Ratio, Proportion & Compound Measures — Year 9 Revision Notes
These notes cover harder ratio and proportion problems and the compound measures speed and density — all at Year 9 (Stage 9) level.
Harder ratio and proportion
Year 9 ratio problems often need more than one step: simplifying, sharing, then scaling. Keep track of what one 'part' is worth, and check your answer fits the original total. Direct proportion problems are solved by finding the value of one unit first.
Key Facts & Formulas
- One part = amount ÷ total parts
- Direct proportion: find one unit, then scale
Tips
- Work out the value of one part or one unit first.
- Check your answer against the original total.
Speed, distance and time
Speed is distance divided by time: speed = distance ÷ time. Rearranging gives distance = speed × time and time = distance ÷ speed. A car travelling 150 km in 3 hours has a speed of 150 ÷ 3 = 50 km/h. Always check the units match.
Key Facts & Formulas
- speed = distance ÷ time
- distance = speed × time
- time = distance ÷ speed
Tips
- Make sure the time units match the speed units.
- Use a formula triangle to rearrange.
Density, mass and volume
Density is mass divided by volume: density = mass ÷ volume. Rearranging gives mass = density × volume and volume = mass ÷ density. An object of mass 60 g and volume 20 cm³ has density 60 ÷ 20 = 3 g/cm³.
Key Facts & Formulas
- density = mass ÷ volume
- mass = density × volume
- volume = mass ÷ density
Tips
- Density uses mass on top, volume underneath.
- Watch the units, such as g/cm³.
Revision Checklist
- I can solve multi-step ratio and proportion problems
- I can use speed = distance ÷ time and rearrange it
- I can use density = mass ÷ volume and rearrange it
- I can convert units within a compound measure
Frequently Asked Questions
How does a formula triangle work?
Write the three quantities in a triangle with the 'top' quantity above the line and the other two below. Cover the one you want: if the other two are side by side you multiply; if one is above the other you divide.
Build strong foundations in Ratio, Proportion & Compound Measures
A free trial class with Teacher Rig helps your Year 9 child master Ratio, Proportion & Compound Measures now — so IGCSE Maths feels familiar, not frightening, later.
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