Past paper questions

Peter invests $P$ at the beginning of each month in a year at an interest rate of $6\%$ per annum, compounded monthly. If he gets \10\,000$at the end of the year, find$P$ correct to 2 decimal places.

The figure shows a cuboid $ABCDEFGH$. If the angle between the triangle $ACE$ and the plane $ABCD$ is $\theta$, then $\tan\theta =$

In the figure, $A$, $B$ and $C$ are points lying on the circle. $TA$ is the tangent to the circle at $A$. The straight line $CBT$ is perpendicular to $TA$. If $BC = 6\text{ cm}$, find the radius of the circle correct to the nearest $0.1\text{ cm}$.

Let $a$ be a constant and $-90^\circ < b < 90^\circ$. If the figure shows the graph of $y = a\cos(x^\circ + b)$, then

Bag A contains 2 red balls, 3 green balls and 4 white balls while bag B contains 2 red balls, 3 green balls and 4 yellow balls. If one ball is drawn randomly from each bag, then the probability that the two balls drawn are of different colours is

2 girls and 5 boys randomly form a queue, find the probability that the two girls are next to each other in the queue.

A set of numbers has a mode of 32, an inter-quartile range of 27 and a variance of 25. If $3$ is added to each number of the set and each resulting number is then doubled to form a new set of numbers, find the mode, the inter-quartile range and the variance of the new set of numbers.