Saturday 19 September 2026: lessons restarted about two weeks ago and in IV ginnasio (the first year of the Italian liceo classico, the classical high school) the natural science teacher is introducing (or about to introduce) the scientific method, physical quantities and density. The first test typically arrives between late October and early November — about six weeks from now. This is the right moment to set the topic up properly, not the moment for the last-night review.
Why science at the classical high school is different from what you imagine
At the liceo classico the timetable in IV ginnasio is heavily tilted towards the ancient languages: 5 hours of Latin, 4 of Greek, 3 of maths and only 2 hours of natural science a week. With only two hours, every topic is seen once and that’s it: very little time for exercises in class, almost everything devoted to explanation and definitions. The result is a pattern that repeats every year: the student arrives at the test with a notebook full of definitions learned by heart and zero practice on conversions, which require automatic skills, not repeated theory.
Then there is a second feature of the classical high school that changes the way you study: the science test here is almost always multiple choice — ticked answers plus a few short calculations — not an open essay as happens more often elsewhere. Studying for a multiple-choice test means recognising the right answer among plausible distractors and doing a quick calculation without getting a single step wrong, not just being able to “explain” the topic aloud. It is also, frankly, the subject that classical high school students underestimate most because “it isn’t Latin” — and it is the one where I most often see an unexpected failing grade at the start of the year.
Scientific method and physical quantities: the basics
The scientific method proceeds through observation, hypothesis, experiment and conclusion (or theory, if the hypothesis holds up under several independent checks). In a multiple-choice test you are almost always asked to recognise which stage of the method corresponds to a described situation, rather than to list the stages by heart.
A physical quantity is anything that is measured with an instrument and expressed with a number plus a unit of measurement. The International System (SI) fixes seven base quantities — among them length (metre), mass (kilogram), time (second), temperature (kelvin) — from which all the others, called derived, are obtained: density, for example, is , that is mass divided by volume in cubic metres.
To avoid writing numbers with too many zeros we use scientific notation: a number is written as , with . It is the tool that makes both very large numbers (the Earth–Sun distance, ) and very small ones (the diameter of an atom, of the order of ) manageable.
Conversions: the real stumbling block
This is where more marks are lost than in any other part of the test, because with two hours a week you rarely get to do enough of them in class. The wrong way to go about it is to learn “the little rule” (move the decimal point by so many places); the way that doesn’t fail is to reason with powers of ten every time.
From cm to m, and from cm³ to m³. If , then cubing both sides of the equality also cubes the power of ten: . You don’t divide by 100, you divide by a million — the most common mistake of all comes precisely from forgetting that the exponent 3 of the volume applies to the conversion factor too, not just to the unit.
From g/cm³ to kg/m³. The same principle, applied to a density: and , so
To go from g/cm³ to kg/m³ you always multiply by 1000. This is why the density of water can be read equally as or : it is exactly the same physical value, written in two different units.
Litres and dm³. For volumes of liquids there is an equality that should be learned by heart because it comes up everywhere: . A litre of water occupies exactly one cubic decimetre — a cube with 10 cm sides.
Density: definition and the three ways to use it
Density is the ratio between the mass and the volume of a substance:
It is a characteristic property of the substance: it does not depend on how much material you have (a gram of gold and a gold bar have the same density), and that is why it is used to identify a material or to predict how it behaves.
From the same formula you get the other two, and it is good to be able to use all three without having to “reinvent” them each time:
A classic application that often comes up in tests: why does ice float on water? Because, unlike almost all substances, water in the solid state is less dense than water in the liquid state (about against ): when water freezes, the molecules arrange themselves in a more “open” crystal lattice, taking up more space for the same mass. An object floats in a liquid when its density is lower than that of the liquid: it is exactly the same reasoning, applied to a case — that of water — which is an exception to the general rule.
States of matter and changes of state
Matter comes in three states of aggregation: solid (own shape and volume), liquid (own volume, shape of the container) and gas (neither own shape nor own volume, it fills all the available space). The change from one state to another has a precise name in each direction, and mixing them up means a wrong tick:
| From → to | Name |
|---|---|
| solid → liquid | melting |
| liquid → solid | freezing (solidification) |
| liquid → gas | vaporisation (boiling or evaporation) |
| gas → liquid | condensation |
| solid → gas | sublimation |
| gas → solid | deposition |
One point that often appears in the multiple-choice test as a question of its own: during a change of state, while the two phases coexist, the temperature stays constant even though you keep supplying heat. If you draw a heating curve (temperature on the vertical axis, heat supplied or time on the horizontal axis), the graph rises, then shows a horizontal stretch — the plateau — at melting, rises again, and shows a second plateau at boiling. The heat supplied during the plateau is not used to warm the substance: it is used to break the bonds holding the particles together in the starting state.
