Flashcards · J560 · Topic 5

Ratio, proportion and rates of change flashcards

16 cards on Topic 5, subtopics 5.01 to 5.03. Pick a subtopic or study them all.

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Ratio: Compares quantities, written a : b. Order matters. 2 : 5 is not 5 : 2.
Ratio in simplest form: Whole numbers with no common factor other than 1.
Ratio in the form 1 : n: The first part is 1; n can be a decimal or fraction. Divide both parts by the first: 25 : 40 = 1 : 1.6.
Share £510 in the ratio 1 : 2 : 3: Total parts 6; one part = 510 ÷ 6 = £85. Shares: £85, £170, £255. Check: they add to £510.
Two shares are in the ratio 5 : 2 and differ by 36. Find them.: The difference is 3 parts, so one part = 36 ÷ 3 = 12. Shares: 60 and 24.
Size check for a ratio answer: The larger ratio number must get the larger share. If it does not, you have swapped the order.

Direct proportion: y = kx, so y ÷ x is constant. The graph is a straight line through the origin. Doubling x doubles y.
Inverse proportion: y = k/x, so x × y is constant. The graph is a curve that never meets the axes. Doubling x halves y.
8 painters take 6 days. How long do 12 painters take, at the same rate?: Inverse proportion: the job is 8 × 6 = 48 painter-days. 48 ÷ 12 = 4 days.
If x doubles, what happens to y when y ∝ x², y ∝ x³ or y ∝ 1/x²?Higher: y ∝ x²: y × 4. y ∝ x³: y × 8. y ∝ 1/x²: y ÷ 4.
y is inversely proportional to √x, and y = 4 when x = 9. Find x when y = 3.Higher: y = k/√x, so 4 = k/3 and k = 12. 3 = 12/√x, so √x = 4 and x = 16.

Simple interest compared with compound interest: Simple: P × r × n / 100, the same amount added every year. Compound: start × multiplierⁿ, so the amount added grows each year.
A value falls by 10% and then by 20%. What is the overall change?: Multiply the multipliers: 0.9 × 0.8 = 0.72, a 28% fall overall (not 30%).
After a 20% rise a price is £360. Find the original price.: Divide by the multiplier: 360 ÷ 1.2 = £300.
Growth and decay formula A = A₀ × rⁿHigher: A₀ is the starting amount, r the multiplier per period and n the number of periods. r > 1 is growth; 0 < r < 1 is decay.
V = 900 × 0.9ⁿ. What does it describe, and what is V when n = 3?Higher: A start of 900 falling by 10% each period. V = 900 × 0.9³ = 900 × 0.729 = 656.1