Number worksheet — GCSE Higher

1.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

2.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

3.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.

4.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

5.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

6.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

7.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

8.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

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

10.Work out ⁴√16

11.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

12.Work out −4.5 + 2.8.

13.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

14.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

15.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.