Higher November 2018 Paper 1 Q22
22 There are only green pens and blue pens in a box.
There are three more blue pens than green pens in the box.
There are more than 12 pens in the box.
Simon is going to take at random two pens from the box.
The probability that Simon will take two pens of the same colour is \(\dfrac{27}{55}\)
Work out the number of green pens in the box. (6)
| Answer | Mark | Mark scheme |
|---|---|---|
| 21 | P1 | for a relevant probability, eg P(green) \(= \dfrac{x}{2x + 3}\) or P(blue) \(= \dfrac{x + 3}{2x + 3}\) |
| P1 | for a relevant product, eg. \(\text{``}\dfrac{x}{2x + 3}\text{''} \times \text{``}\dfrac{x - 1}{2x + 2}\text{''}\) or \(\text{``}\dfrac{x + 3}{2x + 3}\text{''} \times \text{``}\dfrac{x + 2}{2x + 2}\text{''}\) OR \(\left(\text{``}\dfrac{x}{x + 3}\text{''}\right)^2 + \left(\text{``}\dfrac{x + 3}{2x + 3}\text{''}\right)^2 = \dfrac{27}{75}\) | |
| P1 | forms an appropriate equation, eg. \(\text{``}\dfrac{x}{2x + 3} \times \dfrac{x - 1}{2x + 2}\text{''} + \text{``}\dfrac{x + 3}{2x + 3} \times \dfrac{x + 2}{2x + 2}\text{''} = \dfrac{27}{55}\) | |
| P1 | (dep P3) process to reduce equation to \(ax^2 + bx + c = 0\) eg. \(x^2 - 25x + 84 = 0\) | |
| P1 | process to solve quadratic equation eg. \((x - 21)(x - 4) = 0\) | |
| A1 | cao |
Additional guidance
the number of green and blue pens could be \(x - 3\) and \(x\) or equivalent
probabilities must be in an algebraic form in a single variable
This is an exception using replacements. No further credit is available