Course Description

INTRODUCTORY ALGEBRA is the first or beginning course of mathematics in high school level. It is the introduction of algebra that serves as the foundation to all the courses of mathematics to be encountered in next years of high school. This will develop the skills applied to problem solving. The discussions focus on set theory and number theory, algebraic expressions and polynomials, linear equations, rectangular coordinate system, and translating word problems to mathematical expressions as applied to real-life situations.


Sunday, July 10, 2011

Lesson 2 MEASURING LENGTHS


CENTIPEDE DIAGRAM











This 'centipede' diagram is used to convert metric to metric units.

How to use the 'centipede' diagram?

Given: 13.2 m = ____ km

known: 13.2 m
unknown: ____ km

STEP 1: Identify the location of the decimal point on the known measurement.
The known measurement is 13.2 m. The decimal point is placed between the numbers 3 and 2.


STEP 2: Referring to the 'centipede' diagram, count the number of curve lines from the known measurement to the unknown measurement. The number of curve lines
serves as decimal places.
There are 3 curve lines from m to km. (3 decimal place)



STEP 3: Determine the direction in counting the curve lines -- left or right. The direction is to the LEFT.

STEP 4: Having these ideas from STEP 1 to 3. You will be able to convert the given measurements.
  • STEP 1: decimal point is between 3 and 2
  • STEP 2: 3 curve lines
  • STEP 3: left
T
herefore, from the location of the decimal point between numbers 3 and 2, you need to move to three decimal places to the left to convert the given.





Lesson 1 METRIC SYSTEM and ENGLISH SYSTEM

English System
  • originated from England
  • has several names for its units
Example:
length: inches, feet, yard, mile, furlong
weight: ounces, pounds, ton, metric ton
volume: fluid ounces, cup, pint, quart, gallon
  • has indefinite values for conversion


Metric System



Advantages of using Metric System over English System
  • metric units are easier to identify/recognize
  • metric units are easier to convert

Saturday, July 09, 2011

Lesson 1 BASIC PROPERTIES FROM SET THEORY

WHAT IS A SET?

1. A set is a well-defined collection of distinct objects.

· Well-defined means clearly stated or clearly defined.

· Distinct means different or distinguished from others.

· Objects are called ELEMENTS.

· Є(epsilon) is used to denote elements.


2. A set is enclosed in a curly brace{} and objects/elements are separated by a comma.

· (ellipsis) is used to indicate infinite set or continuity of elements with the same pattern.


3. A set is denoted by a capital letter of the English alphabet.

· Null or empty set is a set with no element. Ф or {}

· Singleton is a set with only one element.

· Pair is a set with two elements.


Assessment: Check Your Understanding on page 5

HOW TO DESCRIBE A SET?

1. Roster Method – listing all the elements of the set exactly once.

Ex. A = {a,e,i,o,u}

2. Set-Builder Method – stating one determining feature of its elements.

Ex. A = {x|x is a vowel in the English alphabet}

· | - is read as “such that”

Assessment: Check Your Understanding on page 5

SUBSETS AND PROPER SETS

1. Proper Subset – if all the elements of set A is obtained in set B but there are elements of set B that is not obtained in set A.

Ex. A = {a,c,e} B = {a,b,c,d,e} AB or BA

2. Subset – parts of a set. It is an element or group of elements that are parts of a certain set. Its notation is. To solve for the number of subsets a set has, use the formula 2n where n is the number of elements of the set.

Ex. A = {a,c,e} Its subset are {}, {a}, {c}, {e}, {a,c}, {a,e}, {c,e}, {a,c,e}.

· The collection of the subsets of a set is called power set.

REMEMBER: A null set is a subset of all subsets and a set is a subset of itself.


HOW TO COMPARE SETS?


1. Equal Sets (=) – sets with the same elements.

Ex. A = {m,a,l,l} B = {a,l,m} C = {m,a,m,m,a,l}

Remember: elements of a set should be distinct

A = {m,a,l} B = {a,l,m} C = {m,a,l}

In this case, we notice that all sets has elements of a,l and m, therefore A = B, A = C or B = C

1. Equivalent Sets (~) – sets with the same cardinality.

· Cardinality of set means the number of elements in a set.

Ex. A = {m,y,r,a} The cardinality of set A is 4 because it has four elements.

Ex. X = {1,2,3,4,5} Y = {6,5,4,3,2}

The cardinality of set X is 5 and the cardinality of set Y is also 5, therefore X~Y.