Percentages, Ratio & Proportion

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Corbett MathsCompound interest and depreciation

Corbett MathsReverse percentages

Corbett MathsRatio — dividing and problem solving

GCSE Maths TutorCompound Interest (Higher & Foundation) | GCSE Maths Revision | GCSE Maths Tutor

GCSE Maths TutorReverse Percentages using the Bar Method (Non-Calculator) | GCSE Maths Tutor

GCSE Maths TutorRatios, Fractions and Percentage Problems! Common Exam Questions | Grade 5+ | GCSE Maths Tutor

Key facts & methods

Percentages

Percentage multiplier: 20% increase → multiply by 1.20. 15% decrease → multiply by 0.85.
Compound interest: Amount = P × (1 + r/100)ⁿ. E.g. £500 at 3% for 4 years = 500 × 1.03⁴.
Depreciation: same formula but (1 − r/100)ⁿ. E.g. car worth £12,000 depreciates 8% per year.
Reverse percentage: given the value AFTER a % change, find the original.
After 20% increase: value = 120% of original. Original = value ÷ 1.2.
After 15% decrease: value = 85% of original. Original = value ÷ 0.85.

Ratio and proportion

Dividing in a ratio: total parts = sum of ratio. E.g. share £45 in ratio 2:3 → 5 parts, each part = £9. Shares: £18 and £27.
Direct proportion: y = kx. If y doubles, x doubles. Graph is a straight line through origin.
Inverse proportion: y = k/x. If x doubles, y halves. Graph is a reciprocal curve.
Algebraically: y ∝ x → y = kx. y ∝ 1/x → y = k/x. y ∝ x² → y = kx². Find k using given values.

Exam questions — 5 questions · 12 marks · Edexcel 4MA1 style

3 marksCompound interestGrade 7 Booklet style 🔢 Calculator

Hannah invests £3500 in a savings account. The account pays compound interest at 2.4% per year. How much will Hannah have after 3 years? Give your answer to the nearest penny. (3 marks)

Hint: Compound interest: P × (1 + r/100)ⁿ. Here P=3500, r=2.4, n=3. So 3500 × 1.024³. Use your calculator.

+30 XP

3 marksReverse percentageGrade 7 Booklet style 🔢 Calculator

A jacket costs £63 after a 30% discount. What was the original price? (3 marks)

Hint: £63 is what REMAINS after 30% off. So £63 = 70% of original. Divide by 0.7 (not multiply by 1.3).

+30 XP

4 marksRatio problem4MA1 Set 1 P1H Q7 style ✏️ No calculator

Talil mixes cement, sand and gravel in ratio 1:3:5 by weight to make 180 kg of concrete. He has 15 kg cement, 85 kg sand, 100 kg gravel. Does he have enough of each material? Show all working. (4 marks)

Hint: Find the value of 1 part (total ÷ sum of ratio). Multiply by each ratio number. Compare with what he has. State conclusion clearly.

+40 XP

4 marksProportion4MA1 style ✏️ No calculator

y is inversely proportional to x². When x = 3, y = 4. (a) Find the equation connecting y and x. (b) Find y when x = 6. (4 marks)

Hint: (a) Write y = k/x², substitute the given values to find k. (b) Use your equation with x=6.

+40 XP

1 markPercentage increase4MA1 style

A car was bought for £8000. It depreciated by 12% per year. Which calculation gives its value after 3 years?

A 8000 × 0.88³

B 8000 × 0.12³

C 8000 − (8000 × 0.12 × 3)

D 8000 × 1.12³

Percentages, Ratio & Proportion

Percentages

Ratio and proportion

Module complete! 🎉