Tubman University Placement Exam cheat sheet

Main idea = the single point the whole passage supports; supporting details answer who, what, when, where, why, how.

Topic sentence usually appears first or last in a paragraph; a sentence that only adds an example is a detail, not the main idea.

Inference rule: a valid inference must be forced by the text; if it needs outside knowledge, it is not an inference.

Context-clue types: definition (is, means), contrast (but, however), example (such as, for instance), cause-effect (because, therefore).

Tone words to recognize: neutral, critical, sympathetic, humorous, nostalgic, objective, sarcastic; tone is the author's attitude, mood is the reader's feeling.

Fact vs. opinion test: a fact can be verified; an opinion contains value words such as best, should, beautiful, unfair.

Pronoun reference: the nearest preceding noun that agrees in number and gender is usually the antecedent.

Sequence markers (first, then, finally, meanwhile, after) signal chronological order; comparison markers (similarly, unlike) signal compare-contrast structure.

Order of operations: Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right.

Percent change = (new − old) ÷ old × 100%; percent of a number = rate × base (e.g., 15% of 80 = 0.15 × 80 = 12).

Slope m = (y₂ − y₁)/(x₂ − x₁); slope-intercept form y = mx + b; parallel lines share m, perpendicular slopes multiply to −1.

Area formulas: rectangle A = lw; triangle A = ½bh; circle A = πr², circumference C = 2πr; trapezoid A = ½(b₁ + b₂)h.

Pythagorean theorem a² + b² = c² for right triangles, with c the hypotenuse; common triples: 3-4-5, 5-12-13, 8-15-17.

Mean = sum ÷ count; median = middle value of an ordered list; mode = most frequent value; range = max − min.

Simple interest I = Prt; distance = rate × time; average speed = total distance ÷ total time.

Exponent rules: xᵃ·xᵇ = xᵃ⁺ᵇ; xᵃ/xᵇ = xᵃ⁻ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1 for x ≠ 0; x⁻ᵃ = 1/xᵃ.

Factoring: a² − b² = (a + b)(a − b); a quadratic ax² + bx + c = 0 has roots x = [−b ± √(b² − 4ac)] ÷ 2a.

Cell theory: all living things are made of cells, the cell is the basic unit of life, and cells arise from existing cells.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts; respiration reverses it in mitochondria.

Newton's laws: inertia (no net force means no change in motion), F = ma, and equal-and-opposite action-reaction pairs.

States of matter: solid (fixed shape and volume), liquid (fixed volume, variable shape), gas (variable shape and volume); heating increases particle motion.

Atomic structure: protons (+) and neutrons in the nucleus, electrons (−) in shells; atomic number = protons; mass number = protons + neutrons.

Water cycle stages: evaporation, transpiration, condensation, precipitation, collection/runoff.

Food chain order: producer → primary consumer → secondary consumer → decomposer; energy decreases at each level (roughly 10% transferred).

Human body: heart pumps blood through arteries away from the heart and veins toward it; lungs exchange oxygen and carbon dioxide in alveoli.

Density = mass ÷ volume; an object denser than its fluid sinks, less dense floats.

Liberia was founded by the American Colonization Society; freed African Americans arrived beginning in 1822, and independence was declared on 26 July 1847.

Liberia's capital is Monrovia, named after U.S. President James Monroe; the country lies on the West African coast and borders Sierra Leone, Guinea, and Côte d'Ivoire.

Three branches of government: executive (president enforces laws), legislative (makes laws), judicial (interprets laws); checks and balances prevent concentration of power.

A constitution is the supreme law of a state; statutes are passed by the legislature, and courts may review them.

Basic civic duties include obeying laws, paying taxes, jury or voting participation where eligible, and respecting others' rights.

U.S. history markers: Declaration of Independence 1776, Constitution 1787, Civil War 1861–1865, civil rights movement of the 1950s–1960s.

Major international bodies: the United Nations (founded 1945, headquarters New York), African Union (2002, headquarters Addis Ababa), ECOWAS (1975, headquarters Abuja).

Map skills: latitude lines run east-west and measure north-south position; longitude lines run north-south and measure east-west position; the Equator is 0° latitude.

A paragraph needs unity (one controlling idea), coherence (logical order and transitions), and adequate development.

Sentence fragment = missing subject, verb, or complete thought; run-on = two independent clauses joined without proper punctuation or conjunction.

Comma rules: separate items in a series, set off introductory elements, join a dependent clause to an independent clause, and mark nonessential information.

Subject-verb agreement: a singular subject takes a singular verb; intervening phrases do not change the number (e.g., 'The box of books is heavy').

Active voice puts the doer first ('The committee approved the plan'); passive voice puts the receiver first ('The plan was approved').

Formal writing avoids contractions, slang, and second-person 'you' in academic essays; it prefers precise nouns and verbs over vague ones.

Transition words by function: addition (moreover), contrast (however), cause (therefore), example (for instance), sequence (subsequently).

An essay structure: introduction with a thesis, body paragraphs each with a topic sentence and evidence, and a conclusion that restates rather than introduces.

Ratio and proportion: set up a/b = c/d and cross-multiply (ad = bc) to solve for an unknown.

Work-rate rule: if one worker finishes a job in a hours, the rate is 1/a per hour; combined rate = 1/a + 1/b, and time = 1 ÷ combined rate.

Number series: check differences first, then ratios, then alternating patterns; Fibonacci-type series add the two previous terms.

Probability = favorable outcomes ÷ total outcomes; independent events multiply (P(A and B) = P(A) × P(B)).

Combinations count unordered selections: C(n, r) = n! ÷ [r!(n − r)!]; permutations count ordered arrangements: P(n, r) = n! ÷ (n − r)!.

Logical statements: the contrapositive (not B implies not A) is equivalent to 'if A then B'; the converse is not equivalent.

Averages shortcut: if every value increases by k, the mean increases by k; total = mean × count.

Data interpretation: read axis labels and units before computing; a percentage-point change (e.g., 20% to 25%) differs from a percent change (25% increase).