Number worksheet — GCSE Higher

1.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

2.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

3.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

4.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

5.4ˣ = 64. Work out the value of x.

6.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

7.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

8.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

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

10.Work out (−2)³ + (−3)² − (−4)

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

12.Simplify (y³)⁴, giving your answer as a single power of y.

13.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

14.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

15.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.