Conduct grade 5 and 6: what law 150 changes
What happens with a 5 or 6 in conduct in Italian secondary school after law 150: non-admission, civic education paper, school credit and what families can do.
Blog
Notes from the notebook.
Guides, worked examples and study method, translated from our Italian blog.
The blog grows out of our lessons: every article answers a question a student has actually asked us, with step-by-step worked examples, the reasoning before the formulas and the typical mistakes to avoid.
The topics follow the Italian secondary-school syllabus and the first years of university — maths, physics, science and computer science — plus preparation for admission tests such as the TOLC, the IMAT and the Bocconi test. We are translating the Italian articles into English one batch at a time; each English article links to its Italian original.
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Evolution: Darwin, natural selection and Hardy-Weinberg
Evolution in Year 5: Lamarck versus Darwin, natural selection, the modern synthesis, Hardy-Weinberg with a worked numerical exercise, speciation and evidence.
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First law of thermodynamics with worked exercises
The first law in Year 4 of high school: internal energy, work on the p-V plane and gas transformations, with three worked exercises and sign mistakes.
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First school report with failing grades: what to do, calmly
How the report grade is formed, how to read a 4 or a 5 mid-year and what to do in the eight weeks before the class council, without family drama.
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Geometric optics: mirrors, refraction and lenses
Geometric optics for Year 4 of high school: spherical mirrors, Snell's law, total internal reflection and thin lenses, with three worked sign exercises.
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Indefinite integrals: standard, substitution, by parts
Indefinite integrals for Year 5: table of standard integrals, substitution, integration by parts with LIATE and rational functions. Three checked exercises.
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Linear equations: method and worked examples
How to solve a linear equation step by step: brackets, fractions, impossible and indeterminate cases, checking and word problems. Three worked examples.
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Minerals and rocks: the rock cycle explained
Minerals, the Mohs scale, igneous, sedimentary and metamorphic rocks and the rock cycle: diagrams, examples and worked exercises for the Year 1 test.
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Orientation advice in Year 8: what it means
What the Year 8 orientation advice says and doesn't say, how to read it and what to do if it doesn't match your child's choice of secondary school.
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Lists, tuples and dictionaries in Python: worked exercises
Lists, tuples and dictionaries in Python for the first two years: methods, slicing, typical mistakes and three worked exercises with checked output.
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Atmosphere and hydrosphere: pressure, winds, water cycle
Layers of the atmosphere, pressure in hPa and atm, how winds form, the greenhouse effect and the water cycle: notes and exercises for a Year 1 science test.
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Circulatory and respiratory systems: diagram and questions
The heart, pulmonary and systemic circulation, vessels, alveoli and gas exchange in one clear outline, with four typical test questions and model answers.
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Cryptography: Caesar, Vigenère and RSA explained
Caesar cipher in Python, Vigenère, symmetric and asymmetric cryptography, RSA worked by hand with small numbers, digital signatures and HTTPS explained.
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Eigenvalues and eigenvectors: how to diagonalise
Eigenvalues, eigenvectors and diagonalisation in linear algebra: the procedure, multiplicities, a non-diagonalisable matrix and a symmetric one, worked.
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German subordinate clauses: weil, dass, wenn
German subordinate clauses: why the verb goes to the end with weil, dass, wenn and ob, modals and Perfekt, weil versus denn, inversion, with worked exercises.
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Latent heat and thermal expansion: worked exercises
Thermal expansion, latent heat and changes of state for Year 2 physics: three worked exercises and the typical mistakes that cost marks in the test.
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Limits and indeterminate forms: how to solve them
How to solve limits with 0/0, infinity over infinity and infinity minus infinity forms: a scheme to recognise them, the technique and three worked exercises.
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Trig equations: elementary, linear, homogeneous
How to solve trigonometric equations in Year 4: elementary, quadratic, linear and homogeneous, with three worked examples and the typical mistakes.
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Newton's method and bisection in Python
The bisection and Newton-Raphson methods for finding the zeros of a function, with complete Python code, stopping criteria and a comparison of convergence.
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Numerical series: convergence tests and exercises
Numerical series in Calculus 1: necessary condition, comparison, ratio, root, Leibniz and absolute convergence, with four worked exercises.
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Photosynthesis, fermentation and cellular respiration
Photosynthesis, fermentation and cellular respiration compared: where each happens, ATP yields, a summary table and typical mistakes in oral tests.
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Plasma membrane and transport: diffusion and osmosis
Plasma membrane and transport for Year 2: diffusion, osmosis, hypotonic and hypertonic solutions, sodium-potassium pump, endocytosis. Table and exercises.
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Strings and files in Python: exercises for your test
Strings, slicing, methods and reading files in Python for Year 3: three exercises with complete code and output, plus the mistakes to avoid.
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Quadratic systems: methods and worked exercises
Quadratic systems by substitution, the discriminant and number of solutions, line and parabola, symmetric systems: four worked exercises for Year 3.
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