MIP1502 Assignment 4 (COMPLETE ANSWERS) 2025 (721016) - DUE 15 August 2025

,MIP1502 Assignment 4 (COMPLETE
ANSWERS) 2025 (721016) - DUE 15 August
2025
MIP1502 FULL ASSIGNMENT RESPONSE: FUNCTIONS,
MISCONCEPTIONS & TEACHING STRATEGIES


Question 1: Functional Relationships and Teaching
Misconceptions
1.1 Real-world Function Analysis
Situation 1 (Linear):
 1.1.1
o Independent Variable (Input): Kilometres driven
o Dependent Variable (Output): Total cost of renting
the van
 1.1.2
o Function rule: f(k)=230+4.30kf(k) = 230 + 4.30k,
where kk is the number of kilometres.
 1.1.3
| Kilometres (k) | Cost (R) |
|----------------|----------|
| 0 | 230.00 |
| 50 | 445.00 |

, | 100 | 660.00 |
| 150 | 875.00 |
 1.1.4
Graph would be a straight line starting at (0, 230),
increasing linearly. X-axis: kilometres, Y-axis: total cost.
Situation 2 (Non-linear):
 1.1.1
o Independent Variable: Radius of the circle
o Dependent Variable: Area of the circle
 1.1.2
o Function rule: A(r)=πr2A(r) = \pi r^2
 1.1.3
| Radius (r) | Area (A) (approx.) |
|------------|---------------------|
| 1 | 3.14 |
| 2 | 12.57 |
| 3 | 28.27 |
| 4 | 50.27 |
 1.1.4
Graph would be a curve starting at (0,0), curving
upwards. X-axis: radius, Y-axis: area.
1.2 Thabo’s Misconception