1999 年

The method of bisection is used to find the root of $\sin x+x-1=0$ starting with the interval $[0,2]$. After the first approximation, the interval which contains the root becomes $[0,1]$. Find the interval which contains the root after the third approximation.

John goes to school and returns home at speeds $x$ km/h and $(x+1)$ km/h respectively. The school is $2$ km from John's home and the total time for the two journeys is $54$ minutes. Which of the following equations can be used to find $x$ ?

In the figure, find the point $(x,y)$ in the shaded region (including the boundary) at which $bx-ay+3$ attains its greatest value.

The sum of the first two terms of a geometric sequence is $3$ and the sum to infinity of the sequence is $4$. Find the common ratio of the sequence.

It is given that $y$ varies inversely as $x^3$. If $x$ is increased by $100\%$, then $y$ is

$\dfrac{\cos(90^\circ-A)\cos(-A)}{\sin(360^\circ-A)}=$

If $0\le\theta\le 2\pi$, solve $(\cos\theta-3)(3\sin\theta-2)=0$ correct to 3 significant figures.

The figure shows five sectors. Which of the marked angles measures $2$ radians?

In the figure, $ABCDEFGH$ is a rectangular block. Find the inclination of $EM$ to the plane $ABCD$ correct to the nearest degree.

In the figure, $AT$ is tangent to the circle at $T$ and $ABC$ is a straight line. Find $AT$.