O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2020 · Q1010 Marks

10 Amira drives 40 km to work. (a) Amira takes x minutes to drive the first 30km of the journey. Show that her average speed in km/h for the first 30 km of the journey is 1800/x .

(a)Amira takes x minutes to drive the first 30km of the journey. Show that her average speed in km/h for the first 30 km of the journey is 1800/x .[1]
(b)Amira's average speed in km/h for the final 10km of the journey is 600 / (x-25) . Her average speed for the first 30km of the journey is 8 km/h slower than her average speed for the final 10km. Form an equation in x and show that it simplifies to x² +125x-5625 = 0.[3]
(c)Solve the equation x²+125x-5625 = 0. Show your working and give each answer correct to 1 decimal place.[3]
(d)It takes Amira 25 minutes less to drive the final 10km than it takes for the first 30km. Calculate Amira's average speed, in km/h, for the whole journey.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[1] Show that average speed is 1800/x km/h; e.g. Speed = Distance/Time = 30km / (x minutes / 60 min/hr) = 30 * 60 / x = 1800/x km/h.
[3] M1 for setting up equation: 600/(x-25) - 1800/x = 8 (or equivalent); M1 Strict FT correct elimination of fractions and brackets (e.g., 600x - 1800(x-25) = 8x(x-25)); A1 for correct rearrangement to x² + 125x - 5625 = 0 (A0 if any errors/omissions in working).
[3] B2 for quadratic formula applied correctly: (-125 ± sqrt(125² - 4(1)(-5625))) / (2×1) oe; (B1 for discriminant 125² - 4(-5625) = 15625 + 22500 = 38125 seen); B1 for each correct answer 35.1, -160.1 (to 1 d.p.).
[3] M1 for finding total time for journey (sum of first 30km time and final 10km time), using the positive x value from (c); M2 for overall speed = Total Distance / Total Time; Final answer 53[.0] to 53.1 km/h nfww.

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.