Free Praxis Core Exam Flashcards

The central point or most important concept in a passage. Often stated in the first or last paragraph, but may be implied. Ask: 'What is the author's primary message?' Distinguish from supporting details, which provide evidence.

The reason an author writes a text. Common purposes include to inform (provide facts), persuade (convince readers), entertain (amuse), or explain (clarify). Identify through word choice, tone, and content selection.

A conclusion drawn from evidence and reasoning rather than explicit statements. Requires reading between the lines using textual clues and prior knowledge. Valid inferences must be supported by the text.

The author's attitude toward the subject, revealed through word choice and style. Examples: objective, critical, humorous, sarcastic, sympathetic, formal. Different from mood (the reader's feeling) or topic (the subject).

Information surrounding an unfamiliar word that helps determine its meaning. Types include definition (direct explanation), example, contrast, synonym, and inference clues. Essential skill for vocabulary questions on standardized tests.

Facts are verifiable statements that can be proven true or false. Opinions are personal beliefs, judgments, or interpretations. Signal words for opinions: 'I think,' 'should,' 'best,' 'probably.' Critical for evaluating arguments.

The organizational pattern of a passage. Common structures: chronological (time order), cause-effect, compare-contrast, problem-solution, and description. Recognizing structure aids comprehension and prediction.

A sentence that expresses the main argument or claim of an essay. Should be specific, arguable, and provide direction for the essay. Typically appears at the end of the introduction. All body paragraphs should support the thesis.

The sentence that states the main idea of a paragraph. Usually appears first in the paragraph and introduces what the paragraph will discuss. Should connect to the thesis and be supported by details in the paragraph.

The logical flow and connection of ideas in writing. Achieved through transitional words, consistent point of view, logical organization, and clear pronoun references. Reader should easily follow the progression of ideas.

Words and phrases that connect ideas and show relationships. Examples: however (contrast), therefore (conclusion), furthermore (addition), similarly (comparison), consequently (cause-effect). Improve flow and coherence.

Using the same grammatical form for items in a series or comparison. Example: 'She likes hiking, swimming, and biking' (not 'hiking, swimming, and to bike'). Creates rhythm and clarity in writing.

Subjects and verbs must match in number. Singular subjects take singular verbs; plural subjects take plural verbs. Watch for intervening phrases: 'The box of cookies is on the table' (box is the subject, not cookies).

Pronouns must agree in number and gender with their antecedents. 'Each student must bring his or her book' or 'All students must bring their books.' Avoid unclear references where the antecedent is ambiguous.

Two or more independent clauses joined without proper punctuation or conjunction. Fix with: period and capital letter, semicolon, comma with coordinating conjunction, or subordinating one clause. Example error: 'I was tired I went to bed.'

Incomplete sentences lacking a subject, verb, or complete thought. Common fragments: dependent clauses alone, phrases without verbs, or -ing words without helping verbs. Every sentence must express a complete idea.

Error where two independent clauses are joined with only a comma. Fix with: semicolon, period, comma with conjunction, or subordination. Incorrect: 'I was tired, I went to bed.' Correct: 'I was tired, so I went to bed.'

A modifying phrase that doesn't clearly connect to the word it modifies. Example: 'Walking to school, the rain started' (the rain wasn't walking). Fix: 'Walking to school, I got caught in the rain.'

Words often mixed up: affect/effect (verb/noun), their/there/they're, its/it's, then/than, accept/except, principal/principle, who/whom. Know the distinctions for both usage and spelling questions.

Introduction (hook, background, thesis), body paragraphs (topic sentence, evidence, analysis), counterargument and rebuttal, conclusion (restate thesis, broader significance). Each body paragraph should focus on one main point.

Information used to support claims: facts, statistics, examples, expert opinions, and personal anecdotes. Evidence must be relevant, sufficient, and properly integrated. Always explain how evidence supports your point.

Acknowledging and responding to opposing viewpoints. Strengthens your argument by showing you've considered alternatives. Follow with rebuttal explaining why your position is stronger. Shows critical thinking.

Effective openings include: surprising fact or statistic, relevant anecdote, thought-provoking question, quotation, or vivid description. Avoid dictionary definitions and overly broad statements. Hook should connect to thesis.

Effective conclusions: restate thesis in new words, synthesize main points, call to action, broader implications, or return to opening image. Avoid introducing new arguments or simply summarizing. Leave lasting impression.

PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Example: 3 + 4 × 2 = 3 + 8 = 11, not 14. Critical for correctly solving multi-step problems.

