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Generator Worksheets by grade Printables Blog Pricing

Math Sheet Studio

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We pick the skills and settings; every question and answer is still computed, so the key stays correct.

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Unit test: 20 questions, easy to hard, 2 points each, roomy spacing. Keeps your selected skills.

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Limits

Limits by direct substitutionLimits by factoring (0/0 forms)Limits at infinityOne-sided limits and continuity

Derivatives

Derivatives with the power ruleThe product and quotient rulesThe chain ruleDerivatives of trigonometric, exponential and logarithmic functionsEquations of tangent lines

Applications of derivatives

Critical points, extrema and increasing intervalsPosition, velocity and accelerationOptimization problemsRelated ratesConcavity and inflection points

Integrals

Indefinite integrals (antiderivatives)Definite integralsIntegration by substitutionArea between curvesRiemann sums and the trapezoidal rule

Differential equations

Differential equations: initial value problemsExponential growth and decay models (dy/dt = ky)

Each skill gets its own section. Up to 8 skills per sheet.

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Number optionsNo negative numbersWhole-number answers only (no fractions or decimals)

Largest number in a question

Applies to new and unlocked questions. Questions you edited by hand are left as typed.

Step-by-step answer keyPro: each answer shows its working in the PDF.QR code for the answersPrints a code that opens the answer key on a phone, so work can be checked at home.

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Set each section’s count and difficulty. Use the arrows to change its position. Locked questions stay in selected sections; unlock them to reduce counts or change their difficulty.

1. Related rates

Questions

Difficulty

Planned: 12 / 60 questions

12 questionsSign in to download PDFsSettingsShow answers

Name ______________________Date ____________Score ____ / 12

Related rates practice

Related rates · 1–12

Find the rate. Give answers with π in terms of π.

Medium

1.The radius of a circle grows at 2 cm/s. How fast is its area growing when the radius is 9 cm?

Medium

2.The radius of a circle grows at 4 cm/s. How fast is its area growing when the radius is 8 cm?

Medium

3.The radius of a circle grows at 3 cm/s. How fast is its area growing when the radius is 10 cm?

Medium

4.The radius of a circle grows at 2 cm/s. How fast is its area growing when the radius is 12 cm?

Medium

5.The radius of a circle grows at 2 cm/s. How fast is its area growing when the radius is 3 cm?

Medium

6.The radius of a circle grows at 1 cm/s. How fast is its area growing when the radius is 9 cm?

Medium

7.The radius of a circle grows at 3 cm/s. How fast is its area growing when the radius is 11 cm?

Medium

8.The radius of a circle grows at 5 cm/s. How fast is its area growing when the radius is 2 cm?

Medium

9.The radius of a circle grows at 3 cm/s. How fast is its area growing when the radius is 5 cm?

Medium

10.The radius of a circle grows at 2 cm/s. How fast is its area growing when the radius is 11 cm?

Medium

11.The radius of a circle grows at 4 cm/s. How fast is its area growing when the radius is 9 cm?

Medium

12.The radius of a circle grows at 5 cm/s. How fast is its area growing when the radius is 9 cm?

Answer key — Related rates practice

Related rates

1.36π cm²/s

2.64π cm²/s

3.60π cm²/s

4.48π cm²/s

5.12π cm²/s

6.18π cm²/s

7.66π cm²/s

8.20π cm²/s

9.30π cm²/s

10.44π cm²/s

11.72π cm²/s

12.90π cm²/s

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