Review for Final Exam

1
Review for Final Exam

• Take out your list of questions!

2
Chapter 2

• Consider
• 1 2 2(3)/2
• 1 2 3 3(4)/2
• 1 2 3 4 4(5)/2
• If this pattern continues, what are the next two
  equations?
• 123455(6)/2 1234566(7)/2
• If this pattern continues, what is the sum of the
  first n numbers?
• 1 2 3 n n(n 1)/2

3
Chapter 2

• What is the nth term in this growing sequence?
• 3n 3 or 3(n 1)

4
Chapter 2

• A printing company charges 10.00 to print the
  first 100 copies of a document, and 0.08 for
  each copy beyond 100.
• Write a formula to determine the amount you pay
  for 145 copies.
• Write a formula to determine the amount you pay
  for n copies.
• Price 10.00 0.08(45) 13.60
• Price 10.00 0.08(n - 100)

5
Chapter 2

• Is each an example of a function?
• In general, of pets and your age?
• If all tickets are the same price, number of
  tickets and amount of money?
• Age of a plant in days and height of the plant.
• No--one eight-year old may have 3 fish, and
  another eight-year old may have 1 dog yes yes

6
Chapter 2

• Describe this graph.
• Mitchells bicycle trip

7
Chapter 7

• When can you use each type of graph?
• Box and whisker plot
• Stem and leaf plot
• Line (Dot) plot
• Scatterplot
• Pictograph
• Circle Graph vs. Bar Graph
• Histogram
• Line Graph

8
Chapter 7

• List the characteristics of good graphs
• Neat
• Title
• Axes labeled
• Axes numbered appropriately--constant intervals
• Circle graph--list the number of people/things
• Stem and Leaf Plot and Pictograph key
• Bar Graphs--bars same thickness and distance from
  each other
• Appropriate graph for the data set.

9
Chapter 7

• Find the mean, median, mode, and range of this
  data set
• 0, 4, 5, 6, 7, 8, 9, 9, 9, 9, 10, 11, 14, 14, 50
• What is special about 50?
• Mean 11 median 9 mode 9
• 45 is an outlier
• If you make a box and whisker plot 0, 6, 9, 11,
  50

10
Chapter 7

• 8 students join the biggest loser club at
  school. Their job is to lose an average of 12
  pounds. At the 10th meeting, they see if they
  have reached their goal. The first 7 students
  have an average weight loss of 11 pounds. How
  much weight must the 8th student lose for the
  club to reach its goal?
• First 7 students lose 11 pounds each 77 pounds.
• So, (77 x)/8 12. The 8th student needs to
  lose 19 pounds. Good luck.

11
Chapter 7

• Mean, median, mode?
• When the data are tightly clustered?
• When the data are roughly normal?
• When the data are skewed?
• When there are outliers?

12
Chapter 7

• Know how to make all the graphs.
• Know how to interpret all the graphs.

13
Chapter 7

• Which type of graph(s) could you use?
• The favorite pet of each child in a class.
• The number of pencils each child has in his/her
  backpack.
• The score of each student on the last exam.
• Comparing students test scores on the last two
  tests.
• Bedtime last night for each student.
• Comparing height and weight of each student.
• Temperature outside for the year.

14

• The favorite pet of each child in a class. Bar,
  picto, circle if all students choose just one
  pet.
• The number of pencils each child has in his/her
  backpack. Dot, stem and leaf, frequency table,
  box and whisker, histogram
• The score of each student on the last exam.Dot,
  stem and leaf, frequency table, box and whisker,
  histogram
• Comparing students test scores on the last two
  tests. Scatterplot
• Bedtime last night for each student. Dot, stem
  and leaf, frequency table, box and whisker,
  histogram
• Comparing height and weight of each
  student.Scatterplot
• Temperature outside for the year. Line graph

15
Chapter 7

• If a data set has a mean of 200 and a standard
  deviation of 12,
• What can you say about a data point of 224?
• What can you say about a data point of 188?
• Name an interval that contains half the data.
• Name an interval that contains about 68 of the
  data.
• Nearly all the data are contained within ___
  standard deviations of the mean.

16
Chapter 7

• Suppose I have a bag with 4 red balls, 3 black
  balls, and 3 green balls.
• Name the possible outcomes and their theoretical
  probabilities if I pick a single ball at random.
• P(r) 4/10 P(b) 3/10 P(g) 3/10
• Name the possible outcomes and their theoretical
  probabilities if I pick two balls of the same
  color at random without replacing them.
• P(rr) 4/103/9 P(gg) P(bb) 3/102/9

17
Chapter 7

• In one sentence, explain how you know that a game
  is fair using the concept of expected value.
• If the expected value of winning a game is 0,
  then the game is fair.

