Number worksheet — GCSE Higher

1.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

2.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

3.Work out (−6) + (−4) × 3

4.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

5.Simplify ⁴√(16a⁸b¹²)

6.Work out the value of 2⁻⁴

7.Write 0.325 as a fraction in its simplest form.

8.Work out ⁴√81

9.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

10.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

11.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

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

13.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

14.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.