DAT QR 1 - Numbers and Ops - Scientific Measurement - Algebra - Geometry)

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DAT QR 1 - Numbers and Ops - Scientific Measurement - Algebra - Geometry)
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2015-08-28 22:37:03
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DAT quantitative reasoning review flashcards QR
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Flashcards for DAT QR Section review
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  1. 1 inch = ________ cm
    2.54 cm
  2. 1 meter = _____ yards
    1.09 yards
  3. 1 mile = _____ yards
    1760 yards
  4. 1 mile = _____ km
    1.6 km
  5. 1 kg = _____ lbs
    2.2 lbs
  6. 1 kg = _____ oz
    35.27396 oz
  7. 1 g = _____ oz
    0.0353 oz
  8. 1 oz = _____ liter
    0.0295735 liter
  9. 1 gallon = _____ fl oz
    128 fl oz
  10. 1 hr = _____ seconds
    3600 seconds
  11. 1 yard =
       a) _____ ft
       b) _____ m
    • a) 3 ft
    • b) 0.9144 m
  12. 1 mile = _____ ft.
    5,280 ft.
  13. 1 foot =
       a) _____ inches
       b) _____ m
    • a) 12 inches
    • b) 0.3048 m

    Hint: 1 foot = ___ m

    - Three (.3) men set foot through the door (0) and "foraged" (48) through Demeter's house.
  14. Formula for converting °F to °C
  15. Formula for converting °C to °F
  16. Mnemonic for prefixes of metric units
    King Henry Died Unexpectedly Drinking Chocolate Milk

    • Kilo = 103
    • Hecto = 102
    • Deca = 101
    • Unit Base
    • Deci = 10-1
    • Centi = 10-2
    • Milli = 10-3
  17. Decimal equivalents of fractions:

    1/2 = _____
    1/3 = _____
    1/4 = _____
    1/5 = _____
    1/6 = _____
    1/7 = _____
    1/8 = _____
    1/9 = _____
    • 1/2 = 0.5
    • 1/3 = 0.33
    • 1/4 = 0.25
    • 1/5 = 0.2
    • 1/6 = 0.167
    • 1/7 = 0.143
    • 1/8 = 0.125
    • 1/9 = 0.111
  18. Mnemonic for prefixes of metric units (greater increments of powers of 10)
    The Great Mancini Usually Makes Navy-guys Pee

    • Tera = 1012
    • Giga = 109
    • Mega = 106
    • Unit Base
    • Micro = 10-6
    • Nano = 10-9
    • Pico = 10-12
  19. Domain of a function
    Set of possible values an independent variable(s) (input) can have.

    Note: Determine if there are any real value for x (as in f(x)) for which the expression is undefined.
  20. Range of a function
    Set of possible values that the output of a function can have.

    Note: Are there any numbers the output cannot equal?
  21. Inequalities

    What happens to an inequality sign when one multiplies or divides both sides of an equation by a negative number?
    The inequality symbol changes direction.

    Note: squaring a negative number also falls into this category; you are multiplying by that same negative number.
  22. Absolute Inequalities

    If the symbol is > (or ≥) (absolute value is > the number on the other side of the inequality, what is the "connecting word?"
    Connecting word in the inequality is: "or"

    - if a >0, then the solutions to |x| > a are x > a or x < -a.

    Hint: "great-or"

    Ex: |x + 2| > 7

    • ⇒ x + 2 > 7 or x + 2 < -7
    • ⇒ x > 5 or x < -9

    Note: "Absolute value" is how far "x" is from zero along the number line.


  23. Absolute Inequalities

    If the symbol is < (or ≤) (absolute value is < the number on the other side of the inequality, what is the "connecting word?"
    Connecting word in the inequality is: "and"

    - if a < 0, then the solutions to |x| < a are x < a and x > -a.

    - also written as -a < x < a.

    Hint: "less-and"

    Note: "Absolute value" is how far "x" is from zero along the number line.
  24. What is a linear equation?
    An equation that describes relationships between variables in which every term is a scalar or a scalar multiple of a variable.

