| Topics | |
|---|---|
| 1 | Number & Algebra |
| 2 | Functions |
| 3 | Geometry & Trigonometry |
| 4 | Statistics & Probability |
| 5 | Calculus |
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| Topic 1: Number and Algebra (part of the topic) | |
|---|---|
| 1.1 | Numbers – rounding – scientific form |
| 1.2 | Sequences in general – Series |
| 1.3 | Arithmetic sequences |
| 1.4 | Geometric sequences |
| 1.5 | Applications of G.S. – Percentage growth) |
| 1.6 | The Binomial theorem – (a+b)ⁿ |
| 1.7 | Deductive proof |
| 1.8 | Methods of proof |
| 1.9 | Mathematical induction |
| Topic 2: Functions | |
|---|---|
| 2.1 | Lines (or Linear functions) |
| 2.2 | Quadratics (or Quadratic functions) |
| 2.3 | Functions, domain, range, graph |
| 2.4 | Composition of functions: fog |
| 2.5 | The inverse function: f^{-1} |
| 2.6 | Transformations of functions |
| 2.7 | Asymptotes |
| 2.8 | Exponents – the exponential function a^x |
| 2.9 | Logarithms – the logarithmic function log_ax |
| 2.1 | Exponential Equations |
| At this point a quick introduction to complex numbers (only the Cartesian part) as well as a reference to the fundamental theorem of algebra is needed. See paragraphs 1.10-1.11 from Topic 1. A full treatment of complex numbers will take place in year 2. | |
| 2.11 | Polynomial functions |
| 2.12 | Sum and Product of roots |
| 2.13 | Rational functions – Partial fractions |
| 2.14 | Polynomial and rational inequalities |
| 2.15 | Symmetries of f(x) – More transformations |
2.16 | Modulus equations and inequalities |
| Topic 3: Trigonometry (part of the topic) | |
|---|---|
| 3.1 | 3D Geometry |
| 3.2 | Triangles – Sine and Cosine rules |
| 3.3 | Applications in 3D Geometry – Navigation |
| 3.4 | The trigonometric circle – Arcs and Sectors |
| 3.5 | sinθ, cosθ, tanθ on the unit circle |
| 3.6 | Trigonometric identities and equations |
| 3.7 | Trigonometric functions |
| 3.8 | More trigonometric equations – identities |
| 3.9 | Inverse trigonometric functions |
| Topic 5: Calculus (part of the topic) | |
|---|---|
| 5.1 | The limit f(x) – The derivative f'(x): A rough idea |
| 5.2 | Derivatives of known functions – Rules |
| 5.3 | Tangent line – Normal line at some point x_0 |
| 5.4 | The chain rule |
| 5.5 | Monotony – max, min |
| 5.6 | Concavity – points of inflection |
| 5.7 | Optimization |
| 5.14 | Implicit differentiation (without kinematics) |
| 5.15 | Rate of change problems |
| 5.8 | The indefinite integral |
| 5.9 | Integration by substitution |
| 5.16 | Further integration by substitution |
| 5.1 | The definite integral – Areas between curves |
| 5.18 | Further areas between curves – Volumes |
| Topic 5: Calculus (part of the topic) | |
|---|---|
| 5.12 | Continuity and differentiability |
| 5.13 | L'Hôpital's rule |
| 5.11 | Kinematics (+last paragraph of 5.14) |
| 5.19 | Differential equations |
| 5.20 | Maclaurin series – Extension of Binomial Theorem |
| Topic 4: Statistics and Probability | |
|---|---|
| 4.1 | 4.1 Basic concepts of Statistics |
| 4.2 | 4.2 Measures of central tendency – Measures of spread |
| 4.3 | 4.3 Frequency tables – Grouped Data |
| 4.4 | 4.4 Regression |
| 4.5 | 4.5 Elementary Set Theory |
| 4.6 | 4.6 Probability |
| 4.7 | 4.7 Conditional probability – Independent events |
| 4.8 | 4.8 Tree diagrams |
| 4.9 | 4.9 Distributions – Discrete random variables |
| 4.10 | 4.10 Binomial distribution – B(n, p) |
| 4.11 | 4.11 Normal distribution – N(μ, σ) |
| 4.12 | 4.12 Continuous random variables |
| 4.13 | 4.13 Counting – Permutations – Combinations |
| Topic 1: Number and Algebra (part of the topic) | |
|---|---|
| 1.10 | Systems of linear equations |
| Topic 3: Vectors (part of the topic) | |
|---|---|
| 3.10 | Vectors: Geometric representation |
| 3.11 | Vectors: Algebraic representation |
| 3.12 | Scalar (or Dot) product – angle between vectors |
| 3.13 | Vector equation of a line in 2D |
| 3.14 | Vector equation of a line in 3D |
| 3.15 | Vector (or Cross) project |
| 3.16 | Planes |
| 3.17 | Intersection among lines and planes |
| 3.18 | Distances |
| Number and Algebra (part of the topic) | |
|---|---|
| 1.11 | Complex numbers – basic operations |
| 1.12 | Polynomials over the Complex field |
| 1.13 | The complex plane |
| 1.14 | De Moivre's theorem |
| 1.15 | Roots of z^n=a |
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