GMAT Math

Ordered Pair

(x,y) Set of numbers that identify the location of a point. X always comes first.

Circles on a coordinate plane

(x-h)²+(y-k)²=r² (h,k) = Circle center

Quadratic Formula

Way to solve quadratic equations when quadratic equation cannot be easily factored

Scientific Notation

1.2 x 10^-2 = 0.012 Negative means move decimal left & positive means omve decimal right

General Rule of Addition

2 events that can happen together P(A ro B)= P(A)+P(B) -P(A and B) Probability of drawing a card that is a Q or J

Special Rule of Multiplication

2 events that happen at the same time but are independent P(A and B)= P(A) x P(B) Probability of rolling a 5&6 on one roll of two dice

General Rule of Multiplication

2 events when the occurrence of the 1st event impacts the 2nd P(A and B)= P(A) x P(A/B) Drawing Q and leaving it out of the next to draw a J

Central Tendency

A value that picks a typical or representative of a group of numbers or other information Average/ "Arithmetic mean" = Sum of all #/ number of members Median- Middle value among list. If two remain, average both. Mode-Value that occurs most frequently Weighted Average- Multiply weight by value then average by total weight

Area of a triangle

A= 1/2 bh

Area of a circle formula

A=πr²

Fraction Tips

Always simplify fractions Cannot add fractions with different denominators so must multiply by the lowest common denominator Eliminate fractions by multiplying by the LCM

% Change

Amount a number increases or decreases by (new-old)/old

Distance Problems

Any problem involving distance, speed, or time spent traveling Distance = (Rate x time)

Work Problems

Asks how much work gets done in a certain amount of time Production = (Rate x Time)

Strategy for solving data sufficiency questions

Asks you to evaluate the evidence vs solve the problem & deals ONLY with the data presented in the problems. Do not overthink these problems Do not actually solve for problem Strategy: Evaluate questions and decide on what info is needed Evaluate first statement and decide Y/N Evaluate second statement and decide Y/N Evaluate Y/N for both statements Statement1- Y Statement2 Y or N Y/Y = D Y/N = A Statement1- N Statement2 Y N/Y = B Statement2 N Statement 1 & 2 N/N/Y = C N/N/N = E

Adding & Subtracting Exponents

Base AND exponent must be the same (Ex 4a^2 - a^2 = 3a^2)

Cube Bisect & Diagonal

Bisect = a(square root 2) Diagonal= a(square root 3)

Circumference of a circle

C=2πr

Linear Equations

Contains an unknown variable & no exponent greater than 1 y= mx + b

Converting Mixed Number

Convert to improper fraction by multiplying denominator by whole number then adding the numerator.

Dividing Fractions

Dividing fractions-

Problem Solving Questions Strategy

Examine all data in question & isolate the problem ask Eliminate obvious incorrect Use the info in the question Find the equation Know when to move on

Exponent = 0? Exponent = 1?

Exponent = 0 equation is always 1 & when exponent = 1 value is the base An even exponent or power can't product a negative number

standard deviation

Expresses variation by measuring how spread out the distribution is from the mean. This is more reliables than the range because it considers all data points.

Stacking Method

Faster way to solve equations that have multiple variables

Accrual Equation

Final Amount = (Initial #) x (1 + Rate) ^n N = number of years

Range

Highest & lowest of values of the dependent variables (y) Range Tipes: Absolute value of a number Make sure to distinguish between range and domain in questions

Slope

How steep the line is (Rise over run) Slope = (y2-y1)/(x2-x1) Horizontal line have a slope of 0 and vertical lines have no slope

Inequalities

If you multiple or divide by a negative number you must flip the sign

Inscribed vs Circumscriberd Figure

Inside another figure vs outside another figure

Prime Numbers

Integers that can not be divided by themselves. 0 & 1 are not prime numbers

Midpoint coordinates of a line segment on a coordinate plane

M =((x1+x2)/2),(y1+y2)/2)

Probability

Measure of how likely a particular event will occur. This is expressed as a percentage, fraction, or decimal. Probability deals with outcomes & events) P(E) = # of outcomes involving E / Total possible # of outcomes

Parallelogram & Area

Most commonly tested quadritaleral. Adjacent sides measure 180 degrees & diagonals bisect each other. A = bh

Multiply fractions

Multiply numerators across then multiple denominators across Cross multiplication saves time

Square Roots (Also known as radicals)

Must be >= 0 ALWAYS and stuff in house before taking the root. Treat as a parenthesis. If n{512} =4n{2}, then n = ? n{2 x 256} =4n{2} N{256} = 4

Multiply/Divide Square Roots

Must happen within the room Must be >= 0

Special Rule of Addition

Mutually exclusive events P(A or B)= P(A)+P(B) Probability of rolling a 5 on a 6-sided dice

