Number worksheet — GCSE Higher

1.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

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

3.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

4.Work out (−36) ÷ (−6) × 2

5.Work out 100 − 4 × 5²

6.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

7.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

8.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.

9.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

10.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

11.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

12.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

13.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

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

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