OCR C1 2014 June — Question 1 4 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2014
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicCompleting the square and sketching
TypeComplete the square
DifficultyModerate -0.8 This is a straightforward completing the square question with simple coefficients. It requires factoring out the coefficient of x², completing the square, and simplifying—all standard C1 techniques with no problem-solving or conceptual challenges beyond routine algebraic manipulation.
Spec1.02e Complete the square: quadratic polynomials and turning points
Express \(5x^2 + 10x + 2\) in the form \(p(x + q)^2 + r\), where \(p\), \(q\) and \(r\) are integers. [4]
AnswerMarks Guidance
\(5x^2 + 10x + 2 = 5(x + 2x) + 2 = 5[(x+1)^2 - 1] + 2 = 5(x+1)^2 - 3\)B1, B1, M1, A1 [4] If \(p, q\) and \(r\) found correctly, then ISW slips in format. \(5(x+1)^2 + 3\) B1 B1 M0 A0; \(5(x+1) - 3\) B1 B1 M1 A1 (BOD); \(5(x+1)^2 - 3\) B1 B0 M1 A0; \(5(x^2 + 1)^2 - 3\) B1 B0 M1 A0; \(5(x-1)^2 - 3\) B1 B0 M1 A0; \(5x(x+1)^2 - 3\) B0 B1 M1 A0 
$5x^2 + 10x + 2 = 5(x + 2x) + 2 = 5[(x+1)^2 - 1] + 2 = 5(x+1)^2 - 3$ | B1, B1, M1, A1 [4] | If $p, q$ and $r$ found correctly, then ISW slips in format. $5(x+1)^2 + 3$ B1 B1 M0 A0; $5(x+1) - 3$ B1 B1 M1 A1 (BOD); $5(x+1)^2 - 3$ B1 B0 M1 A0; $5(x^2 + 1)^2 - 3$ B1 B0 M1 A0; $5(x-1)^2 - 3$ B1 B0 M1 A0; $5x(x+1)^2 - 3$ B0 B1 M1 A0
Express $5x^2 + 10x + 2$ in the form $p(x + q)^2 + r$, where $p$, $q$ and $r$ are integers. [4]

\hfill \mbox{\textit{OCR C1 2014 Q1 [4]}}
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Q1 4 Q2 5 Q3 5 Q4 4 Q5 8 Q6 6 Q7 7 Q8 9 Q9 12 Q10 12