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OCR MEI C3 Mathematics June 2016 - Official Thread

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How many marks was 8ii and iii and does anyone have a pic of the paper? Or can post an unofficial mark scheme with the mark breakdown in each question :smile:

Reply 321

rupertmenneeer

Original post by fazee

UNOFFICIAL MARK SCHEME:

1. Integrate 1 + cos(0.5x) between limits of 0 and pi/2. Answer is pi/2 + root2

2. Solve for x. Answer is x = ln2

3. Can't remember the context. Answer is 4ln4 - 4 - alternatively may be written as 4(ln4 -1) or ln256 - 4 or any equivalent form.

4. |2x+1| = -x. First case, 2x+1 = -x, gives 3x+1 = 0, 3x = -1, x = -1/3
Second case, -(2x+1) = -x, negate both sides to give 2x+1 = x, x+1 = 0, x = -1
Alternative approach, square both sides, 4x² + 4x + 1 = x², 3x² + 4x + 1 = 0, (x+1)(3x+1) = 0, x= -1, x = -1/3 as before

5i. V = 4root(h³+1) - 4. dV/dh using chain rule gives 4*1/2(h³+1)^-1/2 * 3h² = 6h² * (h³+1)^-1/2. Substituting h=2 gives dV/dh = 8 (feel free to check this for yourself).
5ii. dh/dt = dh/dV * dV/dt = 1/8 * 0.4 = 0.4/8 = 0.05

6i. Can't remember the context. Answer is root3 /3
6ii.Transformation is first translate 1 unit to the right, THEN stretch parallel to y-axis, scale factor 1/2

7. x²ⁿ-1 = (xⁿ+1)(xⁿ-1). Substituting for x=2, 2ⁿ has to be even, so it's a product of two consecutive odd numbers, so one of those must be divisible by 3, so their product is divisible by 3. That's why I put anyway, I've seen someone say it's not right, so not completely sure about this one.

8i. Differentiate using quotient rule, then multiply your result by 2root(x+4), to obtain dy/dx in the form given.
8ii. Using equation for y, asymptote is x= -4, so x coordinate of P is -4. Use dy/dx for x=0, to show that tangent is y = 0.5x (y-intercept c is 0). Then y = 0.5 * -4 = -2, so P is (-4,-2)
8iii.Area under the curve is found by integration to be 14/3. Area of triangle with vertices O,Q and (5,0) is 1/2 * 5 * 5/2 = 25/4
So area of required region is 25/4 - 14/3 = 19/12

9i. y = e^2x + ke^-2x. When x=0, y = 1 + k*1 = 1+k
9ii. Answer is 2rootk
9iii. Answer simplifies to (0.5k - 1/2) - (1/2 - 0.5k) = 0.5k - 1/2 - 1/2 + 0.5k = k - 1
9ivA. Replace x with (x+ 0.25lnk), to give g(x) = rootk(e^2x + e^-2x).
9ivB. g(-x) = g(x), so g(x) is an even function.
9ivC. f(x) is symmetrical about the line x = 0.25lnk. This can be deduced because g(x) is f(x) translated 0.25lnk units to the left. g(x) is even, so is symmetrical about the y-axis i.e. symmetrical about line x=0. f(x) is g(x) translated 0.25lnk units to the right, therefore its line of symmetry is x = 0.25lnk. Full reasoning will probably be required for all 3 of these marks.

These are the answers of my friend, who does Additional Further Maths, so I think they should all be right, or most of them anyway. Of course, feedback is more than welcome, if I've made a mistake please point it out.

I think boundaries will be 88 or 89 for 100 UMS (out of 90, for exam and coursework). 90% should be 80 or 81, and A should be 72 or 73. Difference between each grade will be about 7 or 8 marks.

