FTCE Math Review

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  1. Image Upload
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  2. Image Upload
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  3. Image Upload
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  4. Image Upload
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  7. Image Upload
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  8. Image Upload
    Image Upload
  9. Image Upload
    Image Upload
  10. Image Upload
    Image Upload
  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
  15. For inequalities, reverse the inequality symbol when ________.
    multiplying or dividing by a negative number
  16. What is the binomial theorem formula?
    • Image Upload
    • where Image Upload
  17. Image Upload = ____
    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
  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 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)
  22. Formula to factor the difference of perfect cubes: Image Upload
    Image Upload
  23. Formula to factor the sum of perfect cubes:  Image Upload
    Image Upload
  24. Formula for factoring in pairs: Image Upload
    Image Upload
  25. For any polynomial P(x) with root=r, what is one known factor?
    x-r
  26. Formula for the quadratic equation?
    Image Upload
  27. Image Upload 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 is a __________.
    parabola
  32. The formula for the axis of symmetry for a parabola is ________.
    Image Upload
  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
    Image Upload
  37. Multiplying vector coordinates by a scalar changes the ___________ of the vector.
    magnitude
  38. Image Upload
    Image Upload
  39. Image Upload
    Image Upload
  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
    Image Upload
  46. If a function is odd, fImage Upload
    Image Upload
  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
  51. Reflection over the y-axis changes the coordinates from (x,y) to _____ and results in the function _________.
    (-x,y), Image Upload
  52. Reflection over the axis y=x changes the coordinates (x,y) to _____ and results in the function __________.
    (y,x), Image Upload
  53. Horizontal translation of a graph by Image Upload changes the coordinates from (x,y) to ________ and the function to ________.
    (x+h,y), Image Upload
  54. Vertical translation of a graph by Image Upload changes the coordinates from (x,y) to ________ and the function to ________.
    (x,y+k), Image Upload
  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
  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
  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
  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
    5 & 7; 1 & 3; 6 & 8; 2 & 4
  77. Name the alternate interior angles in the image below:
    Image Upload
    6 & 3; 2 & 7
  78. Name the alternate exterior angles in the image below:
    Image Upload
    1 & 8; 4 & 5
  79. Name the consecutive interior angles in the image below:
    Image Upload
    6 & 7; 2 & 3
  80. Name the consecutive exterior angles in the image below:
    Image Upload
    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
    State the relationship between the lengths of the chords shown.
    Image Upload
  92. Image Upload
    State the relationship between the tangent and the secant of the circle shown above.
    Image Upload
  93. Image Upload
    State the relationship between the 2 secants drawn in the circle above.
    Image Upload
  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
  98. For equiangular polygons, an interior angle = ?
    Image Upload
  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
  103. Formula for the length of an arc = ?
    Image Upload
  104. Parallelogram: A=?
    Image Upload
  105. Square:  A=?
    Image Upload
  106. Rectangle:  A=?
    Image Upload
  107. Triangle:  A=?
    Image Upload
  108. Kite:  A=?
    Image Upload
  109. Rhombus: A=?
    Image Upload or Image Upload
  110. Trapezoid: A=?
    Image Upload
  111. Circle:  A=?
    Image Upload
  112. Sector:  A=?
    Image Upload
  113. The line from the center of a regular polygon perpendicular to a side is called a(n) _______________.
    apothem
  114. Polygon:  A=?
    Image Upload
  115. Right Prism:  
    LA=?
    TA = ?
    Image Upload

