OCR C1 2011 June — Question 4 5 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2011
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting quadratic curve
DifficultyModerate -0.8 This is a straightforward simultaneous equations question requiring substitution of the linear equation into the quadratic, expanding to get a quadratic equation, and solving. It's a standard C1 exercise with clear structure and routine algebraic manipulation, making it easier than average but not trivial since students must correctly expand and solve the resulting quadratic.
Spec1.02c Simultaneous equations: two variables by elimination and substitution

4 Solve the simultaneous equations $$y = 2 ( x - 2 ) ^ { 2 } , \quad 3 x + y = 26$$

AnswerMarks Guidance
\(2x^2 - 8x + 8 = 26 - 3x\)M1 Attempt to eliminate x or y
\(2x^2 - 5x - 18(=0)\)A1 Correct 3 term quadratic (not necessarily all in one side)
\((2x-9)(x+2)(=0)\)M1 Correct method to solve quadratic
\(x = \frac{9}{2}, x = -2\)A1 x values correct
\(y = \frac{25}{2}, y = 32\)A1, 5 y values correct
SR If A0 A0, one correct pair of values, spotted or from correct factorisation wwwB1
$2x^2 - 8x + 8 = 26 - 3x$ | M1 | Attempt to eliminate x or y | Must be a clear attempt to reduce to one variable. Condone poor algebra for first mark.

$2x^2 - 5x - 18(=0)$ | A1 | Correct 3 term quadratic (not necessarily all in one side) | If x eliminated: $y = 2(\frac{26-y}{3} - 2)^2$ leading to $2y^2 - 89y + 800 = 0$ or $(2y-25)(y-32)=0$ etc.

$(2x-9)(x+2)(=0)$ | M1 | Correct method to solve quadratic |

$x = \frac{9}{2}, x = -2$ | A1 | x values correct |

$y = \frac{25}{2}, y = 32$ | A1, 5 | y values correct |

SR If A0 A0, one correct pair of values, spotted or from correct factorisation www | B1 |
4 Solve the simultaneous equations

$$y = 2 ( x - 2 ) ^ { 2 } , \quad 3 x + y = 26$$

\hfill \mbox{\textit{OCR C1 2011 Q4 [5]}}