AQA GCSE Maths: Ratio, Proportion and Rates of Change

Aisha, Ben and Carl share a sum of money in the ratio $3 : 5 : 7$3:5:7.

(a) Carl receives £84 more than Aisha. Work out the total sum of money shared. (3 marks)

(b) Ben gives one fifth of his share to a charity. Work out how much money Ben has left. (2 marks)

$d$d is inversely proportional to the square of $t$t. When $t = 4$t=4, $d = 5$d=5.

(a) Find a formula for $d$d in terms of $t$t. (3 marks)

(b) Find the value of $d$d when $t = 10$t=10. (1 mark)

A solid metal cylinder has a mass of $1560$1560 g and a volume of $200 \text{ cm}^3$200 cm3.

(a) Work out the density of the metal, stating the units. (2 marks)

(b) A different solid, made of the same metal, has a mass of $4.68$4.68 kg. Work out the volume of this solid, in $\text{cm}^3$cm3. (2 marks)

Shop A sells a $750$750 g jar of coffee for £6.30. Shop B sells a $450$450 g jar of the same coffee for £3.96. Determine which shop offers the better value for money. You must show your working. (3 marks)

The value of a car is £18000. Each year the value falls by $12\%$12% of its value at the start of that year. Work out the value of the car after $3$3 years, to the nearest pound. (2 marks)

A train travels $150$150 km in $2$2 hours $30$30 minutes. Work out the average speed of the train, in km/h. (1 mark)