ESSLCE cheat sheet

Cell theory: all living things are made of cells, cells come from pre-existing cells, and the cell is the basic unit of life; prokaryotes lack a nucleus and membrane-bound organelles, eukaryotes have both.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂; occurs in chloroplasts, with light-dependent reactions in thylakoid membranes and the Calvin cycle in the stroma.

Cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP; glycolysis in cytoplasm, Krebs cycle in mitochondrial matrix, electron transport chain on inner mitochondrial membrane.

Mendelian genetics: dominant allele masks recessive; monohybrid cross of heterozygotes gives 3:1 phenotype ratio and 1:2:1 genotype ratio; test cross uses a homozygous recessive to reveal genotype.

Newton's laws: (1) inertia unless net external force acts, (2) F_net = ma, (3) every action has an equal and opposite reaction; weight = mg where g ≈ 9.8 m/s² on Earth.

Kinematics equations (constant acceleration): v = u + at; s = ut + ½at²; v² = u² + 2as; average velocity = (u + v)/2.

Ohm's law: V = IR; power P = VI = I²R = V²/R; resistors in series add (R_total = R₁ + R₂), in parallel 1/R_total = 1/R₁ + 1/R₂.

Mole concept: 1 mole = 6.022 × 10²³ particles = molar mass in grams; molarity = moles of solute / liters of solution; at STP 1 mole of ideal gas occupies 22.4 L.

Acid-base: pH = −log[H⁺]; strong acid fully dissociates, weak acid partially; neutralization acid + base → salt + water; pH < 7 acidic, pH = 7 neutral, pH > 7 basic.

Quadratic formula: for ax² + bx + c = 0, x = [−b ± √(b² − 4ac)] / (2a); discriminant Δ = b² − 4ac: Δ > 0 two real roots, Δ = 0 one repeated root, Δ < 0 no real roots.

Logarithm rules: log(ab) = log a + log b; log(a/b) = log a − log b; log(aⁿ) = n log a; log_b x = ln x / ln b; log_b b = 1 and log_b 1 = 0.

Trigonometry: sin²θ + cos²θ = 1; sin(A ± B) = sinA cosB ± cosA sinB; cos(A ± B) = cosA cosB ∓ sinA sinB; law of sines a/sinA = b/sinB = c/sinC; law of cosines c² = a² + b² − 2ab cosC.

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

Derivative rules: d/dx(xⁿ) = n xⁿ⁻¹; product rule (uv)' = u'v + uv'; quotient rule (u/v)' = (u'v − uv')/v²; chain rule d/dx f(g(x)) = f'(g(x))·g'(x).

Definite integral: ∫ₐᵇ f(x) dx = F(b) − F(a) where F' = f; area under curve between a and b equals this integral when f(x) ≥ 0.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A ∩ B) = P(A)P(B|A); independent events P(A ∩ B) = P(A)P(B); complementary P(A') = 1 − P(A).

Combinations and permutations: nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!); number of subsets of an n-element set is 2ⁿ.

Ethiopian historical sequence: Aksumite Empire (c. 1st–7th century CE), Zagwe dynasty (c. 1137–1270), Solomonic dynasty restored 1270, Battle of Adwa 1896, Italian occupation 1936–1941, Derg 1974–1991, Federal Democratic Republic from 1991/1995 constitution.

Battle of Adwa (1 March 1896): Ethiopian forces under Emperor Menelik II and Empress Taytu defeated Italy, preserving sovereignty and becoming a symbol of African anti-colonial resistance.

Scramble for Africa: Berlin Conference 1884–1885 set rules for European partition; Ethiopia and Liberia remained independent by the early 20th century.

Earth's structure: crust (continental ~30–70 km, oceanic ~5–10 km), mantle, outer core (liquid), inner core (solid); plate tectonics explains earthquakes, volcanoes, and mountain belts.

Climate controls: latitude, altitude, distance from sea, ocean currents, and prevailing winds; Ethiopia's highlands are cooler due to altitude; the Intertropical Convergence Zone drives seasonal rainfall.

Map scale: scale = map distance / ground distance; large scale shows small area in detail, small scale shows large area with less detail; contour lines connect points of equal elevation.

Civics: rule of law requires government bound by law; separation of powers divides legislature, executive, judiciary; human rights are universal and inalienable; democratic principles include participation, accountability, transparency, and majority rule with minority rights.

Ethical education: values such as honesty, responsibility, respect, justice, and tolerance; civic virtue involves obeying just laws, paying taxes, and participating in community affairs.

English tenses: present simple for habits/facts; present continuous for ongoing actions; present perfect (have/has + past participle) for past actions with present relevance; past simple for finished past events.

Subject-verb agreement: singular subject takes singular verb (he goes), plural subject takes plural verb (they go); indefinite pronouns like everyone, each, nobody are singular.

Conditionals: zero (if + present, present) for general truths; first (if + present, will + base) for real future; second (if + past, would + base) for unreal present; third (if + had + past participle, would have + past participle) for unreal past.

Passive voice: be + past participle; use when the doer is unknown or unimportant, e.g., 'The letter was written yesterday.'

Direct vs indirect speech: shift tense back one step (present → past, past → past perfect), change pronouns, and adjust time/place words (now → then, here → there).

Amharic (Ge'ez script) is written left to right with an abugida system; each consonant has vowel-modified forms; the language is Semitic and uses subject-object-verb order.

Affan Oromoo uses the Latin alphabet (Qubee) with digraphs such as ch, dh, ny, ph, sh; it is a Cushitic language with subject-object-verb order and grammatical gender.

Tigrigna uses the Ge'ez script like Amharic; it is a Semitic language with subject-object-verb order and a system of grammatical gender; the definite article is a suffix.

Reading comprehension strategy: identify main idea, supporting details, author's purpose, tone, and inference; distinguish fact from opinion; use context clues for unfamiliar vocabulary.

Number series: check differences (constant, increasing, alternating), ratios, squares/cubes, primes, and Fibonacci-type patterns; test each rule against at least three terms before committing.

Percentage: part = percent × whole; percent change = (new − old)/old × 100%; successive changes multiply, e.g., +10% then −10% gives net −1%.

Ratio and proportion: if a:b = c:d then ad = bc; to divide a quantity Q in ratio a:b:c, shares are Q·a/(a+b+c), Q·b/(a+b+c), Q·c/(a+b+c).

Work and rate: if A finishes a job in a days and B in b days, together they finish in ab/(a+b) days; rate = work / time.

Speed, distance, time: distance = speed × time; average speed for equal distances = 2v₁v₂/(v₁ + v₂), not the arithmetic mean.

Syllogism validity: an argument is valid if the conclusion follows necessarily from the premises; a valid argument with true premises is sound; watch for undistributed middle and illicit conversion.

Analogy and classification: identify the relationship (part-to-whole, cause-effect, synonym, function) and apply the same relation to the answer pair; for odd-one-out, find the shared property of all but one item.

Data interpretation: read axes and units carefully; compute totals, averages, and percentages from tables or bar/line charts; check whether the question asks for absolute value or percent.