OCR C1 2010 June — Question 7 6 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2010
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting general conic
DifficultyModerate -0.3 This is a straightforward simultaneous equations problem requiring substitution of a linear equation into a quadratic (conic), then solving the resulting quadratic. While it involves multiple steps and algebraic manipulation, it's a standard C1 technique with no conceptual difficulty—slightly easier than average due to the clean numbers and routine method.
Spec1.02c Simultaneous equations: two variables by elimination and substitution
7 Solve the simultaneous equations $$x + 2 y - 6 = 0 , \quad 2 x ^ { 2 } + y ^ { 2 } = 57 .$$
Question 7:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(2(6-2y)^2 + y^2 = 57\)M1* Substitute for \(x/y\) or attempt to get an equation in 1 variable only
\(2(36 - 24y + 4y^2) + y^2 = 57\)A1 Correct unsimplified expression
\(9y^2 - 48y + 15 = 0\)A1 Obtain correct 3 term quadratic
\(3y^2 - 16y + 5 = 0\)
\((3y-1)(y-5) = 0\)M1 dep Correct method to solve 3 term quadratic
\(y = \frac{1}{3}\) or \(y = 5\)A1
\(x = \frac{16}{3}\) or \(x = -4\)A1 6 SC If A0 A0, one correct pair of values, spotted or from correct factorisation www B1 
# Question 7:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $2(6-2y)^2 + y^2 = 57$ | M1* | Substitute for $x/y$ or attempt to get an equation in 1 variable only |
| $2(36 - 24y + 4y^2) + y^2 = 57$ | A1 | Correct unsimplified expression |
| $9y^2 - 48y + 15 = 0$ | A1 | Obtain correct 3 term quadratic |
| $3y^2 - 16y + 5 = 0$ | | |
| $(3y-1)(y-5) = 0$ | M1 dep | Correct method to solve 3 term quadratic |
| $y = \frac{1}{3}$ or $y = 5$ | A1 | |
| $x = \frac{16}{3}$ or $x = -4$ | A1 | **6** SC If A0 A0, one correct pair of values, spotted or from correct factorisation **www** B1 |

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7 Solve the simultaneous equations

$$x + 2 y - 6 = 0 , \quad 2 x ^ { 2 } + y ^ { 2 } = 57 .$$

\hfill \mbox{\textit{OCR C1 2010 Q7 [6]}}
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