AMPERAVON INSTITUTE FOR MATHEMATICS 26.04.2017
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Teaching Curriculum (subjects), School Algebra, Matrices, Tensors. School Geometry, Statistics, Probability Theory/ Statistics, Analytical Geometry/ Vector Analysis, Differential Equations, Integral Equations, Complex Numbers, Spherical Geometry, Functions of a complex variable, Theory of Functions, Set theory, Calculus, Group theory, functional analysis, quaternions.
International Baccalaureate Mathematics HL/SL/MS. 26.04.2017
1. Functions 2. Sequences and Series 3. Exponents 4. Logarithms 5. Natural Logarithms 6. Graphing and Transforming functions 7. Quadratic equations and functions 8. Complex numbers and Polynomials 9. Trigonometry 10. General Triangles 11. Periodic functions 12. Counting and Binomial Theorems 13. Mathematical Induction 14. Matrices 15. Vectors in 2 and 3 Dimensions 16. Complex numbers 2. 17. Lines and Planes in Space, 18. Statistics 19. Probability 20. Calculus 1 21. Differential Calculus 22. Applications of Differential Calculus. 23. Derivatives of logarithmic and exponential functions. 24. Derivatives of circular and hyperbolic functions. 25. Integration of functions. 26. Applications of integration, calculation of areas and volumes. 27. Integration of circular functions. 28. Further integration methods and differential equations. 29. Statistical distributions, Binomial, Poisson, and Normal distributions.
IB Syllabus Mathematics SL, 2015.
1. Functions. Domain and range of relations, Composite and inverse functions, Transforming functions.
2. Quadratic functions and solution of quadratic equations. Applications.
3. Probability. Venn diagrams, conditional probability, tree diagrams and applications.
4. Properties and laws of exponential and logarithmic functions. Solution of exponential and logarithmic equations. Applications.
5. Rational functions, reciprocal functions.
6. Patterns and sequences, geometric, arithmetic sequences and series. Convergent sequences and their sum. Applications, Pascal's triangle and binomial expansion. Sum notation and series.
7. Limits, convergence and derivatives. Rules of differentiation. Product chain and quotient rules. Higher order derivatives. Graphs and derivatives. Extrema and opimization problems. Graphs of f(x), f'(x), and f''(x). Maximum, minima, and points of inflection, f''(x) = 0. Motion on a straight line. Applications.
8. Discriptive statistics. Univariate analysis. Presenting data. Measures of central tendency, dispersion. Cumulative frequency. Variance, standard deviation, mean values.
9. Integration. Inverse derivatives, indefinite integrals. Areas and definite integrals. Fundamental theorem of calculus. Area between two curves. Volume of revolution. Definite integrals and linear motion.
10. Bivariate analysis. scatter diagrams, line of best fit. Least squares regression and correlation .
11. Right angled triangles, sine, cos and tan functions. Applications. General triangles, sine and cosine rules.
Area of triangles. Circles, sectors, arcs and radians.
12. Basic concepts of vectors. Addition and subtraction of vectors. Scalar products. Vector equation of a line.
14. Derivatives of trigonometric functions. Problems involving derivatives. Integration of sine and cosine functions. Linear motion on a line revisited.
15. Probability distributions, binomial and normal distributions. Random variables.
16. Graphic display calculations. Functions, differential and integral calculus. Vectors, statistics and probability calculations.
HL Syllabus 2015. Only topics that are additional to SL topics will be listed.
1. Algebra: Logarithms, change of base. Counting principles, including permutations and combinations. The binomial theorem and expansion of (a + b) to the power n (integer). Circular arrangements. Proof of binomial theorem.
Proof by mathematical induction. Complex numbers, a +ib, sums, products and quotients thereof. Real, imaginary parts, conjugate, modulus and argument. Polar form. The complex plane. Powers of complex numbers. De Moivre's theorem. nth roots of complex numbers. Conjugate roots of polynomial equations with real coefficients. Solutions of linear equations with 3 equations and 3 unknowns.
2. Functions and equations. Rational functions y= (ax + b) / (cx + d). Functions y = a to the power x, y = log(base a) (x).
3. cos, sin, tan, sec, csc, and cot. Compound angle identities. Double angle identities. Pythagoras identities.
4. Vectors. 3-dimensional vectors. The vector product of two vectors and its properties. Vector equation of a plane. Normal form equation of a plane and the cartesian equation of a plane.
5. Statistics and Probability. Conditional probability. Independent events, P(A/B) = P(A) = P(A/B').
P(A geschnitten mit B) = P(A)xP(B) shows independence. Use of Bayes' theorem for a maximum of three events.
Poisson distribution, its mean and variance.
6. Calculus. Implicit differentiation. Derivatives of sec(x), csc(x), cot(x), a to the power x, log(base a) (x),
arcsin x, arccos x, arctan x. Kinematic problems. Integration by substitution. Integration by parts.
Options. These are only for HL.
7. Option Statistics and probability.
8. Option. Sets relations and groups.
9. Option. Calculus.
10. Option. Discrete mathematics.