Optimisation problems test, 12 grade

Question Nr. 1 out of 10

An open-top box has square base side x and volume V = 500. Which function gives surface area?

S(x) = x² + V

S(x) = x² + 4V/x

S(x) = 4x + V/x

S(x) = Vx²

Question Nr. 2 out of 10

What general strategy is suitable for a word optimisation problem?

Use every number in one product

Choose the first critical point automatically

Ignore units

Translate the context into an objective function and constraints, then verify the result

Question Nr. 3 out of 10

A rectangle against a wall uses 80 m of fence on three sides. What perpendicular side maximises area?

63 m

20 m

68 m

37 m

43 m

Question Nr. 4 out of 10

For x > 0, f(x) = x + 36/x has its minimum at which x?

10

8

1

6

5

Question Nr. 5 out of 10

Profit is P(x) = −2x² + 20x. Which x maximises profit?

5

6

18

22

24

Question Nr. 6 out of 10

Why must endpoints also be checked on a closed interval?

Because an absolute optimum on a closed interval may occur at an endpoint

Only endpoints can be extrema

Endpoints never matter

The derivative is undefined at every endpoint

Question Nr. 7 out of 10

For x > 0, f(x) = x + 49/x has its minimum at which x?

7

6

4

19

18

Question Nr. 8 out of 10

What must first be defined when building an optimisation model?

Maximise every expression

Ignore physical restrictions

State the variable, its feasible domain, and the objective function

Differentiate before defining variables

Question Nr. 9 out of 10

A rectangle has perimeter 28 cm. What should one side be for maximum area?

16 cm

7 cm

6 cm

2 cm

28 cm

Question Nr. 10 out of 10

A rectangle has perimeter 32 cm. What should one side be for maximum area?

8 cm

13 cm

15 cm

27 cm

17 cm

Test: Optimisation problems

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Test: Optimisation problems

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Related mathematics tests

Function analysis using derivatives

Lines and planes in space

Tangent and physical meaning of derivative

Prisms and pyramids