Professional Mathematics teacher for all grades / levels , IGCSE and IB. A-level and AP. Excellent exam preparations, mock exams and past papers practice. Experience in teaching the following:
British Curriculum (Edexcel, Cambridge and AQA):
- IGCSE
- AS & A-level:
C1, C2, C3, C4, M1 & M2, S1 & S2
IB:
- Standard level
- Advanced level
American curriculum:
- Middle Years Program (MYP) year 6-10
- Diploma Program (DP) year 11-12
- Advanced Placement (AP)
My teaching experience include, but not limited to, the following topics:
1. FUNCTIONS
1.1 The domain and range of a relation on a Cartesian plane
1.2 Function notation
1.3 Composite functions
1.4 Inverse functions
1.5 Inverse trig functions
1.6 Transforming functions
1.7 Periodic functions
1.7 Modulus function
2. LINEAR ALGEBRA
2.1 Simultaneous equations
2.2 Solving quadratics and completing the squares
2.3 Surds / Indices
2.4 Inequalities
2.5 Polynomials (factor / remainder theorems)
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2.6 Binomial expansion
2.7 Partial fractions
2.8 Solving linear systems using Gaussian elimination
2.9 Gauss-Jordan row reduction and reduced row echelon form
2.10 Equivalent systems, rank, and row space
2.11 Determinants and row reduction
2.12 Eigen values and diagonalization
3. TRIGONOMETRY
3.1 Sine rule
3.2 Cosine rule
3.3 Radians
3.4 Arc length and sector
3.5 Exact values of Sin
3.6 Cosine and tan of standard angles
3.7 Sec, Cosec, Cot, Sin, Cos and Tan
3.8 Compound /double angle formulae
4. EXPONENTIAL & LOGARITHMIC FUNCTIONS
4.1 Exponents
4.2 Solving exponential equations
4.3 Exponential functions
4.4 Properties of logarithms
4.5 Laws of logarithms
4.6 Exponential and logarithmic equations
4.7 Application of exponential and logarithmic functions
5. CURVE SKETCHING
5.1 Graphs of quadratics
5.2 Polynomials (from the factorized form)
5.3 Relationships between Graphs of y = f (x), y = f (x + a) and y = f (ax)
6. SEQUENCES & SERIES
6.1 Arithmetic sequences
6.2 Geometric sequences
6.3 Series
6.4 Sigma notation
6.5 Sequences
6.6 Defined recursively
7. COORDINATE GEOMETRY
7.1 Equations of straight lines
7.2 Gradient
7.3 Parallel and perpendicular lines
7.4 Equation of a circle
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7.5 Circle theorems
8. PARAMETRIC EQUATIONS
8.1 Finding gradients
8.2 Conversion from Cartesian to parametric equations
9. CALCULUS I and II
9.1 Differentiation of powers of x, e(x), ln(x), sin(x), cos(x) and tan(x)
9.2 Product rule and quotient rule
9.3 Chain rule
9.4 Trapezium rule
9.5 Differential equations
9.6 Implicit differentiation
9.7 Sequences of real numbers
9.8 Convergent and divergent sequences
9.9 Tests for convergence (ratio, root, and comparison tests)
10. VECTORS
10.1 Dot product
10.2 Cross product
10.3 Scalar product
10.4 Equations of lines
10.5 Intersection of lines
10.6 Multiplication of matrices
11. NUMERICAL METHODS
11.1 Roots by sign change
11.2 Fixed point iteration
12. COMPLEX NUMBER
12.1 Definitions
12.2 Basic arithmetic
12.3 Argand diagram
12.4 Polynomial equations with complex roots
12.5 Polar form
12.6 Exponential notation
12.7 Roots of complex numbers
13. MATRICES
13.1 Definitions
13.2 Basic arithmetic
13.3 Fundamental operations with matrices
13.4 Matrices as linear transformation
13.5 Composition
13.6 Determinant
13.7 Inverse
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13.8 Use in solving linear simultaneous equations
13.9 Equations of planes and geometric interpretation
13.10 Characteristic polynomial
13.11 Transpose of matrices
14. DESCRIPTIVE STATISTICS
14.1 Univariate analysis
14.2 Presenting data
14.3 Measures of central tendency
14.4 Measures of dispersion
14.5 Cumulative frequency
14.6 variance and standard deviation
15. PROBABILITY DISTRIBUTION
15.1 Random variable
15.2 The binomial distribution
15.3 The normal distribution
16. BIVARIATE ANALYSIS
16.1 Scatter diagrams
16.2 The line of best fit
16.3 Least squares regression
16.4 Measuring correlation
17. INTEGRATION
17.1 Antiderivatives and the indefinite integration
17.2 Area and indefinite integration
17.3 Integration by inspection
17.4 Integration by trigonometric substitution
17.5 Integration by parts
17.6 Fundamental theorem of calculus
17.7 Area between two curves
17.8 Volume of revolution
17.9 Definite integration with linear motion
17.10 Integration using trigonometric functions
17.11 Integration of improper integrals
17.12 Integration of average value of a function
17.13 Integration to find length of a curve
17.14 Double and triple integrals in rectangular and polar coordinates
18. ENGINEERING MATHEMATICS
18.1 Arrange and separate first order and second order differential equations
18.2 Laplace equation
18.3 Laplace transformation
18.4 Find general solution of partial differential equations