Math AI HL All Topics

Topic 1 All

Read All Questions Under Topic 1. Number & Algebra

Topic 1.1

1.1 Approximation and scientific notation.

Topic 1.2

1.2.1 Arithmetic Sequence/series.
1.2.2 Arithmetic Sequence/series-Sigma Notation/Applications/ including approximate difference.

Topic 1.3

1.3.1 Geometric Sequence/Series.
1.3.2 Geometric Sequence/series-Applications.

Topic 1.4

1.4 Compound Interest/Annual depreciation
1.4* Arithmetic and Geometric Sequence/series.

Topic 1.5

1.5 Laws of Exponents with integer exponents.
1.5* Introduction to logarithms–base 10 and e.

Topic 1.6 & 1.7

1.6 Approximations/Estimations/Lower and Upper bounds.
1.7 Amortization and Annuities using technology

Topic 1.8 & 1.9

1.8 Use of technology to solving systems of linear equations/polynomials.
1.9 Laws of Logarithms.

Topic 1.10 & 1.11

1.10 Expressions involving rational exponents.
1.11 Sum of infinite Geometric sequence

Topic 1.12 & 1.13

1.12 Complex numbers_Catersian form.
1.13 Complex numbers_Polar form.

Topic 1.14 & 1.15

1.14 Matrices and Matrix Algebra.
1.15 Eigenvalues/eigenvectors/Diagonalization of 2×2 matrices.

Concept Quiz 1
Test 1 HL –No Calculator.
Test 2 HL –Calculator.
Test 3 HL –No Calculator.
Test 4 HL –Calculator

Topic 2

Functions

Topic 2 All

Read All Questions Under Topic 2. Functions

Topic 2.1, 2.3 & 2.3

2.1 Linear functions.
2.2 Concepts of functions.
2.3 graph of functions

Topic 2.4

2.4 Analytic properties of graphs of functions (Using the GDC calculator).
2.4 Composition and inverse functions

Topic 2.5, 2.6 & 2.7

2.5 Models.
2.6 Modelling/Parameters/validity/Reliability.
2.7 Composition of functions/Inverse

Topic 2.8, 2.9 & 2.10

2.8 Transformation of functions.
2.9 Further models.
2.10 Log transforms and scaling.

Concept Quiz 2
Test 1 HL –No Calculator.
Test 2 HL –Calculator.
Test 3 HL –No Calculator.
Test 4 HL –Calculator

Topic 3

Geometry and trigonometry

Topic 3 All

Read All Questions Under Topic 3. Geometry and trigonometry

Topic 3.1

3.1.1 Coordinate geometry.
3.1.2 Right angled trigonometry_SOH CAH TOA.
3.1.3 3D Analysis. Volume and surface area of solids

Topic 3.2 & 3.3

3.2.2 Non-Right angled trigonometry_Sine and Cosine Rule.
3.3 Applications of Basic Trigonometry. (elevations, bearings and 3D trig)

Topic 3.4 & 3.5

3.4 Circles, sector, segment and arc-length.
3.5 Equation of perpendicular bisectors.

Topic 3.6 & 3.7

3.6 Voronoi Diagram
3.7 : Radian measure of angle, area of sector, arc-length.

Topic 3.8

3.8 Unit Circle and Graphs of basic trigonometric functions.
3.8.2 Graphical methods for solving trig equations.
3.8.3 Applications of trig functions and Ferris Wheel

Topic 3.9 & 3.10

3.9 Matrix transformation.
3.10.1 Vectors (definition and forms)
3.10.2 Position vectors. Properties of vectors. HL

Topic 3.11 & 3.12

3.11 Vector equation of a line in 2D and 3D.
3.12 Vector application to Kinematics

Topic 3.13

3.13.1 Scalar dot products. Angle between two vectors.
3.13.2 Cross product. Area of a parallelogram.

Topic 3.14, 3.15 & 3.16

3.14 Graph theory.
3.15 Adjacency matrices etc.
3.16 Trees and cycle algorithm with undirected graphs.

Concept Quiz 3
Test 1 HL –No Calculator.
Test 2 HL –Calculator.
Test 3 HL –No Calculator.
Test 4 HL –Calculator

Topic 4

Statistics and probability

Topic 4 All

Read All Questions Under Topic 4. Statistics and probability

Topic 4.1, 4.2 & 4.3

4.1 Terminologies and sampling.
4.2. Data handling and presentation.
4.3 Central measures and dispersion

Topic 4.4 & 4.5

4.4 Linear correlation and regression
4.5 Definition of probability

Topic 4.6

4.6 Venn diagram and combined events.
4.6.2 Conditional probabilities and tree diagram

Topic 4.7 & 4.8

4.7 Probability distribution of a discrete random variable.
4.8 Binomial distribution.

Topic 4.9 & 4.10

4.9.1 Normal distribution
4.9.2 Inverse normal distribution.
4.10 Spearman’s rank correlation coefficient.

Topic 4.11

4.11.1 Chi-square test of independence.
4.11.2 Chi-square goodness of fit test
4.11.3 t-test

Topic 4.12 & 4.13

4.12 Design of data collection. Validity and reliability.
4.13 Nonlinear regression. R-squared

Topic 4.14 & 4.15

4.14 Linear transformation of a single random variable.
4.15 Sampling distribution of the mean/Central limit theorem.

Topic 4.16 & 4.17

4.16 Confidence Interval for the mean of normal population.
4.17 Poisson Distribution.

Topic 4.18 & 4.19

4.18 Test of population parameters.
4.19 Transition matrices/ Markov chains

Concept Quiz 4
Test 1 HL –No Calculator.
Test 2 HL –Calculator.
Test 3 HL –No Calculator.
Test 4 HL –Calculator

Topic 5

Calculus