IP Maths Notes (Lower Sec, Year 1-2): 03) Ratio, Rate & Percentage Reasoning
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Structure ratio simplifications, rate conversions, percentage change chains, and mixture questions with full working.
Last updated 30 Nov 2025
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- Start Here
- Learning targets
- 1 Ratio fundamentals
- 2 Rate conversions
Q: What does IP Maths Notes (Lower Sec, Year 1-2): 03) Ratio, Rate & Percentage Reasoning cover?
A: Structure ratio simplifications, rate conversions, percentage change chains, and mixture questions with full working.
Start Here
| Read time | What to take away |
| 1 second | Ratio, rate, and percentage questions are about consistent parts, units, and multipliers. |
| 10 seconds | Simplify ratios by scaling all parts equally, convert rates with units visible, and handle percentage change with multipliers such as 1.20 or 0.85. |
| 100 seconds | Follow the examples to practise average speed, reverse percentage, and mixtures, then check each answer by asking whether the size and unit are reasonable. |
Mastery of ratio and percentage reasoning saves marks across chemistry mixtures, physics rates, and finance contexts. This post trains systematic setups and calculator-free checks.
These notes align with MOE Lower Secondary Mathematics syllabus used in IP pathways (aligned to O-Level Mathematics 4052 foundations).
Status: MOE Lower Secondary Mathematics syllabus (latest release) checked 2025-11-30 - scope unchanged; remains the reference for these lower-sec notes.
New to the Integrated Programme? Start with What is IP? | Browse all free IP notes.
Learning targets
- Simplify ratios and express them in different forms (part:part, part:whole).
- Convert between rates (speed, density, unit pricing) with clear units.
- Chain multiple percentage changes and interpret reverse percentages.
- Model mixtures and part-whole distributions using algebraic reasoning.
1 Ratio fundamentals
1.1 Simplification & scaling
- Divide all parts by the highest common factor to simplify.
- To increase a ratio, multiply each part by the same scale factor.
