FTCE Math Review

  1. Image Upload 1
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  9. Image Upload 17
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  10. Image Upload 19
    Image Upload 20
  11. Parallel lines have slopes that are _______.
    equal
  12. What is standard form for a linear equation?
    Ax + By = C where A is not negative
  13. Perpendicular lines have slopes that are __________.
    Negative reciprocals of each other
  14. What is point-slope form for a linear equation?
    Image Upload 21
  15. For inequalities, reverse the inequality symbol when ________.
    multiplying or dividing by a negative number
  16. What is the binomial theorem formula?
    • Image Upload 22
    • where Image Upload 23
  17. Image Upload 24 = ____
    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
  18. i = ?
    Image Upload 25
  19. To rationalize the denominator of a fraction you should _______________.
    multiply by the form of 1 needed to make the denominator a perfect power.
  20. When the denominator is a binomial containing a radical expression, the form of 1 used to rationalize is called the ________.
    conjugate
  21. The conjugate used to rationalize a binomial denominator has the 



    A.  same ration terms with opposite sides
  22. Formula to factor the difference of perfect cubes: Image Upload 26
    Image Upload 27
  23. Formula to factor the sum of perfect cubes:  Image Upload 28
    Image Upload 29
  24. Formula for factoring in pairs: Image Upload 30
    Image Upload 31
  25. For any polynomial P(x) with root=r, what is one known factor?
    x-r
  26. Formula for the quadratic equation?
    Image Upload 32
  27. Image Upload 33 is called the ______________.
    discriminant
  28. If the discriminant of a polynomial is positive the resulting roots are ________.
    2 real, unequal roots
  29. If the discriminant of a polynomial is zero, the resulting roots are __________.
    1 real root
  30. If the discriminant of a polynomial is negative, the resulting roots are _________.
    2 complex roots
  31. The shape of the graph for Image Upload 34 is a __________.
    parabola
  32. The formula for the axis of symmetry for a parabola is ________.
    Image Upload 35
  33. If a>0, a parabola opens ___________.
    upward
  34. If a<0, a parabola opens ____________.
    downward
  35. What are the 2 components of a vector?
    magnitude and direction
  36. For a vector multiplied by a scalar, Image Upload 36
    Image Upload 37
  37. Multiplying vector coordinates by a scalar changes the ___________ of the vector.
    magnitude
  38. Image Upload 38
    Image Upload 39
  39. Image Upload 40
    Image Upload 41
  40. For a function, the set of all input values is called the __________.
    domain
  41. For a function, the set of all output values is called the ___________.
    range
  42. To determine if the inverse of a function is a function, use the _______________.
    horizontal line test
  43. A function that is symmetric about the y-axis is said to be _________.
    even
  44. A function that is symmetric about the origin is said to be __________.
    odd
  45. If a function is even, Image Upload 42
    Image Upload 43
  46. If a function is odd, fImage Upload 44
    Image Upload 45
  47. Rotation 90o about the origin, changes the coordinates (x,y) to _________.
    (y,-x)
  48. Rotation 180o about the origin, changes the coordinates (x,y) to _________.
    (-x,-y)
  49. Rotation 270o about the origin, changes the coordinates (x,y) to _________.
    (-y,x)
  50. Reflection over the x-axis changes the coordinates from (x,y) to ______ and results in the function __________.
    (x,-y), Image Upload 46
  51. Reflection over the y-axis changes the coordinates from (x,y) to _____ and results in the function _________.
    (-x,y), Image Upload 47
  52. Reflection over the axis y=x changes the coordinates (x,y) to _____ and results in the function __________.
    (y,x), Image Upload 48
  53. Horizontal translation of a graph by Image Upload 49 changes the coordinates from (x,y) to ________ and the function to ________.
    (x+h,y), Image Upload 50
  54. Vertical translation of a graph by Image Upload 51 changes the coordinates from (x,y) to ________ and the function to ________.
    (x,y+k), Image Upload 52
  55. Vertical dilation of a graph by factor a changes the coordinates from (x,y) to _________ and results in the function _______.
    (x, ay), Image Upload 53
  56. Horizontal dilation of a graph by factor a changes the coordinates from (x,y) to _________ and results in the function _______.
    (ax, y), Image Upload 54
  57. Angles of equal measure are said to be _________.
    congruent
  58. A ray _________ an angle as the ray divides the angle into 2 congruent angles.
    bisects
  59. Any point on a perpendicular bisector is ___________ from the ends of the segment.
    equidistant 
  60. Angles that sum to 90o are said to be _______.
