Revision Exercise 1

6. Trigonometrical Ratios and Equations

6.1 General Angles in Radians and Degrees

6.2 Trigonometric Ratios of a General Angle

6.3 Trigonometrical Ratios of Special Angles: 30^{o}, 45^{o} , 60^{o} , or ð/6, ð/4, ð/3

6.4 Graphs and Properties of sin x, cos x and tan x

6.5 Further Trigonomtrical Graphs

6.6 Absolute Valued Trigonometrical Functions

6.7 Simple Trigonometrical Equations

6.8 Trigonometrical Ratios of Cotangent, Secant and Cosecant

6.9 Fundamental Identities

6.10 More Trigonometrical Equations

6.11 Proving of Identities

Summary

Review Examples 6

Review Questions 6

7. Further Trigonometrical Identities

7.1 Sum and Difference of Two Angles

7.2 Multiple Angles

7.3 Equations of the type A cos è + B sin è = C

7.4 Factor Formulae

7.5 Further Proving of Identities

Summary

Review Examples 7

Review Questions 7

8. Matrix and Its Application

8.1 Revision

8.2 The Inverse Matrix

8.3 Using Matrices to Solve Simultaneous Equations

Summary

Review Examples 8

Review Questions 8

9. The Binomial Theorem

9.1 Binomial Expansions of the Form (x + y)^{n}

9.2 The Binomial Theorem

Summary

Review Examples 9

Review Questions 9

10. Matrix and Its Application

10.1 Simple Examples in Geometric Proof

10.2 The Midpoint and Intercept Theorem

10.3 The Alternate Segment Theorem, Intersecting Chords Theorem and Tangent-Secant Theorem

10.4 More Proofs in Plane Geometry

Summary

Review Examples 10

Review Questions 10

Revision Exercise 2

11. Further Coordinate Geometry

11.1 Equation of a Circle

11.2 Graphs of Equations

Summary

Review Examples 11

Review Questions 11

12. Differentiation

12.1 The Ideas of Limits

12.2 Gradient of a Curve

12.3 Differentiation of y = ax ^{n}

12.4 Differentiation of a Composite Function

12.5 Differentiation of Products

12.6 Differentiation of Quotients

12.7 Higher Derivatives

Summary

Review Examples 12

Review Questions 12

13. Differentiation and Its Applications

13.1 Increasing and Decreasing Functions

13.2 Stationary Points: Maximum and Minimum Points (First Derivative Test)

13.3 Distinguishing Maximum and Minimum Points Using dy^{ 2}/dx^{2 }(Second Derivative Test)

13.4 Problems on Maximum and Minimum Values

Summary

Review Examples 13

Review Questions 13

14. Further Applications of Differentiation

14.1 Equations of Tangent and Normal to a Curve

14.2 Connected Rates of Change

14.3 Motion with Variable Velocity and Acceleration

Summary

Review Examples 14

Review Questions 14

15. Differentiation of Trigonometrical Functions

15.1 Differentiation of Trigonometrical Functions

15.2 Applications of Differentiation of Trigonometrical Functions

15.3 Further Applications of Differentiation of Trigonometrical Functions

Summary

Review Examples 15

Review Questions 15

Revision Exercise 3

16. Logarithmic and Exponential Functions

16.1 Graphs of Logarithmic Functions

16.2 Differentiation of Logarithmic Functions

16.3 Problems Involving ln x

16.4 Graphs of Exponential Functions

16.5 Differentiation of Exponential Functions

16.6 Problems Involving ln e^{x}

Summary

Review Examples 16

Review Questions 16

17. Integration

17.1 Integration

17.2 Symbol of Integration

17.3 Integration of a Function Involving a Linear Factor

17.4 Integration of Trigonometrical Functions

17.5 Integration of Functions of the Form 1/ ax + b

17.6 Integration of Exponential Functions

17.7 Definite Integral

17.8 Further Examples of Definite Integration

Summary

Review Examples 17

Review Questions 17

18. Applications of Integration

18.1 Area Under a Curve

18.2 Kinematics

Review Examples 18

Review Questions 18

Revision Exercise 4

Answers

Samples

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