Higher June 2024 Paper 1 Q23
23 C is a circle with centre (0, 0)
L is a straight line.
The circle C and the line L intersect at the points \(P\) and \(Q\).
The coordinates of \(P\) are (5, 10)
The \(x\) coordinate of \(Q\) is \(-2\)
L has a positive gradient and crosses the \(y\)-axis at the point \((0, k)\)
Find the value of \(k\). (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(-5\) | P1 | for \(x^2 + y^2 = 125\) or \(5^2 + 10^2\ (= 125)\) |
| P1 | for process to find \(y\) coordinate of \(Q\), eg \((\pm)\sqrt{125 - (-2)^2}\) | |
| P1 | for selecting \(-\sqrt{125 - (-2)^2}\) eg \(y = -11\) | |
| P1 | (dep P2) for process to find \(y\) intercept, eg \(\dfrac{10 - [y]}{5 - -2}\ (= 3)\) and substitutes \(x = 5\), \(y = 10\) in \(y = \text{``}3\text{''}x + k\) or \(\dfrac{10 - [y]}{5 - -2}\ (= 3)\) and \([y] + 2 \times \text{``}3\text{''}\) or \(\dfrac{10 - k}{5} = \dfrac{k - [y]}{2}\) or \([y] + \dfrac{2}{7} \times (10 - [y])\) | |
| A1 | cao |
Additional guidance
Where \([y]\) is their \(y\) coordinate of \(Q\)