A-level真题分享

　　在以往的A-level考试中，出题频率非常高，但还是有很多学生败给了这种类型题。今天带大家来解决一道这种类型题，并且给大家分享一下易错点和难点，让大家以后遇到这种题能“手到擒来”。
　　本题(a)问是一道求值题，我们可以通过把t=0代入式子得值
　　根据examiner’sreport:
　　Most knew that 3500 was the value required. The only mistakes were from those putting t=1 into
　　所以我们要注意，当我们要求the start value,我们带入的t=0，而不是t=1。
　　本题(b)问是一道常考题型，这个主要考查的就是通过对数来解决指数函数power的取值范围。
　　首步, write down inequality.
　　第二步，simplify both sides.
　　第三步，use logarithm to solve the inequality and simplify the answer.
　　根据Examiner’s report:
　　Most students gained the first two marks although occasionally BODMAS rule were misapplied, with students writing, forfeiting these first two marks. Many were also successful in getting to t=30.516… hours, with various correct uses of logarithmic approaches. The most common error was getting from there to the correct number of hours and minutes, as required. Some rounded to 30.5 and obtained 30 hours and 30 minutes, losing the final mark. Some converted to 1831 minutes, losing the final mark. Occasionally an answer of 30 hours and 32 minutes was given, suggesting 100minutes in an hour.
　　这里我们需要注意几个点：
　　对指数函数进行化简时，先对系数进行化简。
　　通过对数来解决指数函数power的不等式时，当底数大于1，不等号不改变，当底数大于0并且小于1时，不等号要发生改变。
　　接后的答案，需要按题目进行化简，不要算错了。
　　本题(c)问是一道常见的微分应用，要记得指数函数的微分共识。
　　首步, differentiate the equation.
　　第二步, put the value into the deviated function.
　　根据Examiner’s report：

　　The requirement to ‘Use Calculus’ was not followed by a significant minority who just worked out N when t was 8, or divided that number by 8, Those who correctly differentiated almost always got an acceptable answer. Those who incorrectly differentiated N, usually to , and then put t=8 could only gain one method mark for this part.
　　这里我们需要提醒学生：
　　对指数函数求导公式一定要掌握，公式本不提供。
　　要注意答案的保留要求，看题目具体说明。