Projectile motion: range, maximum height, formulas
Projectile motion explained as two independent motions: horizontal and angled launches, range, maximum height and time of flight, with three worked exercises.
Blog
Notes from the notebook.
Guides, worked examples and study method, translated from our Italian blog.
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Quadratic inequalities: the parabola and the sign
How to solve quadratic inequalities with the parabola: discriminant, roots and sign in the three cases, systems, typical mistakes and worked examples.
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Sorting algorithms: bubble, selection, insertion sort
Bubble, selection and insertion sort explained with a step-by-step trace on 6 numbers: pseudocode, Python, comparisons, swaps, O(n²) and worked exercises.
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SQL: SELECT, JOIN and GROUP BY with worked examples
SELECT, WHERE, INNER and LEFT JOIN, GROUP BY, HAVING: a small database with three tables, typical mistakes and solved queries with the result tables.
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Uniform and accelerated motion: formulas, graphs
Uniform and uniformly accelerated motion explained with cars, trains and braking: formulas, s-t and v-t graphs, typical mistakes and worked exercises.
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Graph transformations: shifts, reflections, absolute value
How to get the graph of f(x+a), f(x)+b, -f(x), f(-x) and |f(x)| from a known function: rules, direction mistakes and three worked exercises for Year 3.
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Kant explained: the Critique of Pure Reason
Synthetic a priori judgements, the Copernican revolution, the aesthetic and the analytic: the Critique of Pure Reason explained for the Year 4 oral test.
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Leopardi: thought, the Canti and Operette for the oral
Leopardi for the Year 5 oral test: the phases of pessimism, the Canti and Operette morali to link up, the mistakes that cost a grade and two worked outlines.
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Periodic trends: atomic radius and electronegativity
Atomic radius, ionisation energy, electron affinity and electronegativity: how they vary across the periodic table and how to compare two elements.
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Recursion: factorial, Fibonacci and Euclid's GCD
How to write and trace a recursive function: base case, recursive step and call stack, with worked examples on factorial, Fibonacci and Euclid's GCD.
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Seneca in Latin: how to translate a passage in Year 5
Seneca's terse style, sententiae and philosophical vocabulary: an eight-step method for translating an Epistulae passage in Year 5, with worked examples.
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Simple harmonic motion: spring and pendulum
Simple harmonic motion: period and frequency of a spring and a pendulum, energy, position and velocity graphs, typical mistakes and three worked exercises.
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The first tutoring lesson: how to structure it so it works
How to prepare and run a first online tutoring lesson: what to ask, what to explain, and how to close with a recap and a plan for the lessons that follow.
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Getting chosen as a tutor without a portfolio
No reviews or students yet? How to build trust as a tutor: a sample lesson, a clear method, real references and honest communication.
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How much to charge for tutoring: private, platform or agency
How much can you earn from tutoring? How to think about your rate and what changes between working privately, on a platform or with an agency.
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How to find students for online tutoring: a guide
How to find your first online tutoring students: word of mouth, ads, platforms and agencies, what to write and how to reply to people who contact you.
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How to prepare for the healthcare professions test
Healthcare professions test 2026/27: official structure, +1.5/−0.4 scoring, the decree's syllabus and a study plan area by area, with a free mock exam.
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How to start tutoring online: a guide for beginners
Want to tutor online but don't know where to start? Subjects, levels, tools and your first week: a practical guide for students and graduates.
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Health professions test: structure, syllabus, preparation
How the health professions admission test works: 60 questions, +1.5/−0.4 marking, subject weights, worked examples and a study plan.
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TOLC practice test: how to take it and read the result
How to use a TOLC practice test (SU, B, I and the others): timing, penalties, how to sort your mistakes and read the score section by section.
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Logical reasoning in the TOLC: question types and examples
The six types of logic question that keep coming back in the TOLC and other admission tests, each with a worked example and a method to solve them fast.
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English conditionals: the four types explained
Zero, first, second and third conditional: when to use each, the right verb tenses, typical mistakes of Italian speakers and worked exercises for the test.
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German cases: nominative, accusative and dative
Nominative, accusative and dative in German: how to spot the case, the article table and the prepositions that take each case, with worked exercises.
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HACCP and food contamination: a guide to the test
Physical, chemical and biological contamination, the seven HACCP principles and critical control points: the food-science test, with worked examples.
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