Maths F4 — Qalam

1 Chapter 1 13 lessons

1. ANALYTIC TRIGONOMETRY 32 min
2. Analytic Trigonometry: Co-function Identities and Verifying Identities 34 min
3. sum and difference identity for Sine and Tangent 30 min
4. sum and difference identity for Sine and Tangent Part 2 25 min
5. Sum and difference identity Part 3 30 min
6. Double-Angle Identities: Derivations and Applications 30 min
7. Double angle-identities(Lesson 3.2) 24 min
8. Trigonometric Identities: Double-Angle, Product-to-Sum, and Sum-to-Product Formulas 34 min
9. Trigonometric Half-Angle Identities: Derivations and Applications 42 min
10. Exercise 1.4: Half-Angle Identities 30 min
11. Trigonometric Equations Part 1: Linear and Quadratic Methods 41 min
12. Solving Trigonometric Equations: Quadratic Form and Half-Angle Identities 47 min
13. Solving Trigonometric Equations with Double-Angle and Pythagorean Identities 42 min

2 Chapter 2 16 lessons

1. Introduction to Complex Numbers: Definitions, Parts, and Powers of i 33 min
2. Example 22 (CH2 Lesson 11) 36 min
3. Example 211 (CH2 Lesson 12) 22 min
4. Square Roots of Complex Numbers: Algebraic Method and Examples 37 min
5. Polynomial Equations of Degree n and Complex Roots 34 min
6. Introduction to Argand Diagrams and Geometrical Representation of Complex Numbers 23 min
7. Geometrical Representation of Complex Numbers: Example 2.18 23 min
8. Modulus and Argument of Complex Numbers: Definitions and Examples 28 min
9. Modulus and Argument of Complex Numbers: Examples and Applications 34 min
10. Ch 2 2.5.2 Complex numbers in polar form(Lesson 19) 32 min
11. Converting Complex Numbers to Polar Form: Modulus and Argument 37 min
12. MULTIPLICATION AND DIVISION OF TWO COMPLEX NUMBERS IN POLAR FORM 42 min
13. Division of Complex Numbers in Polar Form 23 min
14. Complex Numbers: De Moivre's Theorem and n-th Roots 36 min
15. Finding Square and Cube Roots of Complex Numbers 32 min
16. De Moivre's Theorem: Powers of Complex Numbers 30 min

3 Chapter 3 24 lessons

1. Ch 2 THE BASIC COUNTING PRINCIPLE(Lesson 26) 41 min
2. Ch 2 PERMUTATIONS(Lesson 27) 37 min
3. Ch 2 EXAMPLE 3.6(Lesson 28) 31 min
4. Permutations with Restrictions: Examples and Applications 31 min
5. Permutations with Restrictions: Examples 3.9 and 3.10 26 min
6. Ch3 COMBINATIONS(lesson 31) 35 min
7. Probability of an Event: Sample Space, Events, and Basic Calculations 33 min
8. Probability: Standard Deck of Cards (Example 3.17) 30 min
9. Probability: Using Possibility Diagrams 42 min
10. Probability: Example 3.20 and Exercise 3.5 21 min
11. Probabilities of Mutually Exclusive and Non-Mutually Exclusive Events 35 min
12. Probability: Addition Rule and Independent Events (Examples 3.24 - 3.26) 29 min
13. Ch3 INDEPENDENT EVENTS(lesson 38) 15 min
14. Probability: Using Possibility Diagrams for Two Events 36 min
15. Probability: Example 3.20 and Possibility Diagrams 31 min
16. Probabilities of Mutually Exclusive and Inclusive Events 41 min
17. Probability: Intersection, Union, and Independent Events 37 min
18. Mathematics: Dependent Events and Tree Diagrams in Probability 30 min
19. Probability: Tree Diagram Construction and Examples 34 min
20. Solving Probability Problems: Netball Games and Fruit Selection 28 min
21. Conditional Probability: Concepts, Formulas, and Applications 31 min
22. Conditional Probability: Solving Example 3.35 16 min
23. Conditional Probability: Solving Examples 3.35 and 3.36 15 min
24. Conditional Probability: Examples 3.37 and 3.38 39 min

4 Chapter 4 16 lessons

1. Ch4 MEAN,MEDIAN,MODE OF GROUPED DATA(lesson 50) 39 min
2. Arithmetic Mean for Grouped Data: Finding Missing Frequencies 35 min
3. Statistics: Calculating Median for Grouped Data 31 min
4. Statistics: Calculating Median for Grouped Data and Finding Missing Frequencies 32 min
5. Statistics: Finding Missing Frequencies with Median and Calculating Mode for Grouped Data 38 min
6. Statistics: Calculating the Mode of Grouped Data (Example 4.8) 19 min
7. Ch4 CUMULATIVE FREQUENCY CURVE(OR OGIVE)(lesson 56) 26 min
8. Ch4 METHOD 2(lesson 58) 34 min
9. Drawing a 'More Than' Type Ogive and Finding the Median: Example 4.10 32 min
10. Ch4 EXAMPLE 4.11(lesson 60) 22 min
11. Ch4 MEASURES OF DISPERSION(SPREAD)(LESSON 61) 35 min
12. Standard Deviation and Variance of Ungrouped Data 34 min
13. Calculating Mean, Variance, and Standard Deviation: Examples 4.13 and 4.14 33 min
14. Standard Deviation and Variance of Grouped Data: Example 4.15 20 min
15. Calculating Mean, Variance, and Standard Deviation for Grouped Data (Example 4.16) 21 min
16. Introduction to Stem-and-Leaf Plots 37 min

5 Chapter 5 9 lessons

1. Introduction to Limits: Definitions, Numerical Investigations, and Indeterminate Forms 42 min
2. Theorems of Limits and Evaluation of Algebraic Limits (Example 5.1) 36 min
3. Evaluating Algebraic Limits: Indeterminate Forms and Factorization 31 min
4. One-Sided Limits and the Existence of Limits 58 min
5. Limits at Infinity and Indeterminate Forms 53 min
6. Evaluating Limits at Infinity: Example 5.6 24 min
7. Continuity and Discontinuity of Functions at a Point 39 min
8. Continuity of Functions on Intervals: Definitions and Examples 23 min
9. LIMITS OF TRIGONOMETRIC FUNCTIONS 59 min

6 Chapter 6 15 lessons

1. Introduction to Differentiation and First Principles 41 min
2. Differentiation from First Principles: Example 6.1 (c, d, e) 39 min
3. Differentiation: The Power Rule and Constant Multiple Rule (Example 6.2) 37 min
4. Rules for Differentiation and Applications: Example 6.3 and 6.4 55 min
5. Differentiation: Exercise 6.1 Review, Product Rule, and Quotient Rule 52 min
6. Differentiation: Product Rule and Chain Rule Applications (Example 6.9) 38 min
7. Differentiation: The Chain Rule, Composite Functions, and Second Derivatives 45 min
8. Differentiation: First and Second Derivatives (Example 6.13 & Exercise 6.3) 35 min
9. Differentiation of Trigonometric Functions: Basic Rules and Examples 27 min
10. Differentiation of Trigonometric Functions: Example 6.15 26 min
11. Differentiation: Increasing/Decreasing Functions and Concavity 40 min
12. Maximum and Minimum Points: First and Second Derivative Tests 38 min
13. Finding Stationary Points and Determining Nature (Max/Min) using Second Derivative Test 47 min
14. Differentiation: Applications of Rates of Change 58 min
15. Stationary Point, Maximum Point 25 min

7 Chapter 7 6 lessons