OCR GCSE Maths: Number

A car travels at a constant speed of $24.0$24.0 m/s, measured to the nearest $0.1$0.1 m/s, for a time of $15.0$15.0 seconds, measured to the nearest $0.1$0.1 second.

The distance travelled is given by $\text{distance} = \text{speed} \times \text{time}$distance=speed×time.

(a) Write down the upper bound and the lower bound of the speed. (2 marks)

(b) Calculate the upper bound for the distance travelled. (2 marks)

(c) By considering the bounds, write down the distance travelled to a suitable degree of accuracy. Give a reason for your answer. (1 mark)

(a) After a price increase of $20\%$20%, the cost of a monthly gym membership is £96. Work out the cost of the membership before the increase. (2 marks)

(b) A van is bought for £18 000. Each year its value decreases by $10\%$10% of its value at the start of that year. Work out the value of the van at the end of $3$3 years. (2 marks)

(a) Write $540$540 as a product of its prime factors. Give your answer in index form. (2 marks)

(b) Given that $126 = 2 \times 3^2 \times 7$126=2×32×7, find the highest common factor (HCF) and the lowest common multiple (LCM) of $540$540 and $126$126. (2 marks)

Work out the exact value of $\left(\frac{8}{27}\right)^{-\frac{2}{3}}.$(278​)−32​. Give your answer as a fraction in its simplest form. (3 marks)

Write $\sqrt{72} + \sqrt{50}$72​+50​ in the form $a\sqrt{2}$a2​, where $a$a is an integer. (2 marks)

Write $73\,500\,000$73500000 in standard form. (1 mark)