose one check-in, open the matching lesson, and write down the smallest skill that still feels shaky. That is the next win.
Limits Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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No. It is indeterminate, which means the expression needs more work before you decide.
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5. Substitution works here because the function is continuous at x=2: 2^2+1=5.
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It checks what the function approaches from only the left or only the right. If the two sides disagree, the two-sided limit does not exist.
Continuity Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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f(a) exists, the limit exists, and the limit equals f(a). I like to check these in that exact order.
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A hole. The graph wants to connect there, but the function value is missing or placed incorrectly.
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No. The function cannot be continuous if the graph approaches two different values.
Derivative Rules Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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5x^4. The power rule brings the exponent down, then subtracts 1 from the exponent.
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The product rule: f'g+fg'. Use it when two changing expressions are multiplied together.
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cos(x). This is one of the core trig derivatives worth knowing cold.
Derivative Applications Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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The slope of the tangent line at x=a. In words, it tells you the instant rate of change there.
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The graph is concave up. You can picture the curve opening upward like a smile.
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Define the quantity to maximize or minimize. Then rewrite it using one variable before taking the derivative.
Integrals Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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x^3+C. Differentiate x^3+C to check: you get 3x^2.
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Net signed area or accumulated change. Always ask what the units mean in the original problem.
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The Fundamental Theorem of Calculus. It is the bridge between rate of change and accumulated change.
Series and Advanced Review Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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The series diverges. This is a quick first check before using a more detailed test.
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The p-series test. It is a helpful benchmark for many convergence questions.
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Functions near a chosen center. The closer you are to the center, the more useful the approximation usually is.
A USEFUL NEXT STEP
Calculus Math: study questions
What can I study in this Calculus Math Online Center?
Review limits and continuity, derivative rules and applications, integrals and accumulation, plus advanced topics when your course includes them. The page provides six short practice check-ins, linked worked lessons and calculators; the check-ins are not full-length exams.
How should I use the Calculus Math resources?
Choose a topic or practice activity from this Online Center. Review the linked explanation, try the practice, and use the result to decide what to study next. Check each resource’s directions for its format and access requirements.
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