Number worksheet — GCSE Higher

1.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

2.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

3.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

4.Given that 2⁵ = 32, work out 2⁶.

5.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

6.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

7.Work out how many factors 36 has.

8.A country has an area of 25,000,000 hectares. Write this area in standard form.

9.Work out 5⁰ + 5¹ + 5²

10.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

11.Work out how many factors 100 has.

12.Which of these is written correctly in standard form?

13.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

14.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

15.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.