MATH 10001 Mathematics for Computing
Winter 2015
MATH 10001 Mathematics for Computing, Test 2
Calculators:
Students may use a standard calculator or a scientific calculator.
Formulas:
The future value of an investment:
The future value of an ordinary simp
Annuities
An annuity is a series of payments of the same amount made at regular intervals (weekly, monthly,
semi-annually, etc.).
Payment interval: The length of time between payments, e.g. month, week etc.
Term of the annuity: The time between the first
Interest
Simple interest is interest that is earned on the original amount invested. It is calculated according to
the formula I = Prt, where I is the interest, P is the principal (amount invested), r is the interest rate, and
t is the time.
The total amo
Compound Interest
In most financial transactions (loans, savings etc.), compound interest is used. In compound interest, the
interest is calculated periodically and added to the existing balance. The advantage of compounding lies
in these successive addit
Present Value of periodic payments
When re-paying loans we can calculate the present value (An) of a series of periodic payments (R). The
present value represents the value of a series of future periodic payments, which are all subject to the
interest on
Geometric Series
The sum of the terms in a geometric progression is called a geometric series. For the geometric
progression cfw_a, ar, ar2, ar3, . . . the corresponding geometric series would be: a + ar + ar2 + ar3 + . . .
Let Sn represent the sum of n
Geometric Progressions
A Geometric Progression (GP) is an ordered sequence of numbers such that the ratio of any term to the
preceding term is a constant. This constant ratio, commonly known as the common ratio, is represented
by the symbol r.
Examples:
3
Linear Equations
An equation is a mathematical statement indicating that two expressions are equal.
A linear equation is an equation in which the terms containing the unknown variable are all of first
degree.
An equation has two sides (the left hand side
Graphing Equations
Consider the point P(3, 2) found in the first quadrant. Its horizontal distance from the origin (x
coordinate) is +3 units and its vertical distance from the origin (y coordinate) is +2 units.
The numbers in the ordered pair (3, 2) are
Systems of Linear Equations
A system of linear equations is two or more equations that simultaneously impose conditions on all
variables.
Example: A system of two linear equations with two unknowns is:
x+y=5
xy=3
The solution to a System of Equations is a
Word Problems
A common strategy for solving word problems is to translate the statements that are given into
mathematical expressions and equations. Then solve the problem by solving the equations.
Example 1:
Eight less than a number is equal to the produ
Exponents
Exponents can be used to show how many times a number is used as a factor.
Examples:
2 2 2 2 2 = 32 = 25 the base is 2 and the exponent is 5.
10 10 10 = 1000 =103 the base is 10 and the exponent is 3.
1 1 1
1
=
= 2 = 42 the base is 4 and the ex
Translating English statements into Mathematical Form
Solving problems in mathematics often requires translating statements in English into
mathematical forms involving variables and arithmetic operations.
Example 1:
the sum of x and twice y
We can transl
Truth Tables
A truth table gives the truth value of a logical expression for all possible truth values of the variables in
the logical expression.
Examples:
Here are the truth tables for NOT, AND, OR for all possible truth values of variables p and q:
Neg
Mathematical Logic
Logic is the study of valid reasoning. Logic provides definitions, rules and methods that facilitate clear
and precise expression. Logic can be used to interpret the validity of statements.
Logical Statements
A logical statement can be
Sets
A set is a collection of distinct objects. The objects in a set are called elements, or members, of the set.
Set Notation
To denote that an element a, is a member of the set A, we use the notation: a A
To denote that an element a, is not a member of
Venn diagrams
Venn diagrams are used as a graphical representation of sets and show the relationships between them.
They are constructed using:
- A rectangle which represents the universal set the set of all objects under consideration.
- Circles inside t
Modulus
A modular number system is a "finite" number system because a limited set of numbers is permitted
within the system.
The face of a standard clock represents a modular number system (Modular 12). Consider some
examples in which the current time is
Classification of Numbers
REAL NUMBERS
A real number represents a point on an infinitely long number line. Real numbers include all of the
numbers generally used in arithmetic.
RATIONAL NUMBERS
Rational numbers can be expressed a/b where a and b are integ
Scientific Notation
Scientific notation is used to represent very large numbers or very small numbers. Instead of writing a
number with many zeros either before or after the decimal, we can multiply the number by 10 to an
integer exponent:
1 = 100
1 = 100
Complement Math
Unfortunately, computers do not have the capabilities to subtract binary numbers. Complement math is
used to perform binary subtraction by changing it into binary addition.
The TENS complement of an n-digit number N is 10n N.
TENS complem
Converting Between Number Systems
In computer mathematics, you will be required to convert between the decimal, binary, and
hexadecimal number systems.
Converting from Decimal to Binary/Hexadecimal
There are a number of methods we can employ to convert a
SI (Metric) Prefixes
SI prefix table:
Tera
Giga
Mega
kilo
hecto
deca
x1012
x109
x106
x103
x102
x101
x100
deci
centi
milli
micro
nano
pico
x10-1
x10-2
x10-3
x10-6
x10-9
x10-12
The table above shows how many base units there are in every prefix. If the base
Arithmetic Operations Addition/Subtraction
Addition in the decimal number system:
When the sum of two digits is greater than 9, a carry-out of 1 is added to the next significant digit.
Example:
548 + 723
Addition in the binary number system:
1+1=0
1 + 1 +
Number Systems
In any number system, symbols are used to represent quantitative values. The base of any number
system is equivalent to the number of distinct, admissible symbols.
Decimal Number System (Base 10)
The decimal number system is the predominant
MATH 10001
In Class Group Assignment
Instructor: Josh Schneider
Compound Interest:
The current interest rate for Tangerines savings account is 1.05% per year [1].
[1]
https:/www.tangerine.ca/en/saving/savings-accounts/savings-account/index.html
1. Determi
MATH 10001
In Class Group Assignment
Instructor: Josh Schneider
Due: Wednesday, April 1, In class
Instructions:
- You may work on this assignment in a group of up to four students.
- Write the names of each student in your group on this page.
- Submit thi
MATH 10001
In Class Group Assignment
Instructor: Josh Schneider
Due: Wednesday, March 25, In class
Instructions:
- You may work on this assignment in a group of up to four students.
- Write the names of each student in your group on this page.
- Submit th
MATH 10001
In Class Group Assignment
Instructor: Josh Schneider
Systems of linear equations and word problems:
1. Three data files (file A, file B, and file C) require a total of 1.40 GB to store.
Two copies of file B and a single copy of file C requires
MATH 10001
In Class Group Assignment
Instructor: Josh Schneider
Applications of geometric progressions:
1. The world population in 1990 was about 5.265 billion and in 2008 it was about 6.688
billion[1].
[1]
http:/en.wikipedia.org/wiki/World_population
a)