Number worksheet — GCSE Higher

1.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

2.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

3.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

4.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

5.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

6.After a price increase of 10%, a laptop costs £330. Work out the original price.

7.Work out 10% of 30% of £200.

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 ((−3) + 5) × (−4) − (−6) ÷ 2

10.Work out the value of (1/3)⁻²

11.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

12.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

13.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

14.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

15.Simplify √45.