Higher November 2022 Paper 2 Q27
27 In a class there are
\(n\) boys
a total of 25 students.
Two of the students are chosen at random.
The probability that both students are boys is \(\dfrac{7}{20}\)
Work out the value of \(n\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{n}{25}\) and \(\dfrac{n - 1}{24}\) | M1 | oe may be implied eg \(\dfrac{n(n - 1)}{600}\) |
| \(n^2 - n - 210\ (= 0)\) | M1dep | oe with all terms fully simplified eg \(n^2 - n = 210\) |
| \((n - 15)(n + 14)\) or \(\dfrac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 1 \times -210}}{2 \times 1}\) or \(\dfrac{1}{2} \pm \sqrt{210 + \dfrac{1}{4}}\) | M1 | oe eg \(\dfrac{1 \pm \sqrt{841}}{2}\) or \(\dfrac{1 \pm 29}{2}\) or \(0.5 \pm 14.5\) ft their 3-term quadratic |
| 15 | A1 | 15 and \(-14\) is A0 |
Additional guidance
| Answer 15 with no working or from trial | M3A1 |
| Beware Answer 15 from incorrect working eg \(\dfrac{n}{25} \times \dfrac{n}{25} = \dfrac{7}{20} \qquad n^2 = 218.75 \qquad n = 15\) | M0M0M0A0 |
| Allow \(n\) to be \(N\) or \(x\) etc | |
| 3rd M1 Allow \((-1)^2\) to be \(1^2\) | |
| 3rd M1 Do not allow \((-1)^2\) to be \(-1^2\) unless recovered | |
| 3rd M1 Allow \(\pm\) to be \(+\) | |
| 3rd M1 Square root sign should cover all appropriate work unless recovered eg \(\dfrac{1 \pm \sqrt{1} + 840}{2}\) not recovered | M0 |
| 3rd M1 Fraction line should be under all appropriate work unless recovered eg \(1 \pm \dfrac{\sqrt{841}}{2}\) not recovered | M0 |
| 3rd M1 √((–1)2 – 4 × 1 × –210) is correct for \(\sqrt{(-1)^2 - 4 \times 1 \times -210}\) |