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مقدمة في الرياضيات(1)
Chapter1: Review of Basic Concepts
1.1Sets
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1.1Sets
Set definition: union, intersection, belong, subset.
set operations
1.2Real Numbers and their properties
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1.2Real Numbers and their properties
Set of numbers – real (number) line
Exponents
Order of Operations
Properties of real numbers
order on the number line – absolute value
1.3Polynomials
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1.3Polynomials
Rules of Exponents
Polynomials- Addition and subtraction
multiplication
DIVISION
1.4Factoring polynomials
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1.4Factoring polynomials
Greatest common factor – factoring by grouping
factoring trinomials – factoring binomials – factoring by substitution
1.5Rational Expressions
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1.5Rational Expressions
Rational expressions – Lowest term
multiplication and division – addition and subtraction – complex fractions
1.6rational exponents
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1.6rational exponents
Negative Exponent and quotient rule and rational exponents
Radical Notations – Simplified radicals
1.7Radical Expressions
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1.7Radical Expressions
Radical Notations – Simplified radicals
Operations with radicals – Rationlizing denominators
Test Prep
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Chapter2: Equations and Inequalities
2.1Linear Equations
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2.1Linear Equations
Basic Terminology – Solving Linear Equations
Identities – conditionals and contradictions – Solving for a specified variable
2.2Quadratic Equations
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2.2Quadratic Equations
Solving quadratic equation
Completing square – quadratic formula
solving for specified variable – discriminant
2.3Inequalities
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2.3Inequalities
Linear inequality – three part inequality
quadratic inequality
rational inequality
2.4Absolute Value Equations and Inequalities
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2.4Absolute Value Equations and Inequalities
Basic Concepts – Absolute value equations
absolute value Inequality – special cases
Chapter3: Graphs and Functions
3.1Functions
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3.1Functions
Reltaions and functions – determining wether relations are functions
Domain and range exercises Part (1)
Domain and range exercises Part (2)
function notation
increasing, decreasing and constant functions
3.2Linear Functions
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3.2Linear Functions
Graphing Linear Function
Standard form – slope
average rate of change – linear models
3.3Equations of Lines and Linear Models
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3.3Equations of Lines and Linear Models
Point-slope form
slope – intercept form
vertical and horizontal lines – parallel and perpendicular lines
3.4Graphs of Basic Functions
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3.4Graphs of Basic Functions
Continuity
The identity, squaring, and cubing functions – square root and cube root function – absolute value functions – relation x = y^2 – piecewise defined functions
greatest integer functions
3.5Graphing Techniques
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3.5Graphing Techniques
streching and shrinking -reflecting
symmetry – even and odd functions
translations
3.6Function Operations and Composition
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3.6Function Operations and Composition
arithmetic operations on functions
The difference quotient
composition of functions
Chapter4: Polynomial and Rational Functions
4.1Parabolas
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4.1Parabolas
Conic sections – Horizontal Parabolas
Geometric definition and equations of parabolas
Exercise one
Exercise Two
application of parabolas
4.2Quadratic Functions and Models
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4.2Quadratic Functions and Models
quadratic functions
graphing techniques – completing the square
vertex formula
quadratic models
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1.5Rational Expressions
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1.5Rational Expressions
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Rational expressions – Lowest term
multiplication and division – addition and subtraction – complex fractions
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