Edexcel A-Level Further Mathematics - Further Mechanics 1 - 20 October 2020

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_gcx
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Edexcel Further Mathematics Paper 3C/4C (Further Mechanics 1)


Date: 20 October 2020
Session: PM
Length: 1h30
Marks: 75 (a fourth of the total A-level)

Paper 3C/4C can cover anything on the Further Mechanics 1 part of the specification.

If you want to use old spec resources, there is a content mapping document here. Be aware that the style is different and the old specification does not cover everything.

Content Mapping

A summary of content mapping can be found below.

Spoiler:
Show
  • Momentum in one dimension - M1
  • Momentum in two dimensions - M2
  • Work and energy - M2
  • Elastic strings and springs - M3
  • Elastic collisions in one dimension - M2
  • Elastic collisions in two dimensions - M4
  • Successive oblique impacts with smooth surfaces - M4

[Not sure if successive oblique impacts were marked as new in the mapping document in error, but I found a question on this on the first M4 paper I looked at. (2015) Don't know the frequency that they come up.]
Last edited by _gcx; 2 months ago
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SpiderMan1234434
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How was it?
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Reape
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Thoughts on that paper?

I found half of it okay, some I had some strange methods for. Unfortunately on the “half KE” one i forgot a square root, only realised coming out of the exam. y should’ve been 2, I guess, I got a surd. So annoyed. 14 Mark question

Couldn’t figure out the last one. Got tan(1/2 a) = 9/4tan(b) or something and had no clue where to go from there. So that’s a bunch of marks too.

So, all in all, not feeling amazingly great about it. Might’ve felt better if I didn’t miss out a sqrt:/
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SpiderMan1234434
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So, you guys heard about:

https://ofqual.blog.gov.uk/2020/10/1...autumn-series/
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sivashennaidoo
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(Original post by SpiderMan1234434)
So, you guys heard about:

https://ofqual.blog.gov.uk/2020/10/1...autumn-series/
yea seems likes good news
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Reape
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Do we have enough people to get a bit of an unofficial mark scheme going? Also quite interested in how people solved the very last question? @Jaaaaaack I think you said you were doing mechanics too?
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John_DoeIII
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Lads did you finish every question? Also did anyone use product rule for the restitution question?
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SpiderMan1234434
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(Original post by John_DoeIII)
Lads did you finish every question? Also did anyone use product rule for the restitution question?
Nope and Yep
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SpiderMan1234434
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how did you find it overall. Mark?
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Reape
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Very roughly remembering questions... Pretty tired right now, can't really remember many specifics... Some of the questions may be wrong, or in the complete wrong order. Feel free to fix :

1. (4+5 marks) Finding impulse (vector and angle) I think?
2. Power question. Car moves along with 15kW power. v = 25. Find something (can't remember what). Part b) find V given some conditions I don't remember.
3. (5+6?) Direct collision question of two spheres. Can't remember what you had to find. I think showing that they’re same direction? Final part, three spheres and after B collides with C show that it collides with A again.
4. (4+5 Mark?) Wonky shaped plane. Particle in, deflected. Show a vector was parallel with AB. Part b) I think finding e maybe?
5. Elastic string on a rough plane joined to point, particle launched up slope. lambda = kmg. Distance = 3l. Show that k = 15/38 or something. Part b: Find acceleration at instant it starts going down the slope.
6. (11+3 marks). Oblique collision given vectors, and told to find speed of P, Q, and then e. Given KE after (of Q) is half before. Part b was finding the angle of deflection, I think.
7.(7-9 Mark, 3 Mark) Two parallel planes, show tan(1/2 a) = 1/3. Part b, can't remember.

