1986 年

Let $\mathrm{F}(x)=2x^3+3x^2-11x-6$. Given that $\mathrm{F}(2)=0$ and $\mathrm{F}(-3)=0$, then $\mathrm{F}(x)$ can be factorized as

If $a$, $b$ and $c$ are positive numbers, which of the following is a possible graphical representation of $y=ax^2+bx+c$

If $a>0$ and $b<0$, which of the following is/are negative? I. $\dfrac{1}{a}-\dfrac{1}{b}$ II. $\dfrac{a}{b}+\dfrac{b}{a}$ III. $\dfrac{a^2}{b}-\dfrac{b^2}{a}$

If $2<x<3$ and $3<y<4$, then the range of values of $\dfrac{x}{y}$ is

$ABCDEFGH$ is a cube of side $3\text{ cm}$. A tetrahedron $DACH$ is cut away along the plane $ACH$. The volume of the remaining solid is

The marked price of an article is originally $P$. The marked price is then increased so that when a discount of $10\%$ is made on the new marked price, the selling price is still $P$. What is the new marked price?

The total surface area of a regular tetrahedron of side $3\text{ cm}$ is

Ten litres of a mixture contain $60\%$ of alcohol and $40\%$ of water by volume. How many litres of water should be added so that it contains $30\%$ of alcohol by volume?

If $A$, $B$ and $C$ can finish running the same distance in $3$, $4$ and $5$ minutes respectively, then $A$'s speed : $B$'s speed : $C$'s speed $=$

If the five interior angles of a convex pentagon form an A.P. with a common difference of $10^\circ$, then the smallest interior angle of the pentagon is