Question 9 - A-Level Maths

Exam Board	OCR MEI
Module	C1 (Core Mathematics 1)
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Simultaneous equations
Type	Line intersecting quadratic curve
Difficulty	Moderate -0.8 This is a straightforward simultaneous equations question requiring students to equate the expressions, form a quadratic, and solve for two intersection points. It's a standard C1 exercise with routine algebraic manipulation and no conceptual challenges, making it easier than average but not trivial since it requires multiple steps and solving a quadratic.
Spec	1.02q Use intersection points: of graphs to solve equations

9 Find the coordinates of the points where the curve \(y = x ^ { 2 } - 2 x - 8\) meets the line \(y = x + 2\).

Answer	Marks
i.e. \((-2,0), (5,7)\)	M1, A1, M1, A1

$x + 2 = x^2 - 2x - 8 \Rightarrow x^2 - 3x - 10 = 0$

$\Rightarrow (x - 5)(x + 2) = 0 \Rightarrow x = -2, 5$

i.e. $(-2,0), (5,7)$ | M1, A1, M1, A1 |

9 Find the coordinates of the points where the curve $y = x ^ { 2 } - 2 x - 8$ meets the line $y = x + 2$.

\hfill \mbox{\textit{OCR MEI C1  Q9 [4]}}