Week Syllabus of tutorial
-----------------------------------------------------------------------------1. Sets (integers, whole numbers, rational and irrational numbers, real numbers), intervals, operations on intervals (intersection, union, complement,…), neighbourhood of a point, absolute value.
2. Functions of one real variable (definition, domain, range, graph,…) Operations on functions (sum, difference, product, quotient), composite functions, properties of functions (even and odd functions, monotonic functions, bounded functions), one-to-one and inverse functions.
3. Elementary functions (linear, quadratic, rational and algebraic functions, exponential and logarithmic functions) and their properties. Drawing a sketch of the graph, graphs containing an absolute value.
4. Sine and Cosine functions, trigonometric functions. Definition by means of unit circle, values in radian measure, graphs, goniometric identities.
5. Test 1 (examining time: 20-30 minutes). Rational expressions: polynomials, fractions, exponents and roots.
6. Rational expressions: polynomials, fractions, exponents and roots.
7. Algebraic equations: linear equations (possibly with a parameter), quadratic equations (solutions in real numbers and in the complex plane), irrational equations.
8. Systems of two linear (and non-linear) equations in two unknowns. Linear inequalities (solutions by null point method), system of linear inequalities
9. The Exponential and logarithmic equations (inequalities respectively), properties of logarithms. Inverse functions.
10. Test 2 (examining time:20- 30 minutes). Domains of more complicated functions.
11. Analytic geometry in a geometric plane: point, vector, line (equations and a graph), circle (equations, determining its centre and radius).
12. The conic sections: the ellipse, the hyperbola (as a graph of a linear rational function), the parabola (as a graph of a quadratic function). Properties of conics.
13. Tangents to conic sections. Finding common points of a line and a conic. Test 3 (examining time: 20-30 minutes).
14. Reserve.
---
-----------------------------------------------------------------------------1. Sets (integers, whole numbers, rational and irrational numbers, real numbers), intervals, operations on intervals (intersection, union, complement,…), neighbourhood of a point, absolute value.
2. Functions of one real variable (definition, domain, range, graph,…) Operations on functions (sum, difference, product, quotient), composite functions, properties of functions (even and odd functions, monotonic functions, bounded functions), one-to-one and inverse functions.
3. Elementary functions (linear, quadratic, rational and algebraic functions, exponential and logarithmic functions) and their properties. Drawing a sketch of the graph, graphs containing an absolute value.
4. Sine and Cosine functions, trigonometric functions. Definition by means of unit circle, values in radian measure, graphs, goniometric identities.
5. Test 1 (examining time: 20-30 minutes). Rational expressions: polynomials, fractions, exponents and roots.
6. Rational expressions: polynomials, fractions, exponents and roots.
7. Algebraic equations: linear equations (possibly with a parameter), quadratic equations (solutions in real numbers and in the complex plane), irrational equations.
8. Systems of two linear (and non-linear) equations in two unknowns. Linear inequalities (solutions by null point method), system of linear inequalities
9. The Exponential and logarithmic equations (inequalities respectively), properties of logarithms. Inverse functions.
10. Test 2 (examining time:20- 30 minutes). Domains of more complicated functions.
11. Analytic geometry in a geometric plane: point, vector, line (equations and a graph), circle (equations, determining its centre and radius).
12. The conic sections: the ellipse, the hyperbola (as a graph of a linear rational function), the parabola (as a graph of a quadratic function). Properties of conics.
13. Tangents to conic sections. Finding common points of a line and a conic. Test 3 (examining time: 20-30 minutes).
14. Reserve.
---