# AQA C2 Unofficial Markscheme 24th May 2017Watch

Thread starter 2 years ago
#1
Will post it below
0
Thread starter 2 years ago
#2
AQA MPC2 June 2017 Unofficial Markscheme

1. A sector has a perimeter of cm and an angle of radians. The radius is cm.

(a) Find the value of [2 marks]

(b) Find the area of the sector. [2 marks]
Using ,

2. A triangle ABC has an angle BAC of . There are sides of cm and cm.

(a) Show that the angle ACB is to the nearest degree [3 marks]
Using the sine rule:
, which is to the nearest degree.

(b) Find the area of the triangle. [3 marks]
Other angle is . Hence the area is cm2

3.
(a) Express in the form where is an expression in . [3 marks]

(b) Hence solve the equation . [2 marks]

4. A geometric series has the th term .
(a) Find and . [2 marks]
.

(b) Find the sum to infinity of the series [3 marks]
First term , and common ratio .
Hence sum to infinity is

(c) Find the smallest value of such that . [3 marks]

. The signs change here as is a decreasing function so if , then .

Hence so is at least 13.

5. A curve satisfies , where .
(a) Show that there is only one value of for which there is a stationary point. [2 marks]
At stationary points, (discarding as ). Hence there is only one value of for which there is a stationary point.

(b) Find and show that this is a minimum point. [3 marks]
.
When , this is equal to 1. Hence as the second derivative is positive, the point is a minimum.

(c) The line is a tangent to the curve. Find the equation of the curve. [4 marks]
Must be a tangent at the stationary point. Hence the point (4, 2) lies on the curve (the stationary point). Integrating gives . As , so .

6. There is a curve .
(a) (i) Use the trapezium rule with five ordinates (four strips) to approximate to two decimal places. [4 marks]
Call the integral . Then .

Now, and .

Hence , to two decimal places.

(a) (ii) State how the approximation may be improved. [1 mark]
Use more strips/ordinates.

(a) (iii) The point (1, ) lies on the curve. Use your answer to part (a)(i) to find the area bounded by the curve, the line and the line , to two decimal places. [3 marks]
so, by a sketch, the area is a rectangle with part (a)(i) subtracted. The area is to two decimal places.

(b) The curve may be mapped onto the curve of by a translation and a stretch. Describe:
(i) the translation [2 marks]

Translation in the vector

(ii) the stretch [2 marks]

Stretch parallel to the -axis scale factor .

(c) Use logarithms to solve the equation , giving your answer to three significant figures. [2 marks]

to three significant figures.

7. A curve has the equation .
(a) The region bounded by the curve and the lines and is above the -axis. Show that the area of this region is 16. [5 marks]

Area (as curve is above the -axis) is:

(b) The normal to the curve is parallel to the line . Find the equation of the normal to the curve. [6 marks]
Differentiating gives . Now, the normal has a gradient of . Hence the gradient of the tangent to the curve is . So

. Hence .

So the equation of the normal is .

8.
(a) Solve the equation in the range . Give your answers to the nearest degree. [2 marks]

, to the nearest degree.

(b) (i) Given that , show that . [3 marks]

(ii) Show that there is only one possible value of . [2 marks]
Factorising gives . As , the only possible value of is .

(c) Hence solve the equation in the range , giving your answer to the nearest degree. [4 marks]

Solving in the range .

Use part (a) and then add on to both solutions to give
, to the nearest degree.

So
, to the nearest degree.

9. Given that , express in terms of . [7 marks]

7
2 years ago
#3
One of the trig equations were

48, 312
0
2 years ago
#4
Equation of curve is 2/5x^5/2-x^2+ 26/5

If I am not wrong
1
Thread starter 2 years ago
#5
(Original post by MajorFader)
Equation of curve is 2/5x^5/2-x^2+ 26/5

If I am not wrong
(Original post by MajorFader)
One of the trig equations were

48, 312
I agree I'm writing the markscheme question by question and updating it.
1
2 years ago
#6
(a) (iii) The point (1, ) lies on the curve. Use your answer to part (a)(i) to find the area bounded by the curve, the line and the line , to two decimal places. [3 marks]
so, by a sketch, the area is a rectangle with part (a)(i) subtracted. The area is to two decimal places.

k=8 not 2?
0
Thread starter 2 years ago
#7
(Original post by alextttt)
(a) (iii) The point (1, ) lies on the curve. Use your answer to part (a)(i) to find the area bounded by the curve, the line and the line , to two decimal places. [3 marks]
so, by a sketch, the area is a rectangle with part (a)(i) subtracted. The area is to two decimal places.

k=8 not 2?
Sorry that was a typo
0
2 years ago
#8
all the singles in here say "Resit!"
0
2 years ago
#9
(b) The curve may be mapped onto the curve of by a translation and a stretch.
(i) the translation [2 marks]

Translation in the vector (, 0)

