IBDP Mathematics (AA) : Analysis and Approaches (HL/SL)

The Mathematics: Analysis and Approaches course is designed for students who wish to study mathematics as a subject in its own right or to pursue their interests in areas related to mathematics. It appeals to students who are interested in exploring real and abstract applications of mathematical concepts. There is a strong emphasis on calculus and on algebraic, graphical and numerical approaches. In this course, students will develop strong skills in mathematical thinking and become fluent in the construction of mathematical arguments.

Source: IB Mathematics Analysis and Approaches Guide (AA) 2019

Source: IB Mathematics Analysis and Approaches Guide (AA) 2019

## MODULES : View - Register - Learn

In this module, the students extensively learn about operations with numbers. Modelling real-life situations with the structure of arithmetic and geometric sequences and series allows for prediction, analysis and interpretation. Students gain in-depth knowledge of mathematical financial models such as compounded growth and investments. Students benefit from learning deeper insights to do well in three exam papers.

**Prior Learning: **Students are expected to be well versed with the concepts of arithmetic and geometric sequences: understanding of the difference between both the sequences.

**Technology: **TI-nspire software

**Content:**

- Operation with Numbers
- Arithmetic sequences and series- Use of the formulae for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for sums of arithmetic sequences. Applications on Arithmetic sequences and modelling real life problems
- Geometric sequences-Use of nth term and sum of the first n terms of the sequence. Use sigma notation for the sums of geometric sequences. Applications
- Financial applications based on sequences
- Sum of infinite convergent geometric sequences

**Duration of the module: **6 Hours (Three sessions of 2 hours each)**Fee: **SGD 240/-**Module Code: **IBMAAM1**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn the operations on Exponents and logarithms, Approximations and Bounded numbers. Students learn amortization and annuities using technology. The concept of the system of linear equations in three variables and Polynomials are dealt in detail. This module benefits the student to do well in the three exam papers.

**Prior Learning: **Students are expected to be well versed with the concepts of basic exponent and logarithm

**Technology: **TI-nspire software

**Content:**

- Laws of exponents with integer exponents and logarithms with base 10 and e- Numerical evaluation, solving exponential equations including using logarithms.
- Simple deductive proofs
- The binomial theorem.

**Duration of the module: **6 Hours (Three sessions 2 hours each)**Fee: **SGD 240/**–**

**Module Code:**IBMAAM2

**Mode of Teaching:**Online

**How to enrol:**Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students will be introduced to a very important concept of complex numbers and its properties. Students learn the different ways of representing the data. Students learn De Moivre’s theorem. This module helps the students attempt and do well in three exam papers.

**Prior Learning: **. Students are expected to be well versed with the concepts of Number system,basic geometry

**Technology: **TI-nspire software

**Content:**

Complex Numbers-Modulus-argument form,quadratic and polynomial equations with real coefficients, De Moivre’s theorem, Powers and roots of Complex numbers

**Duration of the module: **8 Hours (Four sessions of 2 hours each)**Fee: **SGD 320/-**Module Code: **IBMAAM3**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn the concepts of counting principles, partial fractions and mathematical proofs. Students develop logical ability to learn and solve permutations and combinations concepts. Students learn binomial theorem and its applications. This module helps the students to do well in the three exam papers.

**Prior Learning: **Students are expected to be well versed with the concepts of basic arithmetic skills

**Content:**

- Counting principles, including permutations and combinations, extension of the binomial theorem to fractional and negative indices
- Partial fractions
- Proof by Mathematical Induction, contradiction and Counter example

**Duration of the module: **4 Hours (Two sessions of 2 hours each)**Fee: **SGD 160/-**Module Code: **IBMAAM4**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn to model real-life events using functions. The students get a clear understanding of how to move from different forms of functions. Students gain a clear insight on function and its inverse and the key features of a graph. This module is very essential to have a successful attempt the three exam papers.

**Prior Learning: **Students are expected to be well versed with forming an equation and solving for the variable. Students also need to have an idea of domain and range.

**Technology: **TI- Nspire

**Content:**

- Lines with gradients: Parallel and Perpendicular lines
- Concept of function and its inverse – Domain, Range and graph
- Inverse Functions
- Sketching graphs and interpreting the key features of the graph.
- Using technology to find: Point of Intersection, Zeros and sums and differences.
- The graph of the function and its key features.
- Composite functions.

**Duration of the module: **6 Hours (Three sessions of 2 hours each)**Fee: **SGD 240/-**Module Code: **IBMAAM5**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn to model real-life events using different functions. The students learn to model various functions: Linear, Quadratic, Cubic, Exponential growth and decay models, Direct and inverse variation and Sinusoidal Models. This module help the students to determine the suitable models in varied contexts and it helps to do well in the three exam papers and IA.

**Prior Learning: **Students are expected to be well versed with forming an equation and solving for the variable. Students also need to have an idea of domain and range.

