OCR C1 2010 June — Question 5 5 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2010
SessionJune
Marks5
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TopicSolving quadratics and applications
TypeQuadratic in higher integer powers
DifficultyModerate -0.8 This is a straightforward quartic-in-quadratic-form question requiring substitution u = x², solving the resulting quadratic 4u² + 3u - 1 = 0, then back-substituting. It's a standard C1 technique with clear structure and no conceptual challenges, making it easier than average but not trivial since students must recognize the substitution and handle both positive and negative square roots correctly.
Spec1.02f Solve quadratic equations: including in a function of unknown
5 Find the real roots of the equation \(4 x ^ { 4 } + 3 x ^ { 2 } - 1 = 0\).
Question 5:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(k = x^2\)M1* Use a substitution to obtain a quadratic or factorise into 2 brackets each containing \(x^2\)
\(4k^2 + 3k - 1 = 0\)
\((4k-1)(k+1) = 0\)M1 dep Correct method to solve a quadratic
\(k = \frac{1}{4}\) (or \(k = -1\))A1
\(x = \pm\frac{1}{2}\)M1 Attempt to square root to obtain \(x\)
A15 \(\pm\frac{1}{2}\) and no other values 
# Question 5:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $k = x^2$ | M1* | Use a substitution to obtain a quadratic or factorise into 2 brackets each containing $x^2$ |
| $4k^2 + 3k - 1 = 0$ | | |
| $(4k-1)(k+1) = 0$ | M1 dep | Correct method to solve a quadratic |
| $k = \frac{1}{4}$ (or $k = -1$) | A1 | |
| $x = \pm\frac{1}{2}$ | M1 | Attempt to square root to obtain $x$ |
| | A1 | **5** $\pm\frac{1}{2}$ and no other values |

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5 Find the real roots of the equation $4 x ^ { 4 } + 3 x ^ { 2 } - 1 = 0$.

\hfill \mbox{\textit{OCR C1 2010 Q5 [5]}}
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