Addition/subtraction: need common denominator. Multiplication: multiply numerators and denominators. Division: multiply by reciprocal. Simplify results. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Use the formula: part = percent × whole. To find percent: (part/whole) × 100. Percent increase/decrease: (change/original) × 100. Convert percents to decimals by dividing by 100.

A ratio compares two quantities (3:4 or 3/4). A proportion states two ratios are equal. Cross multiply to solve: if a/b = c/d, then ad = bc. Used for scaling, unit rates, and similar figures.

Prime numbers have exactly two factors: 1 and themselves (2, 3, 5, 7, 11...). Composite numbers have more than two factors. 1 is neither prime nor composite. 2 is the only even prime number.

Isolate the variable using inverse operations: add/subtract terms to get variable terms on one side, multiply/divide to solve. Example: 2x + 5 = 13 → 2x = 8 → x = 4. Check solution by substituting back.

The rate of change in a linear relationship, calculated as rise/run or (y₂-y₁)/(x₂-x₁). Positive slope rises left to right; negative falls. Slope of 0 is horizontal; undefined slope is vertical.

y = mx + b, where m is slope and b is y-intercept. Used to graph lines and write equations. Example: y = 2x - 3 has slope 2 and y-intercept -3 (crosses y-axis at (0,-3)).

Two or more equations with the same variables. Solve by graphing (intersection point), substitution (solve for one variable, substitute), or elimination (add/subtract equations). Solution is ordered pair satisfying both equations.

Statements using <, >, ≤, ≥. Solve like equations, but flip the inequality sign when multiplying or dividing by a negative. Graph on number line with open (< or >) or closed (≤ or ≥) circles.

Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ. Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Power rule: (aᵐ)ⁿ = aᵐⁿ. Zero exponent: a⁰ = 1. Negative exponent: a⁻ⁿ = 1/aⁿ.

Sum of interior angles = 180°. Exterior angle equals sum of non-adjacent interior angles. Triangle inequality: sum of any two sides must exceed the third side. Types: equilateral, isosceles, scalene; acute, right, obtuse.

In a right triangle, a² + b² = c², where c is the hypotenuse. Used to find missing sides. Common triples: 3-4-5, 5-12-13, 8-15-17. Only applies to right triangles.

Rectangle: A = lw. Triangle: A = ½bh. Circle: A = πr². Parallelogram: A = bh. Trapezoid: A = ½(b₁ + b₂)h. Memorize these formulas for the Praxis Core exam.

Perimeter: sum of all sides. Rectangle: P = 2l + 2w. Circumference of circle: C = 2πr or πd. Units are linear (cm, ft), while area is squared (cm², ft²).

Rectangular prism: V = lwh. Cylinder: V = πr²h. Cone: V = ⅓πr²h. Sphere: V = ⁴⁄₃πr³. Volume is measured in cubic units. Surface area is the total area of all faces.

Congruent figures have same shape AND size (all corresponding parts equal). Similar figures have same shape but may differ in size (corresponding angles equal, sides proportional). Use proportions to find missing lengths in similar figures.

Mean: sum divided by count (average). Median: middle value when ordered (or average of two middle values). Mode: most frequent value. Choose appropriate measure based on data distribution and outliers.

Range: difference between highest and lowest values. Standard deviation: measure of spread from the mean (larger = more spread). These describe data variability, not central tendency.

P(event) = favorable outcomes / total outcomes. Ranges from 0 (impossible) to 1 (certain). Complement: P(not A) = 1 - P(A). Independent events: P(A and B) = P(A) × P(B).

Identify axes, scales, and units. Bar graphs compare categories; line graphs show change over time; pie charts show parts of a whole; scatter plots show relationships. Avoid misinterpreting scales or drawing unsupported conclusions.

Displays five-number summary: minimum, Q1 (25th percentile), median (Q2), Q3 (75th percentile), maximum. The box shows the middle 50% of data (interquartile range). Whiskers extend to min and max.

The relationship between two variables. Positive correlation: both increase together. Negative correlation: one increases, other decreases. No correlation: no relationship. Correlation does not imply causation.

Random sample: every member has equal chance of selection (reduces bias). Bias sources: self-selection, leading questions, non-representative sample. Sample size affects reliability of conclusions.

Read carefully, identify what's asked. Define variables. Translate words to math: 'is' means equals, 'of' means multiply, 'per' means divide. Set up equation, solve, check if answer is reasonable.

Commutative: a + b = b + a. Associative: (a + b) + c = a + (b + c). Distributive: a(b + c) = ab + ac. Identity: a + 0 = a, a × 1 = a. Inverse: a + (-a) = 0, a × (1/a) = 1.