Moderate -0.8 This is a straightforward simultaneous equations problem requiring substitution of y=3x into the circle equation, solving the resulting quadratic, then finding y-coordinates. It's a standard C1 exercise with clear method and no conceptual challenges, making it easier than average but not trivial due to the algebraic manipulation and surd simplification required.
Question 1:
1 | x2 + 9x2 = 25
10x2 = 25
x= ±(√10)/2 or.±√(5/2) or ±5/√10 oe
y = [±] 3√(5/2) o.e. eg y = [±] √22.5 | M1
M1
A2
B1 | for subst for x or y attempted
or x2 = 2.5 o.e.; condone one error from
start [allow 10x2 − 25 = 0 + correct
substn in correct formula]
allow ±√2.5; A1 for one value
ft 3 × their x value(s) if irrational;
condone not written as coords. | 5
Find the coordinates of the points of intersection of the circle $x^2 + y^2 = 25$ and the line $y = 3x$.
Give your answers in surd form. [5]
\hfill \mbox{\textit{OCR MEI C1 Q1 [5]}}