考题5-6 2015 AMC 12A

AMC12是针对高中学生的数学测验，该竞赛开始于2000年，分A赛和B赛，于每年的2月初和2月中举行，学生可任选参加一项即可。其主要目的在于激发学生对数学的兴趣，参予AMC12的学生应该不难发现测验的问题都很具挑战性，但测验的题型都不会超过学生的学习范围。这项测验希望每个考生能从竞赛中享受数学。那么接下来跟随小编来看一下AMC12的官方真题以及官方解答吧：

Problem 5

Amelia needs to estimate the quantity , where  and  are large positive integers. She rounds each of the integers so that the calculation will be easier to do mentally. In which of these situations will her answer necessarily be greater than the exact value of ?

Solution

To maximize our estimate, we want to maximize  and minimize , because both terms are positive values. Therefore we round  down. To maximize , round  up and  down. 

Problem 6

Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be  :  ?

Solution

This problem can be converted to a system of equations. Let  be Pete's current age and  be Claire's current age.

The first statement can be written as . The second statement can be written as 

To solve the system of equations:

Let  be the number of years until Pete is twice as old as Claire.

The answer is .

以上就是小编对AMC12数学竞赛试题及答案的介绍，希望对你有所帮助，更多学习资料请持续关注AMC数学竞赛网！

2015年AMC数学竞赛12A整套其他真题如下：

AMC数学竞赛12A 01-02   AMC数学竞赛12A 03-04   AMC数学竞赛12A 05-06   AMC数学竞赛12A 07-08

AMC数学竞赛12A 09-10   AMC数学竞赛12A 11-12   AMC数学竞赛12A 13-14   AMC数学竞赛12A 15-16

AMC数学竞赛12A 17-17   AMC数学竞赛12A 18-19   AMC数学竞赛12A 20-20   AMC数学竞赛12A 21-22

AMC数学竞赛12A 23-24   AMC数学竞赛12A 25-25