Thread: exam problem

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?

Originally Posted by nazz

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?

Can you tell us what you have done, or what particular difficuties you are having.

RonL

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?

The minimum is -40 and the maximum is 100.

b) What is the minimum number of questions a candidate needs to answer
correctly in order to pass the examination?

Assuming what? The candidate could answer 6 questions correctly and not attempt any of the other questions and still pass with a 30.

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.

(-2*15) + (5*5) = -30 + 25 = -5 marks

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.

20-x

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

-2(20-x) + 5x
Simplified would be: 7x - 40

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

7x - 40 = 44
7x = 84
x = 84/7 = 12

Thus, 12 were answered correctly and 8 incorrectly.
Double check: (5*12) + (-2*8) = 60 - 16 = 44.

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

10

Justification: (5*10) + (-2*10) = 50 - 20 = 30.

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?

See part B as I will answer this question similarly. If 8 questions are answered correctly while the remaining 12 are not attempted, then you answered the minimum number of questions in order to pass (with a score of 32).

ii) If a candidate answers all the questions, how many must a candidate
answer correctly to pass the examination?

(4*11) + (-2*9) = 44 - 18 = 26 [fail]
(4*12) + (-2*8) = 48 - 16 = 32 [pass]

So, 12 is the new minimum number of questions the candidate needs to answer correctly in order to pass (assuming every question attempted).

I hope this helps. Hopefully I fully understood the somewhat vague instructions.
-Andy

Originally Posted by abender

[snip]

I hope this helps. Hopefully I fully understood the somewhat vague instructions.
-Andy

How does it help the student learn if you just do their homework for them?

I was trying to set up a dialogue here!

RonL