GMAT Complete Math | Score Higher for Top Business Schools

Apply the order of operations with pendas to solve expressions, then isolate variables and solve equations by reverse operations, including handling fractions and multiple x terms.

Apply the order of operations using pemdas to simplify expressions with parentheses, exponents, and left-to-right multiplication and division, and practice basic equation solving.

Solve a system of two equations for Y using substitution and elimination, isolating X or Y and substituting or eliminating terms to find Y.

Master substitution and elimination as you solve two-equation systems in GMAT practice, converting x to terms of y, distributing, and canceling coefficients to find variables.

Explore exponents and roots, including negative exponents, fractional bases, and even versus odd powers. Practice root simplification and prime factorization for GMAT-style problems.

Review exponent and root rules with three exercises—six to the third power, nine to the negative one-half, and one over four to the negative two—to reinforce real-solution strategies.

Master distribution and factoring in algebra by applying the FOIL method to multiply two quantities and recognizing factoring as the reverse of distribution, with practical examples.

Practice distribution and factoring using the foil method, identifying common factors, and simplifying expressions, with a quantitative comparison problem to verify equivalence.

Master quadratics by moving to zero and factoring x^2 - 4x -12 into (x+2)(x-6) to reveal two x values, and note undefined results when the denominator vanishes.

Factor quadratics by setting the equation to zero and factoring out the coefficient A, then use two numbers that multiply to C and add to B to find X.

Master three special quadratics: A^2−B^2, (A+B)^2, and (A−B)^2, by recognizing them in problems, factorizing to perfect squares such as (W+8S)^2, and practicing to boost GMAT performance.

Master special quadratics by recognizing patterns like a plus b times a minus b and a plus b squared, enabling quick factorization and time-saving exam strategies.

Learn to solve quadratics with the quadratic formula, memorize X = (-B ± sqrt(B^2 - 4AC)) / (2A), and use it as a backup when factoring fails.

Practice applying the quadratic formula to solve equations in standard form ax^2 + bx + c = 0, compute discriminants, and obtain x-values.

Master completing the square by rewriting ax^2+bx+c=0 as a(x+d)^2+e, using d=b/(2a) and e=c−b^2/(4a), and apply it to find parabola vertices.

Review and apply completing the square using the form A(x + D)^2 + E, with D = B/(2A) and E = C − B^2/(4A), through three exercises.

Explore inequalities by reading and graphing on a number line with open or closed circles; solve by adding or subtracting and flip the sign when multiplying or dividing by negatives.

Solve and explain inequalities by isolating variables, splitting compound inequalities, and applying sign-flip rules when dividing by negatives to compare quantities A and B.

Master absolute value inequalities by solving two scenarios, isolating the absolute value, and checking for extraneous solutions, with practice on plotting on a number line.

Isolate the absolute value and split into two cases for absolute value inequalities. Plot on a number line with open or shaded circles, flipping the sign for negatives.

Explore the basics of functions: inputs and outputs, F(X) notation, and independent and dependent variables, including domain and range. Master solving compound functions by working from inside to outside.

Review exercises on functions and function composition, determine constants, and solve G(6), G(F(3)), and F(G(Y)) versus G(F(Y)) using the quadratic formula and foil method.

Explore the difference between simple and compound interest, using principal, rate, and time formulas, with an example of quarterly compounding and practical guidance for exams.

Explore compound and simple interest through exercises, using principal, rate, and time to compute totals and interest. Compare quantities A and B to distinguish amounts due under different interest schemes.

Identify sequence patterns using recursive and direct definitions, derive formulas like a_n = 2 a_{n-1} + 1 or a_n = n^2 + 1, and predict next terms.

Explore sequences practice by applying recursive rules, calculating successive terms for b_n = 4 b_{n-1} - 3 and h_n, and predicting next terms using a_n = 3 a_{n-1} + 2.

Learn to plot points on the coordinate plane, identify origin and quadrants, and graph lines using slope, intercepts, and the distance formula.

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

Learn how to find the intersection of lines in slope-intercept form by graphing y-intercepts and slopes, then solve by equating the equations, and recognize parallel lines never intersect.

Compute the intersection of lines by setting equations equal and solving for x, then determine y from either equation. Identify parallel lines by converting to slope-intercept form.

Graph inequalities by plotting lines, shading regions, and using solid or dashed boundaries; sketch absolute value graphs, determine vertex, and analyze open upward or downward v-shapes based on coefficients.

Practice graphing inequalities and absolute value functions by converting to slope-intercept form, plotting the y-intercept with slope, shading above or below lines, and locating the vertex of absolute value graphs.

Learn to graph quadratics and parabolas—vertical or horizontal—using axis of symmetry, line intersections, and vertex form via completing the square to locate the vertex (A,B).

Practice finding intersections of a parabola and a line by solving x^2-2 = 5x-8, yielding points (2,2) and (3,7); learn to locate vertices by completing the square and using forms.

Master rates using the rate-time-distance RTD formula, explore RTA variants, and analyze units, distance, and time across opposite, same, and moving-away scenarios; compute average rate.

Apply rate-time-distance and relative motion to solve: two cars collide in 22.5 seconds from 1800 m apart, and a dog catches a cat after 1556 steps, with 66.2 mph average.

Explore lines in geometry, learn parallel and perpendicular relationships, and master angle equivalence and sums when lines intersect, including 360-degree and 180-degree angle rules.