    Ex. 3x +2y = z + 5

    - Cannot have exponents or variables multiplied together

    - "linear" can be represented in a Cartesian graph as a straight line.
  25. Slope-intercept formula
    y = mx + b

    • m = slope (rise / run); (y2- y1)/(x2 - x1)
    • b = y-intercept (x is always zero; line crosses y-axis)
    •    ⋄ Two equations with similar "m" are parallel.
    •    ⋄ Two equations with similar "m" but one is positive and the other is negative are perpendicular.
  26. Format of a quadratic equation?
    ax2 + bx + c = 0

    • - a second-degree polynomial
    • - where a, b, and c are constants
  27. Steps for completing the square in solving for a quadratic equation.
    ax2 + bx + c = 0

    1. Move c to the other side of the equation.

    2. Divide through by the leading coefficient a.

    3. Then take half of b/a (which is the coefficient of x), square it, and add to both sides of the equation.

    4. Take the square root of both sides an solve for x.
  28. Quadratic formula


    Note: If there is no first degree term (ax2 + c = 0), then:

    x2 = -c/a

    Therefore:
  29. What is a vertical angle?
    The angle opposite of each other that is formed by two intersecting lines.

    - the two angles across from each other are equal in measure (angles 1 & 3; 2 & 4)

    - angles 1 & 3 are vert. angles

    - angles 1 & 2 (adjacent vertical angles) are supplementary angles (forming 180°)
  30. What are complementary angles?
    Two angles that add up to 90° (A & B below).

  31. What is the slope of any line perpendicular to a line with a slope of a/b?
    -b/a
  32. What is the formula to find the sum total of all interior angles of a polygon (with x sides).
    S = (x-2)(180°)
  33. Given the total angles for a polygon, how can you determine each interior angle?
    By dividing the sum of the polygon angles by the number of sides.

    Note: assuming that all angles of the polygon have the same measure.
  34. Perimeter of a rectangle?
    P = 2b + 2h (sum of all sides)

  35. Area of a rectangle?
    A = length x width = b x h
  36. Perimeter of a square?
    P = 4a (sum of all sides of same length)
  37. Area of a square?
    A = a2
  38. What is the sum of the interior angles of a triangle?
    180°

  39. What is the sum of the exterior angles of a triangle?
    360°

  40. What is the value of an exterior angle?
    It is equal to the sum of the opposite two interior angles.

    w= x + y

  41. Perimeter of a triangle?
    Sum of all its sides.
  42. Area of a triangle?
  43. Sides of a triangle:

    a) Sum of any two sides _________
    b) Difference between two sides ________
    a) ≥ the length of the 3rd side. (a+b > c)

    Note: if a+b = c, then the triangle is a line segment (triangle inequality property).

    b) < the length of the 3rd side. (a-b < c)
  44. Pythagorean theorem
    c2 = a2 + b2 (for right triangles)
  45. Right triangle special cases:

    What are the ratios of side lengths commonly used so that there's no need to use the Pythagorean theorem?
    • 3 : 4 : 5
    • 5 : 12 : 13
    • 7 : 24 : 25
    • 8 : 15 : 17
    • 9 : 40 : 41
  46. Right triangle special cases:

    What are the ratios of interior angles commonly used with their associated side ratios?
    30° - 60° - 90°

    - corresponding side ratios:

    45° - 45° - 90°

    - corresponding side ratios:
  47. What are equilateral triangles?
    Triangles with all sides equal (thus all angles are 60°).
  48. What are isosceles triangles?
    • Triangles with 2 sides equal.
    • Angles opposite of equal sides are also equal.
  49. What are scalene triangles?
    • Triangles with no equal sides.
    • There are also no equal internal angles.
    • To find the height of the triangle requires the Pythagorean theorem.
  50. What are similar triangles?
    Triangles that have the same values for interior angles, therefore the ratios of corresponding sides are equal.





    Same shape but scaled to different size.
  51. Diameter of a circle?
    D = 2r

    also:     r = radius
  52. Circumference of a circle?
    Formulae:


  53. Area of a circle?
  54. Define length of an arc of a circle.
    What is the formula?
    Piece of circumference formed by an angle of n degrees measured as the arc's central angle in a circle of radius r.

