Calculus Worksheet Maker (Derivatives · Integrals)
Generate derivative and integral practice — polynomials, product and chain rule, indefinite and definite integrals — by level, with answer keys, to print or save as PDF
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Makes printable calculus practice sheets with an answer key: derivatives of polynomials, products, quotients and powers, indefinite and definite integrals, areas, extrema and motion on a line. Use it for homework sets, quizzes and drill before a test.
How to use
- Choose a "Level" and, where offered, the "Problem types". "Trig, exponential and log" is off until you turn it on.
- For polynomial problems, set the "Lowest degree", "Highest degree", "Most terms" and "Coefficients".
- Under "Sheet", set the "Number of problems" (1 to 100), "Columns", "Text size" and "Working space".
- Press "Make a new sheet" for different problems, then "Save as PDF" or "Print". The answer key pages follow the questions.
How it works
- Answers are exact: expanded polynomials with whole or fractional coefficients, and definite integrals and areas as whole numbers or fractions with a denominator of 12 or less.
- Problems are built so the answer comes out clean: definite integrals of polynomials have whole-number limits, areas use curves whose x-intercepts are whole numbers, and cubic functions for extrema have whole-number critical points.
- Quotient rule answers keep the denominator squared, such as (x + 2)², with the numerator multiplied out. Product rule answers add the step u′v + uv′ under the answer.
- The same "Sheet number" and settings always make the same sheet. Settings are kept in this browser.
Questions and answers
- How do I make a power rule worksheet?
- Choose "Derivatives 1 · power rule" and set the degree range, for example 2 to 5. Each problem is a polynomial and the answer is its derivative, such as 15x⁴ + 9x² for 3x⁵ + 3x³.
- Are the area answers exact?
- Yes. The curve is split at its x-intercepts and each part is integrated with exact fractions, so the area of y = x² − 1 between x = −1 and x = 1 is given as 4/3.
- Can I include sine, cosine, eˣ and ln?
- Yes. Turn on "Trig, exponential and log" at "Derivatives 3" or "Trig, exponential, 1/(ax + b)" at "Integrals 3". Definite integrals of sine and cosine use limits such as π/2.
- Does the sheet include the constant of integration?
- Yes. Indefinite integral answers end in + C, and the instruction states that C is the constant of integration.