MIP1502 Assignment 4
(COMPLETE ANSWERS)
2025 (721016) - DUE 15
August 2025
For assistance contact
Email:
,MIP1502 Assignment Solutions (Full Answers)
Question 1: Functions, Misconception, and Teaching Activity
1.1 Situation 1 (Linear): Rental van
Independent variable (input): x = kilometres driven (km).
Dependent variable (output): f(x) = total cost in Rands (R).
Function rule: f(x) = 230 + 4.30x (R).
km (x) Cost R (f(x))
0 R230.00
10 R273.00
50 R445.00
100 R660.00
Graph: see image below.
1.1 Situation 2 (Non-linear): Area of a circle
Independent variable (input): r = radius (units).
Dependent variable (output): A(r) = area in square units.
Function rule: A(r) = π r².
radius r Area A(r)
, 0.5 0.785
1 3.142
2 12.566
3 28.274
Graph: see image below.
1.2 Misconception: Thabo (rental van)
1.2.1 Fundamental error: Thabo treated the linear function as proportional and ignored the fixed
daily cost (R230).
Difference between proportional and non-proportional linear functions: A proportional linear
function passes through the origin (no fixed start cost). A non-proportional linear function has a
constant term (y-intercept) representing a fixed cost or start-up fee.
1.2.2 Corrective feedback (Grade 6 language):
The company charges R230 even if you drive 0 km — this is the starting fee. You then add the
distance cost: 100 km × R4.30 = R430. Total = R230 + R430 = R660. So R430 was only the
distance part.
1.2.3 Doughnut machine teaching intervention (mapping):
- Flour (setup cost) = fixed fee R230.
- Oil/ingredients per doughnut = variable cost per unit R4.30.
- Doughnuts produced = output (total cost).
Activity: Demonstrate starting the machine (paying flour/setup) then producing doughnuts where
each doughnut requires 'oil' (per-unit cost). Discuss total cost = setup + (per-unit × number).
(COMPLETE ANSWERS)
2025 (721016) - DUE 15
August 2025
For assistance contact
Email:
,MIP1502 Assignment Solutions (Full Answers)
Question 1: Functions, Misconception, and Teaching Activity
1.1 Situation 1 (Linear): Rental van
Independent variable (input): x = kilometres driven (km).
Dependent variable (output): f(x) = total cost in Rands (R).
Function rule: f(x) = 230 + 4.30x (R).
km (x) Cost R (f(x))
0 R230.00
10 R273.00
50 R445.00
100 R660.00
Graph: see image below.
1.1 Situation 2 (Non-linear): Area of a circle
Independent variable (input): r = radius (units).
Dependent variable (output): A(r) = area in square units.
Function rule: A(r) = π r².
radius r Area A(r)
, 0.5 0.785
1 3.142
2 12.566
3 28.274
Graph: see image below.
1.2 Misconception: Thabo (rental van)
1.2.1 Fundamental error: Thabo treated the linear function as proportional and ignored the fixed
daily cost (R230).
Difference between proportional and non-proportional linear functions: A proportional linear
function passes through the origin (no fixed start cost). A non-proportional linear function has a
constant term (y-intercept) representing a fixed cost or start-up fee.
1.2.2 Corrective feedback (Grade 6 language):
The company charges R230 even if you drive 0 km — this is the starting fee. You then add the
distance cost: 100 km × R4.30 = R430. Total = R230 + R430 = R660. So R430 was only the
distance part.
1.2.3 Doughnut machine teaching intervention (mapping):
- Flour (setup cost) = fixed fee R230.
- Oil/ingredients per doughnut = variable cost per unit R4.30.
- Doughnuts produced = output (total cost).
Activity: Demonstrate starting the machine (paying flour/setup) then producing doughnuts where
each doughnut requires 'oil' (per-unit cost). Discuss total cost = setup + (per-unit × number).
