The Year 1 syllabus doesn’t start from zero. From October it takes three things from middle school for granted — powers, fractions and first-degree equations — and builds algebra on top of them without re-explaining them. The problem is not that you haven’t understood them: it is that they still cost you half a minute each, and in a one-hour test you pay that half minute twenty times, every time they reappear inside a longer exercise.
The syllabus, block by block
Powers, including negative exponents. The properties of powers never appear on their own: they sit inside the October expressions with fractions and inside the November monomials.
The minus sign of the exponent flips the fraction, it doesn’t change the sign of the result: stays positive.
Fractions, GCD and LCM. The first October test at the science high school (liceo scientifico) is almost only this: a long expression with fractions and powers. The same rules come back identical from November on algebraic fractions, with letters in place of numbers.
(With the LCM of the denominators in place of the numerator changes accordingly: it is the same result, with smaller numbers.)
First-degree equations. You have already seen them in Year 3 of middle school, but in high school they change role: from a topic they become a tool. In March they are needed for geometry problems, and in Year 2 every linear system is, inside, one of these.
Watch out for the two cases that are not calculation mistakes but answers: with is impossible, is indeterminate — and in a test they are worth marks.
The mistakes that cost the most
The minus in front of a power is not inside the power: without brackets, raising to a power comes before the sign, so while . Whoever confuses the two loses marks even when the rest of the calculation is right.
With fractions, the classic mistake is adding the denominators: is not "". You add only the numerators, and only after bringing everything to the LCM: .
In equations, the minus sign in front of a fraction applies to the whole numerator, as if there were an invisible bracket: , not just on the first term. It is a silent mistake: the calculation goes on with no apparent hitch, and you only notice you got it wrong at the end, when the solution doesn’t check.
For practice on the same three topics you’ll find the practice test on numbers, fractions and powers and the one on first-degree equations (questions in Italian); for the method of tackling the first test of the year there is the guide to the first maths test. If among the fractions you also need ratios and percentages, there is ratios and percentages in Year 1; after algebra come the special products: formulas and worked exercises, and for proof-based geometry the triangle congruence criteria: the proofs.
The Italian version of this post comes with a downloadable document that covers all nine topics in full: every formula, one worked example per topic, the typical mistake where needed and twenty-seven exercises with the complete step-by-step solution.
If you would rather have guided revision than go it alone, maths tutoring starts exactly from here — write to me and we’ll see where to concentrate the first lessons.
