Mathematical Modeling

Question 1

What is mathematical modelling?

Accepted Answer

Using maths to represent and solve real-world problems — A mathematical model uses equations, functions or graphs to represent a real situation.

Question 2

Which type of function best models the path of a ball thrown into the air?

Accepted Answer

Quadratic — Projectile motion follows a parabola, modelled by a quadratic function.

Question 3

A phone plan charging a fixed monthly fee plus a rate per minute is best modelled by a:

Accepted Answer

Linear function — A fixed fee plus a constant per-minute rate is a linear relationship, y = mx + c.

Question 4

Population growth or compound interest is often modelled by a(n):

Accepted Answer

Exponential function — Growth that multiplies over time is modelled by an exponential function.

Question 5

What is the final step of the modelling process?

Accepted Answer

Interpret the result in the real context — After solving, you interpret the answer back in the real-world situation and refine if needed.

Question 6

The first step in building a model is to:

Accepted Answer

Identify the variables and assumptions — You start by identifying the variables and assumptions before forming the model.

Question 7

A linear model has the general form:

Accepted Answer

y = mx + c — A linear model is a straight line of the form y = mx + c.

Question 8

A taxi fare is modelled by y = 3 + 2x, where x is the distance in km. Find the fare for a 5 km trip (in RM).

Accepted Answer

13 — y = 3 + 2 × 5 = 3 + 10 = RM13.

Question 9

Which of these is NOT part of the modelling process?

Accepted Answer

Ignoring the real-world context — Modelling must interpret results in context, so ignoring the context is not part of the process.

Question 10

If a model no longer fits the real data well, it should be:

Accepted Answer

Refined or revised — A model that does not fit should be refined or revised to improve it.