Number worksheet — GCSE Higher

1.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

2.Write ∛(x²) as a single power of x.

3.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

4.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

5.Work out 36 ÷ (2 × 3)

6.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

7.Work out (−6) + (−4) × 3

8.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

9.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

10.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.

11.Work out how many factors 36 has.

12.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.

13.Work out 5⁰ + 5¹ + 5²

14.Work out the value of √(16 + 9)

15.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56