Mathematics 0580 · IGCSE · Equations

Equations — practice question

Alfonso covers 10 km at an average speed of $x$ km/h. On the following day, he covers 12 km at an average speed of $(x - 1)$ km/h. The 10 km journey takes 30 minutes less than the 12 km journey.
(a(i))[4]

Form an equation in $x$ and show that it reduces to $x^2 - 5x - 20 = 0$.

(a(ii))[4]

Solve the equation $x^2 - 5x - 20 = 0$ using the quadratic formula. Show all your steps and give the answers correct to 2 decimal places.

(a(iii))[2]

Determine the time Alfonso needs for the 12 km run. State your answer in hours and minutes, correct to the nearest minute.

(b(i))[1]

Calculate the cheetah’s acceleration in the first 10 seconds.

(b(ii))[3]

Calculate the distance covered by the cheetah.

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: $ rac{12}{x-1}- rac{10}{x}=0.5$

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