Thanks for reading :smile:

I had the exact same for every single answer. General consensus seems that these are the correct answers too.
I got 15/18 for coursework + hopefully 65-72 out of 72 for the paper (assuming I made some errors) so hopefully that will put me close to 100ish ums (fingers crossed)
overall I found it quite an easy paper - hope every else did well. no point stressing now as there is nothing that can be done :smile:

(edited 7 years ago)

Reply 322

rupertmenneeer

Also as response to some of the people debating the proof, this is what I put:

(2^n -1)(2^n + 1)
Since 2^n = 2,4,8,16,32,64.... so on
therefore 2^n - 1= 1,3,(7),15,(31),63... every other number is divisible by three
also 2^n + 1 = 3,(5),9,(17),33,(65)... every other number is divisible by three
therefore the product of (2^n -1)(2^n +1) must be divisible by three as one of the factors is divisible by three
the divisible factor alternates between every value of n

that is what I put I'm not sure if that is exactly how you 'prove' the conjecture but makes sense to me

Reply 323

username1258398

Original post by Leechayy

That's the translated one isn't it? :smug:

Posted from TSR Mobile

:P well the un-translated one certainly isn't 2cosh2x

Reply 324

Aph

Out of interest what did people get for the coursework component seeing as that can cripple your grade.

Reply 325

js171

thanks !

Original post by ComputerMaths97

Add the score from your coursework to your raw mark from the exam, giving a score out of 90, then you get corresponding ums out of 100.

Reply 326

1831303

Original post by Aph

Out of interest what did people get for the coursework component seeing as that can cripple your grade.

17/18

Reply 327

kevvvvvv

for question 9.ii i showed that the minimum point has x co ordinate of 1/4ln4 and then i subbed that back into f(x) to find out the y co ordinate but i got an incorrect y co ordinate. how many marks in the question will i lose because of this

Reply 328

WhiteBison

Original post by Aph

Out of interest what did people get for the coursework component seeing as that can cripple your grade.

16/18

Reply 329

Studious_Student

Original post by Aph

Out of interest what did people get for the coursework component seeing as that can cripple your grade.

18/18

Reply 330

y0uSmartass

For question 3 I didn't sketch the graph, how many marks is that out of 4?
And 8iii how many marks is integration of just the curb work out of 9?

Reply 331

y0uSmartass

I think I got 46/72 in this and I got 15/18 in my coursework, what would I average out with?
What does everyone think the grade boundaries for B will be?

Reply 332

fkjames

Can anyone tell me that if i got 69/72 for c3 paper and 13/18 for c3 coursework, what is the UMS out of 100 for c3 please?

Reply 333

Bunderwump

Original post by fkjames

Can anyone tell me that if i got 69/72 for c3 paper and 13/18 for c3 coursework, what is the UMS out of 100 for c3 please?

Since a lot of people are asking this: here's MEI's UMS conversion site. You can estimate based on previous years, but remember that it changes slightly based on the difficulty of the exam. http://www.ocr.org.uk/i-want-to/convert-raw-marks-to-ums/

Reply 334

Aph

Original post by y0uSmartass

I think I got 46/72 in this and I got 15/18 in my coursework, what would I average out with?
What does everyone think the grade boundaries for B will be?

Based on previous years that would be a mid-C

Reply 335

mrbazz12

Original post by mrbazz12

Okay paper apart from 2 things:

1. For the proof question, I wrote down the difference of two squares i.e. (X^n + 1)(X^n - 1) and then had a mind blank, so will I get 1 mark for that? (out of the 4)

2. The modulus question I used the 'square both sides' method only to forget to square one of the sides :s-smilie:

(the X on the other side to the | 2x - 1 |) so got an answer of X = -1 and X = 1/4. How many marks will I lose for this?

Apart from those lost marks^ I thought paper was alright.

Can anyone answer this?

Reply 336

mrbazz12

Can anyone remember question 3? What was the graph you had to draw?

Reply 337

decombatwombat

Original post by mrbazz12

Can anyone answer this?

You would definitely get the first mark as it asked for that in the question.

You would probably lose 2 marks on the second one, the final A1 for the wrong answer, and probably a M1 mark