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Mathematics Fundamentals for Years 10 to 12

Chapter 1 - Algebra and Surds

1. Addition and Subtraction - Basics of Algebra (4:33)
2. Multiplication - Basics of Algebra (4:38)
3. Division - Basics of Algebra (9:04)
4. Removing Grouping Symbols (6:17)
5. Binomial Products (6:25)
6. Difference of Two Squares (3:55)
7. Perfect Squares (7:36)
8. Examples - Expansion using Perfect Square and Difference of Two Squares Rules (8:04)
9. Factorisation (5:44)
10. Examples - Simple Factorisation (7:40)
11. Factorisation Methods - Grouping in Pairs (5:16)
12. Trinomials - factorisation Methods (3:35)
13. Examples - trinomials - Factorisation Methods (4:48)
14. Perfect Squares - Factorisation Methods (4:06)
15. Example - Perfect Squares - Factorisation Methods (2:36)
16. Difference of 2 Squares - Factorisation Methods (2:41)
17. Example 1 - Difference of 2 Squares - Factorisation Methods (2:54)
18. Sum of Two Cubes - Factorisation Methods (3:01)
19. Difference of Two Cubes - Factorisation Methods (2:32)
20. Example 1 - Difference of Two Cubes - Factorisation Methods (7:53)
21. Example 1 - Factorisation (1:34)
22. Example 2 - Factorisation (5:10)
23. Completing the Square Part 1 (4:14)
24. Completing the Square Part 2 (2:12)
25. Example 1 - Completing the Square (3:04)
26. Example 2 - Completing the Square (2:44)
27. Simplifying Fractions (3:35)

Chapter 2 - Geometry

1. Introduction - Geometric Notations Part 1 (7:16)
2. Introduction - Geometric Notations Part 2 (4:52)
3. Example 1 - Finding the Value of an Angle (3:45)
4. Example 2 - Finding the Value of an Angle (5:39)
5. Example 3 - Finding the Value of an Angle (3:16)
6. Special Properties of Angles Formed Between 2 Parallel Lines (6:33)
7. Example 1 - Special Properties of Angles Formed Between 2 Parallel Lines (2:59)
8. Example 2 - Special Properties of Angles Formed Between 2 Parallel Lines (4:05)
9. Names of Triangles (2:04)
10. Angle Sum of a Triangle (1:37)
11. Exterior Angle of a Triangle (1:59)
12. Congruent Triangles (7:22)
13. Example 1 - Congruent Triangles (3:50)
14. Example 2 - Congruent Triangles (5:16)
15. Similar Triangles (5:16)
16. Example 1 - Similar Triangles (6:42)
17. Tests for Similar Triangles (4:58)
18. Example 1 - Similar Triangles (6:57)
19. Example 2 - Similar Triangles (4:44)
20. Ratio of Intercepts (3:36)
21. Example - Similar Triangles and ratio of intercepts (7:10)
22. Pythagoras' Theorem (2:26)
23. Example 1 - Pythagoras' Theorem (3:06)
24. Example 2 - Pythagoras' Theorem (2:29)

