Variation · 1.2.3
Solving inverse variation problems
This standard asks you to apply inverse variation to solve real-life problems, not just find the relation. Using y = k/x, you calculate an unknown value, compare two different situations, or work out how one quantity changes when another quantity is scaled, for example, how the time needed changes when the number of workers changes.
The official learning standard (1.2.3)
“Solve problems involving inverse variation.”
What it means
This standard asks you to apply inverse variation to solve real-life problems, not just find the relation. Using y = k/x, you calculate an unknown value, compare two different situations, or work out how one quantity changes when another quantity is scaled, for example, how the time needed changes when the number of workers changes.
How it is examined
This is commonly tested as a Paper 2 structured question, often as word problems about workers completing a task, or similar contexts where increasing one quantity reduces another. The first part usually finds the relation, while later parts ask for a new value, or how many units are needed to achieve a target.
Worked example
The number of days, D, needed to build a wall varies inversely as the number of workers, m. It takes 8 workers 15 days to build the wall.
Find how many days 12 workers would take, and how many workers are needed to finish it in 6 days.
- Since D varies inversely as m, write D = k/m.
- Substitute m = 8, D = 15: k = mD = 8 × 15 = 120.
- The relation is D = 120/m.
- For m = 12: D = 120/12 = 10 days.
- For D = 6: 6 = 120/m, so m = 20 workers.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I decide whether a word problem is direct or inverse variation?
Think about what happens in real life: if increasing one quantity makes the other increase too, like more items costing more money, it is direct variation. If increasing one quantity makes the other decrease, like more workers finishing a job faster, it is inverse variation.
What if the problem involves more than two variables?
If a variable varies inversely as the product of two others, such as y = k/(xz), find k using the complete set of given values for all the variables at once, then substitute the new values in the usual way to find the unknown quantity.
Can the answer be a non-whole number of workers or days?
Mathematically, yes, the calculation may give a decimal. But for quantities like the number of workers, real situations usually need a whole number, so you may need to round sensibly.
Most SPM questions, however, are designed to give exact whole-number answers.