# MEI Extra Pure resources

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Hey,

I have basically run out of materials for the MEI extra pure A level exams and I was wondering if people had any more to go through. I have looked at all the old specification questions for MEI for FP2 and FP3 (I have even done some more than twice..) 2006-2018. I have done the specimen and all the practice sets provided by the school. I have also looked at the OCR A specimen paper from Additional Pure Maths. If people would be able to supply questions based on multivariable calculus, recurrence relations (actually solving them, kinda like DEs), eigenvectors and eigenvalues and groups, would really appreciate it. If you have access to the practice sets from other boards such as OCR A, Edexcel, even AQA it would help as they could be quite relevant. The main reason being, I have done all the resources that have been provided by my school and I have just one exam left on Monday (we had a week long gap) and I just need to crack on with some new stuff rather than sitting idly and worrying. BTW the new spec is quite different from the old.

Thanks in advance!

I have basically run out of materials for the MEI extra pure A level exams and I was wondering if people had any more to go through. I have looked at all the old specification questions for MEI for FP2 and FP3 (I have even done some more than twice..) 2006-2018. I have done the specimen and all the practice sets provided by the school. I have also looked at the OCR A specimen paper from Additional Pure Maths. If people would be able to supply questions based on multivariable calculus, recurrence relations (actually solving them, kinda like DEs), eigenvectors and eigenvalues and groups, would really appreciate it. If you have access to the practice sets from other boards such as OCR A, Edexcel, even AQA it would help as they could be quite relevant. The main reason being, I have done all the resources that have been provided by my school and I have just one exam left on Monday (we had a week long gap) and I just need to crack on with some new stuff rather than sitting idly and worrying. BTW the new spec is quite different from the old.

Thanks in advance!

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#2

The old spec ocr a fp3 papers have a lot of good questions on group theory https://www.ocr.org.uk/qualification...892-7890-7892/ . There are these 2 sheets on recurrence relations http://www.cimt.org.uk/projects/mepr...crete_ch14.pdf and http://www.cimt.org.uk/projects/mepr...crete_ch15.pdf . There's a short section of eigenvectors and eigenvalues here too http://www.cimt.org.uk/projects/mepr.../fpure_ch9.pdf. I don't have anything on multivariable calc apart from the mei past papers.

Hope this helps and good luck

Hope this helps and good luck

(Original post by

Hey,

I have basically run out of materials for the MEI extra pure A level exams and I was wondering if people had any more to go through. I have looked at all the old specification questions for MEI for FP2 and FP3 (I have even done some more than twice..) 2006-2018. I have done the specimen and all the practice sets provided by the school. I have also looked at the OCR A specimen paper from Additional Pure Maths. If people would be able to supply questions based on multivariable calculus, recurrence relations (actually solving them, kinda like DEs), eigenvectors and eigenvalues and groups, would really appreciate it. If you have access to the practice sets from other boards such as OCR A, Edexcel, even AQA it would help as they could be quite relevant. The main reason being, I have done all the resources that have been provided by my school and I have just one exam left on Monday (we had a week long gap) and I just need to crack on with some new stuff rather than sitting idly and worrying. BTW the new spec is quite different from the old.

Thanks in advance!

**MysteryVader**)Hey,

I have basically run out of materials for the MEI extra pure A level exams and I was wondering if people had any more to go through. I have looked at all the old specification questions for MEI for FP2 and FP3 (I have even done some more than twice..) 2006-2018. I have done the specimen and all the practice sets provided by the school. I have also looked at the OCR A specimen paper from Additional Pure Maths. If people would be able to supply questions based on multivariable calculus, recurrence relations (actually solving them, kinda like DEs), eigenvectors and eigenvalues and groups, would really appreciate it. If you have access to the practice sets from other boards such as OCR A, Edexcel, even AQA it would help as they could be quite relevant. The main reason being, I have done all the resources that have been provided by my school and I have just one exam left on Monday (we had a week long gap) and I just need to crack on with some new stuff rather than sitting idly and worrying. BTW the new spec is quite different from the old.

Thanks in advance!

1

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Well not a lot tbh, but maybe more than average, I guess. It's cuz I didn't work hard during GCSEs and was disappointed with some of my grades, so I'm trying to put in effort this time, just to be extra sure of getting the grade I want.

