What this guide covers
Selected Sec 1 N3 skills: percentage change, reverse checking and percentage points. Longer successive-change comparisons remain in later practice.
Change compared with what?
Percentage increase equals increase ÷ original amount × 100%. Percentage points instead describe the direct difference between two percentages, such as 40% to 55%.
Check the original amount
A price rises from $80 to $92. Find the percentage increase and check by a multiplier.
- The increase is 92−80=$12.
- Use the original $80 as the base: 1280×100%=15%.
- Check: $80×1.15=$92.
Check: Dividing 12 by the new price $92 would answer a different comparison.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
A fee rises from $45 to $54. What is the percentage increase?
The increase is $9. Relative to the original $45, 945×100%=20%. Check: 45×1.20=54.
A survey result rises from 30% to 45%. How many percentage points is the rise, and what is the percentage increase relative to 30%?
The rise is 45−30=15 percentage points. Relative to the original 30%, it is 1530×100%=50%. These are different measures.
Where this connects
- Sec 1 percentage scope →
See where percentages fit among Sec 1 number topics.
- Later: successive percentage changes →
The Upper Secondary guide compares changes with different bases.
Sources and scope
Original Mentora examples and checks, aligned to Sec 1 N3 in the MOE G2/G3 Mathematics syllabus. They are not reproduced school-paper questions.