Units, estimation, rounding and bounds – Year 10 GCSE maths test answers to download as PDF

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1. Answer to Question 1 (4 marks)

   1. \(3.2\times10\,000=\) 32 000 cm² (1) One square metre is 10 000 square centimetres, so we multiply by 10 000.
   2. \(72\,000\div3600\) (1) \(=\) 20 m/s (1) Change kilometres into metres by multiplying by 1000, then divide by 3600 seconds in an hour.
   3. \(850\div1000=\) 0.85 litres (1) There are 1000 cm³ in a litre, so divide by 1000.

   A common error in (a) is to multiply by 100 only, giving 320 cm².

2. Answer to Question 2 (4 marks)

   1. 0.036 (1) The zero after the decimal point is not significant. The first two significant figures are 3 and 5, and the next digit 7 makes the 5 round up to 6.
   2. \(\dfrac{50\times3}{0.5}=\) 300 (1 for rounding, 1 for the answer) Round 49.6 to 50, 3.1 to 3 and 0.52 to 0.5. Then \(50\times3=150\) and \(150\div0.5=300\).
   3. Accurate value is \(295.7\), so the estimate is bigger (1) The estimate is bigger mainly because 49.6 was rounded up and the denominator 0.52 was rounded down.

3. Answer to Question 3 (4 marks)

   1. \(6.65\le x\lt 6.75\) (1 for each end) The length was rounded to 1 decimal place, so it can be up to 0.05 below or above 6.7.
   2. \(3750\le m\lt 3850\) (1 for each end) Rounding 3800 to 2 significant figures means rounding to the nearest 100, so the mass can be up to 50 below or above 3800.

   The upper end uses a strict inequality, because 6.75 would round up to 6.8.

4. Answer to Question 4 (4 marks)

   1. \(12.55\times8.45\) (1) \(=\) 106.0475 m² (1) Each length can be up to 0.05 m more than the measurement, so multiply the two upper bounds. The upper bound of the area is 106.0475 m².
   2. \(2(12.45+8.35)\) (1) \(=\) 41.6 m (1) Use the lower bounds of both lengths: 12.45 m and 8.35 m. The lower bound of the perimeter is 41.6 m.

5. Answer to Question 5 (4 marks)

   1. \(\dfrac{205}{11.5}\) (1) \(=\) 17.83 m/s (1) The greatest speed uses the greatest distance, 205 m, and the shortest time, 11.5 s. The upper bound is 17.83 m/s.
   2. \(\dfrac{195}{12.5}\) (1) \(=\) 15.60 m/s (1) The least speed uses the least distance, 195 m, and the longest time, 12.5 s. The lower bound is 15.60 m/s.

   Using 210 m or 11 s as bounds is a common error: the bounds are half a unit either side.

Total : 20 marks