    complementary
  61. Angles that sum to 180o are said to be ___________.
    supplementary
  62. Triangles with no equal sides are called _________.
    scalene
  63. Triangles with 2 equal sides are called ______.
    isosceles
  64. The unequal side of an isosceles triangle is called the _______.
    base
  65. Triangles with 3 equal sides (and 3 equal angles) are called _______.
    equilateral
  66. A(n) ______ triangle has 1 angle greater than 90o.
    obtuse
  67. A(n) _____ triangle has 3 angles less than 90o.
    acute
  68. A(n) ______ triangle has a 90o angle.
    right
  69. The line segment from a vertex of a triangle perpendicular to the opposite side is called a(n) _________.
    altitude
  70. The line segment from a vertex of a triangle to the midpoint of the opposite side is called the _______.
    median
  71. A line that bisects a triangle side and is perpendicular to the side is called a(n) __________.
    perpendicular bisector
  72. The line segment that joins the midpoints of 2 sides of a triangle is called the _______.
    midline
  73. The midline creates a line that is _______ the size of the 3rd side.
    half
  74. Formula for the pythagorean theorum = ?
    Image Upload 55
  75. A line that intersects 2 or more coplanar lines is called a(n) ________ line.
    transversal
  76. Name the corresponding angles in the image below:
    Image Upload 56
    5 & 7; 1 & 3; 6 & 8; 2 & 4
  77. Name the alternate interior angles in the image below:
    Image Upload 57
    6 & 3; 2 & 7
  78. Name the alternate exterior angles in the image below:
    Image Upload 58
    1 & 8; 4 & 5
  79. Name the consecutive interior angles in the image below:
    Image Upload 59
    6 & 7; 2 & 3
  80. Name the consecutive exterior angles in the image below:
    Image Upload 60
    5 & 8; 1 & 4
  81. For parallel lines crossed by a transversal what 2 types of angles are supplementary?
    consecutive exterior; consecutive interior
  82. For parallel lines crossed by a transversal, which angles are congruent?
    corresponding angles, alternate interior angles, alternate exterior angles
  83. Any two tangent lines of a circle that meet at point P are _______.
    congruent
  84. The radius that extends from the center of the circle to the point of tangency is _________ to the tangent.
    perpendicular
  85. A _________ line intersects a circle at 2 points.
    secant
  86. A _____ joins 2 points on a circle.
    chord
  87. The _________ of a circle is the chord that passes through the center point.
    diameter
  88. 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
  89. 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
  90. 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.
  91. Image Upload 61
    State the relationship between the lengths of the chords shown.
    Image Upload 62
  92. Image Upload 63
    State the relationship between the tangent and the secant of the circle shown above.
    Image Upload 64
  93. Image Upload 65
    State the relationship between the 2 secants drawn in the circle above.
    Image Upload 66
  94. The formula for the sum of the internal angles for a polygon = ?
    (n-2)180where n = number of sides
  95. The sum of the internal and external angles of a polygon = ?
    180n
  96. The sum of the exterior angles of a polygon = ?
    360o
  97. For equiangular polygons, an exterior angle = ?
    Image Upload 67
  98. For equiangular polygons, an interior angle = ?
    Image Upload 68
  99. Polygons in which all corresponding internal angles and corresponding sides are congruent are said to be _________.
    congruent
  100. Name 5 methods used to prove 2 triangles are congruent.
    SSS, SAS, ASA, AAS, HL
  101. Name 3 methods used to prove 2 polygons are similar.
    SSS, SAS, AA
  102. circumference of a circle = ?
    Image Upload 69
  103. Formula for the length of an arc = ?
    Image Upload 70
  104. Parallelogram: A=?
    Image Upload 71
  105. Square:  A=?
    Image Upload 72
  106. Rectangle:  A=?
    Image Upload 73
  107. Triangle:  A=?
    Image Upload 74
  108. Kite:  A=?
    Image Upload 75
  109. Rhombus: A=?
    Image Upload 76 or Image Upload 77
  110. Trapezoid: A=?
    Image Upload 78
  111. Circle:  A=?
    Image Upload 79
  112. Sector:  A=?
    Image Upload 80
  113. The line from the center of a regular polygon perpendicular to a side is called a(n) _______________.
    apothem
  114. Polygon:  A=?
    Image Upload 81
  115. Right Prism:  
    LA=?
    TA = ?
    Image Upload 82

    Image Upload 83
  116. Right Prism:  V=?
    Image Upload 84
  117. Right cylinder:  
    LA=?
    TA=?
    Image Upload 85

    Image Upload 86
  118. Right cylinder: V=?
    Image Upload 87
  119. Right pyramid:
    LA=?
    TA=?
    • sum of areas of triangular faces
    • Image Upload 88
  120. Right pyramid: V=?
    Image Upload 89
  121. Right cone:
    LA=?
    TA=?
    Image Upload 90