**Technology: **TI- Nspire

**Content:**

- Solutions of Quadratic equations and inequations
- Reciprocal functions and their graphs
- Exponential functions , Logarithmic functions and their graphs
- Solving equations analytically and graphically
- Transformations of graphs

**Duration of the module: **8 Hours (Four sessions of 2 hours each)**Fee: **SGD 320/-**Module Code: **IBMAAM6**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn polynomial functions and solutions by algebraic and graphical methods. Students learn remainder and factor theorems Students also learn the inequality of functions and their solutions. This module helps the students to do well in the three three papers and IA.

**Prior Learning: **Students are expected to be well versed with linear, quadratic, cubic and exponential models

**Technology: **TI- Nspire

**Content:**

- Polynomial functions-Solving by graphical method
- Remainder and Factor theorems
- Rational functions in different forms
- Solutions of inequality functions
- Modulus functions

**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee: **SGD 400/-**Module Code: **IBMAAM7**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students explore three dimensional geometry. Students explore trigonometric rules- sine, cosine, tangent and its inverse. They also learn circular trigonometry and its applications. This module helps the students to do well in the three exam papers.

**Prior Learning: **Students should be familiar with the introduction to trigonometry and the unit circle

**Technology: **TI nspire calculator

**Content:**

- Three dimensional geometry
- Volume and surface area, size of an angle between two intersecting lines or between a line and a plane
- Using sine, cosine and tangent ratios in the right angled triangle, sine and cosine rules
- Non right triangle applications, angle of elevation and depression
- Length of an arc, area of sector

**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee: **SGD 400/-**Module Code: **IBMAAM8**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students explore trigonometric ratios – Sine, Cosine and Tangent. Students also learn pythagorean identities and composite functions and its transformations.This module is very integral to do well in the three exam papers and IA.

**Prior Learning:** Students should be familiar with the introduction to trigonometry and the unit circle

**Technology: **TI- Nspire

**Content:**

- Trigonometric ratios
- Pythagorean Identities, Graph of trigonometric functions.
- Transformation, Real-life contexts.
- Solving trigonometric equations.

**Duration of the module: **12 (Six sessions of two hours each)**Fee: **SGD 480/-**Module Code: **IBMAAM9**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn about trigonometric ratios ( inverse . Students will explore the compound angles and its applications in a variety of contexts. Students also explore and learn double angle identity and its use. This module helps the students to do well the three exam papers.

**Prior Learning: **Students should be familiar with angle measurement in degrees. Compass directions and three figure bearings. Right-angle trigonometry. Simple applications for solving triangles. Pythagoras’ theorem and its converse.

**Technology: **TI nspire calculator

**Content:**

- Reciprocal Trigonometric ratios, pythagorean identities, Compound angles
- Double angles
- Properties of Trigonometric graphs

**Duration of the module: **8 Hours (Four sessions of 2 hours each)**Fee: **SGD 320/-**Module Code: **IBMAAM10**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, students learn and explore a very important and integral concept of vectors. The students also learn vector rules, angles between two lines, writing vector equations and applications to kinematics. This module helps the students to do well in the three exam papers.

**Prior Learning: **Basic algebra,arithmetic, coordinate geometry skills

**Technology: **TI nspire CX calculator

**Content: **

- Introduction to Vectors
- Scalar product of two vectors
- Vector equation of line, Angle between to two lines and applications connected with Kinematics, Skew lines, Cross product of vectors, Geometric interpretation
- Vector equation of plane, intersection of line and plane, angle between line and plane, angle between two planes.

**Duration of the module: **16 Hours (Eight sessions of 2 hour each)**Fee: **SGD 640/-**Module Code: **IBMAAM11**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn about the data collection, various data display methods with justifications. Students will be able to explore the various forms: Pictograms and pie charts. This module helps the students understand the basic concepts to explore this unit and attempt the possible questions all the three exam papers.

**Prior Learning: Descriptive statistics: **collection of raw data; display of data in pictorial and diagrammatic forms, including pie charts, pictograms, stem and leaf diagrams, bar graphs and line graphs. Obtaining simple statistics from discrete and continuous data, including mean, median, mode, quartiles, range, interquartile range.

**Technology: **Ti Nspire CX

**Content: **

- Population,Sample, discrete and continuous data
- Sampling techniques and their effectiveness
- Histogram and Box-whisker diagrams.
- Measures of central tendencies
- Linear correlation
- Pearson’s product-moment correlation coefficient
- Regression lines

**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee: **SGD 400/-**Module Code: **IBMAAM12**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn and gain depth understanding of distributions – Binomial and Normal and its curves. Students use technology to determine the properties and applications of the curves. They also learn about inverse normal calculations as well. This module helps the students to do well in the three exam papers and IA.

