Variation · 1.3.2
Problems on combined variation
Students apply combined variation equations to real-life situations by translating a worded scenario into an equation, finding the constant k from given data, and then solving for an unknown quantity. This often involves multiple steps, careful reading of relationships, and sometimes rearranging the equation for a different unknown.
The official learning standard (1.3.2)
“Solve problems involving combined variation.”
What it means
Students apply combined variation equations to real-life situations by translating a worded scenario into an equation, finding the constant k from given data, and then solving for an unknown quantity. This often involves multiple steps, careful reading of relationships, and sometimes rearranging the equation for a different unknown.
How it is examined
This is mainly tested in SPM 1449 Paper 2 as a structured word problem set in a real-world context (such as cost, production, or resource usage), requiring students to form the combined variation equation from the description, solve for the constant k, then answer a follow-up numeric question using that equation.
Worked example
The cost, C, of manufacturing a component varies directly as the number of units, n, and inversely as the number of machines, m, used. When n = 200 and m = 4, C = RM 500.
Find C when n = 300 and m = 5.
- Form equation: C = kn/m.
- Substitute n = 200, m = 4, C = 500: 500 = 200k/4 = 50k, so k = 10.
- Equation: C = 10n/m.
- Substitute n = 300, m = 5: C = 10(300)/5 = 3000/5 = 600.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I set up the equation from a word problem?
Read the sentence carefully and identify each "varies directly as..." (numerator) and "varies inversely as..."
(denominator) phrase, combine them with one constant k, then use the first given data set to solve for k before answering the actual question asked.
What if the question asks for a variable other than the subject?
Rearrange the combined variation equation to make the required variable the subject after finding k. For example, if C = kn/m and the question asks for m given C and n, substitute known values and solve the resulting equation for m.
Do units matter in combined variation problems?
Yes, keep units consistent throughout your equation. If cost is in RM and units are in pieces, k will carry units that make the equation balance; do not mix inconsistent units when substituting values into the combined variation equation.