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