Permutations

Number of ways the elements of a set can be arranged in specific orders nPr= n!/(n-r)! n = # of permutations

Coefficient

Number that is before base 4x^2 4=Coefficient

Base

Number that is impacted by the exponent x^2 x= base

Independent Variable of a Function

Number you want to find the function of f(x) x is the independent variable

Factors

Numbers you multiply together to get a product Extract common factors

Dividend & divisor

Numerator = dividend Denominator = Divisor

Parabolas

Occur when you graph the quadratic equation (Positive is U, Negative is downward facing) y= a(x-h)^2 +k Vertex- Bottom or top of the parabola (h,k) Axis of symmetry- Cut parabola in half vertically Domain = x & Range = y Empty vertex means that you don't count it

Trapezoid & Area

Only one set of parallel sides A= ½(B1+B2)h

Angles of Intersecting Lines

Opposite angles are congruent and adjacent are supplementary

Order of Operations

PEMA Parenthesis, exponents, multiplication/division (left to right), additiona/subtraction (left to right)

Addition/Subtraction Square Roots

Possible if the roots are the same

Factorial

Product of all natural numbers in a number n! != a factorial Example 4! = 4 x 3 x 2 x 1 Cannot simplify factorials

Quadrants & Origin

Quadrants I,II,III,IV- Start in top right and go counter clockwise I (+x,+y), II (-x,+y), III (-x,-y), IV (+x,-y) Origin (0,0)

2 Types of Dispersions

Range- Difference between the highest & lowest values. The smaller the range the less standard deviation. Standard Deviation- Expresses variation by measuring how spread out the distribution is from the mean. This is more reliables than the range because it considers all data points.

Product

Result from multiplying

Difference

Result from subtracting

Dependent Variable of a Function

Results of substituting the independent value into the function f(x)= y

Rhombus & Area

Rhombus- All angles are the same but not right A=½(D1)(D2)

Fractional Exponents

Rule Example If exponent is in fractional form, consider the top number of the fraction as your actual exponent and the bottom number as the root a^⅔ = 3{a^2} A negative exponent takes the positive exponent and then flips the base nd exponent around so that that together they become the reciprocal a^-3 = 1/(a^3)

Dividing Exponents

Rule Example When dividing terms with exponents and same base, subtract the exponents a^5 / a^3 = a^2 If division contains coefficients, divide coefficients but SUBTRACT exponents 9a^5 x 3a^3 = 3a^2 To different exponential terms with different bases, first make sure the exponents are the same. If they are divide the bases and maintain the same exponent (ab^5) / a^5 = b^5

Multiplying Explonents

Rule Example When multiplying with the same base but different exponents, ADD exponents a^2 x a^3=a^5 If multiplication contains coefficients, multiply coefficients but ADD exponents 2a^2 x 8a^3 = 16a^2 To multiple exponential terms with different bases, first make sure the exponents are the same. If they are multiply the bases and maintain the same exponent a^5 x b^5 = (ab)^5

Raising the Power

Rule Example When raising a power to another power MULTIPLY the exponents (a^3)^^5 = a^15 When raising a power to another power MULTIPLY the exponents and distribute same power to coefficient (2a^2)^^3 = 8a^6

Combinations

Same thing as permutations but the order does not matter nCr= n!/(r!(n-r)! Can cross multiply to simplify

Domain

Set of all possible values of the independent variables (x)

Similar vs Congruent Objects

Similar- Objects that have the same shape but may have different sizes Congruent- Objects that are equal size & shape

Quadratic Expression

Simplest way to solve is to factor into two binomials ax^2+bx+c FOIL- Method to multiply binomials by First, Outer, Inner, Last.

Parallel lines intersected by a transversal

The resulting small and larges angles are the same

Grouping questions

They take time and can be solved quicker using the formula Group1 + Group2 - Both Groups + Neither Group = Total

Supplementary Angles

Two angles that total 180 degrees

Complementary Angles

Two angles that total 90 degrees

Set definitions

Union - Everything in venn diagram Intersection- Interlap ONLY Disjoint- No overlap Subset- Inscribed figure

Absolute Numbers

Value away from zero Ex |-3| = 3 |3|= 3 Can produce multiple different numbers

Cylinder Volume & SA

Volume = πr^2h SA = πdh +2πr^2

Cube Volume & SA

Volume= a^3 SA= 6a^2

Rectangular Prism Volume & SA

Volume=lwh or V=bh SA=2lh+2lw+2wh

(x+y)^2

x^2+2xy=y^2

(x-y)^2

x^2-2xy=y^2

(x+y)(x-y)

x^2-y^2

Linear Equation

y=mx+b m= slope & b = y intercept

Pythagorean Theorem Formula

a²+b²=c² - Only works for right triangles.

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Degrees in a regular shape

n-2)x 180 Pentagon = 5 Hexagon = 6 Heptagon = 7 Octogon = 8