Free PMA Entrance Exam Exam Flashcards

Solve expressions using PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Errors here are a top cause of missed arithmetic items.

Isolate the variable by performing the same operation on both sides: combine like terms, then undo addition/subtraction before multiplication/division. Example: 3x + 5 = 20 -> 3x = 15 -> x = 5.

Use substitution (solve one equation for a variable, plug into the other) or elimination (add/subtract equations to cancel a variable). Both methods give the same (x, y) solution.

For ax^2 + bx + c = 0, x = (-b +/- sqrt(b^2 - 4ac)) / 2a. Use it when a quadratic doesn't factor cleanly.

Part = Percent x Whole (as a decimal). To find percent change: (New Value - Old Value) / Old Value x 100%.

A ratio compares two quantities (a:b); a proportion sets two ratios equal (a/b = c/d). Solve by cross-multiplying: a x d = b x c.

Distance = Rate x Time (d = rt). Rearrange to r = d/t or t = d/r depending on what's unknown. Watch for unit conversions (hours vs minutes).

Rectangle: length x width. Triangle: 1/2 x base x height. Circle: pi x r^2. Trapezoid: 1/2 x (base1 + base2) x height.

Perimeter of a polygon = sum of all side lengths. Circumference of a circle = 2 x pi x r (or pi x diameter).

For a right triangle with legs a and b and hypotenuse c: a^2 + b^2 = c^2. Used to find a missing side when two sides are known.

Sum of interior angles = (n - 2) x 180 degrees, where n is the number of sides. A triangle's angles always sum to 180 degrees; a quadrilateral's to 360 degrees.

A singular subject takes a singular verb; a plural subject takes a plural verb. Ignore intervening phrases: 'The list of items is long' (subject is 'list,' not 'items').

A pronoun must match its antecedent in number and gender. Example: 'Each student must bring his or her ID' (singular 'each' takes a singular pronoun, not 'their' in strict formal usage).

their (possessive) vs there (place) vs they're (they are); its (possessive) vs it's (it is); your (possessive) vs you're (you are).

When unsure of a word's meaning, use context clues in the surrounding sentence and eliminate answer choices with the opposite or unrelated meaning first.

Identify the given word's core meaning, then look for the choice that expresses the most direct opposite - not just a loosely related or milder contrast.

Noun, pronoun, verb, adjective, adverb, preposition, conjunction, and interjection - the building blocks tested in grammar and sentence-correction items.

Keep verb tense consistent within a sentence or passage unless a clear time shift is indicated. Watch for shifts like 'She walks to school and finished her homework' (inconsistent).

Active voice: subject performs the action ('The cadet fired the rifle'). Passive voice: subject receives the action ('The rifle was fired by the cadet'). Active voice is usually clearer and preferred.

The main idea is the passage's central point (often in the topic sentence); supporting details are the facts, examples, or reasons that back it up. Don't confuse a supporting detail for the main idea.

'Affect' is usually a verb meaning to influence ('The heat affected performance'). 'Effect' is usually a noun meaning a result ('The heat had an effect on performance').

Simple (one independent clause), compound (two independent clauses joined by a conjunction), complex (independent + dependent clause), compound-complex (two+ independent clauses plus a dependent clause).

When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality sign. Adding or subtracting the same value does not reverse it.

For the same nonzero base, add exponents when multiplying and subtract exponents when dividing: a^m × a^n = a^(m+n), and a^m / a^n = a^(m-n).

For addition or subtraction, first use a common denominator. For multiplication, multiply numerators and denominators. For division, multiply by the reciprocal.

Slope is change in y divided by change in x: (y2 - y1)/(x2 - x1). A horizontal line has slope 0; a vertical line has undefined slope.

A triangle's interior angles total 180°. An exterior angle equals the sum of the two non-adjacent interior angles.

Diameter equals twice the radius. Circumference is 2πr or πd, while area is πr². Keep linear and square units separate.

Round inputs to convenient values and predict the answer's sign, size, and unit. Estimation helps eliminate options and catches calculator-free arithmetic slips.

Items in a series or comparison should use matching grammatical forms. If one item begins with a gerund or infinitive, coordinate items should match unless meaning requires otherwise.

Place a descriptive phrase next to the word it modifies. If the nearest noun creates an illogical meaning, revise the sentence so the modifier clearly attaches to its target.

Scan each figure for one changing attribute at a time - rotation direction/angle, added or removed lines/shapes, size change, or shading - then predict the next logical step in that single pattern.

First define the precise relationship between the first pair (e.g., part-to-whole, cause-effect, synonym), then find the answer choice that reproduces that exact relationship with the second pair.

In a 3x3 grid, check for a rule that holds consistently across each row AND each column (e.g., shapes rotate, elements are added, or attributes alternate) before selecting the missing piece.

Test the differences between consecutive terms first (constant, increasing, or decreasing), then test ratios or alternating patterns (e.g., +2, x2, +2, x2) if a simple difference doesn't fit.

Identify the shared property among most items in a set (category, function, or attribute) and eliminate the one item that breaks that shared rule.

A reflected figure flips across an axis (line of symmetry) - left and right (or top and bottom) elements swap position and orientation without changing size.

A syllogism draws a conclusion from two premises (e.g., 'All A are B; all B are C; therefore all A are C'). Check that the conclusion follows strictly from the given premises, not from outside assumptions.

Track how many degrees a figure rotates each step (e.g., 45, 90, or 135 degrees clockwise or counterclockwise) and apply the same consistent rotation to find the next figure.

Some series use alphanumeric substitution (A=1, B=2, ... Z=26). Convert letters to numbers to reveal an underlying numeric pattern, then convert the answer back to a letter.

Every pronoun should point clearly to one antecedent and agree with it in number. Rewrite when two possible antecedents make the reference ambiguous.

Use the comparative form for two items and the superlative for three or more. Adverbs modify actions, so choose forms such as more clearly rather than more clear.

Read the sentence before and after an unfamiliar word, identify contrast, definition, example, or cause clues, then test each option in the original sentence.

An inference must follow from passage evidence. Reject choices that may be true generally but add claims, causes, or certainty the text does not support.

State the relationship in the first pair as a short sentence, then choose the second pair that preserves the same direction and degree.

Check consecutive differences first, then ratios, alternating operations, and interleaved sequences. Prefer the simplest rule that explains every transition.

When one rule does not fit adjacent terms, split odd-position and even-position terms into two sequences and test each independently.

Track count, position, direction, shading, size, and combination one attribute at a time. The correct option must satisfy every active change.

A rotation turns every point around a center while preserving orientation order; a reflection flips the figure across an axis and reverses handedness.

Accept only conclusions that must follow from the stated premises. Do not import outside facts or assume the converse of a one-way statement.