GRE Math Complete | High Scores for Top Grad Schools

Master the order of operations using pendas and learn to solve basic equations by isolating variables, combining like terms, and handling fractions and roots.

Practice order of operations using PEMDAS with parentheses, exponents, and left-to-right rules. Solve basic equations for variables like v and b, including fractions and square roots.

Solve systems of two equations by substitution and elimination, isolating a variable, substituting or eliminating terms, and practice solving for y as shown in the lecture.

Solve linear systems from two equations using substitution and elimination: express x in terms of y, substitute into the other equation, and use elimination to find the remaining variables.

Explore exponent rules and roots, applying base and exponent concepts to simplify expressions, square and cube roots. Learn to handle negative and fractional exponents, and simplify roots via prime factorization.

Review and apply exponent and root rules, including negative exponents, reciprocals, fourth and cube roots, and simple x cubed equations, to sharpen GRE math skills.

learn how to distribute and factor algebra expressions using the foil method, multiplying every term in parentheses and pulling out common factors.

Learn distribution and factoring through foiling, applying first, outside, inside, and last steps, factor polynomials by extracting common factors, and compare expressions for equality.

explore quadratics: factor and solve by zero product, foil, and factoring strategies; identify two roots (or one, in a perfect square), and beware undefined values from denominators.

Learn to solve quadratics by factoring and setting the equation to zero. Factor out a and use two numbers that multiply to c and add to b to find x.

Master three special quadratics: (a+b)(a-b)=a^2-b^2, (a+b)^2=a^2+2ab+b^2, and (a-b)^2=a^2-2ab+b^2, then recognize and factor quickly with practice and double-check by foiling.

Recognize special quadratics to save time: apply A+B times A-B equals A^2-B^2 and A±B squared formulas to solve exercises like (x+7)(x-7), (x+7)^2, (x-7)^2, and factor T^8+6T^4V^3+9V^6 as (T^4+3V^3)^2.

Learn how to solve quadratic equations using factoring and the quadratic formula, compare methods, memorize the formula, and apply it as a backup for tricky problems.

Explain solving quadratic equations using the quadratic formula by identifying a, b, c, setting the equation to zero, and obtaining two solutions from the plus/minus root.

Learn to complete the square by rewriting ax^2+bx+c as a(x+d)^2+e, with d=b/(2a) and e=c−b^2/(4a). Practice with nonunit leading coefficients and use this method to find parabola vertices.

Master completing the square by turning ax^2+bx+c into a(x+d)^2+e, with d=B/(2A) and e=C-B^2/(4A), and apply this to 2x^2+20x+50 using the two numbers that multiply to C and add to B.

Explore inequalities and their symbols, learn to interpret number lines, and master solving methods, noting the sign flip when multiplying or dividing by negatives and handling compound inequalities.

Isolate variables, solve inequalities, and determine x in [10,40] and y in [4,12] to find the minimum x times y as 40, noting the sign flip when dividing by negatives.

Explore absolute value inequalities by treating absolute value as distance from zero, solving by splitting into two cases, flipping inequalities when multiplying by negatives, and checking for extraneous solutions.

Solve absolute value inequalities by isolating absolute value, splitting into two inequalities, flipping the sign when dividing by negatives, and plotting the solution on a number line with circles.

Explore how functions map inputs to outputs with f(x), and distinguish domain and range while applying inside-out reasoning to solve compound functions and compare f(g(x)) and g(f(x)).

Detail function compositions and quadratic solving by deriving c from G(4)=20 and evaluating F and G to find where F(G(y)) equals G(F(y)).

Identify and apply strange symbol functions by determining the operation, plug in values for a and b, and evaluate inside-out, doing the parentheses first for compound symbol questions.

Review exercises on strange symbol functions using down arrow notation, perform substitutions in the expressions, and compute results for three practice problems.

Understand simple and compound interest, including how principal, rate, and time determine amounts. Apply P×R×T for simple interest and P×(1+R/N)^(NT) for compound interest to compare outcomes across frequencies.

Explore compound and simple interest calculations with real-world loan examples, including quarterly compounding, total amount due, and the key distinction between interest and principal.

Learn to identify patterns in sequences and distinguish direct from recursive sequences. Convert these patterns into formulas, such as a_n = 2 a_{n-1} + 1, to predict terms.

