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Question

I've been given homework to do for a level maths and i'm really stuck on the one question if you decide to answer it could you please tell me how you got the answer not just the answer? thank you

Q. In a multiple-choice examination of 25 questions, four marks are given for each correct answer and two marks are deducted for each wrong answer. One mark is deducted for any question which is not attempted. A candidate attempts 'q' questions and gets 'c' correct.

Write an expression for the candidates total mark in terms of 'q' and 'c'.

Thank you so much if you can answer this question. :)

Answer 1

Let c be correct,

w be wrong answers,

q attempted questions

u unattempted questions



c+w = q, so w = q-c

c+w+u = 25, so u = 25-(q-c)-c = 25-q



Total Marks given by

4c - 2w - u

Substitute for w and u gives:

4c - 2(q-c) - (25-q) = 6c - q - 25

Answer 2

Since he got "c" correct answers and each correct answer is worth 4 marks, 4c is the total marks for his correct answers.



Which means that he got the remaining attempted questions (q-c) wrong and since each wrong answer results in a 2 mark deduction. 2(q-c) is the total marks deducted for wrong answers.



And he didn't attempt (25-q) questions which results in one mark deducted for each of those.



So his grand total will be:

4c - 2(q-c) -(25-q)

4c -2q + 2c - 25 +q

6c -q - 25

Answer 3

the candidate answers c questions correctly

So, he gets 4*c marks for it.

This means his answers of remaining questions he attempted were wrong. So, 2(q-c) marks are deducted.

Similarly, since he did not attempt some questions, (25 - q) marks are deducted.



His total marks is thus given by 4*c-2(q-c)-(25-q)

simplifying it gives 6c-q-25

Answer 4

total marks=100

qs un attempted = 25 -q

qs wrong = q-c

marks for correct ams=4c

marks deducted for unattempted = 1*[25-q]

marks deducted for wrong ans = 2[q-c]

total marks= 4c - 1*[25-q] - 2[q-c]

solve to get expression



M= 4c -25 +q -2q +2c

=6c -q -25

Answer 5

Total questions in the examination=25,



Marks awarded/deducted per question:

-Correct answer=4 marks (Added),

-Wrong answer=2 marks (Deducted),

-Unattempted question=1 mark (Deducted),



-Questions attempted:

-Total questions attempted=q,

-Correctly answered questions=c,

-Wrongly answered questions=q-c,

-Unattempted questions=25-q,



-Total marks added or deducted:

-Total marks added= No: of correct answers * marks per correct

answer

=4 * c =4c,

-Total marks deducted due to wrong answers=

=No: of wrong answers * mark per wrong answer

=(q-c) * 2 =2q-2c,

-Total marks deducted due to unattempted questios=

=No: of unattempted questions * marks per unattempted

question

=(25-q) * 1 =25-q,



-Total marks awarded in the exam=

=(Total marks added due to correct answers)-( Total



marks deducted due to wrong answers)_ ( Total



marks deducted due to unattempted questions),



=[ 4c ]-[2q-2c]-[25-q] = 4c-2q+2c-25+q = 6c-q-25,



Conclution:

The required expretion is: 6c-q-25.

Answer 6

For correct answers score1 = c



For wrong answers score2 = - 2(q-c)



For non-attempts score3 = -(25-q)



Toatal score is sum of these

= c -2(q-c) - (25-q)

= c -2q + 2c -25 + q



= 3c - q -25



Check if he answers all correctly c=q=25 score = 25

Answer 7

total mark is (c x 4) - (q - c)2 - (25 - q)1

= 4c - 2q + 2c - 25 - q

= 6c - 3q -25



the working should be clear enough

Answer 8

=4c-2(q-c)-(25-q)



4c is the points u get for right answers

2(q-c) is the deduction from getting wrong answer

(25-q) is the other deductions for leaving it blank

Answer 9

T is the total mark

T=(25-q)(-1)+4c+(q-c)(-2)