Cambridge 3 Unit Mathematics Year 12

Preface; How to use this book; About the authors; Chapter one - The inverse trigonometric function: 1A. Restricting the domain, 1B. Defining the inverse trigonometric functions, 1C. Graphs involving inverse trigonometric functions, 1D. Differentiation, 1E. Integration, 1F. General solutions of trigonometric equations; Chapter two - Further trigonometry: 2A. Trigonometric identities, 2B. The t-formulae, 2C. Applications of trigonometric identities, 2D. Trigonometric equations, 2E. The sum of sine and cosine functions, 2F. Extension - Products to sums and sums to products, 2G. Three-dimensional trigonometry, 2H. Further three-dimensional trigonometry; Chapter three - Motion: 3A. Average velocity and speed, 3B. Velocity and acceleration as derivatives, 3C. Integrating with respect to time, 3D. Simple harmonic motion - the time equations, 3E. Motion using functions of displacement, 3F. Simple harmonic motion - the differential equation, 3G. Projectile motion - the time equations, 3H. Projectile motion - the equation of path; Chapter four - Polynomial functions: 4A. The language of polynomials, 4B. Graphs of polynomial functions, 4C. Division of polynomials, 4D. The remainder and factor theorems, 4E. Consequences of the factor theorem, 4F. The zeroes and the coefficients, 4G. Geometry using polynomial techniques; Chapter five - The binomial theorem: 5A. The Pascal triangle, 5B. Further work with the Pascal triangle, 5C. Factorial notation, 5D. The binomial theorem, 5E. Greatest coefficient and greatest term, 5F. Identities on the binomial coefficients; Chapter six - Further calculus: 6A. Differentiation of the six trigonometric functions, 6B. Integration using the six trigonometric functions, 6C. Integration by substitution, 6D. Further integration by substitution, 6E. Approximate solutions and Newton's method, 6F. Inequalities and limits revisited; Chapter seven - Rates and finance: 7A. Applications of APs and GPs, 7B. Simple and compound interest, 7C. Investing money by regular instalments, 7D. Paying off a loan, 7E. Rates of change - differentiating, 7F. Rates of change - Integrating, 7G. Natural growth and decay, 7H. Modified natural growth and decay; Chapter eight - Euclidean geometry: 8A. Points, lines, parallels and angles, 8B. Angles in triangles and polygons, 8C. Congruence and special triangles, 8D. Trapezia and parallelograms, 8E. Rhombuses, rectangles and squares, 8F. Areas of plane figures, 8G. Pythagoras' theorem and its converse, 8H. Similarity, 8I. Intercepts on transversals; Chapter nine - Circle geometry: 9A. Circles, chords and arcs, 9B. Angles at the centre and circumference, 9C. Angles on the same and opposite arcs, 9D. Concyclic points, 9E. Tangents and radii, 9F. The alternate segment theorem, 9G. Similarity and circles; Chapter ten - Probability and counting: 10A. Probability and sample spaces, 10B. Probability and venn diagrams, 10C. Multi-stage experiments, 10D. Probability tree diagrams, 10E. Counting ordered selections, 10F. Counting with identical elements and cases, 10G. Counting unordered selections, 10H. Using counting in probability, 10I. Arrangements in a circle, 10J. Binomial probability; Answers to exercises; Index.