FTCE Math Review

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akrell
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231660
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FTCE Math Review
Updated:
2013-09-03 10:54:59
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math calculus trig
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Review for Florida Teacher Certification Exam
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  1. Parallel lines have slopes that are _______.
    equal
  2. What is standard form for a linear equation?
    Ax + By = C where A is not negative
  3. Perpendicular lines have slopes that are __________.
    Negative reciprocals of each other
  4. What is point-slope form for a linear equation?
  5. For inequalities, reverse the inequality symbol when ________.
    multiplying or dividing by a negative number
  6. What is the binomial theorem formula?
    • where 
  7.  = ____
    a.  When a is positive and k is even?
    b.  When a is positive and k is odd?
    c.  When a is negative and k is even?
    d.  When a is negative and k is odd?
    e.  When a is zero?
    • a.  positive
    • b.  positive
    • c.  imaginary
    • d.  negative
    • e.  zero
  8. i = ?
  9. To rationalize the denominator of a fraction you should _______________.
    multiply by the form of 1 needed to make the denominator a perfect power.
  10. When the denominator is a binomial containing a radical expression, the form of 1 used to rationalize is called the ________.
    conjugate
  11. The conjugate used to rationalize a binomial denominator has the 
    A.  same rational terms
    B.  reciprocal rational terms with opposite signs
    C. reciprocal rational terms
    D.  same rational terms with opposite signs
    D.  same ration terms with opposite sides
    (this multiple choice question has been scrambled)
  12. Formula to factor the difference of perfect cubes: 
  13. Formula to factor the sum of perfect cubes:  
  14. Formula for factoring in pairs: 
  15. For any polynomial P(x) with root=r, what is one known factor?
    x-r
  16. Formula for the quadratic equation?
  17.  is called the ______________.
    discriminant
  18. If the discriminant of a polynomial is positive the resulting roots are ________.
    2 real, unequal roots
  19. If the discriminant of a polynomial is zero, the resulting roots are __________.
    1 real root
  20. If the discriminant of a polynomial is negative, the resulting roots are _________.
    2 complex roots
  21. The shape of the graph for  is a __________.
    parabola
  22. The formula for the axis of symmetry for a parabola is ________.
  23. If a>0, a parabola opens ___________.
    upward
  24. If a<0, a parabola opens ____________.
    downward
  25. What are the 2 components of a vector?
    magnitude and direction
  26. For a vector multiplied by a scalar, 
  27. Multiplying vector coordinates by a scalar changes the ___________ of the vector.
    magnitude
  28. For a function, the set of all input values is called the __________.
    domain
  29. For a function, the set of all output values is called the ___________.
    range
  30. To determine if the inverse of a function is a function, use the _______________.
    horizontal line test
  31. A function that is symmetric about the y-axis is said to be _________.
    even
  32. A function that is symmetric about the origin is said to be __________.
    odd
  33. If a function is even, 
  34. If a function is odd, f
  35. Rotation 90o about the origin, changes the coordinates (x,y) to _________.
    (y,-x)
  36. Rotation 180o about the origin, changes the coordinates (x,y) to _________.
    (-x,-y)
  37. Rotation 270o about the origin, changes the coordinates (x,y) to _________.
    (-y,x)
  38. Reflection over the x-axis changes the coordinates from (x,y) to ______ and results in the function __________.
    (x,-y), 
  39. Reflection over the y-axis changes the coordinates from (x,y) to _____ and results in the function _________.
    (-x,y), 
  40. Reflection over the axis y=x changes the coordinates (x,y) to _____ and results in the function __________.
    (y,x), 
  41. Horizontal translation of a graph by  changes the coordinates from (x,y) to ________ and the function to ________.
    (x+h,y), 
  42. Vertical translation of a graph by  changes the coordinates from (x,y) to ________ and the function to ________.
    (x,y+k), 
  43. Vertical dilation of a graph by factor a changes the coordinates from (x,y) to _________ and results in the function _______.
    (x, ay), 
  44. Horizontal dilation of a graph by factor a changes the coordinates from (x,y) to _________ and results in the function _______.
    (ax, y), 
  45. Angles of equal measure are said to be _________.
    congruent
  46. A ray _________ an angle as the ray divides the angle into 2 congruent angles.
    bisects
  47. Any point on a perpendicular bisector is ___________ from the ends of the segment.
    equidistant 
  48. Angles that sum to 90o are said to be _______.
    complementary
  49. Angles that sum to 180o are said to be ___________.
    supplementary
  50. Triangles with no equal sides are called _________.
    scalene
  51. Triangles with 2 equal sides are called ______.
    isosceles
  52. The unequal side of an isosceles triangle is called the _______.
    base
  53. Triangles with 3 equal sides (and 3 equal angles) are called _______.
    equilateral
  54. A(n) ______ triangle has 1 angle greater than 90o.
    obtuse
  55. A(n) _____ triangle has 3 angles less than 90o.
    acute
  56. A(n) ______ triangle has a 90o angle.
    right
  57. The line segment from a vertex of a triangle perpendicular to the opposite side is called a(n) _________.
    altitude
  58. The line segment from a vertex of a triangle to the midpoint of the opposite side is called the _______.
    median
  59. A line that bisects a triangle side and is perpendicular to the side is called a(n) __________.
    perpendicular bisector
  60. The line segment that joins the midpoints of 2 sides of a triangle is called the _______.
    midline
  61. The midline creates a line that is _______ the size of the 3rd side.
    half
  62. Formula for the pythagorean theorum = ?
  63. A line that intersects 2 or more coplanar lines is called a(n) ________ line.
    transversal
  64. Name the corresponding angles in the image below:
    5 & 7; 1 & 3; 6 & 8; 2 & 4
  65. Name the alternate interior angles in the image below:
    6 & 3; 2 & 7
  66. Name the alternate exterior angles in the image below:
    1 & 8; 4 & 5
  67. Name the consecutive interior angles in the image below:
    6 & 7; 2 & 3
  68. Name the consecutive exterior angles in the image below:
    5 & 8; 1 & 4
  69. For parallel lines crossed by a transversal what 2 types of angles are supplementary?
    consecutive exterior; consecutive interior
  70. For parallel lines crossed by a transversal, which angles are congruent?
    corresponding angles, alternate interior angles, alternate exterior angles
  71. Any two tangent lines of a circle that meet at point P are _______.
    congruent
  72. The radius that extends from the center of the circle to the point of tangency is _________ to the tangent.
    perpendicular
  73. A _________ line intersects a circle at 2 points.
    secant
  74. A _____ joins 2 points on a circle.
    chord
  75. The _________ of a circle is the chord that passes through the center point.
    diameter
  76. For an angle with a vertex on a circle, the measure of the angle is equal to _________.
    1/2 the measure of the arc created
  77. For an angle with a vertex inside a circle, the measure of the angle is equal to ________.
    1/2 the sum of the arcs created
  78. For an angle with a vertex outside a circle, the measure of the angle is equal to __________.
    1/2 the difference of the arcs create.

