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Grade 12 Challenge: Optimization & Rates of Change Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 6: 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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Challenge: Optimization & Rates of Change

Grade 12 · Math

Score___ / 12

Name

Class

Date

Learning goal: Real-World Challenges

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Equal squares are cut from the corners of a 18 cm × 18 cm sheet of card and the sides folded up to make an open box. What is the largest possible volume, in cm³?

Answer: 432

1
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 work
Answer
2
A concert charges $11 a ticket and sells 575 tickets. Market research shows every $1 increase in price loses 25 sales. What ticket price maximizes revenue (in dollars)?
Show your work
Answer
3
A closed cylindrical can must hold 500 cm³. To use the least metal, what should the ratio height ÷ radius be?
Show your work
Answer
4
A concert charges $24 a ticket and sells 1150 tickets. Market research shows every $1 increase in price loses 25 sales. What ticket price maximizes revenue (in dollars)?
Show your work
Answer
5
A 10 m ladder leans against a wall. Its foot slides away from the wall at 3 m/s. How fast is the top sliding down the wall when the foot is 6 m from the wall? Give an exact answer in m/s.
Show your work
Answer
6
A 15 m ladder leans against a wall. Its foot slides away from the wall at 1 m/s. How fast is the top sliding down the wall when the foot is 9 m from the wall? Give an exact answer in m/s.
Show your work
Answer
7
A closed cylindrical can must hold 1000 cm³. To use the least metal, what should the ratio height ÷ radius be?
Show your work
Answer
8
A farmer has 760 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 work
Answer
9
A closed cylindrical can must hold 355 cm³. To use the least metal, what should the ratio height ÷ radius be?
Show your work
Answer
10
A ball's height is h(t) = −4.9t² + 9.8t + 1 metres, t seconds after it is thrown. What is its maximum height, in metres to 1 decimal place?
Show your work
Answer
11
A farmer has 296 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 work
Answer
12
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 work
Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/challenge_optimization

Answer key (click to show)

1.13.0
2.17
3.2
4.35
5.9/4
6.3/4
7.2
8.72200
9.2
10.5.9
11.10952
12.21.6

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