Skill — Ragionare per casi.
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Linked atoms
136 linked atoms.
04 Percentuali
05 Equazioni di primo grado
06 Sistemi di equazioni lineari
07 Teoria degli insiemi
- Checking an equivalence with the truth table
- Distinguishing equivalences and orders
- Negation of a universal proposition
- Truth table and the hidden connective
- Truth table of the connectives
08 Fondamenti di geometria euclidea
09 Metodo di lavoro — come risolvere un problema
10 Equazioni di secondo grado e fratte
11 Disequazioni
- A typical literal inequality
- Case a negative, Delta negative — always negative
- Case Delta negative — parabola always positive
- Case Delta zero — tangent parabola
- Constructing an inequality given the sign table
- First-degree fractional inequality
- The six cases of the parabola
12 La parabola
- Equations with absolute value
- (x-2) ≤ 0)
- Functions with absolute value
- General splitting method
- Inequality with the absolute value of a trinomial (|x²-5x+6| ≥ 2x-3)
- Intersections between a parabola with an absolute value and a line
- Mixed cases with two absolute values
- Special case - modulus greater than or equal to B(x)
- Sum of three absolute values less than 4 (|x|+|x-1|+|x-2| < 4)
- Sum of two absolute values less than or equal to 6 (|x-1|+|x+2| ≤ 6)
13 Radicali ed equazioni irrazionali
- Existence conditions of radicals
- Inequality with the root on the greater side
- Inequality with the root on the smaller side
- Non-strict inequality
- Type I — root greater
- Type II — root smaller
17 Disequazioni irrazionali
- Decision map — what type of inequality am I facing?
- Example — root larger than a line
- Recognising always-non-negative sums
- The method for the larger root — Type II
- The method for the smaller root — Type I
- Worked exercise — Fractional inequality with a radical
- Worked exercise — Sum of two radicals
- Worked exercise — Type I with a strict root
- Worked exercise — Type II with a semicircle
18 Fasci di rette
20 Circonferenza nel piano cartesiano
22 Iperbole e funzione omografica
23 Funzioni, linguaggio e proprietà
- Continuity at the junction points
- Continuity of the integer part
- Graph and image of |x-1|-|x+1|
- Natural domain
- Parameters for continuity
- Solving f(x)=3 piecewise
25 Funzione esponenziale
26 Funzione logaritmica
27 Metodi unificanti per equazioni e disequazioni
- A checklist for the oral exam
- Idea 1: substitution
- Idea 2: applying an injective function
- Idea 3: applying a monotonic function (inequalities)
- Inequality with absolute value
- Irrational inequality
- Logarithmic inequality
28 Circonferenza goniometrica e funzioni sin, cos, tan
- Conversion between polar and Cartesian
- Domain, range and sign
- 2
- From Cartesian to polar
- How to reduce an angle to the first quadrant
- Values using associated arcs
31 Equazioni goniometriche
32 Disequazioni goniometriche
- Absolute value of the cosine
- Factorisation with the double-angle formula
- Inequalities with absolute value and roots
- Product of factors and sign table
- Product of factors with sign table
- The sign-study method
34 Combinatoria
35 Probabilità avanzata
- Bertrand’s Paradox
- Dominant and dominated strategy
- Example — Prisoner’s dilemma
- Monty Hall paradox
- Problem — Bertrand’s three answers
- Problem — Monty Fall variant
- Problem — Simulating Monty Hall with a die
- Problem — The paradox of the two children born on a Tuesday
- Sum at least 9 with the first die even
- The two children paradox
37 Geometria analitica nello spazio
- Example - skew lines
- Line-plane and plane-plane distances
- Relative position of two lines
- Relative positions of line and plane and angles
- Sphere and plane
- Sphere-plane position
- The four cases
- Three planes and a common point
38 Geometria sintetica nello spazio
39 Successioni numeriche
40 Limiti di funzioni
- Accumulation points of sets
- Examples of accumulation points
- Indeterminate forms
- Isolated point and membership of the domain
- When the limit makes sense
41 Continuità e discontinuità
- x
- Continuity at the junction point
- Determining the parameters for continuity
- Examples of classification
- |x|
- Newton versus bisection and cases of failure
- Parameters for continuity and differentiability
- The three types of discontinuity
42 Derivate
- Classification of non-differentiability points
- Classifying points of non-differentiability
- Corner point
- Corner point of |ln x|
- Derivative of ln of the absolute value of x
- Differentiability and continuity
- Differentiability of x·∛x
- Graph with corner, cusp and vertical tangent
- Non-differentiability and the search for maxima and minima
- Parameter for differentiability
- Parametric study of x over (x²+k)