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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                                                                                                              Answers                                                                                                         Glossary/Index