问题 填空题

一个篮球运动员投篮一次得3分的概率为a,得2分的概率为b,不得分的概率为c(a、b、c∈(0,1)),已知他投篮一次得分的数学期望为2(不计其它得分情况),则ab的最大值为______.

答案

由题意,投篮一次得3分的概率为a,得2分的概率为b,不得分的概率为c(a、b、c∈(0,1)),
∴3a+2b=2,
∴2≥2

6ab

∴ab≤

1
6
(当且仅当a=
1
3
,b=
1
2
时取等号)
∴ab的最大值为
1
6

故答案为:
1
6

单项选择题
阅读理解

E

Most of us are used to seasons. Each year, spring follows winter, which follows autumn, which follows summer, which follows spring. And winter is colder than summer. But the earth goes through temperature cycles over much longer periods than those that we experience.

Between 65,000 and 35,000 years ago, the planet was much colder than it is now. During that time the temperature also changed a lot, with periods of warming and cooling. Ice melted during the warm periods, which made sea levels rise. Water froze again during the cold periods.

A new study from Switzerland sheds light on where ice sheets melted during the ice age.

It now seems that the ice melted at both ends of the earth, rather than just in either northern or southern areas. This surprised the researchers from the University of Bern.

Scientists have long assumed(认为) that most of the ice that melted was in the Northern hemisphere(半球) during the 30,000-year-long ice age. That belief was held because the North Pole is surrounded by land, while the South Pole is surrounded by the Antarctic Ocean. It is easier for ice sheets to grow on land. If surrounded by sea, the ice can easily just slip to the ocean instead of building up.

The researchers used a computer model to look at the ways the ice could melt and how it might affect sea levels. They compared these results to evidence(迹象) of how temperatures and currents actually changed during that time.

The model showed that if it was only in the Northern hemisphere that ice melted, there would be a bigger effect on ocean currents(洋流) and sea temperatures than what actually happened. Studies suggest that melting just in the Southern hemisphere would have been impossible, too.

The only reasonable conclusion, the scientists could make, was that the ice melted equally in the North and the South.

It is still a mystery(谜) as to what caused the temperature changes that caused the ice to melt.

72. We can learn from the text that _____.

A.we have experienced temperature cycles since they began

B.what caused ice to melt is still unknown

C. the planet was much colder than it is now between 65,000 and 35,000 years ago, during which time temperature hardly changed

D. before the new study, scientists long believed that ice melted just in either northern or southern areas

73. The underlined phrase "sheds light on" (in Paragraph 3) can be replaced by _____.

A. throws doubts on B. beats down on C. makes it clear D. makes light of

74. The first two paragraphs were written _____.

A. to lead up to the subject that ice melted during the 30,000-year-long ice age

B. to describe what the weather was like during the ice age

C. to compare climate nowadays with that of the ice age

D. to explain what a temperature cycle is

75. Which of the following best shows the relationship between ice, ocean currents and temperatures according to the text?

A. Ice can easily slip into the ocean.

B. Temperature and currents changed as a result of ice melting.

C. Temperature changes lead to ice melting or water freezing, which in turn has an effect on ocean currents and temperature.

D. Ice melted and then froze again due to temperature.