RS Mala Matura cheat sheet

Poland joined the European Union on 1 May 2004; it has held the rotating Council presidency twice, in 2011 and 2025.

NATO was founded on 4 April 1949 in Washington; Article 5 on collective defence has been invoked once, after the 11 September 2001 attacks.

The UN has 193 member states; the Security Council has five permanent members holding veto power: China, France, Russia, UK, USA.

Poland's Sejm has 460 deputies and the Senate 100 senators; both chambers are elected for four-year terms.

The Nobel Prize was first awarded in 1901; Polish-born laureates include Marie Curie (physics 1903, chemistry 1911) and Wisława Szymborska (literature 1996).

A leap year must be divisible by 4, except centuries must be divisible by 400; thus 1900 was not a leap year but 2000 was.

The European Parliament has 720 seats after the 2024 election; Poland elects 53 MEPs, one of the largest national delegations.

Inflation is measured as the annual percentage change in a price index such as CPI; deflation is a negative rate, not merely a slowdown.

Polish has seven grammatical cases: mianownik, dopełniacz, celownik, biernik, narzędnik, miejscownik, wołacz.

Aspect pairs are a core feature: imperfective (czytać, pisać) describes ongoing or repeated action; perfective (przeczytać, napisać) describes completion.

The Jan Kochanowski work 'Treny' (1580) is a cycle of 19 funeral laments written after the death of his daughter Urszula.

'Pan Tadeusz' by Adam Mickiewicz was published in Paris in 1834; its full title calls it the last foray in Lithuania, in twelve books of verse.

Epoki literackie in order: średniowiecze, renesans, barok, oświecenie, romantyzm, pozytywizm, Młoda Polska, dwudziestolecie międzywojenne, postwar and contemporary.

Pozytywizm programme slogans: praca organiczna, praca u podstaw, asymilacja Żydów, emancypacja kobiet; key prose writers include Bolesław Prus and Eliza Orzeszkowa.

Wisława Szymborska won the Nobel Prize in Literature in 1996; Czesław Miłosz won it in 1980.

An argumentative essay (rozprawka) requires a thesis, textual evidence with citations, and a conclusion that returns to the thesis rather than introducing new claims.

Quadratic formula: for ax²+bx+c=0 with a≠0, x = (−b ± √(b²−4ac)) / 2a; the discriminant Δ=b²−4ac gives two, one, or no real roots as Δ>0, Δ=0, Δ<0.

Arithmetic sequence: aₙ=a₁+(n−1)r; sum Sₙ=n(a₁+aₙ)/2. Geometric: aₙ=a₁qⁿ⁻¹; Sₙ=a₁(1−qⁿ)/(1−q) for q≠1.

Derivative rules: (xⁿ)′=nxⁿ⁻¹, (sin x)′=cos x, (eˣ)′=eˣ, (ln x)′=1/x; the chain rule gives (f(g(x)))′=f′(g(x))·g′(x).

Probability: P(A∪B)=P(A)+P(B)−P(A∩B); conditional P(A|B)=P(A∩B)/P(B) for P(B)>0.

Logarithm rules: logₐ(xy)=logₐx+logₐy, logₐ(x/y)=logₐx−logₐy, logₐ(xᵏ)=k·logₐx; changing base: logₐb=log꜀b/log꜀a.

Trigonometric identity: sin²x+cos²x=1; the sine rule a/sin A = b/sin B = 2R and cosine rule a²=b²+c²−2bc·cos A.

Volume formulas: sphere V=(4/3)πr³, cone V=(1/3)πr²h, cylinder V=πr²h; cone and sphere surface areas use slant height l=√(r²+h²).

Combinatorics: permutations P(n,k)=n!/(n−k)!, combinations C(n,k)=n!/(k!(n−k)!); the binomial theorem expands (a+b)ⁿ with coefficients C(n,k).

Conditionals: second conditional uses past simple in the if-clause and would + base verb in the main clause (If I knew, I would tell you).

Third conditional uses had + past participle and would have + past participle; it describes unreal past situations.

Reported speech shifts tense back one step: present→past, past→past perfect; time markers change (now→then, tomorrow→the next day).

Passive voice forms be + past participle; the object of the active clause becomes the subject (They built the bridge → The bridge was built).

Present perfect (have/has + past participle) links past action to present relevance; use it with for, since, already, yet, ever, never.

Countable/uncountable: much, little, a few with uncountables versus many, few, a number of with countables; 'a few' means some, 'few' means almost none.

Relative clauses: defining clauses take no commas and allow 'that'; non-defining clauses take commas and never use 'that'.

Formal writing avoids contractions and phrasal verbs where a single Latinate verb exists (find out → determine, get rid of → eliminate).

Mitosis produces two genetically identical diploid cells; meiosis produces four haploid gametes with crossing-over in prophase I.

DNA replication is semi-conservative: helicase unwinds, polymerase adds complementary bases, A pairs with T and C with G.

Mendel's law of segregation: alleles separate during gamete formation; the law of independent assortment applies to genes on different chromosomes.

Cellular respiration: glycolysis in cytoplasm, Krebs cycle in mitochondrial matrix, oxidative phosphorylation on the inner mitochondrial membrane.

Photosynthesis light reactions occur in thylakoid membranes, the Calvin cycle in the stroma; chlorophyll absorbs mainly red and blue light.

Human blood groups follow multiple alleles (Iᴬ, Iᴮ, i); type AB is codominant, type O is recessive and a universal donor for red cells.

Enzymes lower activation energy; activity rises with temperature up to an optimum, then denatures as hydrogen bonds in the active site break.

Classification hierarchy: domena, królestwo, typ, gromada, rząd, rodzina, rodzaj, gatunek (domain down to species).