Chapter 3 - Functions and Graphs

1. Definition of a Function Part 1 (5:14)
2. Definition of a Function Part 2 (9:22)
3. Definition of a Function Part 3 (5:27)
4. Example 1 - Ordered Pairs and Definition of a Function (1:23)
5. Example 2 - Which Curves are Functions (3:06)
6. Function Notation Part 1 (3:37)
7. Function Notation Part 2 (3:53)
8. Example 1 - Function Notation (1:36)
9. Example 2 - Function Notation (2:24)
10. Example 2 - Function Notation (2:31)
11. Example 4 - Function Notation (3:27)
12. Introduction - Graphing Techniques (2:46)
13. Intercepts - Graphing Techniques (2:44)
14. Example - Intercepts - Graphing Techniques (4:18)
15. Domain - Graphing Techniques (4:08)
16. Range - Graphing Techniques (4:59)
17. Increasing and Decreasing Functions (5:02)
18. Example - Increasing and Decreasing Functions (2:31)
19. Even and Odd Functions (4:49)
20. Example - Odd and Even Functions (4:40)
21. Sketching a Linear Function and Finding its Domain and Range (6:44)
22. Domain and Range of Linear Functions (2:36)
23. Domain and Range of Special Lines (6:25)
24. Example - Domain and Range of Quadratics (6:37)
25. Example 2 - Quadratic Functions (10:17)
26. Absolute Value Functions (5:23)
27. Example 1 Part 1 - Sketching Absolute Value Functions (6:35)
28. Example 1 Part 2 - Sketching Absolute Value Functions (3:55)
29. Example 1 Part 3 - Domain and Range of Absolute Value Functions (1:57)
30. Example 2 Part 1 - Sketching Absolute Value Functions (5:16)
31. Example 2 Part 2 - Sketching the Graph of an Absolute Value Function (3:04)
32. Example 3 - Graphically Solving Equations Involving Absolute Values (5:08)
33. Example 4 - Graphically Finding the Solution to an Inequality Involving Absolute Values (6:27)
34. The Hyperbola (6:12)
35. Asymptotes of a Hyperbola (4:29)
36. Sketching the Graph of a Hyperbola (7:34)
37. Example - Sketching the Graph of a Hyperbola (6:21)
38. Equation of a Circle - Part 1 (6:07)
39. Equation of a Circle - Part 2 (2:24)
40. Example 1 - Graph of a Circle (3:38)
42. Example 3 - Equation of a Circle (3:29)
41. Example 2 - Equation of a Circle (5:24)
43. Equation of a Semi-Circle (4:04)
44. Example 1 - Graph of a Semi-Circle (2:48)
45. Example 2 - Graph of a Semi-Circle (3:02)
46. Graph of Exponential Functions (6:46)
47. Exponential and Logarithmic Functions Part 2 (6:11)
48. Cubic Function (1:56)
49. Example - Domain and Range of Square Root (3:18)
50. Example - Graphing a Cubic Function (6:21)
51. Limits (4:57)
52. Example 1 - Limits (3:29)
53. Example 2 - Limits (2:30)
54. Example 3 - Limits (1:31)
55. Continuity (1:43)
56. Example 1 - Graphing a Discontinuous Function (8:05)

Chapter 4 - Trigonometry

1. Trigonometric Ratios (5:32)
2. Example 1 - trigonometric Ratios (4:47)
3. Example 2 - Trigonometric Ratios (4:30)
4. Complementary Angles (6:08)
5. Example 1 - Complementary Angles (4:14)
6. Example 2 - Complementary Angles (2:26)
7. Example 1 - Finding a Side (3:25)
8. Example 2 - Finding a Side (3:41)
9. Finding an Angle Using Trig Ratios - Example 1 (3:20)
10. Finding an Angle Using Trig Ratios - Example 2 (2:00)
11. Angle of Elevation (3:15)
12. Angle of Depression (1:26)
13. Example 1 - Angle of Depression (4:49)
14. Bearings (2:55)
15. Example 1 - Bearing (1:18)
16. Example 2 - Bearing (4:29)
17. Example 3 - Bearing (4:52)
18. Example 4 - Bearing (4:27)
19. Exact Ratios - 45 degrees (4:53)
20. Exact Ratios - 30 and 60 degrees (5:30)
21. Example 1 - Using Exact Ratios (2:38)
22. Introduction to Trig Ratios for Angles of any magnitude (4:46)
23. Example 1 - Introduction to Trig Ratios for Angles of any Magnitude (7:32)
24. Example 2 - Introduction to Trig Ratios for Angles of any Magnitude (4:07)
25. Trig Ratios for Any Angle Part 1 (6:54)
26. Trig Ratios for any Angle Part 2 (7:20)
27. Sign of Trig Ratios - 2nd Quadrant (3:54)
28. Sign of Trig Ratios - 3rd Quadrant (3:12)
29. Sign of Trig Ratios - 4th Quadrant (2:52)
30. ASTC Rule Part 1 (8:58)
31. ASTC Rule Part 2 (4:37)
32. Example 1 - Sign of Trig Ratios (6:23)
33. Example 2 - Sign of Trig Ratios (3:03)
34. Example 3 - Sign of Trig Ratios (3:41)
35. Example 4 - Sign of Trig Ratios (2:35)
36. Example 5 - Sign of Trig Ratios (5:17)
37. Example 6 - Sign of Trig Ratios (3:34)
38. Negative Angles (3:21)
39. Example - Negative Angles (3:13)
40. Trigonometric Equations (5:08)
41. Example 1 - Trigonometric Equations (6:53)
42. Example 2 - Trigonometric Equations (6:08)
43. Example 3 - Trigonometric Equations (6:45)
44. Trigonometric Identities (7:50)
45. Trigonometric Identities - Proof (8:30)
46. Example 1 - Using Trig Identities (1:09)
47. Example 2 - Using Trig Identities (1:33)
48. Example 3 - Using Trig Identities (1:19)
49. Example 4 - Using Trig Identities (3:44)
50. Example 5 - Using Trig Identities (4:15)

