2006 年

A circle $C$ cuts the $y$-axis at $A$ and $B$. If $AB=8$ and the coordinates of the centre of $C$ are $(-3,5)$, then the equation of $C$ is

One letter is chosen randomly from each of the two words ‘FORTY’ and ‘FIFTY’. Find the probability that the two letters chosen are the same.

There are two questions in a test. The probability that David answers the first question correctly is $\dfrac{1}{4}$ and the probability that David answers the second question correctly is $\dfrac{1}{3}$. Given that David answers at least one question correctly in the test, find the probability that he answers the second question correctly.

The standard deviation of the five numbers $10a+1$, $10a+3$, $10a+5$, $10a+7$ and $10a+9$ is