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DIM5058

MATHEMATICAL TECHNIQUES 1

TOPIC 1

Topic 1: Fundamental Concepts of Algebra
Sub topics:
1
...
2
Exponents
1
...
4
Polynomials
1
...
6
Rational Expressions
-----------------------------------------------------------------------------------------------------------Objectives:
1
...

2
...

3
...

4
...

5
...

6
...

7
...

8
...

-----------------------------------------------------------------------------------------------------------1
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The objects in a set are called the elements of the set
...

For example: {1, 3, 5, 7, 9}

Important Subsets of the Real Numbers
Name
Natural
numbers, ℕ
Whole
Numbers, 𝕎
Integers

ℤ
Rational
numbers

ℚ

Description
These numbers are used for counting
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{0, 1, 2, 3, 4, 5, …}

Consist of:
{
...
}

...
, -3, -2, -1}
- zero
{0}
Numbers that can be expressed as a quotient of 2
two integers
...
375

a
8
a and b are integers, b  0 
Q
3
b

 0
...
 0
...

Irrational numbers cannot be expressed as a
quotient of integers
...
414213
...
14159
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 The lesser of two real numbers is the one farther to the left on a number line
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Inequalities




less than
less than or equal to

Symbols

ab

Meaning
a is less than or equal to b

ab

b is greater than or equal to a




greater than
greater than or equal to

Example

58
88
85

 4  4

Explanation
Because 5 < 8
Because 8 = 8
Because 8 > 5
Because – 4 = – 4
2

DIM5058

MATHEMATICAL TECHNIQUES 1

TOPIC 1

Absolute Value

 x
x 
 x

x

if x  0
if x  0

represents the distance to the origin from the point x
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a 0

4
...


a  a

5
...


a a

6
...

Examples of algebraic expressions:

x + 6, x – 6, 6x, x/6, 3x + 5
...
Perform operations within the innermost parentheses and work outward

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