IB Mathematics AA

Introduction

IB Math 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 mathematical rigour. Students should wherever possible apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context. The majority of students will expect to need a sound mathematical background as they prepare for future studies in subjects such as Physics, Chemistry, Analytics, Economics and Business Administration,…

Objectives

Systematize the core knowledge of the subject

Become familiar with most IB exam formats

Reduce pressure and study time

Improve scores effectively

Enhance independant thinking

Create a solid foundation for higher education

Characteristics

Quality teachers with extensive knowledge about students psychology

Teaching programs are based on international standards

Exclusive materials that closely follow the IB formats

Personalized teaching method according to student progress

Commitment on IB pass grade

EE, IA, TOK completion support

Course content

Topic 1: From patterns to generalizations: sequences, series and proof

1.1 Sequences, series and sigma notation

1.2 Arithmetic and geometric sequences and series

1.3 Proof

1.4 Counting principles and the binomial theorem

Topic 2: Representing relationships: functions

2.1 Functional relationships

2.2 Special functions and their graphs

2.3 Classification of functions

2.4 Operations with functions

2.5 Function transformations

Topic 3: Expanding the number system: complex numbers

3.1 Quadratic equations and Inequalities

3.2 Complex numbers

3.3 Polynomial equations and Inequalities

3.4 The fundamental theorem of algebra

3.5 Solving equations and inequalities

3.6 Solving systems of linear equations

Topic 4: Measuring change: differentiation

4.1 Limits, continuity and convergence

4.2 The derivative of a function

4.3 Differentiation rules

4.4 Graphical interpretation of the derivatives

4.5 Applications of differential Calculus

4.6 Implicit differentiation and related rates

Topic 5: Analysing data and quantifying randomness: statistics and probability

5.1 Sampling

5.2 Descriptive statistics

5.3 The justification of statistical techniques

5.4 Correlation, causation and linear regression

Topic 6: Relationships in space: geometry and trigonometry.

6.1 The properties of three-dimensional space

6.2 Angles of measure

6.3 Ratios and identities

6.4 Trigonometric functions

6.5 Trigonometric equations

Topic 7: Generalizing relationships: exponents, logarithms and integration

7.1 Integration as antidifferentiation and definite integrals

7.2 Exponents and logarithms

7.3 Derivatives of exponential and logarithmic functions; tangents and normals

7.4 Integration techniques

Topic 8: Modelling change: more calculus

8.1 Areas and volumes

8.2 Kinematics

8.3 Ordinary differential equations (ODES)

8.4 Limits revisited

9 Modelling 3D space: Vectors

9.1 Geometrical representation of Vectors

9.2 Introduction to vector algebra

9.3 Scalar product and its properties

9.4 Vector equation of a line

9.5 Vector product and properties

9.6 Vector equation of a plane

9.7 Lines, planes and angles

9.8 Application of vectors

Topic 10: Equivalent systems of representation: more complex numbers

10.1 Forms of a complex number

10.2 Operations with complex numbers in polar form

10.3 Powers and roots of complex numbers in polar form

Topic 11: Valid comparisons and informed decisions: probability distributions

11.1 Axiomatic probability systems

11.2 Probability distributions

11.3 Continuous random variables

11.4 Binomial distribution

11.5 The normal distribution

Topic 12: Exploration

12.1 Practice exam paper 1

12.2 Practice exam paper 2

12.3 Practice exam paper 3

Choose a form of study

Small class

Private tutoring group

1 plus 1

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