# GRE review and prep

 Acute angle is Angles that measure less than 90° are called Obtuse angles is .... Angles that measure more than 90° A right angle always measures... exactly 90° and indicated by a little square where the angle measure is 40 + n = 180 degress = straight line Complementary Angles - because they add up to 90°. Supplementary Angles, because they add up to 180°.   Angles 1, 4, 5, and 8 are equal to one another. 2, 3, 6, and 7 are equal to one another. The sum of any two adjacent angles, such as 1 and 2 or 7 and 8, equals 180ºCorresponding angles; Tranversal line intersects When two lines intersect, the angles that lie opposite each other, called vertical angles, are always equal. Angles in a triangle equals... 180 degrees An equilateral triangle has three equal sides and three equal angles An isosceles triangle has two equal sides and two equal anglesNotice that the two equal angles are the ones opposite the two equal sides A triangle with no equal sides and angles ... Scalene The exterior angle of a triangle plus the interior angle with which it shares a vertex is always 180°. The exterior angle is also equal to the sum of the measures of the remote interior angles. rule of sidesx is greater than the difference of the sides (10-4= 6)but less than the addition of the sides (10+4 = 14) side a is the longest side and A is the largest angle. side c is the shortest side and c is smallest angle. Pythagorean theorem is a2 + b2 = c232 + b2 = 529 -25 = b216 = b2 = b = 4 what are pythogoream's triples? {3, 4, 5} {5, 12, 13} {7, 24, 25} {8, 15, 17}therefore z would be 5 x 10 = 50 how do know x and the value of the angles inside? pythagoream ratio: s:s: s√2therefore x = 5√2 30 60 90 triangle means ratio is s:s√3:2stherefore 1:2:1√3 Area of a Triangle is ? 1/2 x base x height What is the total degrees inside a sqaure? 360 area of a square (2 formulas) base x height1/2 diagonal 2 area? 2 equal sides and 2 equal sides all right anglesarea = length x width area? area is base x height2 and 2 sides not necessarily right angles BE= ED and AE = EC∆ABD = ∆BCD∆AEB = ∆DEC and ∆BEC = ∆AED area? 1/2d1 x d2or base x height area? area = 1/2 (b1 + b2) x h Formula to calcuate degrees in polygons (all equal sides) and average for angle (n-2) 180 = total degrees for average divide by number of sides (n) triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon... how many sides for each? 3, 4, 5, 6, 7, 8, 9, 10, 12 volume of a rectangle? l x w x h surface area of a rectangle? 2lw + 2lh +2wh. volume and surface area of cube? Volume = s3sa = 6s2 volume and surface area? volume =πr2hsurface are = circumference x h x 2area of circle circumference = 2πrarea= πr2 circumference? perimeter of a circle : 2πr Area of a circle is ? area = πr2     AB = chordtangent linescentral angle = cuts arch at same angle An inscribed angle will always cut out an arc in the circle that is twice the size of the degree of the inscribed angle. For example, if an inscribed angle is 40º, it will cut an arc of 80º in the circle. a central angle in an inscribed angle will be twice the size AB? arc length = need c = 60AB is twice because it is an inscribed angle120/360 area of sector? central angle so 70/360 If 2x + 3y = –6 and –4x + 16y = 13, what is the value of y? can add or subtract equations, if variables do not cross out think about mulitpling or dividing each side of one equation by the same number base to a power of 0 equals? 1 number to a negative exponent means? X-4 1/X4 x2+2xy +y2 = ???? x2 +6xy + 9 (a+b)2(x +3)2 x2 – 2xy + y2 x2–10xy + 25 (x –y )( x – y) = (x –y)2(x –5)2 (x +y)(x – y) (x + 4)(x – 4) x2-y2x2 - 16 ratios: we are told ratio of boys to girls are 4 to 5 and there are 12 boys in the classes, how many girls are there? boys = boys 4 = 12 4x = 12 x5 x= 60/4 girls girls 5 x x= 15 Probability formula? In a bag containing 12 red, 13 white, and 15 black marbles, what is the probability of selecting a red marble on a single draw? number of desired outcomestotal number of possible outcomes 12/12+13+15 = 12/40 = 3/10 distance formula? rate x time = distance work formula If you knit 2 sweaters per hour, and knit for 8 hours rate x time2 per hour x 8 hours = 16 What is a prime number? positive number; divideable by itself and one other number only2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97solution : estimate square of number and then check all number below that number97 = 10 = check 2, 3, 5, 7, How to add or subtract fraction? need common denominator and numerators are added together or subtracted Multiplying fractions? 4 x 1 x10 5 8 11 numerators times and denominatorscancelling out = if any numerators are can be divided by the same number as a denominator 4 and 8 divide by 4 and 5 and 10 divide by 51 x 1x2 / 1 x 2 x 11 Divide fractions? 1 x 4 2 5 all you have to do is flip the second fraction and then multiply58 ratios? For every 40 games a baseball team plays, it loses 12 games. What is the ratio of the team’s losses to wins? red, blue, and green marbles ratio of 5:4:3, and he has a total of 36 marbles. How many blue marbles? 40 - 12 = won 28 games = 12:28 = 3:7 5 + 4 + 3 = 12 = 36/12 = 3 times each by 3 to find how many 5 Percentages 4 is what percent of 20? What percent of 2 is 5? 4 = 20x = 400 =20x = 20% 100 5 = 2x/100 = 2x = 500 = x = 250% To convert .3875 into a fraction delete decimal and has four digits after the decimal point, put four zeros in the denominator following the number 1:3875/10000 and reduce percentage increase or decrease Sam pays \$1.65 for a banana that was originally priced at \$2.00 Sam pays \$2.00for a banana that was originally priced at \$1.65 percentage increase percentage decrease % increase or decrease = # increase or decrease divide by original number Exponents Adding or subtacting? multiplying? Dividing? factions to an exponent 1 to the exponent 3 2 need to be same base 2x2 + 3x2add exponents together dividing subtracting exponents1x1x1 over 2x2x2 roots multiple and divide roots single number under a radical sign can be split into two numbers whose product is the original number average if do not have all numbers average of class marks is 74. B got 50%; C got 60%; D got 90% and E got ?? average = sum divide by number of terms74 = 50 + 60+ 90 + x divided by 4 Interest principle x rate x time Median? median of a group of numbers is the middle term when the numbers are written in either ascending or descending order.if two numbers are in the middle you take the mean (average) of two numbers mode number that occurs most frequently range? difference between the largest term and the smallest term Authorerica.kumar ID2167 Card SetGRE review and prep DescriptionGRE prep and review Updated2009-12-04T19:00:22Z Show Answers