Mixtures, elements and compounds
Every sample of matter is either a mixture (several substances physically mixed) or a pure substance (fixed, definite composition).
- Homogeneous mixture: a single phase visible, even to the naked eye or under the microscope — water with dissolved salt, air, sea water.
- Heterogeneous mixture: several distinguishable phases — water and oil, sand and water, granite.
Pure substances are in turn divided into:
- elements: they cannot be broken down into simpler substances by chemical means (oxygen, iron, gold);
- compounds: they can be broken down into two or more elements (water, ; carbon dioxide, ).
To separate the components of a mixture you choose the technique according to which physical property differs between the components:
- Filtration: separates an insoluble solid from a liquid, exploiting particle size (a fine-mesh filter holds back the solid and lets the liquid through).
- Distillation: separates the components of a homogeneous liquid mixture exploiting their different boiling temperatures — you heat it, the more volatile component evaporates first and condenses separately.
- Chromatography: separates different substances dissolved together exploiting the different speed at which they move across a support (typically paper) carried by a solvent.
- Centrifugation: separates a finely dispersed solid in a liquid exploiting the different density, using centrifugal force to speed up the sedimentation that would otherwise take a long time.
The Earth in the Solar System
A note that often closes the syllabus of the first term: the Earth makes two main motions. Rotation, about its own axis, in about 24 hours, is responsible for the alternation of day and night. Revolution, around the Sun, in about 365 and a quarter days (hence the leap year), is responsible, together with the tilt of the Earth’s axis (about 23.5° relative to the plane of the orbit), for the alternation of the seasons.
Here lurks the classic multiple-choice trap: the seasons do not depend on the Earth–Sun distance. The Earth is in fact slightly closer to the Sun in early January (in the depth of winter in the northern hemisphere) than in early July. The seasons depend on how much a hemisphere is tilted towards the Sun at a given point in the orbit: when the northern hemisphere is tilted towards the Sun, it receives more direct light and for more hours a day — it is summer there, while in the southern hemisphere, tilted the other way, it is winter. If a test question offers “the seasons depend on the distance from the Sun” as an option, it is almost always the wrong answer placed there on purpose.
How to study for a multiple-choice science test
With two hours a week and a test made of ticked answers, the effective study method is different from the one for an open essay:
- Isolate the ambiguous definitions (melting/freezing, element/compound, homogeneous/heterogeneous): in the test the distractors are almost always the “twin” concept of the right one.
- Redo every conversion in your head, starting from reasoning with powers of ten, not from the memorised little rule: a doubt about “do I multiply or divide” costs more than a calculation slip.
- Build summary tables for the topics with long lists (changes of state, separation techniques): the test often asks you to match technique and property exploited.
- Train against the clock: a multiple-choice test has tight timing, and speed on the easy questions leaves room for the calculation ones.
Two worked exercises
1. Density of an aluminium cube, with conversion
An aluminium cube has side and mass . Calculate the density in g/cm³ and then in kg/m³.
The volume of the cube is:
The density is:
It is exactly the known density of aluminium: a good sign that the calculation is correct. Converting to kg/m³ (you multiply by 1000):
2. From density to weight, with a conversion in the middle
A container is full of an oil with density . How much does the oil in it weigh, in grams and in kilograms?
First the volume is converted to cm³, using :
Then you apply :
Without the intermediate step from litres to cm³, the number 1.5 and the number 0.92 cannot be multiplied directly: this is exactly the kind of mistake — skipping the conversion in the middle — that a multiple-choice test isolates with a dedicated question.
How I work on this topic
With students starting science in Year 1 at the classical high school, the problem is rarely understanding the theory: it is getting to the test having done enough conversion exercises, which two hours a week do not allow. In lessons we work mostly on that — conversions repeated until they become automatic, density in all three directions, summary tables for the topics learned by heart — with the same practical approach described in the post on chemistry in Year 1 of the technical track: same time of year and nearby topics, but there the focus is — new for 2026/27 — “Experimental Sciences” as a single subject with a laboratory, while at the classical high school there are still two hours a week, no laboratory and a test that is almost always multiple choice. The same reasoning on conversions, applied to physics, is in the post on measurements and significant figures in Year 3. The part on the Earth and the seasons has a post of its own, The Earth in the Solar System: motions and seasons in Year 1; for experimental data and uncertainties, Measurement errors and error propagation.
An honest note on the free practice tests: at the moment they cover maths and physics, not yet science — I won’t promise it will arrive soon, but if you want to train against the clock on other subjects you will already find material there, with the same logic: the correct answer is free, the guided solution is unlocked with your first lesson.
If you want to set the topic up properly before the late-October test, or you already have a marked test to go over together, the most direct way to start is the science page or directly the contact page.
