Number worksheet — GCSE Higher

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

2.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.

3.Write 0.35 as a fraction in its lowest terms.

4.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

5.Work out how many factors 36 has.

6.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.

7.Find the missing number: 17 × ▢ = 391

8.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

9.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

10.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

11.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

12.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

13.Simplify ⁴√(16a⁸b¹²)

14.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

15.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.