GRE Complete Prep: How to Score 330+ for Top Grad Schools

Learn the order of operations using pendas, solve basic equations, and isolate variables by reversing the order of operations, with examples of combining coefficients and roots.

Master the order of operations using PEMDAS, including parentheses, exponents, multiplication, division, addition, and subtraction, and practice solving basic equations with variables and fractions.

Master solving systems of two equations using substitution or elimination, isolate variables, compare methods, and practice solving for Y in varied problems.

Practice solving two-equation systems using substitution and elimination. Derive y from 6y-4x=12 and find c = -27 via elimination in 4b+3c=-17 and -38-b=c.

Explore exponents and roots, including base and exponent notation, negative exponents as reciprocals, and fractional exponents that define roots. Apply exponent rules for multiplication, division, and prime factorization in roots.

Practice solving exponents and roots by applying reciprocal rules for negative exponents and simplifying roots. Learn quick reasoning to solve equations with odd roots without calculators.

Master distribution and factoring by applying the foil method to multiply polynomials, identify common factors, and verify results by distributing.

Review distribution and factoring using foil on (2 w^2 + 3 x^3)(y^4 - 5 z^3) and explore factoring by greatest common factor, plus a quantitative comparison showing both expressions are equal.

Identify quadratics by moving all terms to one side and factoring. Apply the zero-product property and factor pairs to solve for x.

Explore quadratic factoring to solve for X. Set the equation to zero, factor out A, choose two numbers that multiply to C and add to B, yielding two solutions.

Master three special quadratics: a^2 - b^2 = (a+b)(a-b); a^2 + 2ab + b^2 = (a+b)^2; a^2 - 2ab + b^2 = (a-b)^2. Memorize, recognize, and practice to solve quickly.

Recognize and factor special quadratics by identifying a^2 - b^2, and a^2 + 2ab + b^2, then use the foil method to factor (t^4 + 3v^3)^2.

Master the quadratic formula and know when to use it as a backup for solving quadratics. Compare it with factoring, and practice to get two possible values for x quickly.

Review the quadratic formula to solve quadratic equations in standard form. Identify a, b, c and compute x values using the plus and minus cases.

master completing the square to rewrite quadratics as a squared binomial, using d and e formulas and factoring out a. apply techniques to find vertices and solve varied equations.

Transform AX^2 + BX + C into A(X + D)^2 + E using D = B/(2A) and E = C - B^2/(4A), and complete the square through exercises.

Master inequalities by interpreting symbols and translating statements into algebra. Solve with sign rules, handle compound inequalities, and plot solutions on a number line.

Learn to solve inequalities by isolating variables and flipping signs for negatives, using X bounds 10–40 and Y bounds 4–12 to compare the minimum X times Y to 45.

Explore absolute value inequalities by treating the absolute value as distance from zero, isolating it, splitting into two cases, and verifying solutions to avoid extraneous results on a number line.

Practice solving absolute value inequalities for GRE prep: isolate the absolute value, split into two cases, and graph solutions on a number line.

Define and apply functions as relationships between inputs and outputs, using F(X), domain and range, and work from the inside to the outside when solving compound functions.

Explore function practice by solving nested functions and compositions, such as F(G(y)) and G(F(y)), using the quadratic formula and foil method to compare results.

Explore strange symbol functions in algebra, where symbols represent functions and you evaluate inside the parentheses first, then substitute A and B to compute results.

Solve practice exercises on strange symbol functions by substituting values for h, p, a, b, y, and z, and evaluating results for three problems step by step.

This algebra lecture explains simple and compound interest, defines principal, rate, and time, and applies the formulas P×R×T and P×(1+R/N)^(N×T) with a 10,000-dollar loan.

Explore compound and simple interest through loan calculations: apply the compound interest formula with quarterly compounding, compare with simple interest, and determine total amounts due.

Identify patterns in sequences and convert them into formulas, distinguishing direct from recursive types. Learn how terms relate to position or prior terms to predict large terms.

Explore sequence patterns and recurrence relations, compute successive terms from formulas like b_n = 4 b_{n-1} - 3 and a_n = 3 a_{n-1} + 2, and determine term differences.

