One type of the test is sometimes called an objective test.I

One type of the test is sometimes called an objective test.It is designed to deal with facts,not personal opinions.To make up an objective test the teacher write a number of questions,each of which has only one correct answer.Along with each question,the teacher writes the correct answer and also three statements that look alike answers to students who have never learned the material properly.
请问:1.第一个write为什么不用writes?
2.最后一句的理解方式是the teacher writes...to students还是that look alike answers to students