OCR MEI C1 2010 June — Question 1 3 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2010
SessionJune
Marks3
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Mark schemeDownload PDF ↗
TopicStraight Lines & Coordinate Geometry
TypeParallel line through point
DifficultyEasy -1.2 This is a straightforward application of the parallel lines property (same gradient) and point-slope form. It requires only recalling that parallel lines have equal gradients (m=3) and substituting into y-mx=c or y-y₁=m(x-x₁), making it easier than average with minimal problem-solving demand.
Spec1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships
Find the equation of the line which is parallel to \(y = 3x + 1\) and which passes through the point with coordinates \((4, 5)\). [3]
AnswerMarks Guidance
\(y = 3x + c\) or \(y - y_1 = 3(x - x_1)\)M1 allow M1 for 3 clearly stated/used as gradient of required line
\(y - 5 = \text{their } m(x - 4)\) o.e.M1 or \((4, 5)\) subst in their \(y = mx + c\); allow M1 for \(y - 5 = m(x - 4)\) o.e.
\(y = 3x - 7\) or simplified equiv.A1 condone \(y = 3x + c\) and \(c = -7\) or B3 www 
$y = 3x + c$ or $y - y_1 = 3(x - x_1)$ | M1 | allow M1 for 3 clearly stated/used as gradient of required line

$y - 5 = \text{their } m(x - 4)$ o.e. | M1 | or $(4, 5)$ subst in their $y = mx + c$; allow M1 for $y - 5 = m(x - 4)$ o.e.

$y = 3x - 7$ or simplified equiv. | A1 | condone $y = 3x + c$ and $c = -7$ or B3 www
Find the equation of the line which is parallel to $y = 3x + 1$ and which passes through the point with coordinates $(4, 5)$. [3]

\hfill \mbox{\textit{OCR MEI C1 2010 Q1 [3]}}
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Q1 3 Q2 5 Q3 3 Q4 5 Q5 5 Q6 5 Q7 4 Q8 4 Q9 2 Q10 12 Q11 12 Q12 12