Some answers perhaps:

1. Can't remember.
2. Can't remember answers.
3. First part find velocities, note 0-e-1. So direction same. In case it jogs anyone’s memory to fix this, Only part I remember is 30-10e or something. Second collision I think the direction (from my assumption) was negative (ie same direction) and it was faster than A. But can’t remember.
4. Impulse vector is perpendicular to AB. Find impulse. Dot the vector with the given one. Dot product is 0, therefore perpendicular to impulse, so it's parallel with AB.
5. Resolve for friction, find energies, and then WD = change in energy. k = 15/38 pops out.
6. After correction: Magnitude of Q (velocity) after was 0.5, I think solving you get the vector to be (2,1). Find P, then e. Can't remember acceleration
7. Find momentum on two collisions to get tan(1/2 a) = 4/9tan(a). Then, from Cathy_Zheng, use tan2a=2tan(a)/1-tan^2a to find answer.

Again, I probably have question numbers mixed up.
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Cathy_Zheng
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I got tan(1/2a)=4/9tan(a) and use tan2a=2tan(a)/1-tan^2a to find the answer
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Jaaaaaack
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(Original post by Reape)
Do we have enough people to get a bit of an unofficial mark scheme going? Also quite interested in how people solved the very last question? @Jaaaaaack I think you said you were doing mechanics too?
I am here. Im rlly sorry peeps, I have such a shocking memory so cant remember exact answers. But the test went very well for me so very happy for you to fire me questions. I think I got everything
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Reape
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(Original post by Cathy_Zheng)
I got tan(1/2a)=4/9tan(a) and use tan2a=2tan(a)/1-tan^2a to find the answer
Ah, that sounds right! Nice!

I thought a double angle formula might come in handy but I just could t remember it. Couldn’t find it in formula book at a skim either? Spent 15 mins trying to think of it. Aw, I’m so annoyed at that. Got up to the 4/9tan part, so hopefully got a few method marks.
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Jaaaaaack
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(Original post by Reape)
Ah, that sounds right! Nice!

I thought a double angle formula might come in handy but I just could t remember it. Couldn’t find it in formula book at a skim either? Spent 15 mins trying to think of it. Aw, I’m so annoyed at that. Got up to the 4/9tan part, so hopefully got a few method marks.
Than tan a = 9/4 , you then divide through by tan 0.5A as its given tan 0.5 A =/ 0 and then the rest simplifies nicely to a 1/3 so youd only lose 2/3 marks there
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Jaaaaaack
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(Original post by Jaaaaaack)
Than tan a = 9/4 , you then divide through by tan 0.5A as its given tan 0.5 A =/ 0 and then the rest simplifies nicely to a 1/3 so youd only lose 2/3 marks there
Tan a=9/4tan0.5 A. ****
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John_DoeIII
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For the vector and slanted line I didn’t find the impulse I just found the change in speed would that be right considering I got the answer?
Also for the sphere momentum did you let get root 6 for q.
And for the last question the loss in energy is 21.9%?
For the question with the two spheres traveling in the same direction for part B) I got a quadratic, 3e^2-8e+10 and the function was positive for all e so there’s a second collision.
1b) 70° or so was the angle
For the power question I got 5/48 for deceleration and 15.4 for speed.
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SpiderMan1234434
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(Original post by John_DoeIII)
For the vector and slanted line I didn’t find the impulse I just found the change in speed would that be right considering I got the answer?
Also for the sphere momentum did you let get root 6 for q.
And for the last question the loss in energy is 21.9%?
For the question with the two spheres traveling in the same direction for part B) I got a quadratic, 3e^2-8e+10 and the function was positive for all e so there’s a second collision.
1b) 70° or so was the angle
For the power question I got 5/48 for deceleration and 15.4 for speed.
I got 174 (I used the dot product) for the angle and 2ms^-1 for V
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John_DoeIII
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(Original post by SpiderMan1234434)
I got 174 (I used the dot product) for the angle and 2ms^-1 for V
174 for the trucks speed?
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SpiderMan1234434
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(Original post by John_DoeIII)
174 for the trucks speed?
no angle 1b
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John_DoeIII
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How did people get 2ms^-1 wasn’t q 0.2 kg and 4i plus 2j
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