18
Chapter 7

• We flip four coins. I get a point if there are 0
  or 1 head. You get a point if there are 2 or 3
  heads. No one gets a point for all 4 heads.
• Is this game fair?
• P(0 heads) P(4 heads) 1/16
• P(1 head) P(3 heads) 4/16
• P(2 heads) 6/16
• So (5/16) 1 (10/16) 1? Not fair.

19

• We flip 4 coins. I get 4 points if 0 heads are
  showing and 2 points if 2 heads are showing. You
  get 1 point if 1 head is showing, 3 points if 3
  heads are showing, and 4 points if 4 heads are
  showing. Is this game fair?
• 5 (1/16) 2 (6/16) 1 (4/16) 3 (4/16)
  4 (1/16)?
• 5/16 12/16 4/16 12/16 1/16. Yes, this
  game is fair.

20
Chapter 7

• Suppose I roll a 6-sided die two times. How can
  I find the probability of not rolling a double
• Using a tree diagram?
• Using the Fundamental Counting Principle?
• P(not double, not double) 30/36 30/36 25/36

21
Chapter 7

• If I am arranging 12 different books on a
  bookshelf
• Is this an example of permutation or combination?
• permutation
• How many ways can I place 4 of these books on the
  first shelf?
• 12 11 10 9 11880.

22
Chapter 7

• If I am arranging 12 students into cooperative
  groups
• Is this an example of permutation or combination?
• combination
• How many ways can I place 4 of these books into a
  group?
• 12 11 10 9 11880/24 495.1 2 3 4

23
Chapter 8

• Draw or given an example of
• 3 collinear points
• 3 concurrent lines
• 2 skew lines
• 3 parallel lines
• 3 non-coplanar lines
• 2 perpendicular lines

24
Chapter 8

• Explain the difference between
• A segment, ray, and line.
• Vertical and adjacent angles.
• Supplementary and complementary angles.
• Vertical and corresponding angles.

25
Chapter 8

• Name 5 things you know about triangles
• 3 sides, 3 angles
• Interior angle sum 180
• Scalene, isosceles, equilateral
• Acute, right, obtuse
• Regular triangle is an equilateral triangle,
  which has 60 angles.
• All equilateral triangles are similar.

26
Chapter 8

• Name 5 things you know about polygons
• At least 3 straight lines, closed, no overlaps or
  gaps, no curves
• Triangle, quadrilateral, pentagon, hexagon,
  octagon, decagon, duodecagon, etc.
• Number of diagonals n(n - 2)/2
• Convex and non-convex
• Sum of interior angles n(n - 2) 180
• Exterior and interior angles.
• Regular polygons all sides and angles are
  congruent.

27
Chapter 8

• List characteristics of quadrilaterals
• Trapezoid
• Isosceles Trapezoid
• Kite
• Parallelogram
• Rectangle
• Rhombus
• Square

28
Chapter 8

• Draw a triangular prism.
• Find the number of vertices, edges, and faces.
• 6 vertices, 9 edges, 5 faces
• Eulers formula vertices faces edges 2

29
Chapter 8

• Explain the difference between
• Polygon and polyhedron
• Prism and cylinder
• Prism and pyramid

30
Chapter 8

• Sketch (or describe) the figure that has views
• Front Right side Top

31
Chapter 8

• You can build, draw, or describe

32
Chapter 8

• Sketch the front, side, and top view. Then, use
  Eulers formula to show V F E 2.

33

• Front Right Side Top
• Faces 14 Vertices 24 Edges 36

34
Chapter 9

• Which transformations yield congruent images?
• Translation
• Rotation
• Reflection
• Glide reflection
• Dilation
• Contraction

35
Chapter 9

• If a pre-image point is at (10, -3), what will
  the image point be
• after a translation of T(-2, 6)?
• after a rotation of 90 clockwise?
• after a reflection in the y-axis?
• (8, 3) (-3, -10) (-10, -3)

36
Chapter 9

• Explain each of these symmetries
• Reflection
• 90 rotation
• 120 rotation
• Point symmetry
• Translation symmetry

37
Chapter 9

• If this is a piece of paper folded twice, what
  will it look like when unfolded?

38
Chapter 9

• True or false
• If two figures are congruent, then they are
  similar.
• Squares are always similar.
• Rectangles are always similar.
• If two triangles have 2 pairs of corresponding
  congruent angles, then they are similar.
• Isosceles trapezoids are always similar.
• True, true, false, true, false

39
Chapter 9

• Explain what is wrong.
• ? ABC ? DEF because AB DE BC EF and ?
  BAC ? EDF.