Explore the coordinate plane, plot points with ordered pairs, and graph lines using slope, intercepts, and slope-intercept form, including the distance formula.

Explore graphing practice by plotting ordered pairs, computing slopes, converting to slope intercept form, identifying y intercepts and x intercepts, and applying the distance formula to measure distances between points.

learn to find the intersection of two lines using slope-intercept form and solving when y values are equal, and identify parallel lines or the same line.

Practice solving line intersections by equating y, converting to slope-intercept form, and identifying parallel lines by equal slopes.

Graph inequalities by drawing lines (solid for ≥/≤, dashed for < or >) and shading; absolute values form v shapes with vertex (A, B) opening up or down.

Practice techniques for graphing inequalities and absolute value functions, including slope-intercept form, shading regions, dashed and solid lines, and identifying the vertex.

Graph quadratics and parabolas, noting axis of symmetry, line intersections, and how coefficients influence opening and width. Convert to vertex form by completing the square to locate the vertex.

Review intersections of a parabola and a line, solve quadratics by setting equations equal, and use completing the square and vertex form to locate the vertex and describe graph shape.

Learn to solve rate problems with the RTD formula and units. Explore moving objects toward, away, and in the same direction, and apply weighted average concepts.

Use the rate-time-distance approach to solve collision and pursuit problems, comparing approaching versus same-direction motion, then compute total time and distance to find average speed.

Explore lines in this geometry lecture: straight lines measure 180 degrees, parallel lines never intersect, perpendicular lines form right angles, and opposite and adjacent angles relate to 360 and 180.

Reviews line-angles practice: analyzes two parallel lines, identifies small and large angle pairs, and uses 180/360 degree sums to solve for expressions like x+c+d.

Explore polygons: closed two-dimensional shapes with at least three sides, learn perimeter and area, and apply interior angles sum formula N minus two times 180 to triangles, squares, and pentagons.

Solve polygon angle problems by applying the interior angle sum formula (n-2) times 180, determine missing angles, and compute perimeters when sides are equal.

Master triangles fundamentals, including area and perimeter, angle sums, and the three main types; apply the Pythagorean theorem and memorize key triplets and 30-60-90 and isosceles right ratios.

Review right-triangle problems by applying the pythagorean theorem to find the missing leg, then compute area as one-half base times height, and determine a square's diagonal and 30-60-90 triangles.

Explore quadrilaterals by examining squares, rectangles, parallelograms, and trapezoids, their properties, the sum of interior angles to 360 degrees, and how to compute area and perimeter.

Practice quadrilateral area and perimeter problems by decomposing into triangles and a central quadrilateral, using base, height, and the Pythagorean theorem, then compare area to perimeter.

Learn area optimization: for fixed perimeter, the square maximizes quadrilateral area; for triangles, perpendicular sides maximize area; with x plus y equal to 60 cm, the area is 450 cm².

With a fixed perimeter, maximum area occurs when shapes are as square-like as possible; a right isosceles triangle maximizes area for three sides, and an octagon uses equal sides.

Explore circle basics: label parts, radius, diameter, circumference, and area. Master sectors, arc length, central angles, inscribed angles, and inscribed triangles.

Explore circle geometry through arc length and central angles, using unit fractions and ratios of arc length to circumference, and solve problems on inscribed shapes, diameter relations, and circle area.

Explore three-dimensional shapes and learn to calculate surface area and volume for rectangular solids, cylinders, spheres, and cubes using key formulas and practical examples.

Compute and analyze volumes and surface areas of cylinders and spheres, and determine exposed surface area when a cylinder sits on a cube, using standard formulas.

Master the mean, a measure of central tendency, computed as the sum of items divided by the count. Use weighted averages for differing weights; lectures cover the median and mode.

Review mean calculations and solve for the unknown a in a ten-number dataset. Use mean and median for evenly spaced data, and apply weighted averages to price data.

Explore the median as a measure of central tendency by ordering data, identifying the middle value, and averaging the two center numbers for even datasets.

Review the mean and median calculations, distinguish even and odd data sets, apply the evenly spaced data property, and compute their product as demonstrated.

Explore the mode as a measure of central tendency by identifying the most frequent value in a data set, including cases with multiple or no modes.

