Optimization Quiz
10 questions · easy to harder · Calculus 1 · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 5 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Two positive numbers multiply to 64. Find the smallest possible sum.- A) 16
- B) 1
- C) 64
2 Question 2
Two positive numbers have a product of 49. Find the smallest possible sum.Type the answer.
3 Question 3
A rectangle has an area of 100 cm². Find the smallest perimeter.- A) 2 cm
- B) 100 cm
- C) 40 cm
- D) 200 cm
4 Question 4
A rectangular garden of 50 m² is fenced on three sides. A wall is the fourth side. Find the least fencing needed.Type the answer.
5 Question 5
A rectangular pen of 72 ft² is fenced on three sides. A barn is the fourth side. Find the least fencing needed.- A) 24 ft
- B) 72 ft
- C) 2 ft
- D) 36 ft
6 Question 6
A shop sells 300 cakes a day at $5 each. For every $1 it adds to the price, it sells 20 fewer cakes. What price gives the most money?Type the answer.
7 Question 7
A square sheet of card is 12 cm by 12 cm. A square is cut from each corner and the sides are folded up to make an open box. Find the largest volume.- A) 128 cm³
- B) 0 cm³
- C) 6 cm³
8 Question 8
A square sheet of metal is 18 cm by 18 cm. A square is cut from each corner and the sides are folded up to make an open box. Find the largest volume.Type the answer.
9 Question 9
An open box with a square base must hold 32 cm³. Find the least material needed.- A) 32 cm²
- B) 4 cm²
- C) 48 cm²
- D) 128 cm²
10 Question 10
An open box with a square base must hold 108 cm³. Find the least material needed.Type the answer.