The Up to Ten blog offers practical guides for STEM study, strategies for entrance exam preparation (TOLC, SAT, GMAT), and tips to improve academic performance. Articles written by our team of tutors with hands-on experience, updated weekly.
Lagrange's Theorem guarantees a point where the tangent is parallel to the chord; Rolle's Theorem is the special case with a horizontal chord. Statements, geometric intuition, the four-line proof, four worked examples with numbers, and the mistakes we see most often in fifth-year tests.
Read more
Asymptotes come from limits at the edges of the domain: the method for each type, four worked examples, the hole that is not an asymptote and six mistakes.
Read more
There are four rules of differentiation: sum, product, quotient and composite function. A complete table of the standard derivatives, a decision table for working out which rule to use, four worked examples with the numbers, and the five mistakes we see most often in lessons.
Read more
Maths anxiety is not a lack of talent: it is a block that fills up working memory at exactly the moment you need it. Here is how we recognise it in the first lesson and how we dismantle it, one exercise at a time.
Read more
Six standard limits are enough for the Maturità: the problem is recognising them when the question disguises them. A decision table by indeterminate form, worked examples with the numbers, and the mistakes we see most often in lessons.
Read more
"They study so hard, but then they get everything wrong in the test": it is almost never a question of effort. How to recognise passive studying and what concrete routine to suggest at home: exercises redone from scratch, an error log, spaced revision.
Read more
Solving a stoichiometry problem takes four steps: balance the equation, convert to moles, apply the coefficient ratios and convert back. Plus three worked examples.
Read more
Didn't get into Medicine after the filter semester? The three routes — related courses, enrolling elsewhere, a second attempt — and how to choose the right one.
Read more
How many hours a week does the Medicine filter semester take? 15 to 25, depending on your high school, with Physics first. A phased plan, September to November.
Read more
The TOLC-I does not require calculus: no derivatives, no integrals, no limits. The ceiling is the fourth-year scientific high school syllabus. Four worked examples, step by step, show the real level of the questions.
Read more
From €36 to €65 an hour by level: the full one-to-one rates, what they really include and when the 12-hour package pays off. Written by the people who set them.
Read more
A factual comparison of the Cattolica TIEC and the Bocconi Test: 48 vs 50 questions, 60 vs 75 minutes, language, maths share, scoring, attempts allowed, registration windows. Operational differences, dimension by dimension.
Read more
Frequent TOL mistakes at Politecnico di Milano: treating it like the TOLC-I, random guessing, burning an attempt by no-show, ignoring the 75/100 rule, undervaluing English. How to spot them before the test.
Read more
How the SAT works as an alternative to Politecnico di Milano's TOL: which programmes accept it (Engineering only), 2027-28 score thresholds, deadlines, College Board code 7364, and where the SAT does NOT apply.
Read more
The 6-point certifications bonus on the Cattolica TIEC: a B1+ language certificate is worth 4 points, ICDL/EIPASS 2 points. Recognised certifiers, upload rules, role of the school record.
Read more
Mathematics syllabus of Politecnico di Milano's TOL: algebra, functions, geometry, trigonometry, statistics. Why the block is worth 65% of the score and is the ranking tiebreaker.
Read more
How to choose among Bocconi's bachelor programmes for 2027-28: the official lineup, language of instruction, programme profiles and what changed compared to the historical acronyms (CLEAM, CLEF, BIEM, BAI…).
Read more
The full maths syllabus for the Cattolica TIEC: 14 topics from algebra to trigonometry, VPI thresholds to avoid the Maths OFA, preparation strategy.
Read more
Early TOL at Politecnico di Milano: who can sit it, 2026 sessions, and the 75/100 rule that locks in a seat at Engineering one year ahead. The full guide.
Read more
Four failing grades and at risk of repeating the year, but eyes lighting up talking about startups. How to recognise and nurture the hidden talent of labelled students.
Read more
Bocconi's maths section is 24 of 50 questions (48%) inside a single 75-minute timer. Topics, time budget and tactics to go fast without sacrificing accuracy.
Read more
What the TIEC is, the 7 Cattolica Economics bachelor programmes, exam structure, sessions, scoring and VPI: the complete guide to the 2026/2027 admission test in Milan.
Read more
What the TOL is: structure (65 questions, 100 minutes), weighted scoring on a 100 scale, 30/100 minimum threshold, English OFA and 2026 sessions. The full guide to Politecnico di Milano's engineering entrance test.
Read more
The 5 most common TOLC-I mistakes: getting stuck on hard questions, not timing yourself, ignoring sciences. How to recognise and fix them before the test.
Read more
How to tackle GMAT Data Insights: strategies for Data Sufficiency, Multi-Source Reasoning, tables and graphs. The section that makes the difference.
Read more
How the GMAT works: the 3 sections, the 205-805 scoring scale, the adaptive system, and bookmarks. Everything you need to know about the structure before you start preparing.
Read more
How to prepare for the filter semester exams in medicine: strategies for Chemistry, Physics and Biology, study plans for different profiles and time management.
