Number worksheet — GCSE Higher

1.Work out the value of √(16 + 9)

2.Expand and simplify √3(2 + √12).

3.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

4.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

5.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

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

7.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

8.Work out ⁴√81

9.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

10.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

11.Work out √(4 × 9)

12.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

13.Work out 36 ÷ (2 × 3)

14.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

15.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.