Number worksheet — GCSE Higher

1.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

2.√700 lies between which two consecutive integers?

3.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

4.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

5.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

6.Work out how many factors 100 has.

7.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

8.Write ∛(x²) as a single power of x.

9.Work out (5 + 2) × 3²

10.Write 90 as a product of its prime factors.

11.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

12.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

13.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

14.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

15.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.