Advanced Mathematics Grade 12 is one of the titles in the Save Buk series specially written for the new PNG Upper Secondary courses at Grades 11 & 12.

This book gives students concise coverage of the information needed to successfully complete the Grade 12 Advanced Mathematics course. The order of Units in the book follows the order of Units in the Advanced Mathematics Grade 12 syllabus exactly:

Unit 12.1 Patterns and Algebra

Unit 12.2 Trigonometry and Vectors

Unit 12.3 Calculus

The book is written in a manner that best develops an overall understanding of the mathematical concepts and processes set out in the Syllabus.

The Glossary/Index at the end of the book explains the specific terminology that students need to learn for the study of Mathematics.

Unit 12.1 Patterns and Algebra      

Topic 1: Sets - definitions and notation                                                 

Topic 2: Sets - Venn diagrams                                      

Topic 3: Sets - field laws                                  

Topic 4: Using sets to solve problems                                      

Topic 5: Sequences and series                         

Topic 6: Sequences and series - arithmetic sequences                                                   

Topic 7: Sequences and series - geometric sequences                                                   

Topic 8: Applications of geometric sequences                                                                           

Topic 9: Binomial theorem                                                                    

Topic 10: Determinants - simultaneous linear equations                                      

Topic 11: Determinants - simultaneous equations in three unknowns                               

Unit 12.2 Trigonometry and Vectors                                                                     

Topic 1: Basic trigonometry, circular functions and radian measure                                                         

Topic 2: Further trigonometric functions                                                             

Topic 3: Straightforward trigonometric equations                                                                                   

Topic 4: Trigonometric equations including multi-step problems                                                              

Topic 5: Trigonometric identities                                                                        

Topic 6: Properties of vectors

Topic 7: Geometric proofs using vectors                                                                                               

Topic 8: Further properties of vectors

Topic 9: Rectangular components of vectors

Topic 10: Component vectors in three dimensions

Topic 11: The scalar product of vectors

Unit 12.3 Calculus                                                    

Topic 1: The gradient function                                                                

Topic 2:  Derivatives                               

Topic 3: Tangents to curves

Topic 4: Increasing and decreasing functions: turning points

Topic 5: Optimisation (maxima and minima problems)

Topic 6: Rates of change

Topic 7: Derivatives of trigonometric function

Topic 8: The product and the quotient rule for differentiation

Topic 9: Antidifferentiation

Topic 10: Finding the constant of integration

Topic 11: Integration of trigonometric functions                                                 

Topic 12: Definite integrals and area                  

Appendix                                                                                          

Mathematical symbols                                                                                      

Mathematical formulae                                                                                      

Sequences and series                                                                                      

Coordinate geometry                                                                                        

Trigonometry                                                                                        

Calculus                                                                                                           

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