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.