Please help me if you can!
Maths is not my strongest areas and never has been and thats why websites like these are a god send! I'm trying to help my son but want to clarify the following questions with you experts before I can explain all to him.
Please help me I would really appreciate it and let me know how you got to the answers, i.e. the working out ; o ).
1) A Student has obtained marks of 65, 72, 62 and 75 in her first four examinations. She has one examination left to do and hopes to obtain a distinction which requires an average mark of 75 over 5 examinations.
a) Calculate her current average mark. 
b) Explain, giving your reasoning whether she can get a distinction given that the maximum mark available on the final examination is 100? 
2) 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. 
END OF QUESTIONS.
Thank you very much, I appreciate your kind help.
1a) The student has scored 65+72+62+75 = 274 marks in total, so she has scored 274/4 = 68.5 marks on average.
1b) To get an average of 75 over 5 tests, she needs to score a total of 5*75 = 375 marks. She has already scored 274 marks, meaning that she needs 375-274 = 101 more, so it is not possible.
2a) Maximum: 5*20 = 100 marks. Minimum: -2*20 = -40 marks.
2b) The candidate would get 5 marks per question, so they need to answer 30/5 = 6 questions at least.
2c) The candidate would get 20/4 = 5 questions right, meaning they score 5*5 = 25 points, but would also get 20-5 = 15 questions wrong, meaning they score -2*15 = -30 points. Overall, their mark would be 25-30 = -5.
2d i) If he answers x correctly, then the remaining amount would be 20-x.
2d ii) He gets 5 marks for every correct answer and -2 for every incorrect answer, so he would score 5x-2(20-x) = 7x-40 marks.
2d iii) Substitute 44 into the answer from ii): 44 = 7x-40, add 40: 7x = 84, divide by 7: x = 12. The candidate answered 12 correctly.
2d iv) Use the same method as before: 30 = 7x-40, 70 = 7x, x = 10. The candidate must answer at least 10 correctly.
2e i) The candidate gets 4 marks per question, so they need to answer 30/4 = 7.5, but round up to give at least 8 questions correctly.
2e ii) The formula is now 6x-40 marks. Substitute 30 again: 30 = 6x-40, 70 = 6x, x = 11.66..., but round up to give at least 12 questions correctly.
You're welcome for the help, I just hope I haven't just done anyone's homework for them.
Why did the vector cross the road?
It wanted to be normal.