Explore recurrence relations and term predictions in sequences. Identify the rule a_n = 3 a_{n-1} + 2 and the next terms: 323, 971, 2915.

Explore the coordinate plane, plot ordered pairs, and graph lines using slope, intercepts, and the distance between points.

Review and practice graphing by plotting ordered pairs, calculating slope, and identifying the y- and x-intercepts, then apply the distance formula to measure between points.

Explore how to find the intersection of lines using slope-intercept form, graphs, and algebra. Distinguish parallel lines from intersecting lines and solve for the intersection point.

Convert the lines to slope-intercept form, set them equal to solve for x, substitute to find y, and identify parallel lines by matching slopes.

Graph inequalities by plotting lines, shading regions, using solid lines for inclusive inequalities and dashed lines for strict ones; absolute value graphs form a V with vertex (A, B).

Graph inequalities and absolute value functions by converting to slope-intercept form, plotting key points, shading the appropriate region, and identifying the vertex for absolute values.

Master graphing quadratics by analyzing parabolas, their axis of symmetry, and orientation; learn to convert to vertex form via completing the square and locate the vertex for quick graphing.

Explore solving intersections of quadratics and locating parabola vertices through completing the square and vertex form, including the effects of coefficients on direction and width.

Master rate problems using the rate-time-distance formula and unit matching. Explore moving toward, away, or in the same direction, and calculate average rates from total distance and total time.

Review rate-distance-time problems, solving time and distance for approaching objects, pursuit scenarios, and mixed speeds, using the RTD formula and total distance over total time.

Explore lines in geometry: straight lines have 180-degree angles, parallel lines never intersect, and perpendicular lines form right angles. Recognize opposite angles are equal and adjacent angles sum to 180.

Explore angle relationships when a line intersects two parallel lines, distinguishing small and large angles and using 180 and 360-degree sums to solve for expressions like x+c+d and z+c.

Learn how polygons are closed shapes with at least three sides, including triangles, quadrilaterals, pentagons, and trapezoids, and explore perimeter and area. Apply the interior angle sum formula (n-2)×180.

Apply the polygon interior angle sum formula (n-2)×180 to find total angles, then compute individual angles and perimeters for 12- and 6-sided polygons, noting equal sides when angles are equal.

Explore triangle basics, including area as one half base times height, perimeter, angle sums, and key types like isosceles, equilateral, and right triangles with Pythagorean triplets.

Apply the Pythagorean theorem to find missing legs in right triangles, compute area as one-half base times height, and determine a square's diagonal and a 30-60-90 triangle's perimeter.

Explore quadrilaterals, including square, rectangle, parallelogram, and trapezoid, and learn how to compute area and perimeter using base, height, and breakdown into triangles.

Explore solving quadrilateral area and perimeter by decomposing into two triangles and a central shape, applying the Pythagorean theorem to find missing sides, and analyzing rectangle area to perimeter ratios.

learn how area maximization works for polygons: with fixed perimeter, squares maximize area; with fixed area, perimeters decrease toward a square; for triangles, maximize area with perpendicular sides.

Analyze area-optimization exercises: maximize land with a 99-foot fence forming a right triangle with equal legs, then rank shapes by area and perimeter, octagon parking garage with eight equal sides.

Master circle concepts by labeling radius and diameter, applying circumference, area, and arc length formulas with pi, and solving sector and inscribed-angle problems using central angles.

Review circle geometry by solving arc length and circumference from a pizza slice, using central angles, sector areas, and circle area ratios, then examine inscribed shapes and right isosceles triangles.

Explore three-dimensional shapes and calculate their surface areas and volumes. Learn formulas for rectangular solids, cubes, cylinders, and spheres.

Explore cylinder and sphere volumes and surface areas using pi r^2 h, 2 pi r h, and 4/3 pi r^3, plus exposed surfaces when a cylinder sits on a cube.

Learn how to compute the mean, a key measure of central tendency, using the sum divided by count or the equivalent mean times count equals sum, including weighted averages.

Compute the mean using the sum divided by count, solving for unknowns when needed. For evenly spaced data, mean equals the median, and apply weighted averages for diverse values.

Identify the median, a measure of central tendency, by ordering data least to greatest and, for even sets, averaging the two middle numbers.

Compute the mean and median from data sets, distinguish even and odd sizes, and apply the evenly spaced data property by averaging the first and last values to find median.

