Math content for vestibular

MATHEMATICS
1. Numerical Sets
1.1. Natural and integer numbers: operations and properties; divisability; prime factor decomposition; lowest common multiple and greatest common divisor.
1.2. Rational and real numbers: operations and properties; order ratio; absolute value.
1.2.1. Proportionality: ratio, proportion, directly and inversely proportional quantities.
1.3. Complex numbers: representation and operations in algebraic form and trigonometric form.
1.4. Logaritms: definition and properties.
1.5. Sequences: concept of sequence; arithmetic sequence; geometric progression.
2. Financial Math.
2.1. Percent; simple interest; compound interest.
3. Algebraic expressions.
3.1 Equivalents and transformations.
3.2. Notable products.
3.3. Algebraic factoring.
4. Functions
4.1. Relationship between two quantities and function concept.
4.2. Domain and range.
4.3. Algebraic and graph representations.
4.4. Charts: signal analysis; growth; degrowth; function variation analysis; translations and reflections.
4.5. 1st and 2nd degree polynomial functions. 1st and 2nd degree equations and inequalities. Problem solving.
4.6. Exponential Function. Exponential equations and inequalities. Problem solving.
4.7. Logarithm function. Logarithmic equations and inequations. Problem solving.
4.8. Modular function. Composite function. Reverse function.
5. Polynomials and Algebraic Equations.
5.1. Polynomials: concept; degree; roots; operations; binomial division of the form x-a; theorems.
5.2. Algebraic equations: definition, root concept, root properties; Fundamental Theorem of Algebra; relations between
coefficients and roots; search for rational roots; real and imaginary roots.
6. Matrices, Determiners and Linear Systems.
6.1. Matrices: operations; invert of a matrix.
6.2. Determinant: computation and properties.
6.3. Linear systems: solution and discussion. Scaling.
7. Combinatory analysis.
7.1. Multiplication and additive principles.
7.2. Arrays, combinations and permutations.
7.3. Newton binomial.
8. Probability.
8.1. Finite sample space. Events
8.2. Probability of an event in an equiprobable sampling space.
8.3. Probability of event union.
8.4. Probability of events intersection.
8.5. Conditional probability. independent events
8.6. Binomial distribution
9. Statistics
9.1. Graphs and tables: calculations and interpretations.
9.2. Central tendency measures: mean, mode and median.
9.3. Dispersion measure: standard deviation. 10. Trigonometric
9.1. Trigonometric ratios in right-angled triangles.
10.2. Trig functions: sine, cosine and tangent. algebraic and graphic representations; periodicity; graphical analysis of functions.
10.3. Trigonometric equations and inequalities.
10.4. Arc addition formulas and their consequences. Transforming sums into products.
10.5. Resolution of triangles: Law of sines; Cosine law.
11. Flat Geometry
11.1 Elements and properties of plane geometric figures: straight line, half-line, segment, angle, polygons, circumferences, circles and circular sectors.
11.2. Thales' Theorem
11.3. Congruency and similarity of flat figures.
11.4. Metric relations in triangles, regular polygons and circles.
11.5. Pythagoras theorem.
11.6. Areas of polygons, circles, coronas and circular sectors.
11.7. Symmetry.
12. Space Geometry.
12.1. Positional geometry: straight lines and planes in space. Parallelism. Perppencularity. Orthogonal projection. distances. angles
12.2. Polyhedra, prisms and pyramids: elements, properties, areas and volumes.
12.3. Cylinders, cones and spheres: elements, properties, area and volumes.
12.4. Pyramid and cone trunks: elements, properties, areas and volumes.
13. Analytic Geometry.
13.1 Point: distance, midpoint, alignment of three points.
13.2 Line: equations and study of coefficients.
13.2.1 Distance between point and line.
13.2.2 Relative positions of two straight lines.
13.3 Circumference: equations.
13.3.1 Relative positions between straight line and circle.
13.3.2 Relative positions between two circumferences.