2003 年

$P(-10,-8)$ and $Q(4,6)$ are two points. If $R$ is a point on the $x$-axis such that $PR=RQ$, then the coordinates of $R$ are

The mean mark of a mathematics test was 63 marks. Peter got 75 marks in the test and his standard score was 0.75. If Mary got 83 marks in the same test, then her standard score would be

The median of the five numbers $15$, $x-1$, $x-3$, $x-4$ and $x+17$ is $8$. Find the mean of the five numbers.

A bag contains 2 black balls, 2 green balls and 2 yellow balls. Peter repeats drawing one ball at a time randomly from the bag without replacement until a green ball is drawn. Find the probability that he needs at most 4 draws.

$1232\star$ is a 5-digit number, where $\star$ is an integer from 0 to 9 inclusive. The probability that the 5-digit number is divisible by 4 is

$x$ is the mean of the group of numbers $\{a,b,c,d,e\}$. Which of the following statements about the two groups of numbers $\{a,b,c,d,e\}$ and $\{a,b,c,d,e,x\}$ must be true? I. The two groups of numbers have the same mean. II. The two groups of numbers have the same range. III. The two groups of numbers have the same standard deviation.

$\dfrac{10}{x^2+x-6}-\dfrac{2}{x-2}=$

The L.C.M. of $210xy^2$ and $30x^2yz$ is

$x^3-\dfrac{27}{x^3}=$

If $10^{a+b}=c$, then $b=$