Chapter 5 - Linear Functions

1. Distance Between Two Points (7:53)
2. Example - Distance Between Two Points (3:11)
3. Midpoint (2:03)
4. Example - Midpoint (3:35)
5. Gradient (3:20)
6. Example 1 - Gradient (2:32)
7. Positive and Negative Gradient (1:53)
8. Gradient Given 2 Points (2:14)
9. Example 1 - Gradient Given 2 Points (1:13)
10. Example 2 - Gradient Given 2 Points (3:35)
11. Gradient Given the Angle at x-axis Part 1 (2:35)
12. Gradient Given the Angle at the x-axis Part 2 (3:18)
13. Gradient Given an Equation (1:02)
14. Example 1 - Gradient Given an Equation (0:56)
15. Example 2 - Gradient Given an Equation (2:53)
16. Gradient of a General Linear Equation (3:05)
17. Different Ways of Writing the Equation of a Straight Line (4:21)
18. Example 1 - Equation of a Straight Line (2:27)
19. Example 2 - Equation of a Straight Line (3:43)
20. Example 3 - Equation of a Straight Line (2:47)
21. Parallel Lines (4:13)
22. Example 1 - Parallel Lines (4:43)
23. Example 2 - Parallel Lines (5:21)
24. Perpendicular Lines (4:08)
25. Example 1 - Perpendicular Lines (2:01)
26. Example 2 - Perpendicular Lines (5:18)
27. Intersection of Lines (2:35)
28. Example 1 - Intersection of Lines (4:06)
29. Concurrent Lines (6:35)
30. Perpendicular Distance (4:31)
31. Example 1 - Perpendicular Distance (6:25)
32. Example 2 - Perpendicular Distance (5:54)

Chapter 6 - Quadratic Equations

1. Introduction Example - Sketch a Parabola (11:53)
2. Axis of symmetry formula (2:49)
3. Determining the Concavity of a Parabola (5:58)
4. Example 1 - Using Axis of Symmetry and Minimum Value Formula (5:06)
5. Example 2 - Quadratic Equations (3:07)
6. Example 3 - Sketch a Parabola (5:42)
7. Quadratic Inequalities (4:14)
8. Example 1 - Quadratic Inequalities (8:06)
9. Example 2 - Quadratic Inequalities (6:21)
10. The Discriminant Part 1 (4:07)
11. The Discriminant Part 2 (7:28)
12. The Discriminant Part 3 (3:07)
13. Example 1 - Using the Discriminant (1:54)
14. Example 2 - Using the Discriminant (4:09)
15. Example 3 - Using the Discriminant (2:27)
16. Example 4 - Using the Discriminant (3:23)
17. Quadratic Identities Part 1 (4:31)
18. Example 1 - Quadratic Identities (6:45)
19. Example 2 - Quadratic Identities (4:14)
20. Sum and Product of Roots Part 1 (3:16)
21. Example 1 - Sum and Product of roots (1:23)
22. Example 2 - Sum and Product of roots (3:15)
23. Sum and Product of Roots Part 2 (2:29)
24. Example 1 - Sum and Product of Roots Part 2 (4:09)
25. Example 2 - Sum and Product of Roots Part 2 (1:26)
26. Example 3 - Sum and Product of roots Part 2 (4:17)
27. Example 1 - Equations Reducible to Quadratics (3:04)
28. Example 2 - Equations Reducible to Quadratics (4:12)

