Number worksheet — GCSE Higher

1.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.

2.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

3.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

4.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

5.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

6.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

7.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

8.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

9.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

10.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?

11.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.

12.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

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

14.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

15.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.