Percentage change and simple interest – Year 9 maths test answers to download as PDF

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1. Answer to Question 1 (4 marks)

   1. An increase of 15% means the new amount is 115% of the original, which is 1.15 as a decimal (1 mark for the multiplier). Then \(240\times1.15=\)£276 (1 mark).
   2. A decrease of 12% leaves \(100-12=88\%\), so the multiplier is 0.88 (1 mark). Then \(650\times0.88=\)£572 (1 mark).

   Check (a) the long way: 10% of £240 is £24 and 5% is £12, so 15% is £36, and \(240+36=276\). Check (b): 12% of £650 is \(65+13=78\) pounds, and \(650-78=572\). The multiplier method does the whole calculation in one step and is the quickest on a calculator.

2. Answer to Question 2 (4 marks)

   1. The change is \(45-36=£9\), an increase (1 mark). Divide by the original price and multiply by 100: \(\dfrac{9}{36}\times100=\)25% increase (1 mark).
   2. The change is \(50-42=£8\), a decrease (1 mark). Divide by the original price: \(\dfrac{8}{50}\times100=\)16% decrease (1 mark).

   Always divide by the original value, not the new one. Dividing by 45 in part (a) would give 20%, which is wrong. A multiplier check also works: \(36\times1.25=45\) and \(50\times0.84=42\), so both answers are confirmed.

3. Answer to Question 3 (4 marks)

   1. After a 20% reduction the coat costs 80% of the original, so the multiplier is 0.8 (1 mark). £48 is the result of multiplying by 0.8, so divide to go back: \(48\div0.8=\)£60 (1 mark). Check: \(60\times0.8=48\).
   2. After a 5% increase the rent is 105% of the original, so the multiplier is 1.05 (1 mark). Divide: \(630\div1.05=\)£600 per month (1 mark). Check: \(600\times1.05=630\).

   The common wrong method in (a) is to add 20% of £48 to get £57.60. That fails because the 20% was taken from the original price, not from £48.

4. Answer to Question 4 (4 marks)

   1. Simple interest uses \(I=\dfrac{PRT}{100}\) with \(P=2000\), \(R=3.5\) and \(T=4\): \(\dfrac{2000\times3.5\times4}{100}\) (1 mark) \(=\)£280 (1 mark).
   2. Add the interest to the money invested: \(2000+280=\)£2 280. (1 mark)
   3. Each year earns the same interest, \(2000\times3.5\div100=£70\). So £140 needs \(140\div70=\)2 years. (1 mark)

   With simple interest the interest is always worked out on the original £2 000, which is why every year gives exactly £70. Check (a): \(4\times70=280\). Compound interest would give slightly more, because the interest itself would earn interest from the second year.

5. Answer to Question 5 (4 marks)

   1. Apply the 25% reduction first, multiplier 0.75: \(120\times0.75=£90\) (1 mark). Then take a further 10% off the new price, multiplier 0.9: \(90\times0.9=\)£81 (1 mark).
   2. A single 35% reduction uses multiplier 0.65: \(120\times0.65=£78\) (1 mark). This is not £81, so Dev is wrong (1 mark).

   The second discount is 10% of £90, not of £120, so it saves only £9 rather than £12. The two multipliers combine as \(0.75\times0.9=0.675\), which is a 32.5% reduction overall. Successive percentage changes must be multiplied, never added.

Total : 20 marks