10) A multiple choice examination consists of 20 questions each of which have 4 possible answers. A candidate gets 5 marks for a correct answer and has 2 marks deducted for an incorrect answer. (If the candidate does not answer the question no marks are awarded or deducted.) The pass mark is 30.

a) What are the maximum and minimum possible examination marks?

b) What is the minimum number of questions a candidate needs to answer

correctly in order to pass the examination?

c) Estimate the number of marks a candidate would get if he or she answered

each question by picking 1 of the 4 multiple choice answers at random.

d) Assume a candidate answers every question, and let *x *be the number of

questions he answers correctly.

i) Write down an expression in terms of *x *for the number of questions he

answers incorrectly.

ii) Write down an expression in terms of *x *for the number of marks he

obtains.

iii) If the candidate obtained 44 marks, how many answers did he answer

correctly.

iv) How many must he answer correctly to pass the examination?

e) If, instead, 4 marks are awarded for each correctly answered question

i) what is the minimum number of questions a candidate needs to answer

correctly in order to pass the examination?

ii) If a candidate answers all the questions, how many must a candidate

answer correctly to pass the examination?