Free Bachelor of Mathematics: Applied Mathematics Problem Solving Questions and Answers

Question 1

What is the primary focus of applied mathematics?

Accepted Answer

Applying mathematical methods to real-world issues

Answer

Applied mathematics focuses on using mathematical tools and theories to solve practical problems in various fields like science, engineering, economics, and medicine. Unlike pure mathematics, which develops abstract theories, applied mathematics bridges the gap between theoretical concepts and their real-world applications. Its primary goal is to model and understand phenomena in the physical and social sciences.

Question 2

What is the function used to find global and local extrema and stationary points while imposing a constraint?

Accepted Answer

f(x) = x e^x (-x + 1)

Answer

This question likely refers to a specific example or problem discussed within the BMath curriculum where `f(x) = x e^x (-x + 1)` was used to illustrate finding global and local extrema. While the general method for finding extrema with constraints involves techniques like Lagrange multipliers, the function itself is the object being optimized. This particular function is complex enough to demonstrate various calculus techniques for finding critical points and analyzing its behavior.

Question 3

What is the significance of the critical points of a function?

Accepted Answer

They are the points where the function's derivative is zero or undefined

Answer

Critical points of a function are fundamental in calculus for identifying potential locations of local maxima, local minima, or saddle points. These points occur precisely where the first derivative of the function is either equal to zero or is undefined. Analyzing the function's behavior around these critical points helps determine the nature of the extrema.

Question 4

What is the estimated number of baseballs required to fill the interior volume of a Boeing 747?

Accepted Answer

4.8 million baseballs

Answer

This is a classic Fermi problem or estimation question, often used to teach order-of-magnitude calculations. While the exact number can vary based on assumptions about the 747's volume and baseball packing density, 4.8 million baseballs is a commonly cited estimate for this specific problem. It requires estimating the volume of both a baseball and the aircraft, then considering packing efficiency.

Question 5

Which object's volume and packing density are considered when estimating the number of objects required to fill a container?

Accepted Answer

Baseball

Answer

The previous question (ID:114257) specifically asked about filling a Boeing 747 with baseballs. Therefore, when discussing the estimation of objects required to fill a container in the context of that problem, the baseball is the relevant object whose volume and packing density would be considered. This question directly follows up on the specific example.

BMath Bachelor of Mathematics Practice Test

BMath Bachelor of Mathematics Practice Test

Free Bachelor of Mathematics: Applied Mathematics Problem Solving Questions and Answers