The Complete IB Maths Syllabus: SL & HL
The Complete IB Maths Syllabus: SL & HL
If you are going through this syllabus, I suppose you are interested in taking this course or you are presently joined with this course.
In this article, I am going to discuss every topic covered in IB Biology Standard level and IB Biology higher level along with the number of hours dedicated to each topic.
For IB Maths SL, dedicated hours is 140 hours and for IB Maths HL, dedicated hours is 182 hours.
The topics are listed below:
Topic 1: Algebra
Longer Notes:

Packet: Series, Complex Numbers, Differentiation FP

Packet: Complex Numbers, Theorem of Algebra, Modulus, Exponential Form, Nth Roots of Unit

Packet: De Moivre's Theorem, Expansions for Trig Functions, Derivative of sin x
Quick Overview:

Algebraic Sequences

Sequences

Arithmetic Sequences and Series

Geometric Sequences and Series

Complex Numbers

Arithmetics with Complex Numbers

Addition / Subtraction

Multiplication

Division

Argand Diagrams

Modulus of a Complex Number

Polar Form

Multiplication / Division in Polar Form

De Moivre's Theorem

Applications of the Theorem

Roots of Equations

Complex Roots

Long Division

References
Topic 2: Functions and Equations
Longer Notes:

Packet: Indices, Surds, Linear, Quadratics, Cubics, Inequalities

Packet: Functions, Graphs, Polynomials
Quick Overview:

Concept of Functions

Functional Limits

Domain

Range

Number Sets

Integers

Real Numbers

Natural Numbers

Combined Functions

Graphs of Functions

Inverse Function

Modulus Functions

Logarithms and Exponents

Natural Logs

Natural Exponent

Polynomial Functions

Quadratic Formulas and Graphs

Graph Transformations

Translation

Horizontal

Vertical

Stretch

Horizontal

Vertical

Reflection

Horizontal

Vertical

Modulus Transformations

Inverse Transformations

Four Things Graph Sketching
Intercepts
Asymptotes
Millionaire Theory
Table
Calculator
Topic 3: Circular Functions and Trigonometry
Longer Notes:

Packet: Trigonometry

Packet: De Moivre's Theorem, Expansions for Trig Functions, Derivative of sin x
Quick Overview:

Radians

Length of Arc

Area of a Sector

Definitions of Trigonometric Ratios

Special Angles

Definition of Reciprocal Trigonometric Ratios
Secant
Cosecant
Cotangent

Pythagorean Identities

Compound Angle Identities

Double Angle Identities

Manipulation of Trigonometric Functions

Inverse Trigonometric Functions
Arcsin
Arccos
Arctan

Solving Trigonometric Equations

Cosine Rule

Sine Rule

Area of a Triangle
Topic 4: Vectors
Longer Notes:

Packet: Matrices, Vectors
Quick Overview:

Concept of a Vector

Representation of Vectors Using Directed Line Segments

Unit Vectors and Base Vectors

Algebraic and Geometric Vector Calculations

Sum and Difference of Two Vectors

Special Vectors

Scalar Multiplication

Magnitude of a Vector

Position Vectors

Scalar Product of Two Vectors

Properties of the Scalar Product

The angle between two vectors

Perpendicular and Parallel Vectors

Vector Equation of a Line

The Angle Between Two Lines

Distinguishing Between Geometric Cases of Lines Using Vectors

Coincident Lines

Parallel Lines

Intersecting Lines

Skew Lines

Points of Intersection

Vector Product of Two Vectors

Properties of the Vector Product

Vector Equation of a Plane

Vector Equation Normal Form

Cartesian Equation of a Plane

Intersections With Planes

A Line With a Plane

Two Planes

Angle of Intersections with Planes

Line and Plane
 Plane and Plane
Topic 5: Statistics and Probability
Longer Notes:

Packet: Statistics Definitions, Charts and Graphs, Representing data, Standard Deviation

Packet: Sets and Probability, Permutations and Combinations, Distributions
Quick Overview:

Measures of Central Tendency (Year 5 Maths)

Mean

Median

Mode

Measures of Spread

Range

Interquartile Range

Variance

Standard Deviation

Adding and Subtracting Mean/Variance

Discrete Distributions

Uniform / Stick

Binomial

Geometric

Poisson

Negative Binomial

Continuous Distributions

Normal

Zvalue

Probability Density Functions

Central Limit Theorem

Confidence Limits

Hypothesis Testing  Known Variance

Type I and Type II Errors

Unknown Variance

Confidence Limits  Unknown Variance

Hypothesis Testing  Unknown Variance

Matched Pairs

Bivariate Data

Probability Generating Functions (PGF)
Topic 6: Calculus
Longer Notes:

Packet: Differentiation, Max/Min, Parametrics, Kinematics

Packet: Integration, Differentials, Even/Odd Functions, Induction
 Packet: Harder Integration Questions
Quick Overview:

Differentiation

Differentiation by First Principle

Exploring the Gradient Function

Equations of Tangents and Normals

Maximums and Minimums

Points of Inflection

Rates of Change

Kinematics

Parametric Equations

Integration

Exploring the Integral Function

Integration Basics

Finding Areas from Integrals

Volumes of Revolution

Separable Differential Equations

The Trapezium Rule
Options  HL Only 48 hours
IB Math HL students have to study one of the following from the four options:
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