Mathematics extension 2, CambridgeMATHS, Stage 6, Sadler D., Ward D., 2020

Mathematics extension 2, CambridgeMATHS, Stage 6, Sadler D., Ward D., 2020.

   This resource covers the Mathematics Extension 2 syllabus and is designed to be used in conjunction with CambridgeMATHS Mathematics Advanced Year 12 and Extension 1 Year 12. It is based on the authors’ Extension 2 resource developed for the previous syllabus, and retains the same design and structure, but has been re-written to cover the new syllabus implementing in 2020.
The online Curriculum Grid, Scope and Sequence, and Teaching Program are provided to guide you in planning a sound mathematical journey through a complex syllabus.
The Exercises are divided into Foundation. Development and Enrichment to gradually lead you to achieve your highest potential. The Enrichment questions are particularly challenging.




Vectors and the Complex Plane.
The geometry of multiplication and division became evident with the introduction of the modulus-argument form in the previous section. Since the arguments are added or subtracted, it is clear that a rotation is involved. Since the moduli are multiplied or divided, it is clear that an enlargement is involved.

So far, the observed geometry of addition and subtraction has been limited. A better understanding of these two operations is desirable and can be achieved by yet another representation of complex numbers, this time as vectors. In this section, a few vector tools will be introduced to help better understand complex numbers. A more detailed study of vectors is given in the Extension 1 course.

Contents.
Introduction.
Rationale.
About the authors.
1 Complex numbers I.
1A The arithmetic of complex numbers.
1B Quadratic equations.
1C The Argand diagram.
1D Modulus-argument form.
1E Vectors and the complex plane.
1F Curves and regions in the Argand diagram.
1G Polynomials and complex numbers.
1H Chapter review exercise.
2 Proof.
2A The language of proof.
2B Number proofs.
2C Proof by contraposition and by contradiction.
2D Algebraic inequalities.
2E Induction.
2F Inequalities in geometry and calculus.
2G Chapter review exercise.
Appendix: The fundamental theorem of arithmetic.
3 Complex numbers II: de Moivre and Euler.
3A Powers of complex numbers.
3B Trigonometric identities.
3C Roots of complex numbers.
3D Exponential form: Euler’s formula.
3E Applications of exponential form.
3F Chapter review exercise.
4 Integration.
4A The standard integrals.
4B Algebraic manipulation.
4C Substitution.
4D Partial fractions.
4E Denominators with quadratics.
4F Integration by parts.
4G Trigonometric integrals.
4H Reduction formulae.
4I Miscellaneous integrals.
4J Chapter review exercise.
Appendix: A short table of integrals.
5 Vectors.
5A Coordinates in three dimensions.
5B Vectors in three dimensions.
5C The dot product.
5D Applications of the dot product.
5E Vector proofs in geometry.
5F The vector equation of a line.
5G Vector equations of circles, spheres and planes.
5H Chapter review exercise.
Appendix: Some Geometry in 3D.
6 Mechanics.
6A Forces and acceleration.
6B Simple harmonic motion and time.
6C Simple harmonic motion and displacement.
6D Horizontal resisted motion.
6E Vertical resisted motion.
6F Projectile motion.
6G Miscellaneous problems.
6H Chapter review exercise.
Answers.
Index.



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