40
Chapter 9

• True or False
• If an image has 180 rotation symmetry with its
  pre-image, then it also has 90 rotation
  symmetry.
• If an image has 180 rotation symmetry with its
  pre-image, then it also has reflection symmetry.
• If an image has 90 rotation symmetry with its
  pre-image, then it also has 180 rotation
  symmetry.
• Point symmetry is the same as having
  reflection symmetry.
• False, false, true, false

41
Chapter 9

• Use the definition of similarity to explain why
  each pair of figures are NOT similar.

42
Chapter 10

• A student says that 5 gallons is the same as
  about 20 liters because there are 4 quarts in a
  gallon, and a liter is about the same as a quart.
  Respond to the child.
• A student says that 25 inches is about 10
  centimeters because 2.54 cm is exactly one inch.
  Respond to the child.

43
Chapter 10

• Write using a different metric unit.
• 1.5 cm
• 700 g
• 435 mL
• 1.5 cm 15 mm 0.015 m 0.000015 km
• 700 g 0.7 kg 700,000 mg
• 435 mL 0.435 L

44
Chapter 10

• Show a counter-example for the student who
  saysSince a triangle comes from taking half of
  a rectangle, when you find the perimeter of the
  rectangle, just divide by 2 to get the perimeter
  of the triangle.

45
Chapter 10

• Give an example of when you would need to find
  perimeter of a figure.
• Give an example of when you would need to find
  area of a figure.
• Give an example of when you would need to find
  the surface area of a figure.
• Give an example of when you need to find the
  volume of a figure.

46
Chapter 10

• Find the area of this figure two different ways.

17 ft
15 ft
47
Chapter 10

• A student says that the circumference of a circle
  is the same as the perimeter. Is the student
  correct? Explain.

48
Chapter 10

• Find the perimeter and area of this sector
• P 6 6 arc 66(135/360)2p6
• A (135/360)p6 6

49
Chapter 10

• Explain how to find the area of this triangle.

50
Chapter 10

• Tell two different ways for finding the area of
  the region below.

51
Chapter 10

• Think of 3 figures--2 triangles and a rectangle
  or 2 trapezoids and a rectangle.
• Think of a rectangle with a trapezoid missing.

52
Chapter 10

• Explain how you could find the area of the white
  part of the yin-yang symbol.(Ignore the
  smallblack and whitedots, if it helps.)

53
Chapter 10

• An acre is mathematically 43,560 square feet.
  Sketch a rectangle, triangle, parallelogram,
  trapezoid, and circle whose area is approximately
  an acre. Indicate possible dimensions of each
  figure.

54
Chapter 10

• Which has a bigger area?
• An equilateral triangle with perimeter of 36
  feet.
• A square with perimeter of 36 feet.
• A circle with circumference of 36 feet.
• Tri .5 12 6v3 62.35 sq. ft.
• Square 9 9 81 sq. ft.
• Circle C 36 2 p r r 5.73 A p
  (5.73)(5.73) 103.18 sq. ft.

55
Chapter 10

• A child says that the perimeter and area of a
  square that has side length of 2 inches is the
  same. What do you say to this child?

56
Chapter 10

• True or false There are always more vertices
  than edges in a polyhedron.
• False.
• True or false A cone is a polyhedron.
• False.
• True or false A net of a polyhedron can help
  you to find the volume.
• True, but it helps you find the surface area more.

57
Chapter 10

• To find the volume of any prism or cylinder, you
  find the ____, and multiply by the _____.
• To find the surface area of any prism, you double
  the _____ and then multiply the ______ by the
  _____ of the prism.
• To find the surface are of any cylinder, you
  double the _____ and then multiply the _____ by
  the _____ of the cylinder.
• Area of the base, height area of the base,
  perimeter, height area of the base,
  circumference, height.

58
Chapter 10

• Here are formulas. What are they for?
• 2pr2 2prh
• pr2 h
• 2lw 2lh 2wh
• (1/3) pr2 h
• (1/3) area of the base height.
• 2 area of base perimeter of base height
• (4/3) pr3
• lwh

59
Find the surface area and volume
60
Good Luck

• Book 2.2, all of 7, 8, 9, 10
• Explorations
• 2.5, 2.7 7.3, 7.19, 7.21
• 8.1, 8.6, 8.10, 8.11, 8.13, 8.14, 8.15, 8.17,
  8.19
• 9.1, 9.4, 9.5, 9.7, 9.12
• 10.7, 10.10, 10.11, 10.12, 10.14, 10.15