CIE International A-Level Maths: Pure Mathematics 2/3

سرفصل های دوره

Master the content from Papers 2 & 3 (Pure Mathematics 2 & 3) of Cambridge International A-Level Maths

1. Introduction

1. Introduction

2. Whats the Difference Between Paper 2 and Paper 3

2. Algebra

1. The Modulus Function - Graphs - Part 1

2. The Modulus Function - Graphs - Part 1 - quiz.html

3. The Modulus Function - Graphs - Part 2

4. The Modulus Function - Graphs - Part 2 - quiz.html

5. The Modulus Function - Equations and Inequalities - Part 1

6. The Modulus Function - Equations and Inequalities - Part 1.html

7. The Modulus Function - Equations and Inequalities - Part 2

8. The Modulus Function - Equations and Inequalities - Part 2.html

9. Polynomial Division

10. Polynomial Division Intro - quiz.html

11. Polynomial Division - Examples - 1

12. Division Examples - part 1 - quiz.html

13. Polynomial Division - Examples - 2

14. Division Examples - part 2 - quiz.html

15. Remainders - Part 1

16. Remainders - part 1 - quiz.html

17. Remainders - Part 2

18. Remainders - part 2 - quiz.html

19. The Factor Theorem

20. The Factor Theorem - quiz.html

21. The Long Division Method

22. The Long Division Method - quiz.html

3. Logarithms and Exponential Functions

1. Exponential Functions - Intro

2. Exponentials Introduction - quiz.html

3. THE Exponential Function

4. THE Exponential Function - quiz.html

5. Differentiating e^x

6. Differentiating e^x - quiz.html

7. Exponential Modelling

8. Exponential Modelling - quiz.html

9. Logarithms - Intro

10. Logarithms Introduction - quiz.html

11. Simplifying Logarithms

12. Logarithms Laws

13. Using Log Laws

14. Using the Log Laws - quiz.html

15. Logarithmic Equations - Part 1

16. Solving Logarithmic Equations - part 1 - quiz.html

17. Logarithmic Equations - Part 2

18. Solving Logarithmic Equations - part 2 - quiz.html

19. The Natural Logarithm

20. The Natural Log - quiz.html

21. Logarithmic Graph

22. Graphs of Logarithms - quiz.html

23. Non-Linear Data - Exponential Models

24. Non-Linear Data - Exponential Models - quiz.html

25. Non-Linear Data - Polynomial Models

26. Non-Linear Data - Polynomial Models - quiz.html

27. Non-Linear Data - Exam Questions

28. Non-Linear Data - Exam Question - quiz.html

4. Trigonometry

1. Sec, Cosec and Cot

2. Graphs of Sec, Cosec and Cot

3. Graphs of Sec, Cosec and Cot - quiz.html

4. Sec, Cosec and Cot - Simple Identities

5. Sec, Cosec and Cot - Simple Equations

6. Sec, Cosec and Cot - Simple Equations - quiz.html

7. The Pythagorean Identities

8. The Pythagorean Identities - quiz.html

9. The Pythagorean Identities - Proving Identities

10. The Pythagorean Identities - Proving Identities - quiz.html

11. The Pythagorean Identities - Solving Equations

12. The Pythagorean Identities - Solving Equations - quiz.html

13. The Pythagorean Identities - Exam-Style Problems

14. The Pythagorean Identities - Exam Style Problems - quiz.html

15. Inverse Trig Functions - Graphs

16. Inverse Trig Functions - Graphs - Quiz.html

17. Inverse Trig Functions - Calculations

18. Inverse Trig Functions - Calculations - quiz.html

19. The Addition Formulae

20. Using The Addition Formulae

21. Using the Addition Formulae - quiz.html

22. The Double Angle Formulae

23. The Double Angle Formulae - Solving Equations - Part 1

24. The Double Angle Formulae - Solving Equations - Part 1.html

25. The Double Angle Formulae - Solving Equations - Part 2

26. The Double Angle Formulae - Solving Equations - Part 2.html

27. The Double Angle Formulae - Proving Identities

28. The Double Angle Formulae - Proving Identities - quiz.html

29. The Double Angle Formulae - Exam-Style Problems

30. The Double Angle Formulae - Exam-Style Problems - quiz.html

31. Harmonic Form acos(x) + bsin(x)

