Advanced Applications
Name:______________________
Chapters 7-8 Study Guide (Sec. 7.3, 7.4, 8.2, 8.3)
April 19, 2013
Key will be distributed on Monday, April 22.
Actual test on Tuesday, 4-23-13.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine which ratio is the greatest by finding the percentage each represents.
a.
c.
b.
____
d.
2. Determine which ratio is the lowest by finding the percentage each represents.
a.
c.
b.
d.
Short Answer (Show and describe how you found your answers to earn credit for your work).
3. The large square below is divided into smaller squares that are congruent to each other and similar to the large square.
Calculate the perimeter of the small square.
4. The large rectangle below is divided into smaller rectangles that are congruent to each other and similar to the large
rectangle. Calculate the perimeter of the small rectangle.
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5. The large equilateral triangle below is divided into smaller equilateral triangles that are congruent to each other and similar
to the large triangle. Calculate the perimeter of the small triangle.
6. The large rectangle below is divided into smaller rectangles that are congruent to each other and similar to the large
rectangle. Calculate the area of the large rectangle.
7. The large square below is divided into smaller squares that are congruent to each other and similar to the large rectangle.
Calculate the area of the small square.
8. If the perimeter of a triangle is 50 centimeters, what is the perimeter of the triangle if it is scaled by
?
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9. Find the perimeter of the quadrilateral below after it has been scaled by
10. Find the area of the triangle below after it has been scaled by
.
.
11. If the area of a quadrilateral is 500 square units, what is the area of the quadrilateral if it is scaled by
12. Find the area of the triangle below after it has been scaled by a factor of
?
.
13. The two squares below are similar. What is the scale factor from the small figure to the large figure?
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14. The two figures below are similar. What is the scale factor from the large figure to the small figure?
15. Using a scale factor of 4 to build a new structure, what is the correct top-count view of the new structure?
16.
Using a scale factor of 3 to build a new structure, what is the correct top-count view of the new structure?
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17. The scale factor from Figure A to Figure B is 5. If the surface area of the Figure B is 1,000 square units, what is the surface
area of Figure A?
18.
The volume of a right circular cylinder is 108
cm . If it is scaled by a factor of
, what will be the volume of
the scaled cylinder?
19. The volume of a sphere is 512 cubic units. If it is scaled by a factor of
, what would be the volume of the scaled sphere?
20. Figures A and B are similar. The scale factor from Figure A to Figure B is 3. If the volume of Figure A is 75 cubic units,
what is the volume of Figure B ?
21. The figure below is a net for a cylinder. A net similar to this one is drawn using a scale factor of
. Find the surface area
of the scaled object.
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22. Find the volume of the structure below after it has been scaled by a factor of 3.
23. Using cardboard Betty made a box 60 centimeters long, 60 centimeters wide, and 20 centimeters deep. Betty then wanted
to make a new box similar to the first one, so she scaled the box by a factor of
. What is the volume of the scaled box?
24. A doll maker used his own house as a model for a large dollhouse. The scale factor from the real house to the dollhouse is
. If the original house has a volume of 6000 cubic feet, find the volume of the dollhouse.
25. The figures below are similar.
Find the scale factor of the small figure to the large figure.
26. The figures below are similar.
Find the scale factor of the small figure to the large figure.
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27. Consider these rectangles.
Which of the Rectangles B, C, and D have a relationship between lengths and widths proportional to Rectangle A?
28. On the cards below, the top numbers are proportional to the bottom numbers.
Which of the following cards belongs to this set?
Write a proportion that could be used to solve for each variable. Then solve.
29. 7 pints for $2.25
p pints for $6.75
30. 60 pens in 25 boxes
12 pens in y boxes
31. Maya decides to use the method of proportions and similar triangles to find the height of a tower. She measures the length
of the tower’s shadow and finds it is 20 feet long. Then she holds a 12-inch ruler perpendicular to the ground and finds that
it casts a 4-inch shadow. How tall is the tower?
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32. Charles decides to use the method of proportions and similar triangles to find the height of a lamppost. He measures the
length of the post’s shadow and finds it is 10 feet long. Then he holds a 12-inch ruler perpendicular to the ground and finds
that it casts a 4-inch shadow. How tall is the lamppost?
Young Middle School has 750 students, and Carter Middle School has 900 students. Use this percent diagram to estimate
an answer.
33. A survey of Carter school finds that only 225 students prefer cakes to chocolates. What percentage of Carter students prefer
chocolates?
34. Carter school has 396 boys. What is the percentage of girls in the school?
Use the percent proportion to solve each problem. Round to the nearest tenth.
35. 24 is what percent of 120?
36. 30 is 75% of what number.
37. What is 78% of 40?
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How Often We Check Email
76%
23%
1%
Daily
Weekly
Less T han Weekly
38. According to the graph, out of 2500 people, how many would you expect check email daily?
39. Out of 4000 people, how many would you expect check email less than once per week?
Essay
40. A cylinder with height 9 centimeters and radius 18 centimeters is scaled by a factor of 3.
a.
b.
c.
What is the volume of the original cylinder?
What is the volume of the scaled cylinder?
Compare the volumes. Explain how the change in volume seems to be related to the scale factor.
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