Pure Math &#8211; ART SEC &#8211; S2 &#8211; Abdullah Nasr

Lecture 2 (Part 1) – Trigonometry – The cosine rule 4 المواضيع الدرس كعينة

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Introduction to Lecture 2

1- The cosine rule

2- Example (1) on cosine rule

3- Example (2) on cosine rule

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Lecture 3 (Part 1) – Trigonometry – Solution of the triangle 3 المواضيع

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Introduction to Lecture 3

1- cases of solution of triangle

2- The Ambiguous case

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Lecture 5 (Part 1) – Algebra – Real functions (Determination the domain and range – Discuss the monotony) 7 المواضيع

Homework answer – P1

Homework answer – P2

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First term - Unit 1 - Algebra - Functions of a real variable and drawing curves (7 Lectures)

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Introduction Lecture 5

Pre-requirements on unit one

Real function Ex. 1,2

Identifying the domain of the function Part 1

Identifying the domain of the function Part 2

Identifying the domain and the range of the function from its graph

Discussing the monotony of a function from its graph

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Lecture 6 (Part 1) – Algebra – Operations on functions (Composition of functions) 5 المواضيع

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Introduction Lecture 6

Operations on functions part 1

Operations on functions part 2

Composition of functions part 1

Composition of functions (the domain) part 3

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Lecture 7 (Part 1) – Algebra – Some properties of functions ( even and odd functions / one-to-one functions) 5 المواضيع

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Introduction Lecture 7

even and odd functions part 1

even and odd functions part 2

even and odd functions part 3

One-to-one functions

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Lecture 8 (Part 1) – Algebra – Graphical representation of basic functions and graphing piesewise functions 5 المواضيع

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Introduction Lecture 8

Representing the linear function

Grapging the quadratic function

Grapging the piecewise function

The basic forms of some functions

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Lecture 9 (Part 1) – Algebra – Geometrical transformations of basic function curves 7 المواضيع

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Introduction Lecture 9

Vertical and horizontal translation of the function curve part 1

Vertical and horizontal translation of the function curve part 2

Vertical and horizontal translation of the function curve part 3

Reflection of the Function curve in X-axis

Streching of the function curve

More ideas on Vertical and horizontal translation of the function curve

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Lecture 10 (Part 1) – Algebra – Solving absolute value equations and inequalities 7 المواضيع

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Introduction Lecture 10

Solving absolute value equations part 1

Solving absolute value equations part 2

Solving absolute value equations part 3

Solving absolute value inequalities part 1

Solving absolute value inequalities part 2

Solving absolute value inequalities part 3

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Lecture 12 (Part 1) – Algebra – Rational Exponents and exponential equations 5 المواضيع

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First term - Unit 2 - Algebra - Exponents, logarithms and their applications (5 Lectures)

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Introduction Lecture 12

The n-th root & Rational exponents & Exponential rules part 1

The n-th root & Rational exponents & Exponential rules part 2

Exponential Equations part 1

Exponential Equations part 2

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Lecture 13 (Part 1) – Algebra – Exponential function and its applications 6 المواضيع

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Introduction Lecture 13

Definition

Graphical representation of the exponential function

Some geometric transformation of exponential function

Solving the exponential equations graphically

Life applications

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Lecture 14 (Part 1) – Algebra – Logarithmic function and its graph 7 المواضيع

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Introduction Lecture 14

Definition & Remarks

The relation between the exponential and logarithmic functions

Graphical representation of the logarithmic function part 1

Graphical representation of the logarithmic function part 2

Graphical representation of the logarithmic function part 3

Graphical representation of the logarithmic function part 4

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Diverse book Questions

Lecture 15 (Part 1) – Algebra – Some properties of logarithms 6 المواضيع

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Introduction Lecture 15

Some properties of logarithms

Examples on logarithmic functions part 1

Examples on logarithmic functions part 2

Examples on logarithmic functions part 3

Examples on logarithmic functions part 4

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Lecture 17 (Part 1) – Calculus – Introduction to limits of functions “Evaluation of the limit numerically and graphically 3 المواضيع

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First term - Unit 3 - Calculus - Limits and continuity (5 Lectures)

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Introduction Lecture 17

Specified , unspecified and undefined quantities &The concept of limits of a function at a point

General Examples

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Lecture 18 (Part 1) – Calculus – Finding the limit of a function algebraically 4 المواضيع

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Introduction Lecture 18

Theorems (1),(2)

Theorem (3)

more examples on previous theorems

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Diverse book questions (P1)

Diverse book questions (P2)

Lecture 19 (Part 1) – Calculus – Theorem (4) “The law” 4 المواضيع

Homework Lecture 18

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Introduction Lecture 19

Theorem (4) part 1

Theorem (4) part 2

Theorem (4) part 3

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Lecture 20 (Part 1) – Calculus – limit of the function at infinity 4 المواضيع

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Introduction Lecture 20

limit of the function at infinty

Getting the limit of a rational function at infinty

More examples on Getting the limit of a rational function at infinty

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Lecture 1 (Part 1) – Calculus – Rate Of Change 3 المواضيع | 1 اختبار