32. Harmonic Form acosx + bsinx.html

33. Harmonic Form - Solving Equations

34. Harmonic Form - Solving Equations - quiz.html

35. Harmonic Form - Minimum and Maximum Points - Part 1

36. Harmonic Form - Minimum and Maximum - Part 1 - quiz.html

37. Harmonic Form - Minimum and Maximum Points - Part 2

38. Harmonic Form - Minimum and Maximum - Part 2 - quiz.html

39. Modelling With Trigonometric Equations

40. Modelling With Trig Equations - quiz.html

5. Differentiation

1. Differentiating Sin(x) and Cos(x)

2. Differentiating Sinx and Cosx - quiz.html

3. Using the Derivatives of Sin(x) and Cos(x)

4. Using the Derivatives of Sinx and Cosx.html

5. Differentiating Exponential Functions

6. Differentiating Exponential Functions - quiz.html

7. Differentiating Ln(x)

8. Differentiating lnx - quiz.html

9. The Chain Rule - f(x)^n

10. The Chain Rule - f(x)^n - quiz.html

11. The Chain Rule - Trigonometric Functions

12. The Chain Rule - Trigonometric Functions - quiz.html

13. The Chain Rule - Exponential Functions

14. The Chain Rule - Exponential Functions - quiz.html

15. The Chain Rule - Logarithmic Functions

16. The Chain Rule - Logarithmic Functions - quiz.html

17. The Product Rule

18. The Product Rule - quiz.html

19. The Quotient Rule

20. The Quotient Rule - quiz.html

21. Derivatives of Tan, Sec, Cosec and Cot

22. Derivatives of Tan, Sec, Cosec and Cot - quiz.html

23. Using the Derivatives of Tan, Sec, Cosec and Cot

24. Using the Derivatives of Tan, Sec, Cosec and Cot - quiz.html

25. Implicit Differentiation

26. Implicit Differentiation - quiz.html

27. Implicit Differentiation - Stationary and Critical Points

28. Implicit Differentiation - Stationary and Critical Points - quiz.html

29. Second Derivatives - Convex and Concave Functions

30. Second Derivatives - Convex and Concave Functions - quiz.html

31. Parametric Equations - Introduction

32. Converting Parametric Equations to Cartesian Form - Substitution

33. Converting Parametric Equations to Cartesian Form - Substitution - quiz.html

34. Converting Parametric Equations to Cartesian Form - Pythagorean Identities

35. Converting Parametric Equations to Cartesian Form - Pythagorean Identities - qui.html

36. Converting Parametric Equations to Cartesian Form - Double Angles

37. Converting Parametric Equations to Cartesian Form - Double Angle Formulae - quiz.html

38. Intersections of Parametric Equations and Lines

39. Intersection of a Parametric Equation with a Line.html

40. Differentiating Parametric Curves

41. Differentiating Parametric Equations - quiz.html

42. Differentiating Parametric Curves - Stationary Points

43. Differentiating Parametric Equations - Stationary and Critical Points - quiz.html

6. Integration

1. Integrating Standard Functions

2. Integrating Standard Functions - quiz.html

3. Integrating f(ax + b)

4. Integrating f(ax+b) - quiz.html

5. Trigonometric Identities For Integration - Pythagorean Identities

6. Trig Identities for Integration - Pythagorean Identities - quiz.html

7. Trigonometric Identities For Integration - Double Angle Formulae

8. Trig Identities for Integration - Double Angle Formulae - quiz.html

7. Numerical Solutions of Equations

1. Locating Roots

2. Iteration - Part 1

3. Iteration - Part 2

8. Further Algebra

1. Partial Fractions - Two Factors

2. Two Factors - quiz.html

3. Partial Fractions - Three Factors

4. Three Factors - quiz.html

5. Partial Fractions - Repeated Factors

6. Repeated Factors - quiz.html

7. Partial Fractions - Top Heavy Fractions

8. Top Heavy Fractions - quiz.html

9. The Binomial Expansion Formula (When n is Not a Positive Integer)

10. The Binomial Expansion Formula - quiz.html

11. Using the Binomial Expansion Formula

12. Using Binomial Expansion - quiz.html

