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Generator Worksheets by grade Printables Blog Pricing

Generator Worksheets by grade Printables Blog Pricing

Math Sheet Studio

Printable math worksheets you can fix one question at a time.

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Generator Pricing All topics By Common Core standard Blog

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Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Algebra 1 Geometry Algebra 2 Calculus

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Build a worksheet

Changes apply to unlocked questions.

Describe it

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

Templates

Start from a template

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

Choose 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.

Number of questions

Difficulty

Easy to hard within each section

A rectangle with a fixed perimeter

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Working space

Points

Prints the total on the score line and a scoring table on the answer key.

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.

Customize sections

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. Optimization problems

Questions

Difficulty

Planned: 12 / 60 questions

12 questionsSign in to download PDFsSettingsShow answers

Name ______________________Date ____________Score ____ / 12

Optimization problems practice

Optimization problems · 1–12

Use derivatives to find the maximum.

Medium

1.A rectangle has a perimeter of 180 m. What is the largest possible area?

Medium

2.A rectangle has a perimeter of 132 m. What is the largest possible area?

Medium

3.A rectangle has a perimeter of 112 m. What is the largest possible area?

Medium

4.A rectangle has a perimeter of 40 m. What is the largest possible area?

Medium

5.A rectangle has a perimeter of 32 m. What is the largest possible area?

Medium

6.A rectangle has a perimeter of 52 m. What is the largest possible area?

Medium

7.A rectangle has a perimeter of 152 m. What is the largest possible area?

Medium

8.A rectangle has a perimeter of 84 m. What is the largest possible area?

Medium

9.A rectangle has a perimeter of 100 m. What is the largest possible area?

Medium

10.A rectangle has a perimeter of 24 m. What is the largest possible area?

Medium

11.A rectangle has a perimeter of 92 m. What is the largest possible area?

Medium

12.A rectangle has a perimeter of 96 m. What is the largest possible area?

Answer key — Optimization problems practice

Optimization problems

1.2025 m²

2.1089 m²

3.784 m²

4.100 m²

5.64 m²

6.169 m²

7.1444 m²

8.441 m²

9.625 m²

10.36 m²

11.529 m²

12.576 m²

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