Free DCAT Exam Flashcards

A sequence where each term differs from the next by a constant amount (common difference). Find it by subtracting consecutive terms; if the difference is constant, add it to the last term to get the next number.

A quadratic sequence has constant nonzero second differences: subtract consecutive terms, then subtract consecutive first differences. For 2, 5, 10, 17, the first differences are 3, 5, 7 and second differences are 2, 2. The next gap is 9, giving 26.

A sequence where each term is multiplied by a constant ratio to get the next term (e.g., 2, 6, 18, 54... ratio = 3). Find the ratio by dividing a term by the one before it.

Identify the single consistent transformation applied across the figures — rotation, reflection, added or removed elements, size change, or shading — then apply that same transformation to find the missing figure.

Pairs like 'thermometer : temperature :: barometer : pressure' link a tool to the exact quantity it measures. Identify the relationship in the first pair, then find the answer pair with the same relationship.

One word names a part or member of the category named by the other word (e.g., 'petal : flower' or 'chapter : book'). Match the direction of the relationship — part-to-whole, not whole-to-part — in your answer choice.

'All A are B' means every A is inside B, but it does NOT mean all B are A. From 'All A are B' and 'All B are C,' you can validly conclude 'All A are C.'

'Some A are B' means at least one member belongs to both groups, so 'Some B are A' follows with certainty. It does not establish that all A are B. Whether a particular 'some' group overlaps a third category depends on the other premises.

Each letter is shifted a fixed number of positions in the alphabet (e.g., A to D is a +3 shift). Find the shift amount from one known letter pair, then apply it consistently to decode or encode the rest.

For an ordinary 12-hour clock, set H to the hour modulo 12 and M to the minutes. Compute d = |30H - 5.5M| degrees. The smaller angle is min(d, 360 - d). At 3:00 it is 90 degrees; at 11:00, d = 330 and the smaller angle is 30 degrees.

For ax^2 + bx + c = 0 with a not equal to 0, x = (-b +/- sqrt(b^2 - 4ac)) / (2a). The entire numerator is divided by 2a. A negative discriminant gives no real roots.

a^2 - b^2 = (a + b)(a - b). Recognize perfect-square terms separated by subtraction to factor instantly (e.g., x^2 - 9 = (x + 3)(x - 3)).

y = mx + b, where m is the slope (rise/run) and b is the y-intercept. Two points give the slope: m = (y2 - y1) / (x2 - x1). The two-point slope formula requires x2 not equal to x1; a vertical line has undefined slope.

In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse (the side opposite the right angle). Used to find a missing side when the triangle has a 90-degree angle.

Area = (pi)r^2; Circumference = 2(pi)r (or (pi)d), where r is the radius and d is the diameter. Remember d = 2r.

sin(theta) = Opposite/Hypotenuse, cos(theta) = Adjacent/Hypotenuse, tan(theta) = Opposite/Adjacent. Use these to find a missing side or angle in a right triangle.

Distance = Rate x Time (d = rt). Rearrange to solve for rate (r = d/t) or time (t = d/r) depending on what a word problem asks for.

For constant independent work rates, a worker taking a hours has rate 1/a job per hour. Two workers taking a and b hours separately finish together in t hours where 1/t = 1/a + 1/b. Add rates, not completion times.

Percentage change = [(New Value - Original Value) / Original Value] x 100%. A positive result is an increase; a negative result is a decrease.

Mean = sum of values divided by number of values. Median = the middle value when data is ordered (average the two middle values if the count is even). Mode = the value that appears most often.

An atom’s nucleus contains positively charged protons and, usually, neutral neutrons. Negatively charged electrons occupy orbitals around it. Atomic number = protons; mass number = protons + neutrons.

At 25 degrees Celsius, a neutral aqueous solution has pH 7; lower values are acidic and higher values basic. Lower pH means greater hydronium concentration, not necessarily a stronger acid: concentration also matters. The familiar 0–14 scale is not an absolute limit.

Common formula/name pairs: NaCl = sodium chloride (table salt); H2O = water; CO2 = carbon dioxide; NaHCO3 = sodium bicarbonate (baking soda); CaCO3 = calcium carbonate. Use these for general chemistry recall.

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force. Also called the law of inertia.

Force equals mass times acceleration: F = ma. A larger force produces greater acceleration; a larger mass requires more force for the same acceleration.

Length = meter (m), mass = kilogram (kg), time = second (s), temperature = kelvin (K), electric current = ampere (A). SI units standardize scientific measurement worldwide.

