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Edexcel A-Level Further Mathematics - Further Mechanics 1 - 20 October 2020
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Edexcel Further Mathematics Paper 3C/4C (Further Mechanics 1)
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:
[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.]
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- 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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#3
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:/
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:/
Last edited by Reape; 1 month ago
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#5
(Original post by SpiderMan1234434)
So, you guys heard about:
https://ofqual.blog.gov.uk/2020/10/1...autumn-series/
So, you guys heard about:
https://ofqual.blog.gov.uk/2020/10/1...autumn-series/
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#6
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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#7
Lads did you finish every question? Also did anyone use product rule for the restitution question?
Last edited by John_DoeIII; 1 month ago
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#8
(Original post by John_DoeIII)
Lads did you finish every question? Also did anyone use product rule for the restitution question?
Lads did you finish every question? Also did anyone use product rule for the restitution question?
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#10
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.
: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.
Last edited by Reape; 1 month ago
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#12
(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?
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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#13
(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
I got tan(1/2a)=4/9tan(a) and use tan2a=2tan(a)/1-tan^2a to find the answer
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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#14
(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.
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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#15
(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
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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#16
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.
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.
Last edited by John_DoeIII; 1 month ago
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#17
(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.
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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#18
(Original post by SpiderMan1234434)
I got 174 (I used the dot product) for the angle and 2ms^-1 for V
I got 174 (I used the dot product) for the angle and 2ms^-1 for V
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