问题 解答题
某厂从2007年起开始投入技术改进资金,经技术改进后,其产品的生产成本不断降低,具体数据如下表:

年度

2007

2008

2009

2010

投入技改资金x(万元)

2.5

3

4

4.5

产品成本y(万元/件)

7.2

6

4.5

4

(1)请你认真分析表中数据,从你所学习过的一次函数和反比例函数中确定哪种函数能表示其变化规律,说明确定是这种函数而不是其它函数的理由,并求出它的解析式;
(2)按照这种变化规律,若2011年已投人技改资金5万元。
①预计生产成本每件比2010年降低多少万元?
②如果打算在2011年把每件产品成本降低到3.2万元,则还需投入技改资金多少万元(结果精确到0.01万元)?
答案

解:(1)设其为一次函数,解析式为y=kx+b,

当x=2.5时,y=7.2;

当x=3时,y=6,

∴ 解得k=-2.4,b=13.2

∴一次函数解析式为y=-2.4x+13.2

把x=4时,y=4.5代入此函数解析式,

左边≠右边

∴其不是一次函数

设其为反比例函数

解析式为y=

当x=2.5时,y=7.2,

可得:7.2=k/2.5

解得k=18

∴反比例函数是y=

验证:当x=3时,y==6,符合反比例函数

同理可验证x=4时,y=4.5,x=4.5时,y=4成立

可用反比例函数y=表示其变化规律。

(2)①当x=5万元时,y=3.6

4-3.6=0.4(万元),

∴生产成本每件比2010年降低0.4万元

②当y=3.2时,3.2=y=18/x

∴x=5.625

∴5.625-5=0.625≈0.63(万元)

∴还约需投入0.63万元。

单项选择题 A2型题
阅读理解

阅读下列材料, 从所给的四个选项(A、B、C、D) 中,选出符合各小题要求的最佳选项,并在答题卡上将该项涂黑。

The people below are needed to take part in a sport. After the description of these people, there is information about four sports(A-D). Decide which sport would be most suitable for the person mentioned in questions 58-61 and then mark the correct letter(A-D) on your answer sheet.

小题1:Bob is a very active man. He is very strong and healthy. He’d like to take part in an exciting sport. But he is afraid of water.

小题2:Simon is very fat. He would like to lose his weight. But he is not interested in double quick and excitement activity. He enjoys water sports.

小题3:Mathew hates to take part in the violent sports. He is in poor health. He wants to build up his body.

小题4:Jack is brave and risky and a good swimmer. He enjoys water game. He looks for excitement with his friend when they are on holiday.

A.Hiking is a great way to travel. You will get close to nature and take exercise at the same time. Hiking is easy to do and doesn’t have to be very expensive. You can hike close to home or travel to other places. The basic equipment you need for hiking is simple: good shoes, clothes and a backpack. You can hike in the mountains, in a forest or along a river. You can also go for a hike in the city. Hiking is fun and exciting, but you shouldn’t forget safety.

B.Rafting is a good way to experience nature. If you want a normal rafting trip, choose a quiet stream or river that is wide and has few fallen trees or rocks. If you are looking for more excitement you may want to try whitewater rafting. You should always think about your safety and wear good clothes. You also need to learn the basic skills of rafting, such as how to handle the raft, how to paddle and how to get in and out of the raft. You should not go rafting unless you know how to swim, and you should always wear a life jacket.

C.Swimming is a good way for swim lovers. You can reduce your weight and become slim by swimming. You can train your willpower and increase your energy of your lung. You can swim in the swimming pool, in the lake, in the river or even in the sea.

D.Long running is a good sport, for example, Marathom is very popular with young people especially people with strong body and will. If you have hypertension or heart disease, perhaps, it is not suitable for you.