13. Binomial Expansion When the First Term is Not 1

14. When The First Term Is Not 1 - quiz.html

15. Approximations

16. Approximations - quiz.html

17. Binomial Expansion - Algebraic Fractions

18. Binomial Expansion With Algebraic Fractions - quiz.html

19. Binomial Expansion - Partial Fractions

20. Binomial Expansion With Partial Fractions - quiz.html

9. Further Integration

1. Reverse Chain Rule f(x)[f(x)]^n - Part 1

2. Reverse Chain Rule f(x)[f(x)]^n - Part 2

3. Reverse Chain Rule - f(x)[f(x)]^n - quiz.html

4. Reverse Chain Rule - Exponentials

5. Reverse Chain Rule - Exponential Functions - quiz.html

6. Reverse Chain Rule - Logarithmic Functions - Part 1

7. Reverse Chain Rule - Logarithmic Functions - Part 2

8. Reverse Chain Rule - Logarithmic Functions - quiz.html

9. Mixed Reverse Chain Rule Problems

10. Using Partial Fractions For Integration - Part 1

11. Using Partial Fractions For Integration - Part 2

12. Using Partial Fractions for Integration - quiz.html

13. Integration By Parts - Polynomial x Exponential

14. Integration by Parts - Polynomial x Exponential - quiz.html

15. Integration By Parts - Polynomial x Trigonometric

16. Integration by Parts - Polynomial x Trigonometric - quiz.html

17. Integration By Parts - Polynomial x Logarithmic

18. Integration by Parts - Polynomial x Logarithmic - quiz.html

19. Integration By Parts - Exponential x Trigonometric

20. Integration by Parts - Exponential x Trigonometric - quiz.html

21. Integration By Substitution 1 Alternative to Reverse Chain Rule

22. Integration by Substitution 1 - An Alternative to Reverse Chain Rule - quiz.html

23. Integration By Substitution 2 u = f(x)

24. Integration by Substitution 2 u = f(x) - quiz.html

25. Integration By Substitution 3 x = f(u)

26. Integration by Substitution 3 x = f(u) - quiz.html

27. Integration By Substitution - Definite Integrals

28. Integration by Substitution - Definite Integrals - quiz.html

29. Integrating Arctan-Like Functions

30. Problem Solving With Integration

31. Problem Solving With Integration - quiz.html

32. The Trapezium Rule

33. The Trapezium Rule - quiz.html

10. Vectors

1. The Vector Equation of a Straight Line

2. Parallel and Skew Vectors

3. Converting Vector Form to Cartesian Form

4. The Scalar (Dot) Product - Introduction

5. Using the Scalar Product to Find Angles

6. Using the Scalar Product to Find Shortest Distances and Closest Points

11. Differential Equations

1. Differential Equations - Separating Variables - Part 1

2. Differential Equations - Separating Variables - Part 2

3. Differential Equations - Separating Variables - quiz.html

4. Forming Differential Equations

5. Forming Differential Equations - quiz.html

6. Modelling with Differential Equations - Part 1

7. Modelling with Differential Equations - Part 2

8. Modelling with Differential Equations - quiz.html

12. Complex Numbers

1. Complex Numbers - Introduction

2. Addition, Subtraction and Multiplication of Complex Numbers

3. Division of Complex Numbers

4. Square Roots of Complex Numbers

5. Complex Roots of Quadratic Equations

6. Complex Roots of Cubic and Quartic Equations

7. The Argand Diagram

8. Modulus and Argument

9. Modulus-Argument Polar Form of a Complex Number

10. Exponential Form of a Complex Number

11. (Optional!) Explanation of Why the Exponential Form Works

12. Multiplying and Dividing Numbers in Modulus-Argument Exponential Form - Part 1

13. Multiplying and Dividing Numbers in Modulus-Argument Exponential Form - Part 2

14. Multiplying and Dividing Numbers in Modulus-Argument Exponential Form - Part 3

15. Eulers Identity

16. Complex Loci - Circles

17. Complex Loci - Perpendicular Bisectors

18. Complex Loci - Arguments

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