BISHOP ALLEN ACADEMY
MCV 4U
D. Trentadue
Unit 3:
Optimization
TEST
Name:
Date:
Knowledge/
Thinking/Inquiry/
Communication
Understanding Problem Solving
MARK BREAKDOWN
/ 15
Application
/4
Instructions: Show all your work in the space provided to receive full marks. Complete solutions are required.
A total of 4 marks for Communication will be awarded for proper mathematical form and notation.
THINKING, INQUIRY, PROBLEM SOLVING: (20 marks)
1) A gymnasium is designed with a movable partition that extends between the two long sides of the gym. If
the total perimeter (including the partition) is to be 90 m, what dimensions will maximize the enclosed
area? Determine the maximum area.

y
x
Pg. 1 of 3
2) A rectangle is inside the parabola y = 12 − x 2 with its base lying on the x-axis. The other two vertices lie on
the parabola. Find the dimensions of the rectangle with the largest area.

Pg. 2 of 3
3) An open-top rectangular box must contain a volume of 18 m3. The length of the base is three times its
width. Find the dimensions of the box that minimizes the surface area.

Pg. 3 of 3