Number worksheet — GCSE Higher

1.Estimate the value of √45, giving your answer to the nearest whole number.

2.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?

3.Work out 5⁰ + 5¹ + 5²

4.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

5.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

6.Find the missing number: ▢ ÷ 15 = 24

7.Which of these is written correctly in standard form?

8.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

9.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

10.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

11.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

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

13.Simplify ⁴√(16a⁸b¹²)

14.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

15.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.