Percentage and GrowthEdexcel GCSE Maths: Flashcards
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What kind of relationship is a percentage change?
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- What kind of relationship is a percentage change?
- A multiplicative relationship — one quantity is a multiple of the other.
- A price rises from £80 to £100. What is the multiplier?
- 100 ÷ 80 = 1.25 (a 25% increase).
- What is the equation for direct proportion?
- y = kx, where k is a constant.
- If 4 litres of fuel cost £6, what does 10 litres cost?
- k = 6 ÷ 4 = 1.5; cost = 1.5 × 10 = £15.
- Name three types of proportion equation besides y = kx.
- y = kx² (proportional to the square), y = k√x (proportional to the square root), y = k/x (inverse proportion).
- What does it mean if quantity A is 1.5 times quantity B?
- A is 150% of B — bigger than the original, i.e. growth.
- How do you combine a 20% increase followed by a 10% decrease?
- Multiply the multipliers: 1.20 × 0.90 = 1.08, an overall 8% increase.
- Why doesn't a 10% increase followed by a 10% decrease return the original value?
- Because the second percentage is taken from a different (larger) amount than the first.
- What is the constant of proportionality?
- The fixed value k linking two directly or inversely proportional quantities.
- How do you find k in a direct proportion problem?
- Substitute one known pair of x and y values into y = kx and solve for k.
- What happens to y as x increases in inverse proportion (y = k/x)?
- y decreases as x increases.
- Express 120 as a fraction of 80, and as a percentage.
- 120 ÷ 80 = 1.5, i.e. 150%.