Challenging +1.2 This question requires finding a parameter (a=9), then solving x²|9 for integer solutions, which involves factorization and systematic checking. While it needs careful enumeration of divisors and consideration of negative values, it's a straightforward application of divisibility with no deep conceptual insight required—moderately above average difficulty.
8 For a particular value of \(a\), the curve \(\mathrm { y } = \frac { \mathrm { a } } { \mathrm { x } ^ { 2 } }\) passes through the point \(( 3,1 )\).
Find the coordinates of all the other points on the curve where both the \(x\)-coordinate and the \(y\)-coordinate are integers.
A2 for all three points; A1 for one correct point; Ignore \((3,1)\); If other incorrect points A1 max
[3 marks]
## Question 8:
$a = 9$ | M1 (3.1a) | Implied by any of the points
$(-3, 1)$, $(1, 9)$, $(-1, 9)$ | A2 (1.1, 2.2a) | A2 for all three points; A1 for one correct point; Ignore $(3,1)$; If other incorrect points A1 max
[3 marks]
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8 For a particular value of $a$, the curve $\mathrm { y } = \frac { \mathrm { a } } { \mathrm { x } ^ { 2 } }$ passes through the point $( 3,1 )$.\\
Find the coordinates of all the other points on the curve where both the $x$-coordinate and the $y$-coordinate are integers.
\hfill \mbox{\textit{OCR MEI Paper 3 2021 Q8 [3]}}