The International Baccalaureate (IB SL Mathematics) information page for IB Diploma SL Maths Content Page. IB Tuition Centre.

Mathematics Standard Level for the IB Diploma

Herein lies the syllabus of Maths SL IB Diploma Singapore. The topics in Mathematics SL Mathematics IB Diploma books are:

Main Topic: Algebra, Functions and Equations

Quadratic Functions

• Quadratic Form
• Complete the Square
• Factorised form
• Quadratic Formula
• Discriminant
• Intersection of graphs and simultaneous quadratic equations

Exponents and Logarithms

• Laws of exponents
• Exponential functions
• The number e
• Introduction to Logarithms
• Laws and Graphs of Logarithms
• Solving Exponential Equation

Algebraic Manipulations

• Solving Equations by Factorising
• Solving Equations by Substitution
• Features of Graphs
• Using graphical calculator (GDC) to solve equations
• Working with identities

The Theory of Functions

• Function Notation
• Domain and Range
• Composite functions
• Inverse functions
• Rational functions

Transformation of graphs

• Translations
• Stretches
• Reflections
• Consecutive Transformations

Sequence and series

• General sequences
• General series and sigma notation
• Arithmetics and Geometric Series
• Infinite Geometric Series
• Mixed Questions on sequences and series

Binomial Expansion

• Binomial Coefficients
• Applying the Binomial Theorem

Main Topic: Geometry

Circular Measure and Trigonometry

• Measuring angles
• Definitions and graphs of sine and cosine functions
• Definition and graphs of the tangent functions
• Exact Values of trigonometric functions
• Transformations of Trigonometric Graphs
• Modelling using trigonometric functions

Trigonometric Equations and Identities

• Intro to trigonometric equations
• Harder Trigonometric Equations
• Trigonometric Identities
• Using Identities to solve equations
• Double Angle Identities

Geometry of triangles and circles

• Right-angled triangles
• The sine rule
• The cosine rule
•  Area of triangle
• Trigonometry in three dimensions
• Length of an arc
• Area of a sector
• Triangles and circles

Vectors

• Positions and displacements
• Vector algebra
• Distances
• Angles
• Properties of the scalar Product
• Vector equation of a line
• Solving Problems involving lines

Main Topic: Calculus

Basic Differentiation and its applications

• Sketching derivatives
• Differentiation from first principles
• Rules of differentiation
• Interpreting derivatives and second derivatives
• Differentiating trigonometric, exponential and natural logarithm functions
• Tangents and Normals
• Stationary Points
• General Points of Inflexion
• Optimisation

Basic Integration and its Applications

• Integration (Indefinite)
• Constant of Integration
• Integrating inverse x, exponents, trigonometric functions
• Finding the equation of a curve
• Definite Integral
• Geometrical significance of definite integration
• Area between two curves

Further Differentiation

• Chain rule
• Product Rule
• Quotient Rule
• Optimisation with constraints

Further Integration

• Reversing standard derivatives
• Integration by substitution
• Kinematics
• Volumes of revolution

Main Topic: Statistics and Probability

Summarising Data

• Measure of centre of data
• Measures of spread
• Frequency table and grouped data
• Cumulative frequency
• Histograms
• Constant changes to data
• Correlation

Probability

• Empirical Probability
• Theoretical Probability
• Combined events and Venn diagrams
• Tree diagrams and finding intersections
• Independent events
• Conditional probability
• Further Venn diagrams
• Selections with and without replacement

Probability Distributions

• Random variables
• Expectations of a discrete random variable
• The binomial distribution
• The normal distribution
• The inverse normal distribution