A Level Pure Mathematics 1

1.1 Solving Quadratic Equations by Factorisation

16:51 Preview
1.2 Solving Quadratic Equations by Completing the Square

04:27 Preview
1.3 Solving Quadratic Equations by Using Formula

09:32 Preview
1.4 Solving Simultaneous Equations (One Linear and One Quadratic)

09:28
1.5 Solving More Complex Quadratic Equations

05:19
1.6 Maximum and Minimum Values of a Quadratic Function

04:24
1.7 Solving Quadratic Inequalities

03:00
1.8 The Number of Roots of a Quadratic Equation

00:00

2.1 Definition of a Function

27:24
2.2 Composite Functions

14:55
2.3 Inverse Functions

14:12
2.4 The Graph of a Function and its Inverse

13:40
2.5 Translations of Function

20:49
2.6 Reflections of Functions

00:00
2.7 Stretches of Functions

00:00
2.8 Combined Transformation

00:00

3.1 Length of a Line Segment and Midpoint

00:00
3.2 Parallel and Perpendicular Lines

00:00
3.3 Equations of Straight Lines

00:00
3.4 The Equation of a Circle

00:00
3.5 Problems Involving Intersections of Lines and Circles

00:00

4.1 Radians

00:00
4.2 Length of an Arc

00:00
4.3 Area of a Sector

00:00

5.1 Angles Between 0 and 90

00:00
5.2 The General Definition of An Angle

00:00
5.3 Trigonometric Ratios of General Angles

00:00
5.4 Graphs of Trigonometric Functions

00:00
5.5 Inverse Trigonometric Functions

00:00
5.6 Trigonometric Equations

00:00
5.7 Trigonometric Identities

00:00
5.8 Further Trigonometric Equations

00:00

6.1 Binomial Expansion

00:00
6.2 Binomial Coefficients

00:00
6.3 Arithmetic Progressions

00:00
6.4 Geometric Progressions

00:00
6.5 Infinite Geometric Series

00:00
6.6 Further Arithmetic and Geometric Series

00:00

7.1 Derivatives and Gradient Functions

00:00
7.2 The Chain Rule

00:00
7.3 Tangents and Normals

00:00
7.4 Second Derivatives

00:00

8.1 Increasing and Decreasing Functions

00:00
8.2 Stationary Points

00:00
8.3 Practical Maximum and Minimum Problems

00:00
8.4 Rates of Change

00:00
8.5 Practical Applications of Connected Rates of Change

00:00

9.1 Integration as the Reverse of Differentiation

00:00
9.2 Finding the Constant of Integration

00:00
9.3 Integration of Expressions of the Form (Ax + B)^N

00:00
9.4 Further Indefinite Integration

00:00
9.5 Definite Integration

00:00
9.6 Area Under a Curve

00:00
9.7 Area Bounded by a Curve and a Line or by Two Curves

00:00
9.8 Improper Integrals

00:00
9.9 Volume of Revolution

00:00

Course Content

1. Quadratics

1.4 Solving Simultaneous Equations (One Linear and One Quadratic)

1.5 Solving More Complex Quadratic Equations

1.6 Maximum and Minimum Values of a Quadratic Function

1.7 Solving Quadratic Inequalities

1.8 The Number of Roots of a Quadratic Equation

2. Functions

2.1 Definition of a Function

2.2 Composite Functions

2.3 Inverse Functions

2.4 The Graph of a Function and its Inverse

2.5 Translations of Function

2.6 Reflections of Functions

2.7 Stretches of Functions

2.8 Combined Transformation

3. Coordinate Geometry

3.1 Length of a Line Segment and Midpoint

3.2 Parallel and Perpendicular Lines

3.3 Equations of Straight Lines

3.4 The Equation of a Circle

3.5 Problems Involving Intersections of Lines and Circles

4. Circular Measure

4.1 Radians

4.2 Length of an Arc

4.3 Area of a Sector

5. Trigonometry

5.1 Angles Between 0 and 90

5.2 The General Definition of An Angle

5.3 Trigonometric Ratios of General Angles

5.4 Graphs of Trigonometric Functions

5.5 Inverse Trigonometric Functions

5.6 Trigonometric Equations

5.7 Trigonometric Identities

5.8 Further Trigonometric Equations

6. Series

6.1 Binomial Expansion

6.2 Binomial Coefficients

6.3 Arithmetic Progressions

6.4 Geometric Progressions

6.5 Infinite Geometric Series

6.6 Further Arithmetic and Geometric Series

7. Differentiation

7.1 Derivatives and Gradient Functions

7.2 The Chain Rule

7.3 Tangents and Normals

7.4 Second Derivatives

8. Further Diffrentiation

8.1 Increasing and Decreasing Functions

8.2 Stationary Points

8.3 Practical Maximum and Minimum Problems

8.4 Rates of Change

8.5 Practical Applications of Connected Rates of Change

9. Integration

9.1 Integration as the Reverse of Differentiation

9.2 Finding the Constant of Integration

9.3 Integration of Expressions of the Form (Ax + B)^N

9.4 Further Indefinite Integration

9.5 Definite Integration

9.6 Area Under a Curve

9.7 Area Bounded by a Curve and a Line or by Two Curves

9.8 Improper Integrals

9.9 Volume of Revolution

Instructor

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