Higher November 2021 Paper 2 Q24
24 The flight of a plane was in two stages.
The table shows information about the flight.
| Distance (miles) | Speed (mph) | Time (hours) | |
|---|---|---|---|
| 1st stage | 731 | \(x\) | \(\dfrac{731}{x}\) |
| 2nd stage | 287 | \(x - 24\) | \(\dfrac{287}{x - 24}\) |
In total, the flight lasted 2 hours.
Work out the value of \(x\). [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{731}{x} + \dfrac{287}{x - 24} = 2\) | M1 | oe equation |
| \(731(x - 24) + 287x\) or \(731x - 17\,544 + 287x\) | M1dep | oe allow with denominator \(x(x - 24)\) oe |
| \(2x^2 - 1066x + 17\,544\ (= 0)\) or \(x^2 - 533x + 8772\ (= 0)\) | A1 | oe eg \(x^2 - 533x = -8772\) |
| \(\dfrac{-(-1066) \pm \sqrt{(-1066)^2 - 4 \times 2 \times 17\,544}}{2 \times 2}\) or \(\dfrac{1066 \pm \sqrt{1\,136\,356 - 140\,352}}{2 \times 2}\) or \(\dfrac{1066 \pm \sqrt{996\,004}}{2 \times 2}\) or \(\dfrac{1066 \pm 998}{2 \times 2}\) or \((2x - 34)(x - 516)\) or 17 and 516 | M1 | ft their 3-term quadratic oe eg \(\dfrac{-(-533) \pm \sqrt{(-533)^2 - 4 \times 1 \times 8772}}{2 \times 1}\) or \(\dfrac{533 \pm \sqrt{284\,089 - 35\,088}}{2 \times 1}\) or \(\dfrac{533 \pm \sqrt{249\,001}}{2 \times 1}\) or \(\dfrac{533 \pm 499}{2}\) or \((x - 17)(x - 516)\) |
| 516 | A1 | must discard 17 |
Additional guidance
First M1 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts
3rd M1 Allow ft of their 3-term quadratic even if discriminant is \(\leqslant 0\)
In quadratic formula, allow eg \(1066^2\) for \((-1066)^2\)