Mathematics: Analysis & Approaches
5 topics, FE2021
External resources
Number & Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Year 1
By Christos Nikolaidis
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
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 ax
2.9
Logarithms – the logarithmic function logax
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
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
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 x0
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
Year 2
By Christos Nikolaidis
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
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
1.10
Systems of linear equations
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
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 zn=a
My notes
I bought Revision Village for 2 years, it costs $249. I shared stuff with PirateIB, too, so check it out there, too. I'll be sharing my notes too, although math is more practice based so not that much. The recommendation is to keep a seperate notebook for notes and questions.
More
Best textbook is Haese for explanations, where the questions are good for practice, but for exam preparation Revision Village has near infinite drilling. For harder questions, TaskMaker has 400 free questions. Pestle has 1104 pages of questions (no markschemes), and IBdocs has a questionbank available. Cambridge has good explanations but not syllabus coverage. For practice, use Haese's problems, and Cambridge's non-IB style questions. For exam preparation use Haese's trial exam and Cambridge's IB questions. Practice every day!
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