OCR C1 2011 June — Question 1 4 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2011
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCompleting the square and sketching
TypeComplete the square
DifficultyModerate -0.8 This is a straightforward completing the square question with a non-unit coefficient. It requires factoring out the 3, completing the square on the resulting expression, and expanding to find p, q, and r. This is a standard C1 technique with minimal steps and no problem-solving required, making it easier than average.
Spec1.02e Complete the square: quadratic polynomials and turning points

1 Express \(3 x ^ { 2 } - 18 x + 4\) in the form \(p ( x + q ) ^ { 2 } + r\).

AnswerMarks Guidance
\(3(x^2 - 6x) + 4 = 3[(x-3)^2 - 9] + 4 = 3(x-3)^2 - 23\)B1, B1, M1, A1 If \(p, q, r\) found correctly, then ISW slips in format. See guidance for various acceptable forms of final answer.
$3(x^2 - 6x) + 4 = 3[(x-3)^2 - 9] + 4 = 3(x-3)^2 - 23$ | B1, B1, M1, A1 | If $p, q, r$ found correctly, then ISW slips in format. See guidance for various acceptable forms of final answer.
1 Express $3 x ^ { 2 } - 18 x + 4$ in the form $p ( x + q ) ^ { 2 } + r$.

\hfill \mbox{\textit{OCR C1 2011 Q1 [4]}}