Summer 2012 examination
MA107
Quantitative Methods (Mathematics)
Half Unit
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This examination paper contains 5 questions. You may attempt as many questions as you wish,
but only yo
Summer 2012 examination
MA107
Quantitative Methods (Mathematics)
Half Unit
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This examination paper contains 5 questions. You may attempt as many questions as you wish,
but only yo
Summer 2011 examination
MA107
Quantitative Methods (Mathematics)
(Half Unit)
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours.
This paper contains 5 questions. You may attempt as many questions as you wish,
but only the best 4
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 6: Stationary points and Lagrangeans
Exercise 1. We are asked to determine all real numbers, x, that satisfy the inequality
x(x + 1) > 1,
which on rearranging yields the equivalent ine
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 2: Recurrence equations and limits
Exercise 1. Excise tax is discussed in section 1.4 of the Anthony & Biggs book. See also worked
examples 1.3, 1.4 and 1.5.
The supply and demand sets
MA107: Quantitative Methods (Mathematics)
Solutions to the examination (2011)
Question 1.
(a) The equilibrium quantity occurs when pS (q) = pD (q) and so we have
1 + 2q = 6 3q
=
5q = 5
=
q = 1,
and this gives an equilibrium price of pD (1) = 6 3(1) = 3. T
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 10: Integration and Dierential equations
Exercise 1. The basic ideas and meaning of integration can be found in chapter 25 of the Anthony
& Biggs book. Techniques for integration are t
MA107: Quantitative Methods (Mathematics) 201415
Exercises 9: Inverse matrices
For all homeworks in this course please note that no marks will be given for answers only. Always
show the method used to obtain your answers.
Please write clearly. Dont just u
MA107: Quantitative Methods (Mathematics) 201415
Solutions to sample examination question 1
(a) The recurrence equation
3yt + 2yt1 15 = 0
2
yt = yt1 + 5,
3
can be rewritten as
2
and to solve this, because a = 3 = 1, we start by nding the time-independent
MA107: Quantitative Methods (Mathematics)
Solutions to the examination (2014)
Question 1.
(a) The inverse supply and demand functions of a market are
pS (q) = q 2 + 4q + 5
pD (q) = 2q + 12,
and
respectively. For (i), the supply curve has an equation that
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 7: Consumer choice; vectors and matrices
Exercise 1. For information about contours and their gradients see section 12.3 of the Anthony &
Biggs book. See also worked examples 12.3 and
MA107: Quantitative Methods (Mathematics) 201415
Exercises 8: Linear equations
For all homeworks in this course please note that no marks will be given for answers only. Always
show the method used to obtain your answers.
Please write clearly. Dont just u
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 9: Inverse matrices
Exercise 1. Inverse matrices are discussed in chapter 18 of the Anthony & Biggs book. This question
is very similar to worked example 18.1.
For (a), to nd the inver
MA107: Quantitative Methods (Mathematics) 201415
Exercises 10: Integration and Dierential equations
For all homeworks in this course please note that no marks will be given for answers only. Always
show the method used to obtain your answers.
Please write
MA107: Quantitative Methods (Mathematics) 201415
Sample examination question 2
Advice: Read the question, take a look at your notes and then, having put your notes away, do the
question. To get maximum benet, try doing it under exam conditions, i.e. you h
MA107: Quantitative Methods (Mathematics)
Solutions to the examination (2013)
Question 1.
(a) The equilibrium price occurs when supply equals demand and so we have
kp 4 = 10 p
=
(k + 1)p = 14
=
14
,
k+1
p=
and then, using the demand equation (say), this g
MA107: Quantitative Methods (Mathematics)
Solutions to the examination (2012)
Question 1.
(a) We rewrite the given recurrence equation in standard form to get
1
pt = 1 pt1 ,
2
and, as the coecient of the pt1 term is not equal to one, we can nd the time-in
MA107: Quantitative Methods (Mathematics) 201415
Exercises 4: Optimisation
For all homeworks in this course please note that no marks will be given for answers only. Always
show the method used to obtain your answers.
Please write clearly. Dont just use f
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 8: Linear equations
Exercise 1. Information about matrix operations and how to solve systems of linear equations can
be found in chapter 16 of the Anthony & Biggs book. See also worked
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 5: Partial derivatives
Exercise 1. For partial derivatives, see chapter 11 of the Anthony & Biggs book. Note that, when
nding partial derivatives with respect to one variable, we treat
Summer 2014 examination
MA107
Quantitative Methods (Mathematics)
Half Unit
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours.
This paper contains 5 questions. You may attempt as many questions as you wish,
but only the best 4 qu
MA107: Quantitative Methods (Mathematics) 201415
Exercises 1: Sets, functions, graphs, equations
For all homeworks in this course please note that no marks will be given for answers only. Always
show the method used to obtain your answers.
Please write cl
LSE
Summer 2011 examination
MA107
Quantitative Methods (Mathematics)
Half unit
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This paper contains 5 questions. You may attempt as many questions as you wish,
but only your best
Summer 2013 examination
MA107
Quantitative Methods (Mathematics)
(Half Unit)
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours.
This paper contains 5 questions. You may attempt as many questions as you wish,
but only the best 4
Summer 2010 examination
MA107
Quantitative Methods (Mathematics) .
y Half Unit
Suitable for all candidates
Instructions to candidates]
Time allowed: 2 hours
This paper contains 5 questions. You may attempt as many questions as you wish,
but only your best
MA107: Quantitative Methods (Mathematics) 201415
Exercises 2: Recurrence equations and limits
For all homeworks in this course please note that no marks will be given for answers only. Always
show the method used to obtain your answers.
Please write clear