Number worksheet — GCSE Higher

1.Which one of these statements is true?

2.Simplify x⁷ × x⁴, giving your answer as a single power of x.

3.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

4.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

5.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

6.Round 0.006852 to 2 significant figures.

7.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

8.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

9.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

10.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

11.Work out (−2)³ + (−3)² − (−4)

12.Work out −(−3)⁴ + (−3)³

13.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

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

15.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.