# IB Maths HL

The IB Maths HL (higher level) course focuses on introducing important mathematical concepts through the development of mathematical techniques. The intention is to introduce students to these concepts in a comprehensible and coherent way, rather than insisting on the mathematical rigour required for mathematics HL. Students should, wherever possible, apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context.

## Course Description

This course caters for students who already posses knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply simple mathematical techniques correctly. It is expected that the majority of these students will need a sound mathematical background as they prepare for future studies in subjects.

## Syllabus Component of IB Mathematics HL

All topics are compulsory. Students must study all the sub-topics in each of the topics in the syllabus as listed in the IB Mathematics HL guide. Students are also required to be familiar with the topics listed under prior learning.

- Topic 1: Algebra
- Topic 2: Functions and Equations
- Topic 3: Circular Functions and Trigonometry
- Topic 4: Vectors
- Topic 5: Statistics and Probability
- Topic 6: Calculus

## Mathematical Exploration

In the exploration a student should develop his or her own focus with the teacher providing feedback via, for example, discussion, interview and drafting. It should allow the students to develop an area of interest them without a time constraint as in an examination, and allow all to experience a feeling of success.

The exploration is also intended to provide students with opportunities to increase their understanding of mathematical concepts and processes, and develop a wider appreciation of mathematics. These are noted in the aims of the course IB Mathematics HL guide.

## Option Topics

These will be published soon, and we are working on these! Thanks for your patience.

#### Algebra > Arithmetic Sequences

- Number Sequences
- Describing Patterns
- General Term of a Number Sequence
- Identifying Arithmetic Sequences
- Finding the First Term and Common Difference of Arithemtic Sequences
- Finding a Term from a Rule - Arithemtic Sequences
- Set up Rules of Arithmetic Sequences
- Finding number of Terms of Arithmetic Sequences
- Applications of Arithmetic Sequences

#### Algebra > Geometric Sequences

- Identifying Geometric Sequences
- Finding the First Term and Common Ratio of Geometric Sequences
- Finding a Term from a Rule of Geometric Series
- Set up Rules of Geometric Sequences
- Finding number of Terms of Geometric Sequences
- Applications of Geometric Sequences
- Finding Unknown Values from Geometric Sequences

#### Statistics and Probability > Discrete Probability Distributions

- Continuous or Discrete
- Corresponding Probabilities
- Probability Distribution Graphs
- Characteristics of Discrete Probability Distribution
- Find the missing Values From the Discrete Probability Distribution
- Probability Functions
- Using Probability Distributions
- Finding the Variance
- Find the Variance using Expectation Theorems
- Finding unknown value given the Variance

#### Calculus > Drivatives of Trigonometric Functions

- Differentiation of Sine Function : Chain Rule
- Differentiation of Sine Function : Product Rule
- Differentiation of Sine Function : Quotient Rule
- Differentiation of Cosine Function : Chain Rule
- Differentiation of Cosine Function : Product Rule
- Differentiation of Cosine Function : Quotient Rule
- Differentiation of Tangent Function

#### Calculus > Integration Rules

- Using Chain Rule
- Using Derivative of Exponential Functions
- Using Derivative of SINE function
- Using Derivative of COSINE function
- Using Derivative of TANGENT function
- Using Derivative of Logarithmic function
- Using Product Rule
- Using Long Division
- Integration of Logarithmic Functions
- Integration of the Exponential Function