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

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

    Image Upload
  122. Right cone:  V=?
    Image Upload
  123. Sphere:
    TA = ?
    Image Upload
  124. Sphere:  V=?
    Image Upload
  125. If a figure is dilated by factor Image Upload, surface area is dilated by factor _______ and volume is dilated by factor ___________.
    • Image Upload
    • Image Upload
  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
  128. distance between a point (x,y) and a line (Ax+By=C):
    d=?
    Image Upload
  129. Midpoint formula:  MP = ?
    Image Upload
  130. What is the standard formula for the equation of a circle?
    • Image Upload
    • where:
    • center = (h, k) and radius = r
  131. What is the standard form of an ellipse with a horizontal major axis?
    • Image Upload
    • where:
    • center = (h,k)
    • a>b; Image Upload
    • Foci: (h+c, k) and (h-c, k)
  132. What is the standard form of an ellipse with a vertical major axis?
    • Image Upload
    • where:
    • center = (h,k)
    • a>b; Image Upload
    • Foci:  (h, k+c) and (h, k-c)
  133. What is the standard form of a parabola that opens upward?
    • Image Upload
    • 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
    • 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
    • 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
    • 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
    • where:
    • center:  (h,k)
    • difference between vertices:  2a
    • Foci:     (h+c, k) and (h-c, k)
    • Fund. rectangle coord.:  Image Upload
  138. What is the standard form of a hyperbola with a vertical focal axis?
    • Image Upload
    • where:
    • center:  (h,k)
    • difference between vertices:  2a
    • Foci:  (h, k+c) and (h, k-c)
    • Fund. rectangle coord.:  Image Upload
  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

    Image Upload

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

    Image Upload

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

    Image Upload

    Image Upload
  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
    Image Upload
  158. According to the quotient identity:
    Image Upload
    Image Upload
  159. Image Upload
    1
  160. Image Upload
    Image Upload
  161. Image Upload
    Image Upload
  162. This is a graph of the _____ function.
    Image Upload
    sin
  163. This is a graph of the ______ function.
    Image Upload
    • cos
    • Period = 2π
  164. This is a graph of the _____ function.
    Image Upload
    • tan
    • Period = π
  165. This is a graph of the ______ function.
    Image Upload
    • csc
    • Period = 2π
  166. This is a graph of the _____ function.
    Image Upload
    • sec
    • Period = 2π
  167. This is a graph of the _____ function.
    Image Upload
    • cot
    • Period = 2π
  168. This is a graph of the _____ function.
    Image Upload
    arcsin
  169. This is a graph of the ______ function.
    Image Upload
    arccos
  170. This is a graph of the _______ function.
    Image Upload
    arctan
  171. This is a graph of the ________ function.
    Image Upload
    arccsc
  172. This is a graph of the ________ function.
    Image Upload
    arcsec
  173. This is a graph of the _______ function.
    Image Upload
    arccot
  174. The general formula for the transformation of the graph of sin or cos is _________.
    Where:  
    A = ?
    B = ?
    C = ?
    D = ?
    • Image Upload or Image Upload
    • A = amplitude
    • B = reciprocal of horiz. dilation (Image Upload)
    • C = sinusoidal axis (vertical translation)
    • D = phase shift (horizontal translation)
  175. Image Upload
    • Image Upload
    • "sum"thing switches
  176. Image Upload
    • Image Upload
    • "opposite"
  177. Law of Sines
    Image Upload
  178. Law of Cosines
    Image Upload
  179. Mean Image Upload
    Image Upload
  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
  185. Standard deviation:  s = ?
    Image Upload
  186. A 5 number summary contains:
    • minimum
    • maximum
    • median (Q2)
    • Q1
    • Q3
  187. Interquartile range = ?
    Q3 - Q1
  188. Outliers are values < __________ or > _________.
    Image Upload

    Image Upload
  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
  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
  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
    Image Upload
  198. Name 5 types of random samples.
    • simple random
    • stratified random (homogeneous)
    • cluster (heterogeneous)
    • multistage 
    • systematic random
  199. For independent events:  Image Upload
    Image Upload
  200. For dependent events:  Image Upload
    Image Upload
  201. For the probability of M, N, or both M & N: Image Upload
    Image Upload
  202. Permutations (when Position matters):
    Image Upload
    • Image Upload
    • where:
    • n = number of things to choose from
    • r = number chosen
  203. Combinations (order doesn't matter):
    Image Upload
    Image Upload

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

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

    Image Upload
  209. Change of base formula:
    For Image Upload
    Image Upload

Card Set Information

Author:
akrell
ID:
231660
Filename:
FTCE Math Review
Updated:
2013-09-03 14:54:59
Tags:
math calculus trig
Folders:

Description:
Review for Florida Teacher Certification Exam
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