  79. State the relationship between the lengths of the chords shown.

  80. State the relationship between the tangent and the secant of the circle shown above.

  81. State the relationship between the 2 secants drawn in the circle above.
  82. The formula for the sum of the internal angles for a polygon = ?
    (n-2)180where n = number of sides
  83. The sum of the internal and external angles of a polygon = ?
    180n
  84. The sum of the exterior angles of a polygon = ?
    360o
  85. For equiangular polygons, an exterior angle = ?
  86. For equiangular polygons, an interior angle = ?
  87. Polygons in which all corresponding internal angles and corresponding sides are congruent are said to be _________.
    congruent
  88. Name 5 methods used to prove 2 triangles are congruent.
    SSS, SAS, ASA, AAS, HL
  89. Name 3 methods used to prove 2 polygons are similar.
    SSS, SAS, AA
  90. circumference of a circle = ?
  91. Formula for the length of an arc = ?
  92. Parallelogram: A=?
  93. Square:  A=?
  94. Rectangle:  A=?
  95. Triangle:  A=?
  96. Kite:  A=?
  97. Rhombus: A=?
     or 
  98. Trapezoid: A=?
  99. Circle:  A=?
  100. Sector:  A=?
  101. The line from the center of a regular polygon perpendicular to a side is called a(n) _______________.
    apothem
  102. Polygon:  A=?
  103. Right Prism:  
    LA=?
    TA = ?