Homework Lecture 20

Second term - Unit 3 - Calculus

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Introduction to Lecture 1

1 – Definition EX.1,2,3

2 – more examples EX.4,5,6,7

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Lecture 2 (Part 1) – Calculus – Differentiation 4 المواضيع | 1 اختبار

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Introduction to Lecture 2

1 – Definition EX.1,2

2 – Differentiability Of a Function At a Point EX. 3,4,5

3 – more examples EX.6,7,8,9,10

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Lecture 3 (Part 1) – Calculus – Rules Of Differentiation 4 المواضيع | 1 اختبار

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Introduction to Lecture 3

1 – Rules Of Differentiation EX.1,2

2 – Derivative Of The Product Of Two Functions EX.3,4

3 – Derivative Of The Quotient Of Two Functions EX.5,6,7

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Lecture 4 (Part 1) – Calculus – Derivative Of Composite Function (Chain Rule) 4 المواضيع | 1 اختبار

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Introduction to Lecture 4

1 – Theorem EX.1,2,3

2 – Remark EX.4,5

3 – Corollary EX.6,7,8,9

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Lecture 5 (Part 1) – Algebra – Sequences 6 المواضيع | 1 اختبار

Second term - Unit 1 - Algebra - Sequenses And Series

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Introduction to Lecture 5

1 – Definition EX.1

2 – General Term Of a Sequence EX.2,3

3 – Increasing – decreasing – Constant Sequences EX.4,5

4 – Definition EX.1,2,3

5 – The Series EX.4,5,6,7

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Lecture 6 (Part 1) – Algebra – Arithmetic Sequense 5 المواضيع | 1 اختبار

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Introduction to Lecture 6

1 – Definition EX.1,2,3

2 – The General Term Of The Arithetic Sequence EX.4,5,6,7,8

3 – Identifying The Arithmetic Sequence EX.9,10,11,12,13

4 – Arithmetic Means EX.14,15,16,17

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Lecture 7 (Part 1) – Algebra – Arithmetic Series 5 المواضيع | 1 اختبار

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Introduction to Lecture 7

1 – Definition EX.1,2,3,4

2 – Remarks EX.5,6,7,8

3 – more examples EX.9,10,11,12

4 – more examples EX.13,14,15,16,17

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Lecture 8 (Part 1) – Algebra – Geometric Sequence 5 المواضيع | 1 اختبار

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Introduction to Lecture 8

1 – Definition EX.1,2

2 – The General Term Of The Geometric Sequence EX.3,4

3 – Identifying The Geometric Sequence EX.5,6,7,8,9

4 – Geometric Means EX.10,11,12,13,14,15,16,17

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Lecture 9 (Part 1) – Algebra – Geometric Series 3 المواضيع | 1 اختبار

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Introduction to Lecture 9

1 – Definition EX.1,2,3,4,5,6,7

2 – Remarks EX.8,9,10,11,12,13,14,15

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Lecture 10 (Part 1) – Calculus – Applications On Derivatives 4 المواضيع | 1 اختبار

Second term - Unit 3 - Calculus

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Introduction to Lecture 10

1 – Introduction EX.1,2

2 – more examples EX.3,4,5,6,7

3 – more examples EX.8,9,10,11,12

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Lecture 11 (Part 1) – Calculus – Integration 3 المواضيع | 1 اختبار

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Introduction to Lecture 11

1 – Definition EX.1,2,3,4

2 – Rules Of Integration EX.5,6,7

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Lecture 12 (Part 1) – Algebra – Counting Principle – Permutations 5 المواضيع | 1 اختبار

Second term - Unit 2 - Algebra - Permutations And Combinations

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Introduction to Lecture 12

1 – Definition EX.1,2,3,4,5,6

2 – Factorial Of A Number EX.7,8,9

3 – Permutations EX.10,11,12,13

4 – more examples EX.14,15,16,17

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Lecture 13 (Part 1) – Algebra – Combinations 4 المواضيع | 1 اختبار

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Introduction to Lecture 13

1 – Definition EX.1,2,3,4,5

2 – more examples EX.6,7,8,9,10

3 – more examples EX.11,12,13,14,15,16

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Lecture 14 (Part 1) – Probability – Some Basic Terms And Concepts – Events – Operations On Events 5 المواضيع | 1 اختبار

Second term - Unit 2 - Probability

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Introduction to Lecture 14

1 – Definition EX.1,2,3

2 – Remarks EX.4,5

3 – Events EX. 6,7

4 – More Examples 8,9,10,11

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Lecture 15 (Part 1) – Probability – Axioms And Laws Of Probability – Calculating Probability 5 المواضيع | 1 اختبار

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Introduction to Lecture 15

1 – Definitions

2 – Examples 1,2,3,4

3 – More Examples 5,6,7,8

4 – More Examples 9,10,11,12

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Lecture 15 (Part 2) – Diverse Book Questions + Homework 2 المواضيع

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