Explore the mode as a measure of central tendency, the most frequent value in a data set, and learn how data sets can have one, multiple, or no mode.

Demonstrates calculating the mean, median, and mode from data sets, including ordering data, finding the middle value for odd counts, and identifying the most frequent number.

Identify evenly spaced, consecutive integer, and consecutive multiple sets, note their fixed increments, and apply that the mean equals the median while calculating the range.

Learn how to calculate mean, median, mode, and range from data sets, and apply evenly spaced data properties to GRE-style range and sum problems.

Explore how standard deviation measures data spread around the mean using simple examples. Focus on the concept, not the messy formula, and connect variance as standard deviation squared.

Explore standard deviation and variance, the square root relationship, and how data spread around the mean and varying ranges illustrate these concepts.

Explore percentiles and quartiles by ordering data, computing exact percentile values when needed, and identifying the median as the 50th percentile, including p25, p50, and p75.

Review percentiles and quartiles by calculating the 20th, 40th, 60th, and 80th percentiles from ordered data, and apply the median principle.

Explore the normal distribution and bell curve, where the mean equals the median and standard deviation measures spread, with 68, 95, and 99 percent within one to three standard deviations.

Explore normal distribution practice by calculating areas between means and standard deviations, applying 68/95/99 percent ranges, and comparing mean and median in normally distributed data.

Apply the fundamental counting principle to multiply independent choices, such as appetizers, entrees, and desserts. Use factorials, represented by n!, to count arrangements, illustrated with seahorses and a class lineup.

Explore factorials and the fundamental counting principle through practice problems on outfits, gummy bear orders, and marble selections, contrasting permutations and combinations.

Master permutations and combinations by applying factorials to decide when order matters. Use the seahorse examples—nine total, four displayed, and nine choose three—to illustrate the difference and formulas.

Review exercises on combinations and permutations, showing when order matters, using 27 choose 3, 18P5, and 26P2 to compute outcomes and password possibilities.

Learn the fundamentals of probability, including calculating with independent and non-independent events, using union and intersection rules, and applying conditional probability to real-world examples.

Analyze probability practice with dice and pet-store scenarios, identifying outcome pairs that sum to 22, applying non mutually exclusive event rules, and comparing three-die probabilities.

This lecture introduces quantitative comparison, explains the A, B, C, D answer order, and teaches strategies like plugging in values and solving as inequalities, including handling restrictions and negatives.

Review the qc introduction practice exercises using extreme-value reasoning to compare quantities and apply the equal-sign method, noting when indeterminate relationships arise.

Explore techniques for quantitative comparison and math principles, including simplifying fractions, positive and negative numbers, exponents, percentages, ratios, and consecutive numbers.

Review prime factorization of 60 and 70 to identify unique prime factors, compare exponent-based quantities, and apply extreme-value testing and cube-root reasoning to compare expressions.

Learn to solve quantitative comparison problems in algebra using elimination to isolate variables, handle ranges and zero crossings, and apply quadratics and absolute values.

Explore turning word problems into equations, solve a two-equation system by substitution, and compare quantities without needing exact values. Apply this to extreme-value analysis and function compositions like f(g(2)) and g(f(2)).

Learn strategies for quantitative comparison in geometry, from triangles and rectangles to circles and sectors; write and apply area formulas, reason conceptually, and avoid judging by sight.

Review cube and sphere volumes, sector area, and radius from a 60-degree sector. Solve circle-in-square problems using area, arc length, and geometry ratios.

Explore techniques for solving quantitative comparison problems in statistics, including weighted averages, mean, median, and mode, with emphasis on concept-driven reasoning over memorized formulas.

Review quartiles and percentiles, compute the second quartile mean and 25th percentile, compare mean and median, and use standard deviations to interpret data ranges.

Learn to read column and bar charts for data interpretation. Compare stacked and clustered formats, interpret axes, and apply subtraction for totals.

Learn to analyze tables and pie charts to compute percent changes and interpret absolute values and percentages, while understanding their strengths and limitations for data interpretation.

Explore line graphs and scatter plots to visualize trends in continuous data, learn slope interpretation, compare multiple lines, and use trend lines to assess correlations.

Explore histograms and box plots in data interpretation. Learn how histograms show ranges and counts, while box plots reveal the minimum, maximum, median, and quartiles, including the enter cortile range.