  104. Right Prism:  V=?
  105. Right cylinder:  
    LA=?
    TA=?


  106. Right cylinder: V=?
  107. Right pyramid:
    LA=?
    TA=?
    • sum of areas of triangular faces
  108. Right pyramid: V=?
  109. Right cone:
    LA=?
    TA=?


  110. Right cone:  V=?
  111. Sphere:
    TA = ?
  112. Sphere:  V=?
  113. If a figure is dilated by factor , surface area is dilated by factor _______ and volume is dilated by factor ___________.
  114. For the conditional statement p ⇒ q:
    converse = ?
    inverse = ?
    contrapositive = ?
    • q⇒p
    • ~p⇒~q
    • ~q⇒~p
  115. Distance between 2 points formula:  d=?
  116. distance between a point (x,y) and a line (Ax+By=C):
    d=?
  117. Midpoint formula:  MP = ?
  118. What is the standard formula for the equation of a circle?
    • where:
    • center = (h, k) and radius = r
  119. What is the standard form of an ellipse with a horizontal major axis?
    • where:
    • center = (h,k)
    • a>b; 
    • Foci: (h+c, k) and (h-c, k)
  120. What is the standard form of an ellipse with a vertical major axis?
    • where:
    • center = (h,k)
    • a>b; 
    • Foci:  (h, k+c) and (h, k-c)
  121. What is the standard form of a parabola that opens upward?
    • where:
    • focus:   (h, k+c)
    • vertex:  (h,k)
    • directix:  y= k-c
    • axis:  x=h
  122. What is the standard form of a parabola that opens downward?
    • where:
    • focus:     (h,k-c)
    • vertex:   (h,k)
    • directix:  y=k+c
    • axis:      x=h
  123. What is the standard form of a parabola that opens to the right?
    • where:
    • focus:    (h+c, k)
    • vertex:   (h,k)
    • directix:  x=h-c
    • axis:      y=k
  124. What is the standard form of a parabola that opens to the left?
    • where:
    • focus:    (h-c, k)
    • vertex:   (h,k)
    • directix:  x=h+c
    • axis:      y=k
  125. What is the standard form of a hyperbola with a horizontal focal axis?
    • where:
    • center:  (h,k)
    • difference between vertices:  2a
    • Foci:     (h+c, k) and (h-c, k)
    • Fund. rectangle coord.:  
  126. What is the standard form of a hyperbola with a vertical focal axis?
    • where:
    • center:  (h,k)
    • difference between vertices:  2a
    • Foci:  (h, k+c) and (h, k-c)
    • Fund. rectangle coord.:  
  127. Rotation of an image 90o counter-clockwise about the point of rotation changes (x,y) to ____.
    (-y,x)
  128. Rotation of an image 180o counter-clockwise about the point of rotation changes (x,y) to ____.
    (-x,-y)
  129. Rotation of an image 270o counter-clockwise about the point of rotation changes (x,y) to ____.
    (y,-x)
  130. Reflection of an image across the x-axis changes (x,y) to _____.
    (x,-y)
  131. Reflection of an image across the y-axis changes (x,y) to _____.
    (-x,y)
  132. Reflection of an image across the line y=x changes (x,y) to _____.
    (y,x)
  133. Dilation by a factor <1 _______ the image.
    shrinks
  134. Dilation by a factor >1 _________ the image.
    enlarges
  135. The x-coordinate is also referred to as the ______.
    abscissa
  136. The y-coordinate is also referred to as the ________.
    ordinate
  137. 360o = _____ radians
  138. For θ=0:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • 0
    • 1
    • 0
  139. For θ=30o:
    sin θ = ?
    cos θ = ?
    tan θ = ?




