Past paper questions

Simplify $\frac{(m^{5}n^{-2})^{6}}{m^{4}n^{-3}}$ and express your answer with positive indices.

Make $a$ the subject of the formula $\frac{5+b}{1-a}=3b$

Factorize

The cost of a chair is \360$. If the chair is sold at a discount of$20\%$on its marked price, then the percentage profit is$30\%$. Find the marked price of the chair.

The ratio of the capacity of a bottle to that of a cup is $4:3$. The total capacity of 7 bottles and 9 cups is $11$ litres. Find the capacity of a bottle.

In Figure 1, $BD$ is a diameter of the circle $ABCD$. If $AB = AC$ and $\angle BDC = 36^{\circ}$, find $\angle ABD$ (4 marks)

The coordinates of the points A and B are $(-3, 4)$ and $(-2, -5)$ respectively. $A'$ is the reflection image of A with respect to the y-axis. B is rotated anticlockwise about the origin O through $90^{\circ}$ to $B'$.

Let $C$ be the cost of manufacturing a cubical carton of side $x$ cm. It is given that $C$ is partly constant and partly varies as the square of $x$. When $x=20$, $C=42$; when $x=120$, $C=112$.

Figure 2 shows the graphs for Ada and Billy running on the same straight road between town $P$ and town $Q$ during the period 1:00 to 3:00 in an afternoon. Ada runs at a constant speed. It is given that town $P$ and town $Q$ are $16\text{ km}$ apart.

The bar chart below shows the distribution of the most favourite fruits of the students in a group. It is given that each student has only one most favourite fruit.

Distribution of the most favourite fruits of the students in the group

If a student is randomly selected from the group, then the probability that the most favourite fruit is apple is $\frac{3}{20}$.

In Figure 3, $OABC$ is a circle. It is given that $AB$ produced and $OC$ produced meet at $D$.

There are 18 boys and 12 girls in a class. From the class, 4 students are randomly selected to form the class committee.

Figure 4 shows a geometric model $ABCD$ in the form of tetrahedron. It is found that $\angle ACB = 60^{\circ}$, $AC = AD = 20$ cm, $BC = BD = 12$ cm and $CD = 14$ cm.