    Formula:



    Reminder: the measure of an arc of a circle corresponding to a radian angle (central angle) is the same measure as the length of the radius.
  55. What is an area of a sector?
    What are it's formulae?
    It is a portion of the circle formed by an angle of n degree measured as the sector's central angle in a circle of radius r.




    • Area of sector (in radians):

    • Area of sector (in degrees):
  56. What is a trapezoid?
    It is a four-sided figure with one pair of parallel sides and one pair of non-parallel sides.

  57. Formula for the area of a trapezoid.




    Note: formula derived from finding area of 2 combined similar trapezoids (forming a parallelograms (2 pairs of parallel sides)) --> A = bh, but then dividing by two :)
  58. What are the two adjacent (upper and lower) base angles of a trapezoid?
    Supplementary angles (adding up to 180°)

    • Angle A + Angle D = 180°
    • Angle B + Angle C = 180°
  59. These are trapezoids with two equal sides.
    Isosceles trapezoids.

    • - the equal sides are non-parallel.
    • - if the left and right sides are of the same lengths, these angles are the same as well.



    • Angle A = Angle D
    • Angle B = Angle C
    • Diagonal AC = Diagonal BD
  60. What is a parallelogram?
    It is a quadrilateral that has 2 sets of parallel sides.

  61. What is the area of a parallelogram?
    A = b x h

    Note: the height can be solved for by dropping a vertical line from the vertex to the opposite side and evaluating the resulting right triangle.
  62. Other forms of special parallelograms?
    1. Square

    2. Rhombus (four sides of equal lengths but has two different pairs of angle values.

  63. What is the perimeter of a box?
    The sum of all its edges


  64. Surface area of a box?
    • Surface Area = 2lw + 2wh + 2lh
    •                   = 2(lw +wh +lh)
  65. Volume of a box?
    Volume  = l x w x h

    Note:

    - Alternate formula: A x h  (l x w is the area)

    ** Same for prism or cylinder
  66. Surface area of a sphere?


    Note: there are no vertices or edges in a sphere, thus no circumference
  67. Volume of a sphere?
  68. What are cylinders?
    These have two parallel circular faces, and their edges are connected by a smooth, edgeless surface.

    3 parts: two circular faces and the connecting portion.
  69. What is the surface area of a cylinder?
    Surface Area =

    - two areas of a circle plus circumference of a circle times the height of the cylinder.
  70. Volume of a cylinder?


    - area of one of its bases (circle) times the cylinder's height.
  71. 1. What is the slant length of a cone?
    2. What is the height of a cone?
    1. It is the distance from the edge of the circle to the vertex.

    2. It is the distance from the center of the circle to the vertex.
  72. Surface area of a cone?
    Surface Area =

    •                   =
    •                   =

    - solved from the radius (for the area of the base circle), and the area of the lateral portion (1/2 the circumference of the circle times the slant length).
  73. Volume of a cone?


    Note: this is similar to the V of a pyramid, which is where B is the area of the pyramid's base (B=);

    Area of the base circle is .
  74. How do you get the LCM of several integers?
    The LCM of several integers can be found by writing the prime factorization of each of the integers in question and then taking the least number necessary of each prime factor. 

    Ex.

    Let’s find the LCM of 12, 18, and 24:

     

    12 = 2 x 6 = 2 x 2 x 3

    18 = 2 x 9 = 2 x 3 x 3

    24 = 2 x 12 = 2 x 3 x 4 = 2 x 2 x 2 x 3


    Thus,

    •  
    • 12 = 2 x 2 x 3

    18 = 2 x 3 x 3

    24 = 2 x 2 x 2 x 3

         12 has two prime factors of 2, 18 has one prime factor of 2, and 24 has three prime factors of 2.  So the minimum number of prime factors of 2 needed is 3. 

         12 has one prime factor of 3, 18 has two prime factors of 3, and 24 has one prime factor of 3.  So the minimum number of prime factors of 3 needed is 2.

    So the LCM of 12, 18, and 24 is 2 x 2 x 2 x 3 x 3 = 23 x 32 = 8 x 9 = 72.

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