Read more
How to prepare for the GMAT: test structure, sections, scoring, strategies for Quant, Verbal and Data Insights. Study plan and resources for aiming high.
Read more
Digital SAT 2026 guide: structure, 400-1600 scoring, Italy test dates, Reading & Writing and Math prep. For Bocconi, the US and European universities.
Read more
How to prepare for the Bocconi admission test: structure, sections, scoring, sessions and strategies. Everything you need to pass the selection.
Read more
Effective strategies for the 2026 Cattolica Medicine test: how to tackle logic, biology, chemistry, physics and ethical-religious culture in 65 minutes.
Read more
How to prepare for the TOLC-I: test structure, scoring, topics by section, strategies and study plan. Everything you need to get into Engineering.
Read more
What GMAT score do the top business schools really ask for? The averages they publish, the official GMAC percentiles — and the four schools, Bocconi and INSEAD among them, that publish no score at all.
Read more
TOLC-I minimum scores for major Italian universities: Politecnico di Milano, Turin, Bologna, Sapienza. Real thresholds, OFAs and how to interpret your result.
Read more
When to take the GMAT relative to MBA deadlines: preparation timelines for every level, timeline for round 1 and 2, and how to plan your attempts.
Read more
Realistic timelines for TOLC-I preparation based on your starting level: from 2 weeks to 4 months. Study plan for every scenario.
Read more
Effective strategies for the Digital SAT 2026: how to approach Reading & Writing for Italian students, Math techniques, and adaptive module management.
Read more
What SAT score do you need to get into Bocconi? How the alternative to the Bocconi test works, score conversion and the best strategy.
Read more
Complete guide to the Medicine filter semester: exam structure, scoring, 9-section ranking, 2025/26 results and effective preparation strategies.
Read more
Which simulations to use for the TOLC-I, how many to take and how to analyse them. And why a rising score is not always an improvement.
Read more
Structure of the 2026 Bocconi test: 50 questions, 4 sections, 75 minutes. How the scoring works, the penalty, and updates on mathematics and critical thinking.
Read more
Guide to the 2026/27 Cattolica Medicine test: 65 questions in 65 minutes, dates, scoring, places and strategies to pass the Policlinico Gemelli selection.
Read more
All TOLC-I mathematics topics: algebra, analytical geometry, trigonometry, functions. Frequency, difficulty and how to prepare for each area.
Read more
How the TOLC-I works section by section: questions, time, scoring, penalties and OFA thresholds. Strategies for each part of the test.
Read more
TOLC-I and Politecnico di Milano TOL compared: structure, sections, scoring, attempts and which to take. A practical guide.
Read more
First-year physics at the Politecnico di Milano: what is really covered, why it differs from high school, the maths formalism, exams and textbooks.
Read more
What A-Level Further Mathematics is, how it differs from Maths, its modules and exam boards (Edexcel, AQA, OCR), and why it's pivotal for engineering and top STEM.
Read more
All TOLC-I physics topics from the CISIA syllabus: mechanics, optics, thermodynamics and electromagnetism. What actually comes up, level required, common mistakes.
Read more
AA or AI? The definitive guide to the two IB maths courses: content, exams (Paper 1/2/3 + IA), SL vs HL and which universities require AA HL. Choose with confidence.
Read more
The deep link between mathematics and physics: derivatives for velocity, integrals for work, vectors for forces. Understanding one makes the other easier.
Read more
High-school mechanics explained through reasoning, not just formulas. Key concepts, common mistakes, study method and how to actually improve.
Read more
The journey to transform a scientific insight into an effective drug is one of the most complex and expensive human endeavors, requiring on average 12 to 15 years and exceeding one billion dollars in investment.
Read more
We live in a labyrinth of information and misinformation. In this scenario, knowledge and application of the scientific method represent a mental compass that, over the centuries, has unveiled the hidden rules of the cosmos.
Read more
Ultraviolet (UV) radiation is the leading cause of skin damage in humans, including premature aging and skin cancer. Let's discover what lies behind an SPF label and how sunscreens work at the molecular level.
Read more
The Early Session is the first of Bocconi's three admission rounds, and it lets you apply as early as the end of your fourth year of high school. Here's how it works and how to prepare.
Read more
Artificial Intelligence is revolutionizing education, offering personalised tools for more effective learning. Yet the irreplaceable value of human connection remains central.
Read more
The Maturità represents a significant rite of passage in a teenager's life. Understanding the neurobiological dynamics underlying adolescent anxiety is essential for providing effective support.
Read more
Contrary to a widespread belief, by the time of Christopher Columbus most Western scholars did not believe the Earth was flat. Let's explore Columbus's scientific errors and his intuition about the trade winds.
Read more
Inflation is an economic concept present in everyday life, often misunderstood or oversimplified as a mere increase in prices. Let us discover what it really means when inflation rises or falls and how it impacts daily life.