Learn how parallel lines create equal and supplementary angles, distinguish small and large angles, and solve for expressions like two x plus c plus dx using angle properties.

Explore polygons, learn about perimeters, areas, and interior angles, from triangles to pentagons, and apply the sum of interior angles equals (N minus two) times 180 degrees.

Apply the polygon angle-sum rule to find total angles and individual angles, verify 12-sided polygons have total 1800 degrees and 150-degree angles, then solve for missing angles and equal-side perimeters.

Master triangle properties: area equals half base times height, perimeter, angle sums, and the Pythagorean theorem, including 3-4-5, 5-12-13, and 30-60-90 isosceles right patterns.

Use the Pythagorean theorem to find missing legs and compute triangle area, then determine a square diagonal from area 49, and analyze a 30-60-90 triangle for side lengths and perimeter.

Explore quadrilaterals by examining squares, rectangles, parallelograms, and trapezoids; learn their properties and apply area and perimeter formulas with practical breakdowns into triangles and rectangles.

Apply geometric reasoning to compare area and perimeter in quadrilaterals, solve right triangles via the Pythagorean theorem, and compute rectangle area, perimeter, and area-to-perimeter ratios.

Maximize area by approaching a square; with a fixed perimeter, the square has the largest area. In the example, X and Y equal 30 cm, yielding 450 cm².

Study area optimization: maximize land with a three-sided fence forming a right isosceles triangle, and compare areas under fixed perimeters, including an octagon with equal sides.

Explore circle concepts by defining radius, diameter, circumference, and area, applying pi (3.14), and analyzing sectors, arc length, central angles, inscribed angles, and diameter-based right triangles.

Review circle practice using arc length, circumference, central angle, and sector area ratios to find arc lengths and slice areas, then examine an inscribed square and diameter-based triangles.

Learn to analyze three-dimensional shapes by calculating their surface area as the sum of each face and their volumes using formulas for cubes, rectangular solids, cylinders, and spheres.

Review how to calculate the volume and surface area of cylinders and spheres using formulas like pi r^2 h and 4/3 pi r^3, and apply cube surface area concepts.

Learn how to compute the mean, the arithmetic average, and its relation to central tendency, including weighted averages, with practical practice problems.

Review mean practice exercises, solving for an unknown A in a 10-item data set and applying the mean formula; learn about even spacing and weighted averages, yielding 25,750 dollars.

Order data from least to greatest and find middle value to obtain the median, a measure of central tendency; odd datasets yield middle value, even datasets average two middle numbers.

Compute mean and median from data sets, distinguish even and odd cases, apply evenly spaced data properties where mean equals median, and evaluate the product of mean and median.

Identify the mode as the most frequent value in a data set, noting that a data set may have multiple modes or no mode, a measure of central tendency.

Review practice exercises on mean, median, and mode, showing how to compute the mean from a dataset, identify the middle value in ordered data, and determine the most frequent number.

Explore sets and range, including evenly spaced sets, consecutive integer sets, and consecutive multiple sets, and learn to compute mean and median for evenly spaced sequences.

Review practice exercises on sets and ranges, calculating mean, median, mode, and range for data sets, including ascending order and properties of evenly spaced sets.

Describe standard deviation as the spread of data from the mean. Compare datasets that share a mean but differ in spread, and relate standard deviation to variance.

Review standard deviation and variance by confirming that variance equals the standard deviation squared, then compare data sets with the same mean but different ranges to judge spread.

Learn how percentiles divide data sets, order values, and determine exact percentile values, including the 25th, 50th (median), and 75th quartiles.

Review how to compute percentiles and quartiles using data sets, determine the 20th, 40th, 60th, and 80th percentiles, and identify the top 20%.

Master the normal distribution, its bell curve, how the mean equals the median in symmetric data; grasp how standard deviation defines 68 percent, 95 percent, and more than 99 percent.

Explore normal distribution concepts with practice exercises, applying mean and standard deviation to find percentages within 68%, 95%, and 99% ranges, including median-mean relationships.

Apply the fundamental counting principle and factorials to determine possible arrangements. Use meals, seahorses, and lineups as practical examples to see when to multiply choices and when to order items.

Explore factorials and the fundamental accounting principle through practical exercises: counting outfits (6×8×3×4=576), ordering gummy bears (6!), and comparing full ordering vs selecting from two bags (8!, 4×4).

Explore permutations and combinations with seahorse problems, distinguish when order matters versus does not, and apply factorial reasoning.

Review combinations and permutations through practice exercises, using factorial-based formulas and a step-by-step approach to decide if order matters. Explore 27 choose 3, 18P5, and password scenarios.

Explore probability fundamentals, including calculating P(event) as desired over total outcomes, and apply independent, dependent, conditional, and mutually exclusive rules with non mutually exclusive union and intersection examples.

Explore probability through practical exercises with a 20-sided and a 6-sided die, a pet store scenario, and a three-roll experiment, focusing on outcomes and non mutually exclusive events.

Explore data interpretation with column and bar charts. Learn to read axes, estimate values by height, and distinguish stacked from clustered columns for calculating totals and parts.

Master tables display values or percentages and pie charts represent percentages or fractions, and note that tables can make trends hard to observe, while pie charts sum to 100.

Learn how line graphs and scatter plots reveal trends in continuous data. Identify slope, multiple lines, and trend lines to compare datasets.

Learn to interpret data with histograms and box plots. Histograms show ranges and counts but not exact values, while box plots reveal min, max, median, quartiles, and interquartile range.