2011 年

A circle $C$ touches the $x$-axis and passes through the point $(-3,1)$. If the centre of $C$ lies on the $y$-axis, then the equation of $C$ is

A box contains $2$ red cards, $3$ blue cards and $4$ yellow cards. Mary repeats drawing one card at a time randomly from the box with replacement until a red card is drawn. Find the probability that Mary needs at least three draws.

The manager of a popular restaurant designs a questionnaire to collect the opinions from customers about the food provided by the restaurant. The manager has four relatives who are customers of the restaurant and only these four relatives are selected as a sample to fill in the questionnaire. Which of the following are disadvantages of this sampling method? I. The sample size is too small. II. The customers are not randomly selected. III. Not all the customers are selected.

There are three groups of students in a tutorial class. The following table shows the mean mark of each of the three groups of students in a Mathematics test.

Which of the following must be true? I. In the test, the mean mark of all students in the tutorial class is $70$ marks. II. In the test, the mean mark of all students of Group $A$ and Group $B$ is lower than the mean mark of all students of Group $B$ and Group $C$. III. In the test, the student who gets the highest mark is in Group $C$.