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Grade 11 Challenge: Optimization & Rates of Change Worksheet with Answers
Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math
Unit 8: Going FurtherReal-World ChallengesChallenge
Real optimization problems — fencing, open boxes, ticket pricing, sliding ladders and inflating balloons. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.
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Practice Sheetaethelsystems.comChallenge: Optimization & Rates of Change
Grade 11 · Math
Name
Class
Date
Learning goal: Real-World Challenges
Directions: Solve each problem. Show your work, then write your answer in the box.
A ball's height is h(t) = −4.9t² + 24.5t + 1 metres, t seconds after it is thrown. What is its maximum height, in metres to 1 decimal place?
Answer: 31.6
- 1
A farmer has 388 m of fencing to enclose a rectangular field beside a straight river (no fence is needed along the river). What is the largest area she can enclose, in m²?
Show your workAnswer - 2
A farmer has 652 m of fencing to enclose a rectangular field beside a straight river (no fence is needed along the river). What is the largest area she can enclose, in m²?
Show your workAnswer - 3
A ball's height is h(t) = −4.9t² + 29.4t + 1 metres, t seconds after it is thrown. What is its maximum height, in metres to 1 decimal place?
Show your workAnswer - 4
A concert charges $24 a ticket and sells 360 tickets. Market research shows every $1 increase in price loses 10 sales. What ticket price maximizes revenue (in dollars)?
Show your workAnswer - 5
A ball's height is h(t) = −4.9t² + 14.7t + 2 metres, t seconds after it is thrown. What is its maximum height, in metres to 1 decimal place?
Show your workAnswer - 6
A farmer has 408 m of fencing to enclose a rectangular field beside a straight river (no fence is needed along the river). What is the largest area she can enclose, in m²?
Show your workAnswer - 7
A concert charges $10 a ticket and sells 600 tickets. Market research shows every $1 increase in price loses 20 sales. What ticket price maximizes revenue (in dollars)?
Show your workAnswer - 8
A ball's height is h(t) = −4.9t² + 24.5t + 3 metres, t seconds after it is thrown. What is its maximum height, in metres to 1 decimal place?
Show your workAnswer - 9
A ball's height is h(t) = −4.9t² + 19.6t + 2 metres, t seconds after it is thrown. What is its maximum height, in metres to 1 decimal place?
Show your workAnswer - 10
A concert charges $16 a ticket and sells 420 tickets. Market research shows every $1 increase in price loses 10 sales. What ticket price maximizes revenue (in dollars)?
Show your workAnswer - 11
A concert charges $23 a ticket and sells 860 tickets. Market research shows every $1 increase in price loses 20 sales. What ticket price maximizes revenue (in dollars)?
Show your workAnswer - 12
A farmer has 800 m of fencing to enclose a rectangular field beside a straight river (no fence is needed along the river). What is the largest area she can enclose, in m²?
Show your workAnswer
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Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/challenge_optimization
Answer key — Challenge: Optimization & Rates of Change (Grade 11)
- 1.18818
- 2.53138
- 3.45.1
- 4.30
- 5.13.0
- 6.20808
- 7.20
- 8.33.6
- 9.21.6
- 10.29
- 11.33
- 12.80000
Answer key (click to show)
- 1.18818
- 2.53138
- 3.45.1
- 4.30
- 5.13.0
- 6.20808
- 7.20
- 8.33.6
- 9.21.6
- 10.29
- 11.33
- 12.80000
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