Past paper questions

If $m>1$, which of the following are geometric sequences?

I. $2^{m}$, $2^{2m}$, $2^{3m}$, $2^{4m}$
II. $m$, $2m^{2}$, $3m^{4}$, $4m^{8}$
III. $\log m$, $\log m^{2}$, $\log m^{4}$, $\log m^{8}$

Which of the following may represent the graph of $y=f(x)$ and the graph of $y=1-f(x)$ on the same rectangular coordinate system?

For $0^{\circ} \leq x \leq 360^{\circ}$, how many roots does the equation $7\sin^{2}x = \sin x$ have?

In the figure, $AB$ is a vertical pole standing on the horizontal ground $BCD$, where $\angle CBD = 90^{\circ}$. If the angle between the plane $ACD$ and the horizontal ground is $\theta$, then $\tan \theta =$

In the figure, $PQS$ is a circle. $PQ$ is produced to $R$ such that $RS$ is the tangent to the circle at $S$. $I$ is the in-centre of $\Delta QRS$. If $\angle IRQ = 12^\circ$ and $\angle PSQ = 70^\circ$, then $\angle QPS =$

If the straight line $x - y = k$ and the circle $x^2 + y^2 + 2x - 4y - 1 = 0$ intersect at $A$ and $B$, then the x-coordinate of the mid-point of $AB$ is

There are 13 boys and 17 girls in a class. If a team of 2 boys and 3 girls is selected from the class to participate in a voluntary service, how many different teams can be formed?

In an examination, Peter gets $55$ marks and his standard score is $-3$ while Mary gets $95$ marks and her standard score is $2$. Find the mean of the examination scores.

If the variance of the four numbers $a$, $b$, $c$ and $d$ is $9$, then the variance of the four numbers $14-a$, $14-b$, $14-c$ and $14-d$ is