(Original post by

Wow how much work do you do?!!!

**sam23478**)Wow how much work do you do?!!!

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#5

well if you've done that much work you'll be fine

(Original post by

Well not a lot tbh, but maybe more than average, I guess. It's cuz I didn't work hard during GCSEs and was disappointed with some of my grades, so I'm trying to put in effort this time, just to be extra sure of getting the grade I want.

**MysteryVader**)Well not a lot tbh, but maybe more than average, I guess. It's cuz I didn't work hard during GCSEs and was disappointed with some of my grades, so I'm trying to put in effort this time, just to be extra sure of getting the grade I want.

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It was hard, but I think the practice paid off.

(Original post by

how did you find it

**sam23478**)how did you find it

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#9

What answers did you get; I got

1.a. 1,-1

b. (2,1) and (-1,2)

c. y=(1/2)x

2a. Show that

b. Circle radius 3 centre (1/2, -1)

c. a=0.5, c=-3 or 1

c. All the cross sections are circles so it must be a cone so it must be either a max or min not a saddle point. Since there is a cross section if z=42, s.p. at z=6 must be minimum

3. Find inverse of matrix using Cayley Hamilton, can't remember but I checked it with my calculator

4a. e=2 since e*e=e and a*a=2

b. 2*3=3, 1*2=1, 1*1=3*3=2 therefore 1*3 doesn't equal 1/2/3 therefore 1*3=4

c. basically a sudoku

d. Yes it is commutative since a*b=b*a from table

5a. a=alpha/100+1, b=-R

b. u(n)=a^nC+b((a^n-1)/(a-1))

c. show that. lim as n tends to infinity of un =(a^n)C+(b/(a-1))a^n (as a^n-1 tends to a^n)

therefore C+b/(a-1)<0 given answer follows immediately

d. can't remember exactly but 62,000 ish

6a. Show that. a/b=sqrt(7). Since a,b are rational, a/b is rational but root 7 is irrational so no integer solutions

b. Closure as (a+bsqrt7)(c+dsqrt7) belongs to G

associativity as multiplication is associative

identity is 1

inverse of (a+bsqrt7)=(a-bsqrt7)/(a^2-7b^2) this belongs to G

So a group

c. Not a group as (1+csqrt7)(1+dsqrt7)=1+7cd+(c+d)sqrt7, doesn't belong to H as 1+7cd doesn't equal 1 unless one of c,d=0

d. Counter example was <1,-1>. This is the only possible finite subgroup.

Some of those could well be wrong and I might have missed one

1.a. 1,-1

b. (2,1) and (-1,2)

c. y=(1/2)x

2a. Show that

b. Circle radius 3 centre (1/2, -1)

c. a=0.5, c=-3 or 1

c. All the cross sections are circles so it must be a cone so it must be either a max or min not a saddle point. Since there is a cross section if z=42, s.p. at z=6 must be minimum

3. Find inverse of matrix using Cayley Hamilton, can't remember but I checked it with my calculator

4a. e=2 since e*e=e and a*a=2

b. 2*3=3, 1*2=1, 1*1=3*3=2 therefore 1*3 doesn't equal 1/2/3 therefore 1*3=4

c. basically a sudoku

d. Yes it is commutative since a*b=b*a from table

5a. a=alpha/100+1, b=-R

b. u(n)=a^nC+b((a^n-1)/(a-1))

c. show that. lim as n tends to infinity of un =(a^n)C+(b/(a-1))a^n (as a^n-1 tends to a^n)

therefore C+b/(a-1)<0 given answer follows immediately

d. can't remember exactly but 62,000 ish

6a. Show that. a/b=sqrt(7). Since a,b are rational, a/b is rational but root 7 is irrational so no integer solutions

b. Closure as (a+bsqrt7)(c+dsqrt7) belongs to G

associativity as multiplication is associative

identity is 1

inverse of (a+bsqrt7)=(a-bsqrt7)/(a^2-7b^2) this belongs to G

So a group

c. Not a group as (1+csqrt7)(1+dsqrt7)=1+7cd+(c+d)sqrt7, doesn't belong to H as 1+7cd doesn't equal 1 unless one of c,d=0

d. Counter example was <1,-1>. This is the only possible finite subgroup.

