IBDP Mathematics: Analysis and Approaches Higher Level (AAHL)
- Description
- Curriculum
Course description
Mathematics AAHL is a rigorous course designed for students who enjoy Mathematics as it is. It has a nice blend of Pure and Applied Mathematical aspects that include Abstract concepts, Mathematical Proving techniques, Problem solving and Applications into real life situations.
Calculus and its applications and along with Probability calculations require fair use of technology. Students are expected to have strong conceptual understanding and apply the concepts and techniques in unfamiliar contexts.
This course is ideal for students who aim to enroll in Higher Mathematics learning, Engineering courses, Computer Science courses including Machine learning and AI, Some Business and Economics courses. This IB Math course is taught by our experienced teachers in a lively manner through a variety of activities and enrichment tasks that enlighten the young minds and kindle their interest.
Our Approach to Teaching and Learning:
We follow the 5-step process depicted in the picture below.
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1
Number and Algebra- Arithmetic and geometric sequence and series and their applications
- Logarithms
- Mathematical Proofs
- Binomial Theorem
- Counting Principles (Permutation and Combination)
- Partial fractions
- Complex Numbers
- System of linear equations
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2
Functions
- Equation of straight lines, parallel and perpendicular lines
- Function definition and notation
- Domain and Range of functions
- Composition and Inverse functions
- Sketching graphs of functions and determining its key features
- Quadratic functions and its nature of solutions
- Reciprocal and Rational functions
- Asymptotes
- Exponential and Logarithmic functions
- Transformations of functions (or graphs)
- Sum and product of roots of polynomial equations
- Solving inequalities using technology (GDC)
- Absolute function and modulus equations and inequations
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3
Geometry and Trigonometry
- 3D mensuration
- Sine rule, cosine rule and area of a triangle (non-right angled)
- Angle of elevation and depression and its applications
- Bearings
- Circular Measure - Radians, length of arc and area of sector
- Unit circle
- Solving trigonometric equations - linear and quadratic
- Trigonometric identities - double angle and compound angle
- Trigonometric functions and their graphs
- Transformations
- Applications of trigonometry in real world situations
- Reciprocal and inverse trigonometric functions
- Vector Algebra - lines and planes
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4
Statistics and Probability
- Sampling techniques
- Data types and their representations - Cumulative frequency & Box and whisker diagrams
- Measures of central tendency - Mean, Median and Mode
- Measures of spread - Range, Variance/Standard deviation and IQR
- Linear correlation - Bivariate Analysis
- Scatter diagrams
- Pearson Correlation coefficient
- Line of best fit and regression line
- Essentials in Probability and Baye’s Theorem
- Probability calculations in Venn diagrams, Tree diagrams and Two way tables
- Conditional Probability
- Discrete Random Variable and its Expectation/ Mean and Variance
- Binomial Distribution
- Continuous Random Variable and its Mean, Median and Variance
- Normal Distribution
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5
Calculus
- Concept of limit
- Derivative as a gradient function or as a rate of change
- Derivatives from First principles
- Increasing and Decreasing behavior of functions
- Equation of tangents and normals
- Chain rule, product rule and quotient rule
- Implicit Differentiation
- Higher derivatives
- Integration as Ant-differentiation - Indefinite integrals
- Integration as Area under curve - Definite integrals
- Integration by substitution, by parts and by partial fractions
- Area between curves
- Volume of solid of revolution and volume between curves
- First order Differential Equations
- Variables separable method of solving Differential Equations
- Homogeneous Differential Equations
- Solving Linear Differential Equations using Integrating Factor method
- Numerical solutions to Differential Equations by Euler’s Method
- Maclaurin series and its connection to Differential Equations
- L’Hopital’s Rule
- Optimization using Calculus
- Kinematics
- Related rates of change
