Number worksheet — GCSE Higher

1.Work out √25 + 4² − 12 ÷ 3

2.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

3.Write 200 as a product of its prime factors, using index notation.

4.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.

5.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

6.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

7.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

8.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

9.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

10.Work out (−6) + (−4) × 3

11.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

12.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

14.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

15.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.