In what ways did processes of
Catching'Forging Ahead, Catching-Up
preand Falling Behind' differ prepost1914 and post-1945?
TOPIC 6
SNEHA AND
JACOB
US CATCH UP PRE 1914
Britain v America
Basis for US catch up
Increased protection
American tariffs between 1
Summer 2012 examination
MA1~00
Mathematical Methods
Suitable for all candidates
Instructions to candidates
Time allowed: 3 hours
This paper contains 8-questions. You may attempt as many questions as y0u wish,
but only your best 6 answers will count toward
MA103 Slide set 5
Geometric Proofs
Fibonacci Numbers
Using Strong Induction: Egyptian Fractions
1
Roadmap
Geometric proofs
The Fibonacci numbers and solving linear recurrence equations
Strong induction applied to splitting bread
2
The rst n odd numbers su
Introduction to Abstract Mathematics
MA 103
Exercises 1
Deadline for handing in this work : Wednesday of Week 2, 5.00pm.
Relevant parts of the Lecture notes : Sections 2.1 2.7.
Relevant parts of the text books : Biggs : Sections 1.1 1.7 and 3.1 3.5;
Ec
Introduction to Abstract Mathematics
MA 103
Exercises 1
Deadline for handing in this work : Wednesday of Week 2, 5.00pm.
Relevant parts of the Lecture notes : Sections 2.1 2.7.
Relevant parts of the text books : Biggs : Sections 1.1 1.7 and 3.1 3.5;
Ec
Introduction to Abstract Mathematics
MA 103
Exercises 1
Deadline for handing in this work : Wednesday of Week 2, 5.00pm.
Relevant parts of the Lecture notes : Sections 2.1 2.7.
Relevant parts of the text books : Biggs : Sections 1.1 1.7 and 3.1 3.5;
Ec
Review notes EC 102 Chapters 1-16 are on the test Key concepts: Scarcity Choice Opportunity costs (including how to calculate) Ceteris paribus Sunk cost Benefit Marginal cost Marginal benefit the use of graphs Resources: Land Labor Capital Entrepreneurshi
Mark Scheme (Results)
January 2010
GCE
GCE Physics (6PH02) Paper 1
Edexcel Limited. Registered in England and Wales No. 4496750
Registered Office: One90 High Holborn, London WC1V 7BH
Edexcel is one of the leading examining and awarding bodies in the UK an
Mark Scheme (Results)
January 2010
GCE
GCE Physics (6PH04) Paper 1
Edexcel Limited. Registered in England and Wales No. 4496750
Registered Office: One90 High Holborn, London WC1V 7BH
Edexcel is one of the leading examining and awarding bodies in the UK an
Examiners Report
June 2010
GCE Physics 6PH01
Edexcel Limited. Registered in England and Wales No. 4496750
Registered Ofce: One90 High Holborn, London WC1V 7BH
Physics 6PH01
ii
Edexcel is one of the leading examining and awarding bodies in the UK and throu
Mark Scheme (Results)
January 2010
GCE
GCE Physics (6PH01) Paper 1
Edexcel Limited. Registered in England and Wales No. 4496750
Registered Office: One90 High Holborn, London WC1V 7BH
Edexcel is one of the leading examining and awarding bodies in the UK an
ST102
Elementary Statistical Theory
Example workshop:
Point estimation
Dr James Abdey
Department of Statistics
London School of Economics and Political Science
ST102 Elementary Statistical Theory
Dr James Abdey
LT 2015
Example workshop: Point estimation
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Edexcel GCE
Physics
Advanced Subsidiary
Unit 1: Physics on the Go
Wednesday 13 January 2010 Morning
Time: 1 hour 30 minutes
You do not need any other materials.
