Moderate -0.8 This is a straightforward simultaneous equations problem requiring substitution of the linear equation into the quadratic, solving a simple quadratic equation, then finding corresponding y-coordinates. It's a standard GCSE/early A-level technique with no conceptual challenges, making it easier than average for A-level, though the 'show detailed reasoning' requirement adds minimal difficulty.
In this question you must show detailed reasoning.
Find the coordinates of the points of intersection of the curve \(y = x^2 + x\) and the line \(2x + y = 4\). [5]
Question 1:
1 | DR
y(cid:32)4(cid:16)2x
4(cid:16)2x(cid:32)x2 (cid:14)x
(cid:159) x2 + 3x – 4 = 0
(cid:159) x = 1 or x = −4
y = 2 or y = 12
(1,2) and (-4,12) | M1
M1
A1
A1
A1
[5] | 2.1
1.1
1.1
1.1
2.5 | Eliminating x or y must be seen
Form a quadratic equation
n
e
For final A mark, corresponding
values of x and y must be expressed
as coordinates from well set out
correct solution | Or y2(cid:16)14y(cid:14)24(cid:32)0
SC1 for one pair of coordinates
only
1 | 3 | 2 | 0 | 0 | 5 | 0
In this question you must show detailed reasoning.
Find the coordinates of the points of intersection of the curve $y = x^2 + x$ and the line $2x + y = 4$. [5]
\hfill \mbox{\textit{OCR MEI Paper 2 Q1 [5]}}