Chapter 1 ? Number systems: the Real Number System. Exercise 1A ? Classification of numbers. Exercise 1B ? Recurring decimals. Exercise 1C ? Surds. Exercise 1D ? Simplifying surds. Exercise 1E ? Addition and subtraction of surds. Exercise 1F ? Multiplication of surds. Exercise 1G ? The Distributive Law. Exercise 1H ? Division of surds. Exercise 1I ? Rationalising denominators. Exercise 1J ? Rationalising denominators using conjugate surds. Exercise 1K ? Further properties of real numbers ? modulus. Exercise 1L ? Solving equations using absolute values. Exercise 1M ? Solving inequations. Chapter review. Modelling and problem solving. Chapter 2 ? Number systems: Complex numbers. Exercise 2A ? Introduction to complex numbers. Exercise 2B ? Basic operations using complex numbers. Exercise 2C ? Conjugates and division of complex numbers. Exercise 2D ? Radians and coterminal angles. Exercise 2E ? Complex numbers in polar form. Exercise 2F ? Basic operations on complex numbers in polar form. Chapter review. Modelling and problem solving. Chapter 3 ? Matrices. Exercise 3A ? Operations with matrices. Exercise 3B ? Multiplying matrices. Exercise 3C ? Powers of a matrix. Exercise 3D ? Multiplicative inverse and solving matrix equations. Exercise 3E ? The transpose of a matrix. Exercise 3F ? Applications of matrices. Exercise 3G ? Dominance matrices. Chapter review. Modelling and problem solving. Chapter 4 ? An introduction to groups. Exercise 4A ? Modulo arithmetic. Exercise 4B ? The terminology of groups. Exercise 4C ? Properties of groups. Exercise 4D ? Cyclic groups and subgroups. Exercise 4E ? Further examples of groups ? transformations. Chapter review. Modelling and problem solving. Chapter 5 ? Matrices and their applications. Exercise 5A ? Inverse matrices and systems of linear equations. Exercise 5B ? Gaussian elimination. Exercise 5C ? Introducing determinants. Exercise 5D ? Properties of determinants. Exercise 5E ? Inverse of a 3 x 3 matrix. Exercise 5F ? Cramer?s Rule for solving linear equations. Chapter review. Modelling and problem solving. Chapter 6 ? Transformations using matrices. Exercise 6A ? Geometric transformations and matrix algebra. Exercise 6B ? Linear transformations. Exercise 6C ? Linear transformations and group theory. Exercise 6D ? Rotations. Exercise 6E ? Reflections. Exercise 6F ? Dilations. Exercise 6G ? Shears. Chapter review. Modelling and problem solving. Chapter 7 ? Introduction to vectors. Exercise 7A ? Vectors and scalars. Exercise 7B ? Position vectors in two and three dimensions. Exercise 7C ? Multiplying two vectors ? the dot product. Exercise 7D ? Resolving vectors ? scalar and vector resolutes. Exercise 7E ? Time-varying vectors. Chapter review. Modelling and problem solving. Chapter 8 ? Vector applications. Exercise 8A ? Force diagrams and the triangle of forces. Exercise 8B ? Newton?s First Law of Motion. Exercise 8C ? Momentum. Exercise 8D ? Relative velocity. Exercise 8E ? Using vectors in geometry. Chapter review. Modelling and problem solving. Chapter 9 ? Sequences and series. Exercise 9A ? Arithmetic sequences. Exercise 9B ? Geometric sequences. Exercise 9C ? Applications of geometric sequences. Exercise 9D ? Finding the sum of an infinite geometric sequence. Exercise 9E ? Contrasting arithmetic and geometric sequences through graphs. Chapter review. Modelling and problem solving. Chapter 10 ? Permutations and combinations. Exercise 10A ? The addition and multiplication principles. Exercise 10B ? Factorials and permutations. Exercise 10C ? Arrangements involving restrictions and like objects. Exercise 10D ? Combinations. Exercise 10E ? Applications of permutations and combinations. Exercise 10F ? Pascal?s triangle, the binomial theorem and the pigeonhole principle. Chapter review. Modelling and problem solving. Chapter 11 ? Dynamics. Exercise 11A ? Displacement, velocity and acceleration. Exercise 11B ? Projectile motion. Exercise 11C ? Motion under constant acceleration. Chapter review. Modelling and problem solving. Solutions to investigations. Chapter 1. Investigation ? Other number systems. Investigation ? Real numbers ? application and modelling. Chapter 2. Investigation ? Complex numbers in quadratic equations. Investigation ? Multiplication in polar form. Investigation ? Complex numbers: applications. Chapter 3. Investigation ? Matrix powers. Investigation ? Applications of matrices. Investigation ? Matrix multiplication using a graphics calculator. Chapter 4. Investigation ? Application of groups ? permutations. Investigation ? Some applications of group theory. Chapter 5. Investigation ? Solving simultaneous equations. Investigation ? Applications of determinants. Chapter 6. Investigation ? Transformations. Chapter 7. Investigation ? Vectors and matrices. Chapter 8. Investigation ? Three-dimensional non-zero vectors. Investigation ? Vector geometry. Chapter 9. Investigation ? Reward time. Investigation ? Changing shape. Investigation ? Fibonacci numbers. Investigation ? Draw the Mandelbrot Set. Chapter 10. Investigation ? Counting paths.