1.2 Solving Quadratic Equations by Completing the Square – KhanhEdu

Course Content

1. Quadratics

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1.1 Solving Quadratic Equations by Factorisation

1.2 Solving Quadratic Equations by Completing the Square

1.3 Solving Quadratic Equations by Using Formula

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

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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

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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

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4.2 Length of an Arc

4.3 Area of a Sector

5. Trigonometry

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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

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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

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7.1 Derivatives and Gradient Functions

7.2 The Chain Rule

7.3 Tangents and Normals

7.4 Second Derivatives

8. Further Diffrentiation

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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

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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

A Level Pure Mathematics 1

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