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2016 May 25th Edexcel Core 2 Questions and answers. [Unofficial mark scheme] 2016

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USE LINKED MARKSCHEME NOT ATTACHED ONE, THIS ONE IS UPDATED.

1 Geometric series question, prove a=64a=64 given S4=175S_4=175 and r=34r=\frac{3}{4} then workout sum to infinity. Then find the difference between the 9th and 10th term

2 Trapezium rule. y=82x1y=8-2^{x-1} in the interval [0,4][0,4] with 4 trapeziums

3 Circle centred at (7,8)(7,8). Find the equation of it and of a tangent at point (10,13)(10,13)

4 where fx=6x3+13x24f x =6x^3+13x^2-4 find the remainder when divided by (2x+3)(2x+3) then factorise it fully given (x+2)(x+2) is a factor.

5 Expansion of (29x)4(2-9x)^4. The using that expand (1+kx)(29x)4(1+kx)(2-9x)^4 in the form A232x+Bx2A -232x + Bx^2 given the coefficient of xx

6 12cos(θπ5)=01-2\cos(\theta - \frac{\pi}{5})=0 solve for θ\theta and 4cos2x+7sinx2=04\cos^2 x + 7\sin x - 2 = 0

7 This was (3xx32)dx\int (3x-x^{\frac{3}{2}}) dx and then find the limits (where it crossed the xx axis.

8 log3(3b+1)log3(3a2)=1\log_3(3b+1)-\log_3(3a-2)=-1, write b in terms of a then find xx given 22x+57(2x)=02^{2x+5}-7(2^x)=0.

9 Find optimum perimeter of a funny shape which comprised a rectangle, sector and a equilateral triangle, need diagram.
Image by @Cake_Chan
Equations given, that needed proving are, y=500xx24(4π+33)y=\frac{500}{x}-\frac{x}{24}(4\pi+3\sqrt{3})
and P=1000x+x24(4π+3633)P=\frac{1000}{x}+\frac{x}{24}(4\pi+36-3\sqrt{3})


My answers:
1 a) (2 marks) proof
b) (2 marks) 256256
c) (2 marks) 1.6021.602

2 a) (1 mark) 77
b) (3 marks) 20.7520.75
c) (2 marks) 5.755.75

3 a) (2 marks) 34\sqrt{34}
b) (3 marks) (x7)2+(y8)2=34(x-7)^2+(y-8)^2=34
c) (4 marks) 3x+5y95=03x+5y-95=0

4 a) (2 marks) 55
b) (2 marks) f(2)=0f(-2)=0
c) (4 marks) f(x)=(x+2)(3x+2)(2x1)f(x)=(x+2)(3x+2)(2x-1)

5 a) (4 marks) 16288x+1944x216-288x+1944x^2
b) (1 mark) 1616
c) (2 marks) 72\frac{7}{2}
d) (2 marks) 936936

6 i) (3 marks) 8π15\frac{8\pi}{15}or 2π15\frac{-2\pi}{15}
ii) (6 marks)
Unparseable latex formula:

345.5$^{\circ}$

or
Unparseable latex formula:

194.5$^{\circ}$



7 a) (3 marks) 32x225x52+c\frac{3}{2}x^2-\frac{2}{5}x^{\frac{5}{2}}+c
b) (3 marks) 24.324.3

8 i) (3 marks) b=3a59b= \frac{3a-5}{9}
ii) (4 marks) 2.19-2.19

9 a) (2 marks) πx23\frac{\pi x^2}{3}
b) (3 marks) proof
c) (3 marks) proof
d) (5 marks) x=16.63x=16.63 P=120mP= 120m
e) (2 marks) fx=0.437>0 f''x = 0.437 > 0 \therefore is a minimum at xx

This is useful and was spread out over another thread so I thought I would post it here. The missed answers were all either proofs or not suited to a single number response.

EDIT: 9c is P=1000x+x24(4π+3633)P=\frac{1000}{x}+\frac{x}{24}(4\pi+36-3\sqrt{3}) not P=1000x+x24(4π+3634)P=\frac{1000}{x}+\frac{x}{24}(4\pi+36-3\sqrt{4})
8ii is 22x+57(2x)=02^{2x+5}-7(2^x)=0 not 22x+57(2x)=12^{2x+5}-7(2^x)=-1
6a is 12cos(θπ5)=01-2\cos(\theta - \frac{\pi}{5})=0 not 12sin(θπ5)=01-2\sin(\theta - \frac{\pi}{5})=0 thanks for spotting this one @UKoE Luna


FINAL MARK SCHEME UPLOADED C3 next

http://www.thestudentroom.co.uk/showthread.php?t=4117259 <- @AstarAstarA did a very good one here, better break down of the marks.
(edited 7 years ago)

Scroll to see replies

Thanks!
Reply 3


yes
Reply 4
1.b. Is wrong. The answer is -1.602. It has to be negative because in geometric sequence, the biggest term is subtract by the smallest.

Therefore 64(3/4)^9 - 64(3/4)^8 = -1.602 (to three decimal places).

P.S. I don't know if the markscheme would say 'ignore' signs.
Reply 5
Original post by Qweudhs56
1.b. Is wrong. The answer is -1.602. It has to be negative because in geometric sequence, the biggest term is subtract by the smallest.

Therefore 64(3/4)^9 - 64(3/4)^8 = -1.602 (to three decimal places).

P.S. I don't know if the markscheme would say 'ignore' signs.


It asked for the difference I think it would say ignore signs
Reply 6
Original post by X_IDE_sidf
It asked for the difference I think it would say ignore signs


If it asked for difference, I am pretty sure it would be a negative sign. Since when the lower term is minus by the bigger term in order to calculate the difference?
how many marks was 1a?
How many makes would I loose for not putting it in radians. It didn't ask for radians
Reply 9
Original post by Qweudhs56
If it asked for difference, I am pretty sure it would be a negative sign. Since when the lower term is minus by the bigger term in order to calculate the difference?


Difference is absolute. It is asking for how different the numbers are. u9u10=u10u9|u_9-u_{10}| = |u_{10}-u_9| The positive is more correct.
(edited 7 years ago)
Reply 10
Whats 8i)?????
Reply 11
Original post by Verdahf
Whats 8i)?????


Thankyou, sorry I missed that, log3(3b+1)log3(a2)=1\log_3(3b+1)-\log_3(a-2)=-1, write b in terms of a
forgot to encode my answer to 6i how many marks would i lose?
Original post by Verdahf
Whats 8i)?????


the answer was b= (3a+5)/9
Reply 14
Original post by X_IDE_sidf
Thankyou, sorry I missed that, log3(3b+1)log3(a2)=1\log_3(3b+1)-\log_3(a-2)=-1, write b in terms of a


Do you know how many marks this part was for?
Reply 15
Original post by dididid
the answer was b= (3a+5)/9


Do you remember the number of marks this was worth, I think it was 3.
Reply 16
YESSSSS
Original post by X_IDE_sidf
Do you remember the number of marks this was worth, I think it was 3.


yh i think 3 is right
what are your grade boundary predictions?
i got between 70-73 marks how many ums would that be about?
for the first part of the logs

I said 1/3 = 3b+1/a-2

then 1/3a -2/3= 3b+1

1/3a-5/3=3b

1/3a-5/3 all divided by 3 = b

Is this correct and how many marks would i lose if incorrect?

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