ATAR Notes: Forum

HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Standard Mathematics => Topic started by: hagar.a on October 19, 2018, 09:45:36 pm

Title: general maths
Post by: hagar.a on October 19, 2018, 09:45:36 pm: Hey guys
Could someone please explain how to do this question

An assessment task has 25 multiple choice questions each with four alternate answers.
Each question answered correctly is awarded 4 marks, and if any question is answered incorrectly, 2 marks are deducted from the total awarded.
If all questions are attempted on the task:
- Show that if n are answered, the number of marks awarded can be given by: 6n-50

Thankyou
Title: Re: general maths
Post by: RuiAce on October 19, 2018, 09:55:15 pm: Quote from: hagar.a on October 19, 2018, 09:45:36 pm
Hey guys
Could someone please explain how to do this question

An assessment task has 25 multiple choice questions each with four alternate answers.
Each question answered correctly is awarded 4 marks, and if any question is answered incorrectly, 2 marks are deducted from the total awarded.
If all questions are attempted on the task:
- Show that if n are answered, the number of marks awarded can be given by: 6n-50

Thankyou

$\text{Suppose that }n\text{ are correctly answered.}\\ \text{Since each 1 question correctly answered is worth 4 marks,}\\ \text{the }n\text{ questions total up }4n\text{ marks.}$
$\text{Then, there must be }25-n\text{ that are incorrectly answered.}\\ \text{Since each 1 question incorrectly answered costs 2 marks,}\\ \text{the wrong questions total up }2(25-n)\text{ lost marks.}$
$\text{Hence they will receive }\boxed{4n - 2(25-n)}\text{ marks.}\\ \text{Expanding the brackets, we then have}\\ \begin{align*} 4n - 2(25-n) &= 4n - 50 + 2n\\ &= 6n - 50\end{align*}$