47th INTERNATIONAL
CHEMISTRY OLYMPIAD
2015
UK Round One
STUDENT QUESTION BOOKLET
*
The time allowed is 2 hours.
Attempt all 5 questions.
Write your answers in the special answer booklet.
In your calculations, please write only the essential steps in the a
UK Chemistry Olympiad 2016
Examiners Report, Round 1, 2016
The members of the Royal Society of Chemistry (RSC) Olympiad Working Group
would again like to thank teachers for their hard work supporting students and the
RSC to run Round 1 of the UK Chemistry
48th INTERNATIONAL
CHEMISTRY OLYMPIAD
2016
UK Round One
STUDENT QUESTION BOOKLET
*
The time allowed is 2 hours.
Attempt all 5 questions.
Write your answers in the special answer booklet.
In your calculations, please write only the essential steps in the a
Table of Contents:
Table of Contents:
1
Disabled:
2
The Parable of the Old Man and the Young:
5
Anthem for Doomed Youth:
12
A Terre:
16
Arms and the Boy
22
Futility:
25
Dulce et Decorum Est:
28
The Sentry:
33
Strange Meeting:
43
Spring Offensive
51
Exposu
C
L
3
6
Cambridge Chemistry Challenge Lower 6th
June 2014
Student Answer Booklet
Student name
male
female
Email
School
School year (eg year 12)
Subjects taken for AS
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p3
p4
p5
p6
p7
p8
p9
Total
mark
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oxidation states:
Be
H
Si
O
Sirojiddin Abdurasulov
September 19, 2016
Replacing Humans
Professors Blitz and Head
Analysis: Fromm, The Art of Loving and Sales, Tinder and
the Dawn of the Dating Apocalypse
Merriam-Webster defines love as, Attraction that includes sexual desire: The st
JOHN JAY COLLEGE OF CRIMINAL JUSTICE - CUNY
ECO 220-99
MACROECONOMICS
Week 11 Assignment
Important note: Submit your assignments as a Word document. This will allow me to comment
on your assignments and give you feedback. The assignment answers will be po
Sirojiddin Abdurasulov
Professor James Christopher Head and Michael Blitz
November 20, 2016
Who or what are the invaders?
Speaking of the overall background theme, the humanity has been kicked off Earth by the
super-powerful Invaders, who apparently get a
BUSINESS MATHEMATICS
(ACW 110)
Functions
Course Objectives
To develop notion of slope and different forms of
equations of lines
To introduce various forms of functions and their
properties
To sketch graphs arising from different forms of
functions
To deve
-1-
4CCM111A
4CCM111A Calculus I August resit 2013 Solutions
total possible marks: 70(A, 14x5) + 70(B, 5x14) = 140
In section A there are 5 marks for a correct answer, -1 for a wrong
answer, 0 for a blank answer. Put the correct letter in the box.
All the
-1-
4CCM111A
4CCM111A Calculus I January 2013 Solutions
total possible marks: 70(A, 14x5) + 70(B, 5x14) = 140
In section A there are 5 marks for a correct answer, -1 for a wrong
answer, 0 for a blank answer. Put the correct letter in the box.
A1.
1
i2
=
i
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 11
2
60. For the rst two series (which we expect to converge since we know that
converges) we may use
nn
convergence criterium C1, and compare the series at hand to the convergent series n n2 :
(a) Let an = n3
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 10
d
55. Integration by parts on In (x), upon inserting 1 = dx (x), gives:
d
d
x
In (x) = (1+x2 )n
x
x dx =
(1+x2 )n dx
dx
(1+x2 )n
dx
x2 dx
x
+ 2n
=
2 )n
(1+x
(1+x2 )n+1
x
1+x2
dx
=
+ 2n
dx
2 )n
(1+x
(1+x2
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 8
48. All are relations that can be written in the standard form F (x, y) = 0. Standard method: (i) dierentiate
with respect to x (using chain rule), then (ii) solve the result for dy/dx.
dy
d
dy
x2 + y 2 = 0
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 9
52. Just implement the suggested substitutions given. The outcomes can always be checked a posteriori by
dierentiation:
(a)
ex dx
1 + ex
dx/dy = 1/y so dx = y 1 dy
yy 1 dy
dy
=
=
= ln |1 + y| = ln(1 + ex )
1
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 6
39. The substitution suggested leads to the following problem, with now x 0:
1
1 n
1+
= (1 + x)1/x = ex log(1+x)
n
We proved in the lectures that limx0 x1 log(1 + x) = 1, hence
1
1
1 n
= lim ex log(1+x) = el
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 7
44. First the induction proof. We are to prove that An = 0 for all n Z + , with
Z
An =
n
d
dx
n
k=1
n
f (x)
f (x)
fk (x)
=1
fk (x)
k=1
(i) Induction basis:
A1 =
1
d
dx
1
k=1
1
f (x)
f (x)
fk (x)
=1
fk (x)
k=
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 5
35. We dene as usual the dierence between the two sides of the identity: An =
An = 0 for all integer n 0.
0
k=0
(i) basis: A0 =
zk
1z 1
1z
n
k=0
zk
1z n+1
1z .
To prove:
= 1 1 = 0, so the claim is true for
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 4
27. Expressions of the type cos() + b sin() to be written as c sin( + ):
just follow the steps described in lectures,
(a) sin() + cos(): here a = b = 1
c = 12 + 12 = 2,
= arctan(a/b) + n = arctan(1) + n = /
1
CALCULUS 1: SOLUTIONS TO TUTORIAL EXERCISES 3
n
k=1
20. Subtract LHS and RHS of the equality and dene An =
for all n IN.
(i) The basis: A1 =
1
k=1
2k (1 1 ) =
2
1
2
1
2
2k (1 2n ). We have to prove that An = 0
= 0. Thus the statement is correct for n =
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
Kings College London
University Of London
This paper is part of an examination of the College counting towards the award of a degree.
Examinations are governed by the College Regulations under the authority of the Academic
Board.
ATTACH this paper to your
Full Name:
(block capitals)
Student Number:
4CCM111A Calculus 1: Example Test 3
CALCULATORS MAY NOT BE USED
a
b
c
d
e
1
ANSWER GRID: put a cross in
ONE BOX for the correct answer
for each question. If you change
your mind and want to correct
your answer,
CALCULUS I
CM111A
Maple Exercises 5
1. Read through the worksheet giving the solutions to the previous set of problems,
running the example commands as you go, and making sure you understand how
they work.
2. Read through the tutorial worksheet for this w
CALCULUS I
CM111A
Maple Exercises 3
1. Read through the worksheet giving the solutions to the previous set of problems,
running the example commands as you go, and making sure you understand how
they work.
2. Read through the tutorial worksheet for this w
CALCULUS I
CM111A
Maple Exercises 2
1. Read through the worksheet giving the solutions to the previous set of problems,
running the example commands as you go, and making sure you understand how
they work.
2. Read through the tutorial worksheet for this w