| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.8 This is a multi-part question testing basic coordinate geometry: simultaneous equations, perpendicular lines, and circle equations from diameter endpoints. All parts use standard techniques with clear scaffolding. The circle-from-diameter formula is a direct application, and verifying a point lies on the circle is routine substitution. Easier than average A-level content. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(3 \mid x + 3(3x + 1) = 6\) o.e. | M1 | for subst or for rearrangement and multn to make one pair of coefficients the same or for both eqns in form \(y =\) (condone one error) |
| \(10x = 3\) or \(10y = 19\) o.e. | A1 | |
| \((0.3, 1.9)\) or \(x = 0.3\) and \(y = 1.9\) o.e. | A1 |
Total: 3 marks
Question 3:
$3 \mid x + 3(3x + 1) = 6$ o.e. | M1 | for subst or for rearrangement and multn to make one pair of coefficients the same or for both eqns in form $y =$ (condone one error)
$10x = 3$ or $10y = 19$ o.e. | A1
$(0.3, 1.9)$ or $x = 0.3$ and $y = 1.9$ o.e. | A1
graphical soln: (must be on graph paper)
M1 for each line, A1 for $(0.3, 1.9)$ o.e. cao; allow B3 for $(0.3, 1.9)$ o.e.
Total: 3 marks3 Find the coordinates of the point of intersection of the lines $y = 3 x + 1$ and $x + 3 y = 6$.
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\caption{Fig. 7}
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The line AB has equation $y = 4 x - 5$ and passes through the point $\mathrm { B } ( 2,3 )$, as shown in Fig. 7. The line BC is perpendicular to AB and cuts the $x$-axis at C . Find the equation of the line BC and the $x$-coordinate of C .\\
$5 \mathrm {~A} ( 9,8 ) , \mathrm { B } ( 5,0 )$ an $\mathrm { C } ( 3,1 )$ are three points.\\
(i) Show that AB and BC are perpendicular.\\
(ii) Find the equation of the circle with AC as diameter. You need not simplify your answer.
Show that B lies on this circle.\\
(iii) BD is a diameter of the circle. Find the coordinates of D .
\hfill \mbox{\textit{OCR MEI C1 Q3 [3]}}