Number worksheet — GCSE Higher

1.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

2.Work out the exact value of √(2² + 3²)

3.Write down the exact decimal value of the fraction 1/6.

4.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

5.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

6.Work out √25 + 4² − 12 ÷ 3

7.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.

8.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.

9.Work out √(4 × 9)

10.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

11.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

12.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

13.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

14.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

15.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.