Typical plant cells have a cell wall and large central vacuole; photosynthetic plant cells also have chloroplasts. Animal cells lack a cell wall and chloroplasts. Typical plant and animal cells both have a nucleus, mitochondria and a cell membrane.

In a simple complete-dominance model, Bb shows the dominant phenotype and bb shows the recessive phenotype. A dominant allele does not become more common just because it is dominant; not all inherited traits follow this simple model.

Overall aerobic respiration: C6H12O6 + 6O2 -> 6CO2 + 6H2O + released energy. Cells capture part of the released energy in ATP; some is released as heat. This equation describes oxygen-using respiration.

Igneous rock forms from cooled magma/lava; sedimentary rock forms from compacted and cemented sediment layers; metamorphic rock forms when heat and pressure transform existing rock. Each type can transform into another.

A singular subject takes a singular verb; a plural subject takes a plural verb (e.g., 'The list of items is long' — 'list' is singular, so use 'is,' not 'are,' despite 'items' being nearby).

Use subjective pronouns (I, he, she, they, we) as the subject of a verb, and objective pronouns (me, him, her, them, us) as the object of a verb or preposition (e.g., 'Between you and me,' not 'Between you and I').

Items joined in a series or comparison must share the same grammatical form (e.g., 'She likes reading, writing, and swimming' — not 'to read, writing, and swim'). Consistent forms make the list parallel.

Separate three or more items in a list with commas (e.g., 'red, white, and blue'). Also use a comma before a coordinating conjunction (and, but, or) joining two independent clauses.

A semicolon joins two complete, related independent clauses without a conjunction ('I studied hard; I passed the exam'). A comma alone cannot join two independent clauses — that error is called a comma splice.

'Affect' is usually a verb meaning 'to influence' ('Stress can affect your score'). 'Effect' is usually a noun meaning 'a result' ('The effect was clear').

'Its' (no apostrophe) is a possessive pronoun ('The dog wagged its tail'). 'It's' (with apostrophe) is a contraction of 'it is' or 'it has' ('It's raining today').

'Then' refers to time or sequence ('Finish the essay, then review it'). 'Than' is used for comparisons ('Math is harder than English for me').

When asked for a word's synonym, look for the answer choice closest in both meaning and degree/connotation to the given word — not just a loosely related term (e.g., 'furious' is closer to 'enraged' than to 'annoyed').

For antonym items, first define the given word precisely, then find the choice that expresses the opposite meaning — watch for answer choices that are merely unrelated rather than truly opposite.

Recognizing Greek/Latin roots unlocks unfamiliar vocabulary: 'bio-' = life, 'geo-' = earth, '-ology' = study of, 'chrono-' = time, 'phon-' = sound, 'micro-' = small. Break unknown words into roots to estimate meaning.

An idiom's meaning cannot be worked out word-by-word (e.g., 'break the ice' means to ease initial social tension, not to literally break ice). Learn idioms as whole-phrase meanings.

The main idea is the central point the whole passage supports — usually stated or implied in the first or last paragraph. Eliminate answer choices that describe only one supporting detail rather than the passage as a whole.

An inference is a conclusion drawn from clues in the text, not directly stated. The correct inference must be strongly supported by the passage — avoid choices that require outside knowledge or go beyond what the text implies.

The Philippines declared independence from Spain on June 12, 1898, in Kawit, Cavite, under Gen. Emilio Aguinaldo. Independence Day is celebrated as a national holiday every June 12.

A peaceful, mass civilian uprising in February 1986 (Feb. 22-25) that ousted President Ferdinand Marcos Sr. and restored democratic government, installing Corazon Aquino as president.

Luzon is the largest and most populous island in the Philippines, home to Metro Manila. The Philippine archipelago consists of roughly 7,600+ islands grouped into Luzon, Visayas, and Mindanao.

Executive (President, enforces laws), Legislative (Congress: Senate + House of Representatives, makes laws), and Judicial (Supreme Court and lower courts, interprets laws) — a system of checks and balances.

Jose Rizal is widely honored as a Philippine national hero. A writer and reformist, he was executed on December 30, 1896. His novels 'Noli Me Tangere' and 'El Filibusterismo' criticized abuses under Spanish colonial rule.

For situational items on conduct, teamwork, or exam-day decisions, choose the response that follows official rules, prioritizes safety and honesty, and reflects cooperative, professional behavior — not the fastest or most convenient option.