    Image Upload 91
  122. Right cone:  V=?
    Image Upload 92
  123. Sphere:
    TA = ?
    Image Upload 93
  124. Sphere:  V=?
    Image Upload 94
  125. If a figure is dilated by factor Image Upload 95, surface area is dilated by factor _______ and volume is dilated by factor ___________.
    • Image Upload 96
    • Image Upload 97
  126. For the conditional statement p ⇒ q:
    converse = ?
    inverse = ?
    contrapositive = ?
    • q⇒p
    • ~p⇒~q
    • ~q⇒~p
  127. Distance between 2 points formula:  d=?
    Image Upload 98
  128. distance between a point (x,y) and a line (Ax+By=C):
    d=?
    Image Upload 99
  129. Midpoint formula:  MP = ?
    Image Upload 100
  130. What is the standard formula for the equation of a circle?
    • Image Upload 101
    • where:
    • center = (h, k) and radius = r
  131. What is the standard form of an ellipse with a horizontal major axis?
    • Image Upload 102
    • where:
    • center = (h,k)
    • a>b; Image Upload 103
    • Foci: (h+c, k) and (h-c, k)
  132. What is the standard form of an ellipse with a vertical major axis?
    • Image Upload 104
    • where:
    • center = (h,k)
    • a>b; Image Upload 105
    • Foci:  (h, k+c) and (h, k-c)
  133. What is the standard form of a parabola that opens upward?
    • Image Upload 106
    • where:
    • focus:   (h, k+c)
    • vertex:  (h,k)
    • directix:  y= k-c
    • axis:  x=h
  134. What is the standard form of a parabola that opens downward?
    • Image Upload 107
    • where:
    • focus:     (h,k-c)
    • vertex:   (h,k)
    • directix:  y=k+c
    • axis:      x=h
  135. What is the standard form of a parabola that opens to the right?
    • Image Upload 108
    • where:
    • focus:    (h+c, k)
    • vertex:   (h,k)
    • directix:  x=h-c
    • axis:      y=k
  136. What is the standard form of a parabola that opens to the left?
    • Image Upload 109
    • where:
    • focus:    (h-c, k)
    • vertex:   (h,k)
    • directix:  x=h+c
    • axis:      y=k
  137. What is the standard form of a hyperbola with a horizontal focal axis?
    • Image Upload 110
    • where:
    • center:  (h,k)
    • difference between vertices:  2a
    • Foci:     (h+c, k) and (h-c, k)
    • Fund. rectangle coord.:  Image Upload 111
  138. What is the standard form of a hyperbola with a vertical focal axis?
    • Image Upload 112
    • where:
    • center:  (h,k)
    • difference between vertices:  2a
    • Foci:  (h, k+c) and (h, k-c)
    • Fund. rectangle coord.:  Image Upload 113
  139. Rotation of an image 90o counter-clockwise about the point of rotation changes (x,y) to ____.
    (-y,x)
  140. Rotation of an image 180o counter-clockwise about the point of rotation changes (x,y) to ____.
    (-x,-y)
  141. Rotation of an image 270o counter-clockwise about the point of rotation changes (x,y) to ____.
    (y,-x)
  142. Reflection of an image across the x-axis changes (x,y) to _____.
    (x,-y)
  143. Reflection of an image across the y-axis changes (x,y) to _____.
    (-x,y)
  144. Reflection of an image across the line y=x changes (x,y) to _____.
    (y,x)
  145. Dilation by a factor <1 _______ the image.
    shrinks
  146. Dilation by a factor >1 _________ the image.
    enlarges
  147. The x-coordinate is also referred to as the ______.
    abscissa
  148. The y-coordinate is also referred to as the ________.
    ordinate
  149. 360o = _____ radians
  150. For θ=0:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • 0
    • 1
    • 0
  151. For θ=30o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    Image Upload 114

    Image Upload 115

    Image Upload 116
  152. For θ=45o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    Image Upload 117

    Image Upload 118

    1
  153. For θ=60o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    Image Upload 119

    Image Upload 120

    Image Upload 121
  154. For θ = 90o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • 1
    • 0
    • undefined
  155. For θ = 180o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • 0
    • -1
    • 0
  156. For θ = 270o:
    sin θ = ?
    cos θ = ?
    tan θ = ?
    • -1
    • 0
    • undefined
  157. According to the quotient identity:

