Download Final Exam Review KEY

Name ______________________________
pd ________
Final Exam Review KEY
1. Which of the following statements is true?
a. AB = AC
b. BC = DE
AB BD
c.

BC DE
AB AC
d.

BD CE
2. If a point at (3,9) is dilated by a factor of 1/3, what are the new coordinates? _(1,3)_______
3. If two triangles are similar, then their corresponding angles are ___congruent________ and their
corresponding sides are ____proportional____________.
4. Given the following information, how could you prove that DCA
postulate________
A = 46°
B = 44°
AC = 60
AB = 100
5. [????]
6. Given the diagram at the right, if DE is parallel to AC,
what is the value of x? _10________
1
DBC ? ___AA similarity
7. Using information in the diagram below, what is the height of the tree? ___17.5 feet___________
8. If you need to find point P along the line segment with points A (-5, 3) to point B (1, -9) that divides the
segment in the ratio 2:3, what are the coordinates of the point P?
9. Two concentric circles have a diameter of 5 centimeters and 9 centimeters, respectively. Point B lies inside
one circle and outside the other. If B is equidistant from both circles, at what distance is it from the center of
the circle?
3.5 centimeters
10. Describe how to construct (or complete the construction) of the inscribed circle of
Example picture:
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ABC .
11. If the radius is tripled and the height is halved, how does the volume of a cylinder change?
_9/2 the volume___________________________________________________________________________
12. You have 60 cubes, each with a side length of 1 inch. All of the cubes must fit exactly into a box in order
to ship it to your niece, who is in college, and needs cubes. None of the boxes available at the post office can
exceed 10 inches. Which of the following boxes could you purchase to ship the cubes?
Box A
Length – 5 inches
Width – 12 inches
Height - 1 inch
Box B
Length – 0.5 inches
Width – 8 inches
Height – 3 inches
Box C
Length – 4 inches
Width – 4 inches
Height – 5 inches
Box D
Length – 2 inches
Width - 3 inches
Height - 10 inches
13. What is the area of the triangle with the following vertices: D(-3.5, 2), E(2,2), F(-1, 4.5)?
Base = __4.5_______
Height = _2.5_______
Area = __5.625________
14. What happens to the circumference of a circle when the radius is tripled?
Formula for circumference: _C=2  r_______________
___circumference is tripled____________________________________________________________
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15. What are the center and the radius of the circle described by the following equation:
8x + x2 – 2y = 64 – y2
center = (-4, 1)
radius = 9
16. Write the equation of a circle with center at (-5, 10) and a radius of 3.
__(x+5)2 + (y-10)2 = 9 ______________________________________________________________
17. [??]
18. Given the diagram below, what is the measure of CFA ?
57.5˚________________
19. Construct the circle circumscribed in the given triangle.
Example:
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20. What is the solution to the equation cos (2x + 5) = sin (3x + 5) ___x = 16____________________________
21. Which of the following statements is true?
(a) sin (30°) < cos (60°)
(b) sin (30°) > cos (60°)
(c) sin (30°) = cos (60°)
(d) sin (30°) = cos (30°)
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22. (a) Find the value for each of the variables.
a = _8___
h= 4
y = _4 3_
x= 3
b = _5__
(b) Complete the following trig ratios.
sin A = --4/5------cos A = --3/5-----tan A = --4/3-----23. You found a diamond! It has a mass of 5.2812 grams. Diamonds have a density of 3.5211 grams/cm3.
Round to the nearest hundredth. How many grams of diamond do you have? ____18.60 grams___________
24. You are standing in front of a flagpole. The angle of elevation to the top of the flagpole is 50°. If you are
35 feet in front of the flagpole, how high is the flagpole? __42 feet __________
sin 50° = 0.77
cos 50° = 0.64
tan 50° = 1.20
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25. You are standing in front of a building. If the angle of depression is 35°, how tall is the building, to the
nearest foot? __60 feet __________
sin 35° = 0.57
cos 35° = 0.82
tan 35° = 0.70
26. An architect includes wheelchair ramps in her plans for the entrance to a new museum. What is the
angle of elevation between the ramp and the ground? ___4.6˚_____________
27. What is the area of the shaded sector? Round to the nearest
hundredth. __23.93 yard2____________
28. Calculate the sine, cosine, and tangent value, rounded to the nearest hundredth, for A , if a = 7.4, b =
11.2 and c = 15.1.
sin = ___0.49________
cos = ___0.74________
tan = __0.66________
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29. Given the volume formula for a pyramid, what two measurements does the volume depend on?
________area of the base (length and width) and the height__________________________
30. Draw an example of each of the following:
rectangular prism
cylinder
sphere
square pyramid
31. You are building a cardboard playhouse, as shown below. How many square meters of cardboard will you
need to make the house?
____159.14 m2__________________
32. You are trying to reduce a poster whose dimensions are 30 inches (length) by 45 inches (width) so that the
new width is 20 inches. What will be the new length? _____13.3 inches___________
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33. You are given 80 feet of fencing to enclose a yard. Calculate the area of yard you can enclose for each of
the following shapes.
Shape
Square
Rectangle
Circle
Equilateral triangle
Dimensions
20 feet x 20 feet
10 feet x 30 feet
Radius = 13.3 feet
Base = 26 feet , height = 23 feet
Total Area
400 ft2
300 ft2
555.43 ft2
299 ft2
Which one provides the largest area? __circle__________
34. Find the area of the polygon with vertices L(6,-2), M(-2,-4), N(-4,3), and O(2,7).
65 units2
35. Identify the cross sections for the following figures.
_____circle_______
______triangle_____
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___square_______
36. A cylindrical candle has a height of 3.5 inches and contains 135 in3 of candle wax. What is the radius of the
candle? ___3.5 inches___________________
37. Are all circles similar? __yes_____ Why or why not? ___same shape, different size; each circle is a dilation
and a transformation of another
38. The vertices of a quadrilateral L’M’N’O’ are L’(2,4), M’(-6,-4), N’(-3,5), and O’(1,8). If quadrilateral LMNO
was dilated with a scale factor of 4, what are the coordinates of its vertices?
L: __(0.5,1)________
M: __(-1.5,-1)_______
N: __(-0.75,1.25)_______
O: __(0.25,2)_______
39. If you dilate a triangle ABC to form triangle A’B’C’…
(a) draw a picture of the two triangles.
(answers will vary)
(b) identify all of the parts of the triangle that are congruent.
____all angles of the two triangles will be congruent________________________________________
(c) identify all of the parts of the triangle that are proportional.
____corresponding sides of the two triangles will be proportional______________________________
(d) write a similarity statement for the two triangles.
__ ABC
A ' B ' C ' ________________________________
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40. Given the following dilation, compare the lengths of the two line segments.
J
_____JK > J’K’
K
J’
K’
OR J’K’ < JK_____________________________________________________________
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