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
