What this guide covers
Selected Sec 2 N2 skills: map distance and area scale, direct proportion and inverse proportion. The examples do not claim to cover every ratio context.
Name the invariant
For direct proportion yx stays constant; for inverse proportion xy stays constant. On a map, first convert a drawn length to an actual length, then square that length if finding an actual area.
A map square is an area problem
A square plot has side 1.2 cm on a map with scale 1:50,000. Find its actual area in m².
- Actual side =1.2×50,000=60,000 cm=600 m.
- Actual area =600×600=360,000 m².
Check: The linear scale changes each side. Squaring the resulting 600 m gives square metres, not metres.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
y is directly proportional to x. If y=10 when x=4, find y when x=6.
yx=104=2.5 stays constant. At x=6, y=2.5×6=15. Check: 156=2.5.
Six identical machines complete a fixed job in 8 hours. Assuming equal constant rates, how long would four machines take?
The fixed job is 6×8=48 machine-hours. Four machines need 48÷4=12 hours. The product machines×hours stays 48 under the stated assumption.
Where this connects
- Earlier: ratio parts and units →
A consistent unit and ratio order are useful before scale work.
- Later: mixed proportion applications →
The Upper Secondary guide connects proportions with further contexts.
Sources and scope
Original Mentora questions aligned to selected Sec 2 N2 scope in the MOE G2/G3 Mathematics syllabus. The map plot is a new text description, not a reproduced diagram.