OxfordAQA International GCSE Mathematics: Percentage change, interest and exponential growth and decay (9260) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions are aligned to the OxfordAQA International GCSE Mathematics (9260) specification, Version 5.1, for exams from May/June 2018 onwards. They cover N15 (section 3.1.2) and the repeated proportional change and exponential growth and decay parts of N20 (section 3.1.3). Questions 1 to 6 are Core content, which can be assessed at both tiers. Questions 7 to 12 are marked (Extension only).

Read the study guide first if a topic is new, and use the revision notes for quick recall. The course hub and checklist show the rest of the course. Money answers should be given to the nearest penny unless the question says otherwise.

Questions

1. A jacket costs £96. In a sale the price is reduced by 35%. Find the sale price. [2]

2. A monthly phone bill rises from £38.00 to £45.60. Work out the percentage increase. [3]

3. Simple interest is paid on a savings account.

(a) Find the simple interest on £4,500 invested for 5 years at 2.8% a year. [2] (b) Maya invests £2,000. After 2.5 years she has received £150 in simple interest. Find the yearly rate of interest. [2]

4. Compound interest is paid on £6,000. The rate is 3% for the first year, 3% for the second year and 4% for the third year. Find the total interest earned over the three years. [4]

5. A shop raises a price by 20%. A month later it reduces the new price by 15%. Find the overall percentage change in the original price. [3]

6. Ayesha has £3,000 to invest for 3 years. Account A pays 5% a year simple interest. Account B pays 4% a year compound interest.

(a) Find the total in account A at the end of 3 years. [2] (b) Find the total in account B at the end of 3 years. [2] (c) Which account is better, and by how much? [1]

7. (Extension only)

(a) After an 8% pay rise, a salary is £29,160. Find the salary before the rise. [2] (b) A sofa is reduced by 30% in a sale. The sale price is £52.50. Find the original price. [2]

8. (Extension only) £12,500 is invested at 3.6% a year compound interest.

(a) Find the value of the investment after 7 years. [2] (b) Find the smallest whole number of years for the value to exceed £20,000. You must show the values you test. [4]

9. (Extension only) A deposit of £15,000 becomes £17,117.49 after 3 years, with the same percentage of interest added each year. Find that percentage. [3]

10. (Extension only) A machine is bought for £34,000. Its value falls by 15% each year.

(a) Write down a formula for its value, V pounds, after n years. [1] (b) Find its value after 4 years. [2] (c) After how many whole years is the value first below £10,000? [3]

11. (Extension only) A culture starts with 480 bacteria. The number increases by 30% every hour.

(a) Find the number of bacteria after 4 hours, to the nearest whole number. [2] (b) In which hour does the number first exceed 5,000? [3]

12. (Extension only) A rare book gains 6% of its value each year. It is now worth £3,150, exactly 4 years after it was bought.

(a) Find the price paid for the book, to the nearest pound. [3] (b) Find the overall percentage increase in value over the 4 years, to 3 significant figures. [2] (c) How many further years are needed for the value to exceed £4,000? [3]

Answers

1. Multiplier for a 35% decrease = 0.65 [1] 96 × 0.65 = £62.40 [1] [2] Examiner insight: Writing the multiplier as its own line shows your method even if you slip in the multiplication. A bare answer leaves nothing to follow.

2. Change = 45.60 − 38.00 = 7.60 [1] 7.60 ÷ 38 × 100 [1] = 20% increase [1] [3] Examiner insight: Dividing by the original bill is the step that is often lost. Stating “increase” in the answer line also answers the question fully.

3. (a) Interest = 4500 × 0.028 × 5 [1] = £630 [1] (b) 150 = 2000 × (r/100) × 2.5, so r = 150 ÷ 50 [1] r = 3% a year [1] [4] Examiner insight: Show the substitution into the simple interest formula before rearranging. Keeping the units (years, pounds) straight avoids using 2.5 as a percentage by mistake.

4. Multipliers 1.03, 1.03 and 1.04 [1] Total = 6000 × 1.03 × 1.03 × 1.04 [1] = £6,620.02 [1] Interest = 6620.02 − 6000 = £620.02 [1] [4] Examiner insight: The question asks for the interest, not the final amount, so the last subtraction matters. Show a multiplier for each year because the rate changes.

5. Multipliers 1.2 and 0.85 [1] 1.2 × 0.85 = 1.02 [1] Overall change = 2% increase [1] [3] Examiner insight: Adding +20% and −15% gives 5%, which is wrong. Multiplying the multipliers works for any starting price, so you do not need to invent one.

