1984 年

The standard deviation of the five numbers $a-2d$, $a-d$, $a$, $a+d$, $a+2d$ is

$4x^2-9\ge0$ is equivalent to

The graph of $y=x^2+ax+b$ ($a$ and $b$ being constants) cuts the $x$-axis at $(2,0)$ and $(h,0)$, and cuts the $y$-axis at $(0,-2)$. $h=$

If $a$ and $b$ are non-zero real numbers and $a>b$, which of the following must be true? I. $a^2>b^2$ II. $\dfrac1a>\dfrac1b$ III. $a^3>b^3$

If $f(x)=(\log_{10}2x)-x$, then $f(x+1)-f(x)=$

If $a\ne\pm1$, then $1+a^2+a^4+\cdots+a^{2n}=$

Which of the following must be geometric progression(s)? I. $\log_{10}3,\ \log_{10}9,\ \log_{10}27,\ \log_{10}81$ II. $0.9,\ 0.99,\ 0.999,\ 0.9999$ III. $1,\ -3,\ 9,\ -27$

$a$, $b$, $c$ are positive numbers such that $\dfrac ab=\dfrac bc=k$ ($k$ being a constant). Which of the following must be true? I. $b^2=k^2$ II. $\dfrac{a+b}{b+c}=k$ III. $\dfrac ac=k^2$

Last year, a man saved $10\%$ of his income. By how much per cent must his income be increased if his expenditure increased by $20\%$ and he wants to save $20\%$ of his income?

The external and internal radii of a hollow metal sphere are 4 cm and 3 cm respectively. $\dfrac{\text{Volume of metal}}{\text{Volume of the enclosed empty space}}=$