Mathematical Modeling · Form 5
Mathematical Modeling: Worked Examples (Easier)
This set turns short everyday situations into a simple linear or quadratic model, then substitutes a value or solves once. It suits students who are just starting to write a formula from words.
Worked example 1
A stationery shop sells exercise books at RM3 each and adds a fixed delivery charge of RM5 per order. Form a model for the total cost C (RM) for n books, then find the cost of 12 books.
- Variable cost = 3n (RM3 for each of n books).
- Add the fixed delivery charge RM5: C = 3n + 5.
- Substitute n = 12: C = 3(12) + 5.
- C = 36 + 5 = 41.
Worked example 2
A water tank holds 40 litres. Water drains out at a steady 4 litres per minute.
Form a model for the volume V (litres) left after t minutes, then find how long the tank takes to empty.
- Start with 40 litres, lose 4 litres each minute: V = 40 − 4t.
- Tank is empty when V = 0: 0 = 40 − 4t.
- Rearrange: 4t = 40.
- t = 40 ÷ 4 = 10.
Worked example 3
A rectangular flower bed has a length 3 m longer than its width w metres. Form a model for its area A (m²), then find the area when the width is 5 m.
- Length = w + 3, width = w.
- Area = length × width: A = w(w + 3).
- Expand: A = w² + 3w.
- Substitute w = 5: A = 5² + 3(5) = 25 + 15 = 40.
Worked example 4
A taxi charges a fixed RM4 flag-fall plus RM1.20 for each kilometre travelled. Write a model for the fare F(x) in ringgit for a journey of x km, and find the fare for a 15 km journey.
- The fixed charge is RM4 and the variable charge is RM1.20 per km, i.e. 1.20x for x km.
- Model: F(x) = 4 + 1.20x.
- Substitute x = 15: F(15) = 4 + 1.20(15).
- F(15) = 4 + 18 = 22.
Worked example 5
Aina has RM250 in her savings jar and adds RM30 to it every week. Write a model for her total savings S(t) in ringgit after t weeks, and find her savings after 8 weeks.
- The starting amount is RM250 and she adds RM30 each week, i.e. 30t after t weeks.
- Model: S(t) = 250 + 30t.
- Substitute t = 8: S(8) = 250 + 30(8).
- S(8) = 250 + 240 = 490.
Worked example 6
A printer prints at a constant rate of 18 pages per minute. Write a model for the number of pages P(t) printed in t minutes, and find how many pages are printed in 7 minutes.
- The number of pages is directly proportional to the time: 18 pages for each minute.
- Model: P(t) = 18t.
- Substitute t = 7: P(7) = 18(7).
- P(7) = 126.
Worked example 7
A square rug has sides of length x metres. Form a model for its area A (m²) in terms of x, then find the area when x = 4.5 m.
- Area of a square = side × side, so A = x².
- Substitute x = 4.5: A = 4.5² = 20.25.
Worked example 8
A rectangular field has a length that is 6 m more than its width x metres. Form a model for its perimeter P (m) in terms of x, then find the perimeter when x = 8 m.
- Length = x+6, width = x. Perimeter = 2(length + width) = 2[(x+6)+x] = 2(2x+6) = 4x+12.
- Substitute x = 8: P = 4(8)+12 = 32+12 = 44.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What is an easy mathematical-modeling question actually asking me to do?
It gives you a real situation in words and asks you to turn it into a mathematical model, usually a simple equation or formula linking two quantities. At easy level this often means identifying the variables, writing one equation from the given relationship, and using it to find a missing value or check a given one.
What do examiners reward in a basic modeling answer?
Clearly defining what each variable represents before writing the equation, setting up the equation correctly from the words given, and showing the substitution step when using it to answer the question. Marks are lost for a correct final number with no defined variables or no equation shown.
What mistakes happen most at this easy modeling level?
Jumping straight to a number without writing the model as an equation first, misreading which quantity depends on which (reversing the relationship), and forgetting to state the units or check that the answer makes sense in the real situation described. A model that isn't checked against the original problem can go unnoticed as wrong.