GRE review and prep

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erica.kumar
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2167
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GRE review and prep
Updated:
2009-12-04 14:00:22
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GRE
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GRE prep and review
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  1. Acute angle is
    Angles that measure less than 90° are called
  2. Obtuse angles is ....
    Angles that measure more than 90°
  3. A right angle always measures...
    • exactly 90° and indicated by a little square where
    • the angle measure is
  4. 40 + n = 180 degress = straight line
  5. Complementary Angles - because they add up to 90°.
  6. 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 180º
    • Corresponding angles; Tranversal line intersects
    • When two lines intersect, the angles that lie opposite each other,
    • called vertical angles, are always equal.
  7. 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 angles
    • Notice that the two equal angles are the ones opposite the two equal
    • sides
  8. 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 sides
    • x 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.

  9. Pythagorean theorem is
    • a2 + b2 = c2
    • 32 + b2 = 52
    • 9 -25 = b2
    • 16 = b2 = b = 4
  10. 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
  11. how do know x and the value of the angles inside?
    • pythagoream ratio: s:s: s√2
    • therefore x = 5√2
    • 30 60 90 triangle means ratio is s:s√3:2s
    • therefore 1:2:1√3
  12. Area of a Triangle is ?
    1/2 x base x height
  13. What is the total degrees inside a sqaure?
    360
  14. area of a square (2 formulas)
    • base x height
    • 1/2 diagonal 2
  15. area?
    • 2 equal sides and 2 equal sides
    • all right angles
    • area = length x width
  16. area?
    • area is base x height
    • 2 and 2 sides not necessarily right angles
    • BE= ED and AE = EC
    • ∆ABD = ∆BCD
    • ∆AEB = ∆DEC and ∆BEC = ∆AED
  17. area?
    • 1/2d1 x d2
    • or base x height
  18. area?
    area = 1/2 (b1 + b2) x h
  19. 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)
  20. triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon... how many sides for each?
    3, 4, 5, 6, 7, 8, 9, 10, 12
  21. volume of a rectangle?
    l x w x h
  22. surface area of a rectangle?
    • 2lw + 2lh +2wh.
  23. volume and surface area of cube?
    • Volume = s3
    • sa = 6s2
  24. volume and surface area?
    • volume =πr2h
    • surface are = circumference x h x 2area of circle

    • circumference = 2πr
    • area= πr2
  25. circumference?
    perimeter of a circle : 2πr
  26. Area of a circle is ?
    area = πr2
    • AB = chord
    • tangent lines
    • central 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.
  27. a central angle in an inscribed angle will be twice the size
  28. AB?
    • arc length =
    • need c = 60
    • AB is twice because it is an inscribed angle
    • 120/360
  29. area of sector?
    • central angle so 70/360
  30. 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
  31. base to a power of 0 equals?
    1
  32. number to a negative exponent means?
    X-4
    1/X4
  33. x2+2xy +y2 = ????
    x2 +6xy + 9
    • (a+b)2
    • (x +3)2
  34. x2 – 2xy + y2
    x2–10xy + 25
    • (x –y )( x – y) = (x –y)2
    • (x –5)2
  35. (x +y)(x – y)
    (x + 4)(x – 4)
    • x2-y2
    • x2 - 16
  36. 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
  37. 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 outcomes
    • total number of possible outcomes

    12/12+13+15 = 12/40 = 3/10
  38. distance formula?
    rate x time = distance
  39. work formula
    If you knit 2 sweaters per hour, and knit for 8 hours
    • rate x time
    • 2 per hour x 8 hours = 16
  40. What is a prime number?
    • positive number; divideable by itself and one other number only
    • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
    • 61, 67, 71, 73, 79, 83, 89, and 97
    • solution : estimate square of number and then check all number below that number
    • 97 = 10 = check 2, 3, 5, 7,
  41. How to add or subtract fraction?
    need common denominator and numerators are added together or subtracted
  42. Multiplying fractions?
    4 x 1 x10
    5 8 11
    • numerators times and denominators
    • cancelling 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 5
    • 1 x 1x2 / 1 x 2 x 11
  43. Divide fractions?
    1 x 4
    2 5
    • all you have to do is flip the second fraction and then multiply
    • 5
    • 8
  44. 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
  45. 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%
  46. 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
  47. 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
  48. Exponents
    Adding or subtacting?
    multiplying?
    Dividing?
    factions to an exponent 1 to the exponent 3
    2
    • need to be same base 2x2 + 3x2
    • add exponents together
    • dividing subtracting exponents
    • 1x1x1 over 2x2x2
  49. roots
    multiple and divide
  50. roots
    single number under a radical sign can be split into two numbers whose product is the
    original number
  51. 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 terms
    • 74 = 50 + 60+ 90 + x divided by 4
  52. Interest
    principle x rate x time
  53. 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
  54. mode
    number that occurs most frequently
  55. range?
    difference between the largest term and the smallest term

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