Past paper questions

Factorize

The daily wage of Ada is $20\%$ higher than that of Billy while the daily wage of Billy is $20\%$ lower than that of Christine. It is given that the daily wage of Billy is \480$.

There are 132 guards in an exhibition centre consisting of 6 zones. Each zone has the same number of guards. In each zone, there are 4 more female guards than male guards. Find the number of male guards in the exhibition centre. (4 marks)

The box-and-whisker diagram below shows the distribution of the times taken by a large group of students of an athletic club to finish a $100$ m race:

The inter-quartile range and the range of the distribution are $3.2$ s and $6.8$ s respectively.

In Figure 2, the volume of the solid right prism $ABCDEFGH$ is $1020\ cm^{3}$. The base $ABCD$ of the prism is a trapezium, where $AD$ is parallel to $BC$. It is given that $\angle BAD = 90^{\circ}$, $AB = 12\ cm$, $BC = 6\ cm$ and $DE = 10\ cm$.

Tom conducts a survey on the numbers of hours spent on doing homework in a week by secondary students. Questionnaires are sent out and twenty of them are returned. The stem-and-leaf diagram below shows the numbers of hours recorded in the twenty questionnaires:

Let $C$ be the cost of painting a can of surface area $A\ m^2$. It is given that $C$ is the sum of two parts, one part is a constant and the other part varies as $A$. When $A=2$, $C=62$; when $A=6$, $C=74$.

The standard deviation of the test scores obtained by a class of students in a Mathematics test is 10 marks. All the students fail in the test, so the test score of each student is adjusted such that each score is increased by $20\%$ and then extra 5 marks are added.

There are 8 departments in a company. To form a task group of 16 members, 2 representatives are nominated by each department. From the task group, 4 members are randomly selected.

Factorize

The price of 7 pears and 3 oranges is \47$while the price of 5 pears and 6 oranges is$\$49$. Find the price of a pear. (4 marks)

In a polar coordinate system, $O$ is the pole. The polar coordinates of the points $A$ and $B$ are $(26,10^{\circ})$ and $(26,130^{\circ})$ respectively. Let $L$ be the axis of reflectional symmetry of $\Delta OAB$.

In Figure 1, $ABCD$ is a quadrilateral. The diagonals $AC$ and $BD$ intersect at $E$. It is given that $BE = CE$ and $\angle BAC = \angle BDC$.

A pack of sea salt is termed regular if its weight is measured as $100\text{ g }$ correct to the nearest g.

The bar chart below shows the distribution of the numbers of family members of the employees of company $D$.

Distribution of the numbers of family members of the employees of company D

Figure 1

The weight of a tray of perimeter $\ell$ metres is $W$ grams. It is given that $W$ is the sum of two parts, one part varies directly as $\ell$ and the other part varies directly as $\ell^{2}$. When $\ell=1$, $W=181$ and when $\ell=2$, $W=402$.

Let $f(x)=3x^{3}-7x^{2}+kx-8$, where $k$ is a constant. It is given that $f(x)\equiv(x-2)(ax^{2}+bx+c)$, where $a$, $b$ and $c$ are constants.

(4 marks)

In a workshop, 2 identical solid metal right circular cylinders of base radius $R$ cm are melted and recast into $27$ smaller identical solid right circular cylinders of base radius $r$ cm and height $10$ cm. It is given that the base area of a larger circular cylinder is $9$ times that of a smaller one.

A box contains $5$ white cups and $11$ blue cups. If $6$ cups are randomly drawn from the box at the same time,

Simplify $\frac{(xy^{-2})^{3}}{y^{4}}$ and express your answer with positive indices. (3 marks)

The table below shows the distribution of the numbers of calculators owned by some students.

Consider the formula $2(3m+n)=m+7$.

The marked price of a toy is \255$. The toy is now sold at a discount of$40\%$ on its marked price.

Town X and town Y are $80\text{ km}$ apart. Figure 2 shows the graphs for car A and car B travelling on the same straight road between town X and town Y during the period 7:30 to 9:30 in a morning. Car A travels at a constant speed during the period. Car B comes to rest at 8:15 in the morning.

There are 33 paintings in an art gallery. The box-and-whisker diagram below shows the distribution of the prices (in thousand dollars) of the paintings in the art gallery. It is given that the mean of this distribution is $53$ thousand dollars.

The circle C passes through the point $A(6,11)$ and the centre of C is the point $G(0,3)$.