Number worksheet — GCSE Higher

1.Write 12 as a product of its prime factors.

2.Simplify (x⁻²)³, giving your answer as a fraction.

3.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

4.Write 0.325 as a fraction in its simplest form.

5.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

6.Write ∛(x²) as a single power of x.

7.Work out 3 + 4 × (−2).

8.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?

9.Write 7/12 as a decimal, showing clearly which digit is recurring.

10.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

11.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

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

13.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

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

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