  140. For θ=45o:
    sin θ = ?
    cos θ = ?
    tan θ = ?




    1
  141. For θ=60o:
    sin θ = ?
    cos θ = ?
    tan θ = ?




  142. For θ = 90o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • 1
    • 0
    • undefined
  143. For θ = 180o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • 0
    • -1
    • 0
  144. For θ = 270o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • -1
    • 0
    • undefined
  145. According to the quotient identity:

  146. According to the quotient identity:
  147. 1
  148. This is a graph of the _____ function.
    sin
  149. This is a graph of the ______ function.
    • cos
    • Period = 2π
  150. This is a graph of the _____ function.
    • tan
    • Period = π
  151. This is a graph of the ______ function.
    • csc
    • Period = 2π
  152. This is a graph of the _____ function.
    • sec
    • Period = 2π
  153. This is a graph of the _____ function.
    • cot
    • Period = 2π
  154. This is a graph of the _____ function.
    arcsin
  155. This is a graph of the ______ function.
    arccos
  156. This is a graph of the _______ function.
    arctan
  157. This is a graph of the ________ function.
    arccsc
  158. This is a graph of the ________ function.
    arcsec
  159. This is a graph of the _______ function.
    arccot
  160. The general formula for the transformation of the graph of sin or cos is _________.
    Where:  
    A = ?
    B = ?
    C = ?
    D = ?
    •  or 
    • A = amplitude
    • B = reciprocal of horiz. dilation ()
    • C = sinusoidal axis (vertical translation)
    • D = phase shift (horizontal translation)
    • "sum"thing switches
    • "opposite"
  161. Law of Sines
  162. Law of Cosines
  163. Mean 
  164. Median
    • Middle number when values are arranged from smallest to largest.  
    • If there are an even number of values the mean of the middle 2 is taken.
    • The median is a better measure than mean if data contains outliers.
  165. Mode
    number(s) that occur(s) most frequently in a data set
  166. What are the best measures of spread for symmetric data sets?
    standard deviation, variance
  167. What is the best measure for spread for data with outliers?
    interquartile range
  168. Variance: s2 = ?
  169. Standard deviation:  s = ?
  170. A 5 number summary contains:
    • minimum
    • maximum
    • median (Q2)
    • Q1
    • Q3
  171. Interquartile range = ?
    Q3 - Q1
  172. Outliers are values < __________ or > _________.


  173. In a box and whisker plot, the boundaries of the box represent _______.
    Q1 and Q3 with the median line in between
  174. In a box and whisker plot, the "whiskers" represent the _________.
    minimum and maximum
  175. Z-score:  z = ?
  176. Changing the units of a set of data results in ________.
    a change in the center and spread by a ratio of the multiplier
  177. Adding or subtraction a constant to the values of a set of data changes ________.
    the center but not the spread
  178. Analysis of a scatter plot should include these 3 characteristics:
    • shape (linear/nonlinear)
    • direction (+ or - slope)
    • strength (strong/weak)
  179. Correlation coefficient: r = ?
  180. For the correlation coefficient, r, interpret the following results:
    r = -1
    r = 0
    r = 1
    • perfect line
    • no correlation
    • perfect line
  181. Linear regression: 
  182. Name 5 types of random samples.
    • simple random
    • stratified random (homogeneous)
    • cluster (heterogeneous)
    • multistage 
    • systematic random
  183. For independent events:  
  184. For dependent events:  
  185. For the probability of M, N, or both M & N: 
  186. Permutations (when Position matters):
    • where:
    • n = number of things to choose from
    • r = number chosen
  187. Combinations (order doesn't matter):



    • where:
    • n = number of things to choose from
    • r = number chosen
  188. Combinations with repetition:
  189. Sequences in which the difference between sums is constant is called ________.
    arithmetic
  190. Arithmetic sequence:



  191. Sequences in which there is a constant ratio between terms are called __________.
    geometric
  192. Geometric sequence:



  193. Change of base formula:
    For 

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