Translation should be by vector (4/3, 0) as a positive integer as
y = 2^3(x- 4/3)
x - 4 /3 => x = 4/3
0
2 years ago
#10
Impressive getting this up so quick!
2
2 years ago
#11
all the people who failed say "Mc Donald!"
1
2 years ago
#12
i guess im not going to uni and living off your guys taxes
1
2 years ago
#13
Do you think slightly different methods for 7 will still be fully credited? I did the binomial expansion while it was still in log form and found an equation equal to k-1, then factored out 3
0
Thread starter 2 years ago
#14
(Original post by solrowe)
Do you think slightly different methods for 7 will still be fully credited? I did the binomial expansion while it was still in log form and found an equation equal to k-1, then factored out 3
I think that's fine, whether it is in log form or not
0
2 years ago
#15
Why is the translation -4/3 and not +4/3?
0
2 years ago
#16
(Original post by Integer123)
AQA MPC2 June 2017 Unofficial Markscheme

1. A sector has a perimeter of 22cm and an angle of radians. The radius is 8cm.
(a) Find the value of [2 marks]

(b) Find the area of the sector [2 marks]

2. A triangle ABC has an angle BAC of . There are sides of 6cm and 16cm.

(a) Show that the angle ACB is to the nearest degree [3 marks]
, which is 19 degrees to the nearest degree.

(b) Find the area of the triangle. [3 marks]
Other angle is 41 degrees. Hence the area is cm2

3.
(a) Express in the form where is an expression in . [3 marks]

(b) Hence solve the equation . [2 marks]

4. A geometric series has the th term .
(a) Find and . [2 marks]
.

(b) Find the sum to infinity of the series [3 marks]
First term is 108, common ratio is 2/3.
Hence sum to infinity is

(c) Find the smallest value of such that . [3 marks]

.

Hence so is at least 13.

5. A curve satisfies , where .
(a) Show that there is only one value of for which there is a stationary point. [2 marks]
. Hence there is only one value of for which there is a stationary point.

(b) Find and show that this is a minimum point. [3 marks]
.
When , this is equal to 1. Hence it is positive, so the point is a minimum.

(c) The line is a tangent to the curve. Find the equation of the curve. [4 marks]
Must be a tangent at the stationary point. Hence the point (4, 2) lies on the curve (the stationary point). Integrating gives . As , so .

6. There is a curve .
(a) (i) Use the trapezium rule with five ordinates (four strips) to approximate to two decimal places. [4 marks]
Use the trapezium rule formula to find that it is 3.44 to two decimal places.

(a) (ii) State how the approximation may be improved. [1 mark]
Use more strips/ordinates.

(a) (iii) The point (1, ) lies on the curve. Use your answer to part (a)(i) to find the area bounded by the curve, the line and the line , to two decimal places. [3 marks]
so, by a sketch, the area is a rectangle with part (a)(i) subtracted. The area is to two decimal places.

(b) The curve may be mapped onto the curve of by a translation and a stretch.
(i) the translation [2 marks]

Translation in the vector (, 0)

(ii) stretch [2 marks]

Stretch parallel to the -axis scale factor .

(c) Use logarithms to solve the equation , using your answer to three significant figures. [2 marks]

to three significant figures.

7. A curve has the equation .
(a) The region bounded by the curve and the lines and is above the -axis. Show that the area of this region is 16. [5 marks]

Area (as curve is above the -axis) is:
. Substitute in the limits to show that the area is 16.

(b) The normal to the curve is parallel to the line . Find the equation of the normal to the curve. [6 marks]
Differentiating gives . Now, the normal has a gradient of . Hence the gradient of the tangent to the curve is . So

. Hence .

So the equation of the normal is .

8.
(a) Solve the equation in the range . Give your answers to the nearest degree. [2 marks]

The values of are 48 and 312.

(b) (i) Given that , show that . [3 marks]

(ii) Show that there is only one possible value of . [2 marks]
Factorising gives . As , the only possible value of is .

(c) Hence solve the equation in the range . [4 marks]

Solving in the range .

Use part (a) and then add on 360 to both solutions to give

So

9. Given that , express in terms of . [7 marks]

For 6)b)I) I'm pretty sure the translation was with the vector (4/3,0) and for the last question it asked to fine k in the form (c+1)^2 therefore k=3(c+1)^(2) +1
0
2 years ago
#17
Yeah, the translation should be +4/3
0
2 years ago
#18
I used log laws for the first bit and ended up crossing out correct working so 5 marks down drain ?
Also how much do you lose for putting gradient of Q as 1/4. I got x and y fine and used equation right just will it be one accuracy mark gone?
And for trapezium rule for some reason I have no idea I halved the rectangle coz I'm used to doing triangles hahahahha, will I lose 2 or 3 as I still got 8 but then subtracted 3.44 from 4.
0
Thread starter 2 years ago
#19
(Original post by Niallll99)
For 6)b)I) I'm pretty sure the translation was with the vector (4/3,0) and for the last question it asked to fine k in the form (c+1)^2 therefore k=3(c+1)^(2) +1
(Original post by Andrew Dainty)
Yeah, the translation should be +4/3
Ooops, another typo, I put 4/3 on my exam paper
0
2 years ago
#20
(Original post by Niallll99)
For 6)b)I) I'm pretty sure the translation was with the vector (4/3,0) and for the last question it asked to fine k in the form (c+1)^2 therefore k=3(c+1)^(2) +1
I believe it asked to find (c+1)^2 in terms of k.
0
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