GRE Math With Complete Solution A+ Material

GRE Math With Complete Solution A+ Material formula for distance problems - distance=rate×time or d=rt The Perimeter of a rectangle - P=2(l+w) The Perimeter of a Square - P=4s (s=side) Area of a Parallelogram: - A=(base)(height) (x-y)(x+y) - x²-y² (x-y)² - x²-2xy+y² (x+y)² - x²+2xy+y² An Angle that's 180° - Straight Angle The sum of all angles around a point - 360° If a pair of parallel lines is cut by a transversal that's not perpendicular, the sum of any acute angle and any obtuse angle is - 180 Acute Angle an angle that is less than 90° Obtuse Angle:angle that is greater than 90° but less than 180° Distance - (rate)(time) d=rt Rate - d/t (distance)/(time) Time - (distance)/(rate) d/r How do you solve proportions? a/b=c/d - Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60 If a lamp increases from $80 to $100, what is the percent increase? - = 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25% The percent decrease of a quantity - = (actual decrease/Original amount) x 100% If a lamp decreases to $80, from $100, what is the decrease in price? - = (actual decrease/Original amount) x100% = 20/100x100% = 20% To increase a number by x% - multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150 To decrease a number by x% - multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50 THE DENOMINATOR CAN NEVER - BE ZERO! 1/∅=null If ab then - -a-b The reciprocal of any non-zero number is - 1/x Probability of an Event - P(E) = number of favorable outcomes/total number of possible outcomes If Event is impossible - P(E) = ø If E is certain - P(E) = 1/1 = 1 Probability of Event all cases - ∅≤P(E)≤1 Probability of E not occurring: - 1 - P(E) Circumference of a circle - pi(diameter) Circumference of a circle - 2(pi)r Area of a circle - (pi)r² Volume of a rectangular solid - (length)(width)(height) Volume of a cube - edge³ Vertical lines - Do not have slopes! Any Horizontal line slope - zero Slope of any line that goes up from left to right - Positive Slope of any line that goes down as you move from left to right is - Negative Slope - y₂-y₁/x₂-x₁ For any number x - Can be negative, zero, or positive X is the opposite of - -X 3 is the opposite of - -3 The only number that is equal to its opposite - ∅ ∅=∅ Product of any number and ∅ is - ∅ If a product of two numbers is ∅, one number must be - ∅ 7 divided by ∅ - Null ∅ divided by 7 - ∅ The product of odd number of negative numbers - Negative The reciprocal of any non-zero #x is - 1/x The product of any number x and its reciprocal - 1 Dividing by a number is the same as multiplying it by its - Reciprocal ∅ Is neither - Positive or Negative Consecutive integers - x, x+1, x+2 One is (a prime or not?) - NOT A PRIME Positive integers that have exactly 2 positive divisors are - Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23) ∅ Is - EVEN ∅ is a multiple of - Two (∅×2=∅) ∅ is a multiple of - Every number 2 is the only - Even prime number b¹ - 1 bⁿ - b∧b∧b (where b is used as a factor n times) 2⁵+2³ - 2⁸ 2⁵/2³ - 2² (2²)³ - 2⁶ 2³×7³ - (2x7)³ ∅² - ∅ If a is positive, aⁿ is - Positive If a is negative and n is even then aⁿ is (positive or negative?) - aⁿ is positive -3² - 9 -3³ - -27 a(b+c) - ab+ac a(b-c) - ab-ac ab then a - b is positive or negative? - a-b is positive ab then a - b is positive or negative? - a-b is negative If ab, then - a+cb+c ∅ is - Even ∅ is - A multiple of every integer a/∅ - Null 1ⁿ - 1 1 is a divisor of - every number 1 is the - smallest positive integer 1 is an - ODD number 30 60 90 - x, x(SR3), 2x 30 60 90 - 3, 4, 5 30 60 90 - 5, 12, 13 30 60 90 - 3x, 4x, 5x 25^(1/2) or sqrt. 25 = - 5 OR -5 Number of degrees in a triangle - 180 What are the real numbers? - All the numbers on the number line (negative, rational, irrational, decimal, integer). All the numbers on the GRE are real. (-2, 1, .25, 1/2, pi) What are the rational numbers? - All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2, 1, .25, 1/2) What are the irrational numbers? - All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3) What are the integers? - All numbers multiples of 1. 1/2 divided by 3/7 is the same as - 1/2 times 7/3 A number is divisible by 3 if ... - the sum of its digits is divisible by 3. A number is divisible by 4 is... - its last two digits are divisible by 4. A number is divisible by 6 if... - its divisible by 2 and by 3. A number is divisible by 9 if... - the sum of digits is divisible by 9. 10all primes20 - 11, 13, 17, 19 20all primes30 - 23, 29 30 all primes40 - 31, 37 40 all primes50 - 41, 43, 47 50 all primes 60 - 53, 59 60 all primes 70 - 61, 67 70 all primes 80 - 71, 73, 79 1/8 in percent? - 12.5% 1/6 in percent? - 16.6666% 3/8 in percent? - 37.5% 5/8 in percent? - 62.5% 7/8 in percent? - 87.5% 5/6 in percent? - 83.333% x^4 + x^7 = - x^(4+7) = x^11 x^6 / x^3 - x^(6-3) = x^3 (x^2)^4 - x^(2(4)) =x^8 = (x^4)^2 a^0 = - 1 0^0 - undefined Can you add sqrt 3 and sqrt 5? - No, only like radicals can be added. Can you subtract 3sqrt4 from sqrt4? - Yes, like radicals can be added/subtracted. (6sqrt3) x (2sqrt5) = - (6 x 2)(sqrt3 x sqrt5) = 12sqrt15 (12sqrt15) / (2sqrt5) = - (12/2) x (sqrt15 / sqrt5) = 6sqrt3 Can you simplify sqrt72? - Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2. 10^6 has how many zeroes? - 6 To multiply a number by 10^x - move the decimal point to the right x places What does scientific notation mean? - Expressing a number as the product of a decimal between 1 and 10, and a power of 10. Define a "term", - A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x, 4x^2 and 2a/c) Define an "expression". - An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy, 4ab, -5cd, x^2 + x - 1) Define a "monomial" - An expression with just one term (-6x, 2a^2)