Ratio, proportion and rates of change

Amir and Beth share £350 in the ratio 4 : 3. Amir then gives Beth £50. 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 = 3, y = 10. Find y when x = 6.

£6,200 is invested at 2.8% compound interest per year. Work out the value of the investment after 5 years. Give your answer to the nearest penny.

In a sale, prices are reduced by 15%. A coat costs £102.00 in the sale. Work out the price before the sale.

A train travels 171 km in 54 minutes. (a) Work out its average speed in km/h. (b) Convert this speed to metres per second.

The population of a town rose from 36,400 to 41,950. Work out the percentage increase to 1 decimal place.

Pack A has 750 g of cereal for £3.15. Pack B has 500 g for £2.20. Which is better value? Show your working.

A car is bought for £18,500. Its value depreciates by 12% each year. Work out its value after 4 years, to the nearest pound.

Metal A has density 7 g/cm³. A block of metal A has volume 40 cm³ and is melted together with 500 g of metal B to make an alloy of volume 90 cm³ (metal B has density 10 g/cm³). Work out the density of the alloy.

A cyclist accelerates uniformly from rest to 15 m/s in 6 s, travels at 15 m/s until t = 26 s, then decelerates uniformly to rest at t = 36 s. (a) Work out the acceleration. (b) Work out the total distance travelled.

y is inversely proportional to x². When x = 4, y = 20. Find y when x = 10.

A box exerts a force of 1200 N on the floor. Its base is a rectangle 0.8 m by 0.5 m. Work out the pressure in N/m². (pressure = force ÷ area)

The speed of a car (m/s) at 0, 5, 10 and 15 seconds is 0, 6, 10 and 12. Use three trapeziums of equal width to estimate the distance travelled in the first 15 seconds, and state whether this is an under- or over-estimate for a curve that bends downwards (concave).