    Image Upload 122
    Image Upload 123
  158. According to the quotient identity:
    Image Upload 124
    Image Upload 125
  159. Image Upload 126
    1
  160. Image Upload 127
    Image Upload 128
  161. Image Upload 129
    Image Upload 130
  162. This is a graph of the _____ function.
    Image Upload 131
    sin
  163. This is a graph of the ______ function.
    Image Upload 132
    • cos
    • Period = 2π
  164. This is a graph of the _____ function.
    Image Upload 133
    • tan
    • Period = π
  165. This is a graph of the ______ function.
    Image Upload 134
    • csc
    • Period = 2π
  166. This is a graph of the _____ function.
    Image Upload 135
    • sec
    • Period = 2π
  167. This is a graph of the _____ function.
    Image Upload 136
    • cot
    • Period = 2π
  168. This is a graph of the _____ function.
    Image Upload 137
    arcsin
  169. This is a graph of the ______ function.
    Image Upload 138
    arccos
  170. This is a graph of the _______ function.
    Image Upload 139
    arctan
  171. This is a graph of the ________ function.
    Image Upload 140
    arccsc
  172. This is a graph of the ________ function.
    Image Upload 141
    arcsec
  173. This is a graph of the _______ function.
    Image Upload 142
    arccot
  174. The general formula for the transformation of the graph of sin or cos is _________.
    Where:  
    A = ?
    B = ?
    C = ?
    D = ?
    • Image Upload 143 or Image Upload 144
    • A = amplitude
    • B = reciprocal of horiz. dilation (Image Upload 145)
    • C = sinusoidal axis (vertical translation)
    • D = phase shift (horizontal translation)
  175. Image Upload 146
    • Image Upload 147
    • "sum"thing switches
  176. Image Upload 148
    • Image Upload 149
    • "opposite"
  177. Law of Sines
    Image Upload 150
  178. Law of Cosines
    Image Upload 151
  179. Mean Image Upload 152
    Image Upload 153
  180. 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.
  181. Mode
    number(s) that occur(s) most frequently in a data set
  182. What are the best measures of spread for symmetric data sets?
    standard deviation, variance
  183. What is the best measure for spread for data with outliers?
    interquartile range
  184. Variance: s2 = ?
    Image Upload 154
  185. Standard deviation:  s = ?
    Image Upload 155
  186. A 5 number summary contains:
    • minimum
    • maximum
    • median (Q2)
    • Q1
    • Q3
  187. Interquartile range = ?
    Q3 - Q1
  188. Outliers are values < __________ or > _________.
    Image Upload 156

    Image Upload 157
  189. In a box and whisker plot, the boundaries of the box represent _______.
    Q1 and Q3 with the median line in between
  190. In a box and whisker plot, the "whiskers" represent the _________.
    minimum and maximum
  191. Z-score:  z = ?
    Image Upload 158
  192. Changing the units of a set of data results in ________.
    a change in the center and spread by a ratio of the multiplier
  193. Adding or subtraction a constant to the values of a set of data changes ________.
    the center but not the spread
  194. Analysis of a scatter plot should include these 3 characteristics:
    • shape (linear/nonlinear)
    • direction (+ or - slope)
    • strength (strong/weak)
  195. Correlation coefficient: r = ?
    Image Upload 159
  196. For the correlation coefficient, r, interpret the following results:
    r = -1
    r = 0
    r = 1
    • perfect line
    • no correlation
    • perfect line
  197. Linear regression: Image Upload 160
    Image Upload 161
  198. Name 5 types of random samples.
    • simple random
    • stratified random (homogeneous)
    • cluster (heterogeneous)
    • multistage 
    • systematic random
  199. For independent events:  Image Upload 162
    Image Upload 163
  200. For dependent events:  Image Upload 164
    Image Upload 165
  201. For the probability of M, N, or both M & N: Image Upload 166
    Image Upload 167
  202. Permutations (when Position matters):
    Image Upload 168
    • Image Upload 169
    • where:
    • n = number of things to choose from
    • r = number chosen
  203. Combinations (order doesn't matter):
    Image Upload 170
    Image Upload 171

    • where:
    • n = number of things to choose from
    • r = number chosen
  204. Combinations with repetition:
    Image Upload 172
  205. Sequences in which the difference between sums is constant is called ________.
    arithmetic
  206. Arithmetic sequence:
    Image Upload 173
    Image Upload 174
    Image Upload 175

    Image Upload 176
  207. Sequences in which there is a constant ratio between terms are called __________.
    geometric
  208. Geometric sequence:
    Image Upload 177
    Image Upload 178
    Image Upload 179

    Image Upload 180
  209. Change of base formula:
    For Image Upload 181
    Image Upload 182
Author
akrell
ID
231660
Card Set
FTCE Math Review
Description
Review for Florida Teacher Certification Exam
Updated