Number worksheet — GCSE Higher

1.Work out √25 + 4² − 12 ÷ 3

2.Work out the reciprocal of (2 + 3)

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

4.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

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

6.Work out (5 + 2) × 3²

7.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

8.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

9.Work out (2/3)² + (1/2)². Give your answer as a fraction.

10.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

11.√700 lies between which two consecutive integers?

12.Work out the value of 2⁻⁴

13.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

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.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.