Review mean, median, and mode with step-by-step data-set examples, including mean 31.8, median 20, and mode 8.

Explore sets and range, including evenly spaced sets, consecutive integer sets, and consecutive multiple sets, and learn that for evenly spaced sets the mean equals the median.

Review and practice calculating mean, median, mode, and range from data sets, including evenly spaced sets where mean equals median, and compute sums and averages.

Learn how standard deviation describes data spread around the mean, distinguishing tight clusters from dispersion. Compare datasets and connect standard deviation to variance.

Review standard deviation, variance, and the relationship to spread in data sets through practice problems. Apply the mean, range, and standard deviation formula to assess data distribution and interpret results.

Explore percentiles and quartiles, order data, and compute percentile values and the median to analyze data sets.

Explore percentile and quartile calculations using data sets, determine the 20th, 40th, 60th, and 80th percentiles, and identify top 20% cutoffs, such as the 80th percentile around 88.

Learn the normal distribution and bell curve, where mean equals median, and use standard deviation to understand 68%, 95%, and beyond, with practice problems.

Review normal distribution exercises using mean 16 and sd 4 to find the proportion between 8 and 28; confirm mean equals median and compute halves of percentages.

Apply the fundamental counting principle to multiply choices and compute total possibilities, or use factorial for ordering items without constraints; the lecture illustrates with meals, seahorses, and a class lineup.

Review the fundamental counting principle and factorials to count outfits and orders, while practicing permutations and basic combinations with gummy bears and marbles.

Explore permutations and combinations using a seahorse display problem that involves nine seahorses, counting arrangements using factorials when order matters and counting selections when order does not.

Explore combinations and permutations and factorial reasoning through practical exercises: choosing three from twenty-seven where order doesn't matter, and ordering five from eighteen, with order mattering, plus a password problem.

Explore core probability concepts, including independent and dependent events, mutual exclusivity, intersections and unions, and conditional probability, with practical examples and key formulas.

Practice probability with dice: sum 22 from 20-sided and 6-sided dice; apply inclusion-exclusion for cat or black fur; compare even outcomes and not rolling eight on three two-sided throws.

Master quantitative comparison by learning the official four answer choices, plugging in values, and solving as inequalities with attention to negative values and restrictions.

Review explains GRE quantitative comparison: use extremes to compare quantity a and b, treat the relation as an equation, and consider x as negative fractions with sign flips.

Master math principles for quantitative comparison by analyzing signs, exponents, fractions, percentages, and ratios, and learn to simplify expressions, cancel terms, and practice problems.

Review prime factorization of 60 and 70 to identify unique prime factors, and explain how equal unique factors lead to equal quantities. Use extreme values to simplify quantitative comparison problems.

Master algebra for GRE quantitative comparison by using elimination to solve for the needed variable, testing range limits, and applying quadratic and absolute value techniques.

Turn word problems into expressions, solve a system of two equations by substitution, and compare quantities without values while practicing absolute value, ranges, and function composition with f and g.

Develop concept-driven geometry strategies for quantitative comparison by using key area formulas, recognizing shapes, and applying fixed ratios instead of relying on drawings.

Compare volumes of a cube and a sphere with given dimensions, then analyze a circle sector to determine area, radius, and arc length using a 60-degree central angle.

Master quantitative comparison in statistics by applying weighted averages and the mean and other measures of central tendency. Explore mean, median, and mode through conceptual reasoning and practice problems.

Review how to determine quartiles and percentiles, compare the mean and median, and apply the normal distribution with standard deviations to interpret data ranges.

Explore data interpretation with column and bar charts, learning to read axes, estimate heights, and compare stacked versus clustered charts. Use subtraction to find parts and totals accurately.

Learn how tables present absolute values or percentages and how pie charts depict fractions that sum to 100 percent, and note their limitations.

Explore line graphs and scatter plots for data interpretation problems, learn how line slopes reveal trends, compare multiple lines, and use trend lines to understand relationships between variables.

Learn how histograms and box plots visualize data ranges and percentiles, and distinguish histograms from bar charts; extract the minimum, maximum, median, first and third quartiles, and interquartile range.