Paper Reference
6PH01/
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Edexcel GCE
Physics
Advanced
Unit 4: Physics on the Move
Thursday 28 January 2010 Afternoon
Time: 1 hour 35 minutes
You must have:
Ruler
Paper Reference
6PH04/01
Total Marks
Instructi
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Centre
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6 7 5 4
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0 1
Signature
Paper Reference(s)
6754/01
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Salters Horners Physics
Advanced Level
Unit Test PSA4
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1
Wednesday
Mathematical Methods, Lecture Twenty-Nine
Practice Questions and Solutions for Lecture 29
Practice question 29.5.1 Using the simpler notation x1 = x, x2 = y, show that
the function f : R2 R given by
f (x, y) =
x3 + y 3
x+y
is homogeneous of degree n = 2.
ST102
Elementary Statistical Theory
Example workshop:
Random variables
Dr James Abdey
Department of Statistics
London School of Economics and Political Science
ST102 Elementary Statistical Theory
Dr James Abdey
MT 2014
Example workshop: Random variables
Mathematical Methods, Lecture Twenty-Six
Practice Questions and Solutions for Lecture 26
Practice question 26.5.1 Consider the linear transformation S : R2 R2 dened
by
S(
3x y
.
x + 3y
x
)=
y
Also consider the standard basis B for R2 given by
B = cfw_e1 ,
MA103 Slide set 3
Sets and Quantiers
1
Sets
Loosely speaking, a set is a collection of objects.
A set is usually described by listing or describing its members
inside curly brackets (sometimes called braces) cfw_ and .
Example
A = cfw_1, 2, 3 is the set w
Mathematical Methods, Lecture Twenty-Four
Practice Questions and Solutions for Lecture 24
Practice question 24.4.1 T : R2 R2 and S : R2 R2 are linear transformations dened by
T(
x
)=
y
x
y
and
S(
x
)=
y
y
.
x
(a) Sketch the eects of T and S on the standar
Mathematical Methods, Lecture Twenty-Eight
Practice Questions and Solutions for Lecture 28
Practice question 28.4.1 (a) Orthogonally diagonalise the matrix A =
1 2
.
2 1
(b) Use the result in part (a) to sketch the curve xT Ax = 3 in the xy-plane.
Solutio
Mathematical Methods, Lecture Twenty-One
Practice Questions and Solutions for Lecture 21
Practice question 21.3.1
Consider the following matrix A:
1 2 1 3 0
A = 0 1 1 1 1 .
1 3 2 0 1
(a) Find a basis B1 for the row space of A.
(b) Find a basis B2 for the
Mathematical Methods, Revision Lecture
About The Exam
The paper is suitable for all candidates. It contains 8 questions. You may attempt
as many questions as you wish, but only your BEST 6 answers will count towards
the nal mark. All questions carry equal
Mathematical Methods, Lecture Twenty-Five
Practice Questions and Solutions for Lecture 25
Practice question 25.3.1 (a) Show that the following sets, B and C, are bases
for R3 :
1
0
1
0 , 1 , 0
B = cfw_f 1 , f2 , f3 =
1
3
1
and
1
0
1
1 , 1 , 1 .
C
Write your name here
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Centre Number
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Edexcel GCE
Physics
Advanced
Unit 5: Physics from Creation to Collapse
Tuesday 29 June 2010 Afternoon
Time: 1 hour 35 minutes
You do not need any other materials.
Paper Reference
6PH0
Write your name here
Surname
Other names
Centre Number
Candidate Number
Edexcel GCE
Physics
Advanced Subsidiary
Unit 2: Physics at Work
Monday 18 January 2010 Afternoon
Time: 1 hour 30 minutes
You do not need any other materials.
Paper Reference
6PH02/01
Paper Reference
Paper Reference(s)
_
Ell
6755/02
Edexcel GCE
Salters Horners Physics
Advanced Level
Unit Test PSAS (ii)
Thursday 14 June 2007 Morning
Time: 1 hour
Materials required for examination
Nil Nil
IllllIllllllllllllllllllllIllllll
l-l[)004168
Ins
Centre
No.
Surname
Paper Reference
6 7 5 1
Candidate
No.
0 1
Initial(s)
Signature
Paper Reference(s)
6751/01
Examiners use only
Edexcel GCE
Team Leaders use only
Salters Horners Physics
Advanced Subsidiary
Unit Test PSA1
Wednesday 17 January 2007 Afternoo