6. (a) Interest = 3000 × 0.05 × 3 = £450 [1] Total = £3,450 [1] (b) Total = 3000 × 1.04 × 1.04 × 1.04 [1] = £3,374.59 [1] (c) Account A is better, by 3450 − 3374.59 = £75.41 [1] [5] Examiner insight: A comparison question needs a conclusion in words as well as the two totals. Check the totals use the same time period before you compare.

7. (a) Multiplier = 1.08, so original = 29160 ÷ 1.08 [1] = £27,000 [1] (b) Sale price is 70% of the original, so original = 52.50 ÷ 0.7 [1] = £75 [1] [4] Examiner insight: Finding 8% of £29,160 and subtracting is the common error. A quick forward check (27,000 × 1.08) confirms the answer.

8. (a) Value = 12500 × 1.036⁷ [1] = £16,011.36 [1] (b) Value after n years = 12500 × 1.036ⁿ [1] n = 13: £19,796.43, which is below £20,000 [1] n = 14: £20,509.10, which is above £20,000 [1] So the smallest whole number is 14 years [1] [6] Examiner insight: A trial-and-improvement answer should show a value just below and a value just above the target. Stating only the final year gives no evidence of the search.

9. (1 + r/100)³ = 17117.49 ÷ 15000 [1] 1 + r/100 = ∛1.14117… = 1.045 [1] r = 4.5% a year [1] [3] Examiner insight: After the cube root, remember to subtract 1 before converting to a percentage. Giving 1.045 or 104.5% as the rate would not answer the question.

10. (a) V = 34000 × 0.85ⁿ [1] (b) V = 34000 × 0.85⁴ [1] = £17,748.21 [1] (c) n = 7: £10,899.62, which is above £10,000 [1] n = 8: £9,264.68, which is below £10,000 [1] So the value first falls below £10,000 after 8 years [1] [6] Examiner insight: For decay, the multiplier is 0.85, not 0.15. Check that your model gives a smaller value each year before you use it.

11. (a) Number = 480 × 1.3⁴ [1] = 1,371 bacteria (1370.9 rounded) [1] (b) After 8 hours: 480 × 1.3⁸ = 3,916, below 5,000 [1] After 9 hours: 480 × 1.3⁹ = 5,090, above 5,000 [1] The number first exceeds 5,000 in the 9th hour [1] [5] Examiner insight: Read what the question asks: “in which hour” wants a whole number of hours. Rounding the answer to the nearest whole number of bacteria is a separate instruction, given in part (a).

12. (a) Multiplier for 4 years = 1.06⁴ [1] Price = 3150 ÷ 1.06⁴ [1] = £2,495 [1] (b) 1.06⁴ = 1.2625 (4 d.p.) [1] Overall increase = 26.2% [1] (c) 3150 × 1.06⁴ = £3,976.80, which is below £4,000 [1] 3150 × 1.06⁵ = £4,215.41, which is above £4,000 [1] So 5 further years [1] [8] Examiner insight: The book’s age is 4 years, but part (c) starts counting from the value of £3,150 now. Mixing up the starting point is an easy way to give an answer one year out.

Where marks are usually lost

• Dividing by the new amount, not the original, when finding a percentage change.
• Using a multiplier of 1.35 for a 35% decrease, or 0.2 for a 20% increase.
• Adding percentages in a repeated change question instead of multiplying the multipliers.
• Taking a percentage of the final amount when the question asks for the starting amount. Divide by the multiplier.
• Giving the final total when the question asks for the interest earned.
• Using simple interest for a compound question, or the reverse.
• Rounding the multiplier or an intermediate value, which can change the final penny.
• Stating a trial-and-improvement answer without showing the values either side of the target.
• Forgetting to subtract 1 after taking a root when finding a rate.
• Leaving out the words “increase” or “decrease”, or the pound sign on a money answer.

Next steps

• Re-read the study guide for any topic that cost you marks.
• Condense it with the revision notes.
• Return to the OxfordAQA IGCSE Mathematics hub and the course checklist.
• Try all the free 10-minute diagnostics.
• Book a free trial class for help with anything that still feels uncertain.

Official syllabus

OxfordAQA International GCSE Mathematics (9260), Version 5.1, for exams May/June 2018 onwards, published by OxfordAQA. Spec references: N15 (3.1.2) and N20 (3.1.3).