Compare short and long reading comprehension passages and apply time-efficient strategies: preview questions for short passages, summarize long paragraphs, and track the author's opinion to ace gre verbal reasoning.

Develop reading comprehension skills for short and long passages by practicing exam-style questions, using evidence-based reasoning to evaluate answer choices, and mastering strategies for GRE questions.

Identify broad questions about the passage's main point and narrow questions about details. Use active reading and inference strategies to answer choices that fully address the question.

Practice analyzing reading comprehension questions by identifying the main purpose, broad and narrow questions, and inferences, using dating method examples to illustrate precision, applicability, and limitations.

Master GRE reading comprehension techniques, including elimination, reading questions first for short passages, avoiding extreme terminology and trap answers, and using passage-based evidence to justify correct answers.

Practice reading comprehension techniques for the GRE by identifying true statements through evidence, avoiding extreme wording, and applying justification to select correct answer choices.

Discover how to tackle argument structure passages on GRE verbal reasoning by identifying claims, evidence, and assumptions, then answer one-question prompts that infer, strengthen, or weaken arguments and resolve paradoxes.

Master argument structure passages by inferring implications, identifying what strengthens or weakens the argument, and resolving paradoxes with practice questions.

Master Texas text completion by filling blanks with your own words before reviewing options, then rate choices using a two-part approach across single, double, and triple blanks, while boosting vocabulary.

Review exercises for this lecture on text completion practice. Practice solving fill-in-the-blank items by predicting own words, then evaluating choices like soporific, vexatious, and mercurial.

Explore directional words in text completion, identify the mark and direction, apply a two-part approach, and practice moving toward or away from the key term.

Master text-completion strategies by identifying marks and directional words, filling blanks with the best ranked word, and rereading for clarity to improve GRE performance.

Master multiple blank text completion in reasoning by applying an eight-step process: identify easier blanks, focus on one blank at a time, rate options, and verify the text.

Master multiple blank text completion with a step-by-step approach: determine easier blanks, focus on one blank at a time, assess directionality, fill in with your words, and verify all choices.

Learn text completion strategies for verbal reasoning, including simplifying terms with exact definitions and rewriting double negatives. Practice emphasizes emphasis, vocabulary, and elimination to choose the always-correct answer.

Practice text completion strategies by simplifying difficult vocabulary, clarifying sentence meaning, and evaluating answer choices to confidently fill blanks with the correct word.

Learn how to ace sentence equivalence questions by selecting two words that yield two coherent sentences with the same meaning, avoiding traps and expanding vocabulary through practice.

Master sentence equivalence strategies by filling blanks with your own words, then verify with paired choices such as nebulous and ambiguous through clarity checks.

Master sentence equivalence strategies for GRE verbal, compare them with single blank text completion, and learn to identify mark words, word pairs, and standalone options while ranking choices.

Review sentence equivalence exercises, identifying mark and directional words, forming word pairs or stand-alone answers, ranking options, and rereading to ensure clarity for GRE prep.

Master the basics of analytical writing: structure essays with an introduction, body, and conclusion, organize ideas into paragraphs, use transitions, and apply safe vocabulary to boost clarity.

Explore writing basics practice for the GRE, including crafting three body paragraphs with three main points, defending a position with concrete examples, and analyzing prompts for issue and argument tasks.

Learn to tackle the issue task by choosing a side, backing it with evidence, addressing opposing views, and structuring a clear, concise introduction, body, and conclusion.

Develop a clear issue task introduction by stating your position, outlining body points, and delivering a concise thesis statement about present-day issues and future planning, with two to three reasons.

Practice crafting clear thesis statements for GRE issue task introduction paragraphs, choosing a side on prompts about government leadership, elder versus younger advice, and critical thinking versus textbook knowledge.

Learn to craft a persuasive issue task body by selecting a position, developing two to three supporting reasons with concrete examples, addressing counterarguments, and aligning with prompt instructions.

Master issue task strategies for the GRE: learn to argue for or against studying outside one's field, build three body paragraphs, and adapt to prompts, including policy consequences.

Craft a concise issue task conclusion by restating your thesis, briefly summarizing main points, and leaving the reader with something to think, starting with a transition and avoiding new information.