Some of those could well be wrong and I might have missed one

0

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I actually agree with all your answers, I think for the recurrence relation it was n = 21 for the year of repayment? And then you had to take away something like £750 from the £63000. For the first groups question I just used the idea that an order 4 group is either Z4 or Klein and because all the elements were self inverse, you could basically say the group was Klein and do the rest of the question. The CHT had a load of 1/12ths and it was something like A^-1 = 1/12 A^2 + something A + 35/3 I can't remember tbh. Obviously, there might be some different explanations/proofs but for the final numerical answers I think those are good. Well that paper was great then lol

(Original post by

What answers did you get; I got

1.a. 1,-1

b. (2,1) and (-1,2)

c. y=(1/2)x

2a. Show that

b. Circle radius 3 centre (1/2, -1)

c. a=0.5, c=-3 or 1

c. All the cross sections are circles so it must be a cone so it must be either a max or min not a saddle point. Since there is a cross section if z=42, s.p. at z=6 must be minimum

3. Find inverse of matrix using Cayley Hamilton, can't remember but I checked it with my calculator

4a. e=2 since e*e=e and a*a=2

b. 2*3=3, 1*2=1, 1*1=3*3=2 therefore 1*3 doesn't equal 1/2/3 therefore 1*3=4

c. basically a sudoku

d. Yes it is commutative since a*b=b*a from table

5a. a=alpha/100+1, b=-R

b. u(n)=a^nC+b((a^n-1)/(a-1))

c. show that. lim as n tends to infinity of un =(a^n)C+(b/(a-1))a^n (as a^n-1 tends to a^n)

therefore C+b/(a-1)<0 given answer follows immediately

d. can't remember exactly but 62,000 ish

6a. Show that. a/b=sqrt(7). Since a,b are rational, a/b is rational but root 7 is irrational so no integer solutions

b. Closure as (a+bsqrt7)(c+dsqrt7) belongs to G

associativity as multiplication is associative

identity is 1

inverse of (a+bsqrt7)=(a-bsqrt7)/(a^2-7b^2) this belongs to G

So a group

c. Not a group as (1+csqrt7)(1+dsqrt7)=1+7cd+(c+d)sqrt7, doesn't belong to H as 1+7cd doesn't equal 1 unless one of c,d=0

d. Counter example was <1,-1>. This is the only possible finite subgroup.

Some of those could well be wrong and I might have missed one

**sam23478**)What answers did you get; I got

1.a. 1,-1

b. (2,1) and (-1,2)

c. y=(1/2)x

2a. Show that

b. Circle radius 3 centre (1/2, -1)

c. a=0.5, c=-3 or 1

c. All the cross sections are circles so it must be a cone so it must be either a max or min not a saddle point. Since there is a cross section if z=42, s.p. at z=6 must be minimum

3. Find inverse of matrix using Cayley Hamilton, can't remember but I checked it with my calculator

4a. e=2 since e*e=e and a*a=2

b. 2*3=3, 1*2=1, 1*1=3*3=2 therefore 1*3 doesn't equal 1/2/3 therefore 1*3=4

c. basically a sudoku

d. Yes it is commutative since a*b=b*a from table

5a. a=alpha/100+1, b=-R

b. u(n)=a^nC+b((a^n-1)/(a-1))

c. show that. lim as n tends to infinity of un =(a^n)C+(b/(a-1))a^n (as a^n-1 tends to a^n)

therefore C+b/(a-1)<0 given answer follows immediately

d. can't remember exactly but 62,000 ish

6a. Show that. a/b=sqrt(7). Since a,b are rational, a/b is rational but root 7 is irrational so no integer solutions

b. Closure as (a+bsqrt7)(c+dsqrt7) belongs to G

associativity as multiplication is associative

identity is 1

inverse of (a+bsqrt7)=(a-bsqrt7)/(a^2-7b^2) this belongs to G

So a group

c. Not a group as (1+csqrt7)(1+dsqrt7)=1+7cd+(c+d)sqrt7, doesn't belong to H as 1+7cd doesn't equal 1 unless one of c,d=0

d. Counter example was <1,-1>. This is the only possible finite subgroup.

Some of those could well be wrong and I might have missed one

Last edited by MysteryVader; 1 year ago

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#11

yeah sounds like a great paper for both of us!

