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.

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 $G(0,3)$.

It is given that $f(x)$ is the sum of two parts, one part varies as $x^{2}$ and the other part is a constant. Suppose that $f(2)=59$ and $f(7)=-121$.

Figure 3 shows a vessel in the form of a frustum which is made by cutting off the lower part of an inverted right circular cone of base radius $72$ cm and height $96$ cm. The height of the vessel is $60$ cm. The vessel is placed on a horizontal table. Some water is now poured into the vessel. John finds that the depth of water in the vessel is $28$ cm.

Figure 6(a) shows a solid pyramid $VABCD$ with a rectangular base, where $AB = 18\text{ cm}$, $BC = 10\text{ cm}$, $VB = VC = 30\text{ cm}$ and $\angle VAB = \angle VDC = 110^\circ$.

Ada and Billy play a game consisting of two rounds. In the first round, Ada and Billy take turns to throw a fair die. The player who first gets a number '3' wins the first round. Ada and Billy play the first round until one of them wins. Ada throws the die first.

If $p$ and $q$ are constants such that $px(x-1)+x^{2} \equiv qx(x-2)+4x$, then $p=$

Let $a$ be a constant. If the quadratic equation $x^{2}+ax+a=1$ has equal roots, then $a=$

The figure shows the graph of $y=mx^{2}+x+n$, where $m$ and $n$ are constants. Which of the following is true?

If $a>b$ and $k<0$, which of the following must be true?

I. $a^{2}>b^{2}$

II. $a+k>b+k$

III. $\frac{a}{k^{2}}>\frac{b}{k^{2}}$

The solution of $-3x<6<2x$ is

The price of 2 bowls and 3 cups is $506. If the price of 5 bowls and the price of 4 cups are the same, then the price of a bowl is

There are 792 workers in a factory. If the number of male workers is $20\%$ less than that of female workers, then the number of male workers is

If the angle and the radius of a sector are decreased by $x\%$ and $50\%$ respectively so that its area is decreased by $90\%$, then $x=$

The width and the length of a thin rectangular metal sheet are measured as $8\text{ cm }$ and $10\text{ cm }$ correct to the nearest cm respectively. Let $x\text{ cm}^{2}$ be the actual area of the metal sheet. Find the range of values of $x$.

It is given that $\frac{4}{5a} = \frac{5}{7b} = \frac{7}{9c}$, where $a$, $b$ and $c$ are positive numbers. Which of the following is true?