Homework 6: Upload to Courseware by Monday 27th November 11:55 p.m.
Hypothesis Testing for Relationships
Preparation Tasks
A. Before beginning this assignment you should have completed Modules 15, 16
CLAUDIA ESI DENTU
KOBBINA GRAHAM - COHORT B
SOCIAL CONTRACT 1
Student Jailed for Manslaughter
Social contract theory is a concept built on the principles of ethics and moral rules in
order to guide th
BOOK OF EXERCISES
6TH OCTOBER,2016.
LOGIC AN D T HE CON CEP T OF M AT HEM AT ICAL
P ROOF.
1. Which of the following is a proposition,
(a) Abedi pele is the president of Ghana.
(b) 8 + 8 = 20
(c) 2x +
15 Integration 2 Further Techniques
Johann Bernoulli, Jakobs
brother, was born on 27 July
1667 and was the tenth child
of Nicolaus and Margaretha
Bernoulli. Johanns father
wished him to enter the
fami
17 Complex Numbers
Abraham de Moivre was born in
Vitry-le-Franois in France on 26
May 1667. It was not until his late
teenage years that de Moivre had
any formal mathematics training. In
1685 religiou
11 Matrices
The concept of matrices and determinants was probably first understood by the
Babylonians, who were certainly studying systems of linear equations. However, it was
Nine Chapters on the Mat
3 Functions
Calculators are an integral part of school mathematics, and this course requires the
use of a graphing calculator. Although much of the content of this chapter is
ancient mathematics in th
9 Differentiation 2 Further
Techniques
Leonhard Euler is considered
to be one of the most
important mathematicians of
all time. He was born on 15
April 1707 in Basel,
Switzerland, and died on 18
Septe
13 Vectors, Lines and Planes
Stefan Banach was born in Krakw,
Poland (at the time part of the AustroHungarian Empire) on 30 March
1892. During his early life Banach was
brought up by Franciszka Plowa,
7 Trigonometry 2
Consider the equation below. If all angles are in radians
arctan112 arctan122 arctan132 p
Can you prove this?
The mathematics behind the fact
The hint is in the diagram, since we can
1 Trigonometry 1
Although most people
connect trigonometry
with the study of
triangles, it is from the
circle that this area of
mathematics originates.
The study of trigonometry is not new. Its roots
5 Exponential and Logarithmic
Functions
In this chapter we will meet logarithms,
which have many important applications,
particularly in the field of natural science.
Logarithms were invented by John
20 Probability
Have you ever asked around a group of your classmates and been surprised to find
that two of them share the same birthday? At first thought it seems likely that for two
people in the ro
Answers
6 a Consistent. Lines intersect giving unique solution.
7 p3
b Consistent. Same line giving infinite solutions.
Chapter 11
Exercise 4
1 a x 1, y 9, z 13
b x 10, y 10, z 36
c x 2, y 4, z 3
d x
8 Differential Calculus 1 Introduction
The ideas that are the basis for calculus have been with us for a very long time.
Between 450 BC and 225 BC, Greek mathematicians were working on problems that
w
22 Continuous Probability
Distributions
Binomial distributions for 2, 4 and 12 throws
0.7
0.6
Probability
0.5
0.4
0.3
0.2
0.1
0
0
1
2
Number of sixes
0.6
Probability
0.5
0.4
0.3
0.2
0.1
0
0
1
2
Number
14 Integration 1
Jakob Bernoulli was a Swiss
mathematician born in Basel,
Switzerland, on 27 December 1654.
Along with his brother, Johann, he is
considered to be one of the most
important researchers
16 Integration 3 Applications
When students study integral
calculus, the temptation is to see it
as a theoretical subject. However,
this is not the case. Pelageia
Yakovlevna Polubarinova Kochina,
who
2 Quadratic Equations, Functions
and Inequalities
The first reference to quadratic equations
appears to be made by the Babylonians in
400 BC, even though they did not actually
have the notion of an eq
12 Vector Techniques
Bernard Bolzano was born in 1781 in
Prague in what is now the Czech Republic.
During Bolzanos early life there were two
major influences. The first was his father,
who was active
18 Mathematical Induction
Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji was born on 13 April 953 in
Baghdad, Iraq and died in about 1029. His importance in the field of mathematics is
debated by histo
4 Polynomials
The Italian mathematician Paolo Ruffini,
born in 1765, is responsible for
synthetic division, also known as
Ruffinis rule, a technique used for the
division of polynomials that is covere
6 Sequences, Series
and Binomial Theorem
Pascals triangle is constructed by
1
adding together the two numbers
1
1
above as shown (with a 1 on the end
of each row). There are many
1
2
1
interesting res
10 Differentiation 3 Applications
Differential calculus is widely used in both the natural sciences and the human sciences. In
physics, if we want to investigate the speed of a body falling under grav