**Prior Learning: **Calculating probabilities of simple events

**Technology: ** Ti Nspire CX

**Content: **

- Probability introduction
- Representation of probability
- Conditional probability
- Discrete random variables
- Binomial distribution
- Normal distribution

**Duration of the module: **16 Hours ( Eight sessions of 2 hours each)**Fee: **SGD 640/-**Module Code: **IBMAAM13**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn about the very important baye’s theorem, random variables and its classification. Students also explore discrete and random variables. This module helps the students in gaining the most marks under this section in the three exam the papers and IA.

**Prior Learning: **Calculating probabilities of simple event, conditional probability, total probability theorem

**Technology: **Ti Nspire CX

**Content: **

- Use of Bayes’ theorem for a maximum of three events
- Variance of a discrete random variable.
- Mode and Median of continuous random variable.
- Mean,Variance and Standard deviation for both discrete and continuous random variables.
- The effect of linear transformations.

**Duration of the module: **8 Hours ( Four sessions of 2 hours each)**Fee: **SGD 320/-**Module Code: **IBMAAM14**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students learn the differentiation in extension required for the HL and SL course. Students learn derivatives and second derivatives to distinguish between maximum and minimum points. They also explore definite and indefinite integration and area of region and optimisation. They also engage to solve kinematics problems. This module helps the students to do well in the three exam papers and specially IA.

**Prior Learning: **Functions, Algebra, Trigonometry** **

**Technology: **Ti Nspire CX

**Content: **

- Concept of limit
- Concept of Differentiation
- Increasing and Decreasing functions
- Derivatives of the functions
- Tangents and Normals
- Anti differentiation
- Definite Integration using technology
- Chain rule
- Product and Quotient rules
- Second derivative
- Local Maximum and Local Minimum, Optimisation, Point of Inflexion
- Kinematics
- Indefinite Integration
- Definite Integration with analytical approach
- Area under curve and Area between curves

**Duration of the module: **20 Hours (Ten sessions of 2 hours each)**Fee: **SGD 800/-**Module Code: **IBMAAM15**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the students will be learning the differentiation in extension required for the HL course. Students also learn derivatives and second derivatives to distinguish between maximum and minimum points. Students explore definite and indefinite integration and area of region and volume of revolution. They also engage in solving kinematics problems. This module helps the students to do well in the three exam papers and specially IA.

**Prior Learning: **Functions, Algebra, Trigonometry

**Technology: **Ti Nspire CX

**Content: **

- Continuity and Differentiability
- First principle of differentiation
- Higher derivatives
- l’Hospital rule
- Implicit differentiation
- Related rate of change
- Optimization
- Differentiation of Trigonometric functions
- Indefinite Integrals
- Partial fractions to rearrange the integrand
- Integration by substitution
- Integration by parts
- Area and Volume.
- Differential equations
- Maclaurin series

**Duration of the module: **30 Hours (Fifteen sessions of 2 hours each)**Fee: **SGD 1200/-**Module Code: **IBMAAM16**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details** CLICK HERE**

In this module, the student will be provided with a differentiated set of Paper-1 style model paper. They develop skills needed to solve this paper which will be observed and helped to develop the student’s abilities. Time management and organisational skills are focused to develop a comfortable approach to successfully attempt the Paper 1.

**Content:**

- Unit – Number & Algebra
- Unit – Functions
- Unit – Geometry & Mensuration
- Unit – Statistics & Probability
- Unit – calculus

**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee: **SGD 400/-**Module Code: **IBMAAM17**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the student will be provided with a differentiated set of Paper-2 style model paper. They improve skills needed to solve this paper, which will be observed and helped to develop the student’s potential. Time management, technology and organisational skills are focused to develop a comfortable approach to successfully attempt the Paper 2.

**Technology : **TI nspire Calculator

**Content:**

- Unit – Number & Algebra
- Unit – Functions
- Unit – Geometry & Mensuration
- Unit – Statistics & Probability
- Unit – calculus

**Duration of the module: **10 Hours (Five sessions of 2 hours each )**Fee: **SGD 400/-**Module Code: **IBMAAM18**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the student will be provided with a differentiated set of Paper-3 style model paper. They improve skills needed to solve this paper, which will be observed and helped to develop the student’s potential. Time management, technology and organisational skills are focused to develop a comfortable approach to successfully attempt the Paper 3.

**Technology : **TI nspire Calculator

**Content:**

- Unit – Number & Algebra
- Unit – Functions
- Unit – Geometry & Mensuration
- Unit – Statistics & Probability
- Unit – calculus

**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee: **SGD 400/-**Module Code: **IBMAAM19**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE

In this module, the student need to come up with a streamlined IA topic. This module helps the student to progress with the topic and involve all the criteria. The students draft a short report based on a topic chosen and focuses on mathematical connections and concepts.

**Technology : **TI nspire Calculator**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee:** SGD 400/-**Module Code: **IBMAAM20**Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details CLICK HERE