Number worksheet — GCSE Higher

1.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?

2.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

3.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

5.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

6.Work out ⁴√81

7.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

8.Work out the exact value of √(2² + 3²)

9.Which of these statements about −0.7 and −0.25 is true?

10.Simplify ⁴√(16a⁸b¹²)

11.A country has an area of 25,000,000 hectares. Write this area in standard form.

12.Work out √3 × √12, giving your answer as an integer.

13.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

14.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

15.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.