Chapter 7 - Introduction to Calculus

i1. Gradient (3:20)
i2. Example 1 - Gradient (2:32)
i3. Positive and Negative Gradient (1:53)
i4. Gradient Given Two Points (2:14)
i5. Example 1 - Gradient Given 2 Points (1:13)
i6. Example 2 - Gradient Given 2 Points (3:35)
1. Gradient of a curve Part 1 (4:50)
2. Gradient of a curve Part 2 (3:54)
3. Example 1 - Gradient of a curve (5:55)
4. Example 2 - Gradient of a curve (7:49)
5. Example 3 - Gradient of a curve (3:54)
6. Differentiability (6:28)
7. Example 1 - Differentiability (1:12)
8. Example 2 - Differentiability (6:25)
9. Differentiation as a limit (7:28)
10. Example - Estimating the gradient of a curve (6:25)
11. Differentiation from first principles (9:49)
12. Example 1 Part 1 - Differentiation from first principles (8:12)
13. Example 1 Part 2 - Differentiation from first principles (5:27)
14. Example 2 - Differentiation from first principles (6:54)
15. Short Methods of Differentiation Part 1 (4:05)
16. Short Methods of Differentiation Part 2 (5:25)
17. Short method of differentiation Part 3 (7:08)
18. Example 1 - Using differentiation formulas (4:26)
19. Example 2 - Derivative Rules (4:34)
20. Tangent to a curve (2:48)
21. Example 1 - Tangent to the curve (8:06)
22. Example 2 - Equation of a tangent to a curve (7:31)
23. Normal to a curve (3:30)
24. Example 1 - Equation of a normal to a curve (3:09)
25. Example 2 - Equation of a normal to a curve (4:50)
26. More differentiation - converting a function to index form (10:28)
27. Example - Differentiation using indices (5:26)
28. Composite function rule (5:45)
29. Example - Derivative of composite functions (4:20)
30. Differentiation rule for composite functions (4:07)
31. Example - composite function derivative (2:18)
32. Product Rule (4:25)
33. Example 1 - Product Rule (2:56)
34. Example 2 - Product rule (7:56)
35. Quotient Rule (9:50)
36. Example - Quotient Rule (4:13)

8. Locus

1. Definition of a Locus (5:47)
2. Equation of a Locus (4:29)
3. Example 1 - Equation of a Locus (9:56)
4. Example 2 - Equation of a Locus (8:01)
5. Example 3 - Equation of a Locus (7:24)
6. Circle as a Locus (2:17)
7. Example 1 - Circle as a Locus (3:37)
8. Example 2 - Circle as a Locus (6:56)
9. Concave up Parabola with Vertex at (0, 0) as a Focus Part 1 (10:26)
10. Concave up Parabola with Vertex at (0, 0) as a Focus Part 2 (5:20)
11. Example 1 - Parabola as a Focus (2:00)
12. Example 2 - Parabola as a Focus (7:07)
13. Example 3 - Parabola as a Focus (6:39)
14. Concave Down Parabola with Vertex at (0, 0) as a Locus Part 1 (5:43)
15. Concave Down Parabola with Vertex at (0, 0) as a Locus Part 2 (3:00)
16. Example 1 - Concave Down Parabola with Vertex at (0, 0) as a Locus (3:02)
17. Example 2 - Concave Down Parabola with Vertex at (0, 0) as a Locus (2:02)
18. Example 3 - Concave Down Parabola with Vertex at (0, 0) as a Locus (1:41)
19. Parabola with Focus at (a, 0) as a Locus Part 1 (7:41)
20. Example 1 - Parabola with Focus at (a, 0) as a Locus Part 1 (3:12)
21. Example 2 - Parabola with Focus at (a, 0) as a Locus (3:36)
22. Parabola with focus at (-a, 0) as a Locus (2:12)
23. Example 1 - Parabola with Focus at (-a, 0) as a Locus (3:15)
24. Example 2 - Parabola with Focus at (-a, 0) as a Locus (2:47)
25. General Parabola - Concave Up Parabola with Vertex at (h, k) (6:37)
26. Example 1 - General Parabola - Concave Up Parabola with Vertex at (h, k) (6:48)
27. Example 2 - General Parabola - Concave Up Parabola with Vertex at (h, k) (9:25)
28. General Parabola - Concave Down Parabola with Vertex at (h, k) (4:23)
29. General Parabola - Parabola Turning to the right with Vertex at (h, k) (6:05)
30. General Parabola - Parabola Turning to the Left with Vertex at (h, k) (5:24)
31. Example 1 - General Parabola (8:27)
32. Example 2 - General Parabola (10:20)

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53. Example 2 - Limits

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