Read more
Discover the wonders that the August sky has to offer! The queens of summer are undoubtedly the shooting stars from the Perseid meteor shower, which this year will put on a breathtaking show.
Read more
A period abroad represents an adventure, a crossroads of personal, cultural, and academic growth that challenges and enriches fourth-year high school students. Discover the advantages, challenges, and strategies to maximise this experience.
Read more
Discover the science behind Halloween's spooky shadows! From the bioluminescence that makes pumpkins glow to the legends of witches flying on brooms, there is a logical explanation behind every mystery.
Read more
Research shows that dependence on generative AI tools like ChatGPT can lead to reduced brain activity, compromising the capacity for deep cognitive processing.
Read more
The State Exam is approaching and limits are a fundamental pillar. This article offers an essential guide to tackling limits with confidence, from theory to applications.
Read more
Discover the magic of chemistry in the kitchen! Turn your space into a creative lab with exciting experiments like the vinegar and baking soda volcano, slime preparation, and salt crystallization.
Read more
Photographed black holes, galaxies seen as they were 13 billion years ago, gravitational waves: today's astrophysics in real numbers and discoveries, and why it starts with physics and maths.
Read more
AlphaFold and the 2024 Nobel, 5G at 1 millisecond of latency, quantum computing, solar down 90%: today's innovations with real examples and numbers, and the science underneath.
Read more
Behind the notes lie precise numbers: the equation of a sound wave, the frequency ratios that make two sounds consonant, and the Fourier transform behind the MP3. Here's the maths of music.
Read more
Quantum mechanics opens a window onto an invisible universe, revealing concepts such as the uncertainty principle, wave-particle duality, and entanglement.
Read more
Spring is a natural laboratory where solar heat, thermodynamics and fluid dynamics collaborate to drive processes like photosynthesis and the hydrological cycle.
Read more
Maths does not have to be boring! Discover 5 logic games that stimulate reasoning and turn learning into an adventure.
Read more
One subject at a time, one goal at a time. Discover how individual lessons can transform academic performance.
Read more
Recognising and managing emotions helps you study better: from frustration over a hard problem to test anxiety. What emotional intelligence is and how to nurture it in young people.
Read more
Supercomputers and cloud computing are revolutionizing the world of technology. From scientific research to artificial intelligence, these advanced technologies offer unprecedented computing power.
Read more
The speed of light is one of the most fascinating constants in physics. Known as "c", it is approximately 299,792,458 m/s.
Read more
Modern chemistry is a science that fascinates, confuses and sometimes frightens, but it is indispensable for our understanding of the world. But how did it become what it is today?
Read more
Explore common study challenges and discover how to overcome them with our complete guide. Learn time management strategies, proven study techniques and the importance of physical and emotional well-being for achieving academic success.
Read more
Every school year in Italy offers long weekends and holidays to make the most of, balancing study and rest. Here are the fixed dates, how the long weekends form and how to organise yourself.
Read more
Extreme atmospheric phenomena, such as thunderstorms and cumulonimbus clouds, have fascinated humanity for centuries. These imposing clouds form as warm, moist air rises, leading to intense showers and thunderstorms, often accompanied by spectacular lightning.
Read more
Tutoring isn't just about fixing a bad grade. Here's how to tell when it's really needed, what a good tutor changes, and why it's a long-term investment.
Read more
We continue our journey through STEM destinations in Italy! Starting with the spectacular Cascata delle Marmore in Umbria, followed by Città della Scienza in Naples, a place that sparks scientific curiosity.
Read more
What can a parent actually do to support their child's studying? Environment, routine, motivation without pressure and working with the tutor: the practical guide.
Read more
Italy offers extraordinary STEM experiences for students and families. From the Science Museum in Milan to the Grotta Gigante in Friuli, let's discover five unmissable adventures.
Read more
Nuclear energy is a phenomenal force that emanates from the heart of atoms. To understand how it was used in the bombs of Hiroshima and Nagasaki, we must first understand nuclear reactions.
Read more
One of the most important challenges humanity will face in the near future is finding alternative energy sources to fossil fuels. Eyes have turned to the sea.
Read more
Among the fundamental organic molecules for life, the starring role undoubtedly belongs to proteins. Thanks to artificial intelligence, their study is undergoing a revolution.
Read more
The adorable American grey squirrels are taking over Italian cities like Milan. Originally from North America, they have become a threat to the local ecosystem and biodiversity.
Read more
DNA, short for deoxyribonucleic acid, is one of the most incredible and mysterious molecules on our planet. Present in every cell of living organisms, it is the secret archive of life.
Read more
How many times, leafing through a maths textbook, have you wondered what the point of what you are studying is? Today we discover how Lagrange's Theorem is at the heart of how the highway Speed Tutor works.
Read more
For centuries, energy played hide and seek with physicists. One of the best-known arenas where energy plays a fundamental role is sport, and pole vaulting is its queen.
Read more
The movements of the Earth-Sun system are fundamental in governing the rhythm of life on Earth: days, months, seasons and years are all based on these phenomena.
Read more