Ratio, proportion and rates of change

£7,500 is invested at 4.2% compound interest per year. Work out the value of the investment after 6 years. Give your answer to the nearest penny.

In a sale, prices are reduced by 30%. A coat costs £73.50 in the sale. Work out the price before the sale.

A train travels 234 km in 135 minutes. (a) Work out its average speed in km/h. (b) Convert this speed to metres per second.

The population of a town fell from 125,400 to 117,900. Work out the percentage decrease to 1 decimal place.

A car is bought for £24,000. Its value depreciates by 15% each year. Work out its value after 3 years, to the nearest pound.

Pack A has 400 g of cereal for £1.85. Pack B has 650 g for £2.95. Which is better value? Show your working.

£1 = €1.17. A bureau charges 1.5% commission on the amount changed. How many euros does someone receive for £800?

Amir and Beth share £450 in the ratio 7 : 2. Amir then gives Beth £25. Work out the new ratio of Amir's money to Beth's money in its simplest form.

y is inversely proportional to x². When x = 2, y = 18. Find y when x = 6.

In a sale, prices are reduced by 10%. A coat costs £37.80 in the sale. Work out the price before the sale.

A car is bought for £9,600. Its value depreciates by 6% each year. Work out its value after 5 years, to the nearest pound.

Metal A has density 9 g/cm³. A block of metal A has volume 30 cm³ and is melted together with 250 g of metal B to make an alloy of volume 55 cm³ (metal B has density 10 g/cm³). Work out the density of the alloy.

A cyclist accelerates uniformly from rest to 9 m/s in 5 s, travels at 9 m/s until t = 25 s, then decelerates uniformly to rest at t = 33 s. (a) Work out the acceleration. (b) Work out the total distance travelled.

y is inversely proportional to x². When x = 2, y = 36. Find y when x = 3.

£3,000 is invested at 1.9% compound interest per year. Work out the value of the investment after 8 years. Give your answer to the nearest penny.

A box exerts a force of 900 N on the floor. Its base is a rectangle 0.6 m by 0.4 m. Work out the pressure in N/m². (pressure = force ÷ area)

The speed of a car (m/s) at 0, 2, 4 and 6 seconds is 0, 11, 18 and 22. Use three trapeziums of equal width to estimate the distance travelled in the first 6 seconds, and state whether this is an under- or over-estimate for a curve that bends downwards (concave).