MIP1502 Assignment 4 |DETAILED ANSWERS| Semester 2 2025 (721016) - DUE 15 August 2025

, MIP1502 Assignment 4
Semester 2 2025(721016)
DUE 15 August 2025
Use this document as a guide and for references to answer your assignment

Question 1

This question requires you to move beyond simply solving mathematical problems. You will analyse functional
relationships, diagnose a common learner misconception based on the principles in your learning material, and
design a learning activity that aligns with the CAPS curriculum for the Intermediate Phase.

1.1 Consider the two real-world situations below. The first represents a linear function, and the second
represents a non-linear function.

• Situation 1 (Linear): A rental van costs R230 per day plus R4,30 per kilometre driven.

• Situation 2 (Non-linear): The area of a circle depends on the length of its radius.

For each situation, you must:

1.1.1 Identify the independent variable (input) and the dependent variable (output). (2)

 Situation 1 (Linear):

 Independent variable: Kilometres driven (let's denote it as x)
 Dependent variable: Total cost of rental (f(x))

 Situation 2 (Non-linear):

 Independent variable: Radius of the circle (r)
 Dependent variable: Area of the circle (A(r))



1.1.2 Write a function rule using function notation (e.g., 𝑓𝑓(𝑥𝑥)=…). Use the standard
formula for the area of a circle in Situation 2. (2)

 Situation 1:

f(x)=230+4.30x

(R230 fixed cost + R4.30 per km)

,  Situation 2:

A(r)=πr2
A(r)=πr2

(Area of a circle)



1.1.3 Create a table of values showing at least four different, realistic inputs and their
corresponding outputs. (2)

Situation 1 (Linear):

Kilometres (x) Cost f(x) = 230 + 4.30x
0 R230.00
50 R445.00
100 R660.00
150 R875.00

Situation 2 (Non-linear): (Use π ≈ 3.14)

Radius (r) Area A(r) = πr²
1 3.14
2 12.56
3 28.26
4 50.24


1.1.4 Sketch a graph for each function on a separate set of axes. Label your axes clearly
with the variable names. (2)

(Since sketches can't be drawn directly here, describe how the graphs would look:)

 Graph 1 (Linear):
o X-axis: Kilometres
o Y-axis: Total cost (R)
o A straight line starting at (0, 230) and increasing steadily
 Graph 2 (Non-linear):
o X-axis: Radius
o Y-axis: Area
o A curve starting near the origin, increasing rapidly (parabolic shape),
showing that small increases in radius lead to larger increases in area