(Original post by

I actually agree with all your answers, I think for the recurrence relation it was n = 21 for the year of repayment? And then you had to take away something like £750 from the £63000. For the first groups question I just used the idea that an order 4 group is either Z4 or Klein and because all the elements were self inverse, you could basically say the group was Klein and do the rest of the question. The CHT had a load of 1/12ths and it was something like A^-1 = 1/12 A^2 + something A + 35/3 I can't remember tbh. Obviously, there might be some different explanations/proofs but for the final numerical answers I think those are good. Well that paper was great then lol

**MysteryVader**)I actually agree with all your answers, I think for the recurrence relation it was n = 21 for the year of repayment? And then you had to take away something like £750 from the £63000. For the first groups question I just used the idea that an order 4 group is either Z4 or Klein and because all the elements were self inverse, you could basically say the group was Klein and do the rest of the question. The CHT had a load of 1/12ths and it was something like A^-1 = 1/12 A^2 + something A + 35/3 I can't remember tbh. Obviously, there might be some different explanations/proofs but for the final numerical answers I think those are good. Well that paper was great then lol

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#12

can i ask which syllabus is the recursion relation covered? i had found any resources of this topic and it seems to be something technique which would b introduced in math olympiad.

(Original post by

The old spec ocr a fp3 papers have a lot of good questions on group theory https://www.ocr.org.uk/qualification...892-7890-7892/ . There are these 2 sheets on recurrence relations http://www.cimt.org.uk/projects/mepr...crete_ch14.pdf and http://www.cimt.org.uk/projects/mepr...crete_ch15.pdf . There's a short section of eigenvectors and eigenvalues here too http://www.cimt.org.uk/projects/mepr.../fpure_ch9.pdf. I don't have anything on multivariable calc apart from the mei past papers.

Hope this helps and good luck

**yoshbiz**)The old spec ocr a fp3 papers have a lot of good questions on group theory https://www.ocr.org.uk/qualification...892-7890-7892/ . There are these 2 sheets on recurrence relations http://www.cimt.org.uk/projects/mepr...crete_ch14.pdf and http://www.cimt.org.uk/projects/mepr...crete_ch15.pdf . There's a short section of eigenvectors and eigenvalues here too http://www.cimt.org.uk/projects/mepr.../fpure_ch9.pdf. I don't have anything on multivariable calc apart from the mei past papers.

Hope this helps and good luck

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#13

OCR B MEI further maths extra pure. It won't come up in an Olympiad.

(Original post by

can i ask which syllabus is the recursion relation covered? i had found any resources of this topic and it seems to be something technique which would b introduced in math olympiad.

**FrancisKai**)can i ask which syllabus is the recursion relation covered? i had found any resources of this topic and it seems to be something technique which would b introduced in math olympiad.

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#14

**yoshbiz**)

The old spec ocr a fp3 papers have a lot of good questions on group theory https://www.ocr.org.uk/qualification...892-7890-7892/ . There are these 2 sheets on recurrence relations http://www.cimt.org.uk/projects/mepr...crete_ch14.pdf and http://www.cimt.org.uk/projects/mepr...crete_ch15.pdf . There's a short section of eigenvectors and eigenvalues here too http://www.cimt.org.uk/projects/mepr.../fpure_ch9.pdf. I don't have anything on multivariable calc apart from the mei past papers.

Hope this helps and good luck

**MysteryVader**)

Hey,

I have basically run out of materials for the MEI extra pure A level exams and I was wondering if people had any more to go through. I have looked at all the old specification questions for MEI for FP2 and FP3 (I have even done some more than twice..) 2006-2018. I have done the specimen and all the practice sets provided by the school. I have also looked at the OCR A specimen paper from Additional Pure Maths. If people would be able to supply questions based on multivariable calculus, recurrence relations (actually solving them, kinda like DEs), eigenvectors and eigenvalues and groups, would really appreciate it. If you have access to the practice sets from other boards such as OCR A, Edexcel, even AQA it would help as they could be quite relevant. The main reason being, I have done all the resources that have been provided by my school and I have just one exam left on Monday (we had a week long gap) and I just need to crack on with some new stuff rather than sitting idly and worrying. BTW the new spec is quite different from the old.

Thanks in advance!

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