Download GPS Geometry Midterm Review

GPS Geometry Midterm Review
Standard MM1G3
Polygons
1.
2.
3.
4.
5.
6.
Find the sum of the interior angles of a convex heptagon.
Find the sum of the interior angles of a convex pentagon.
What is the measure of each interior angle and exterior angles of a hexagon.
What is the measure of each interior angles and exterior angles of a 11-gon.
How many sides does the regular polygon have whose exterior angles each measure 12˚?
How many sides does the regular polygon have whose exterior angles each measure 15˚?
Triangle Congruence/Triangle Inequalities
7. Could 36, 36, and 36 be 3 sides of a triangle?
8. Could 16, 10 and 7 be 3 sides of a triangle?
9. Could 5, 15, and 29 be 3 sides of a triangle?
10. What are the 2 things you can NOT use to prove triangles are congruent?
11. In TBS , what is the included angle between TB & TS ?
12. In ABC , what is the included angle between AB & BC ?
13. Which 2 things can you NOT use to prove the congruence of triangles?
14. Which statements can you use to prove TUR  KEY by ASA?
I. U  E
A. I, II, and III
II. RU  EY
III. T  K
B. I, III, and IV
IV. TU  KE
C. II, III, and IV
D. I, II, and IV
ABC  WHS by SAS?
III. A  W
IV. AC  WS
15. Which statements can you use to prove
I. B  H
A. I, II, and III
II. AB  WH
B. I, III, and IV
C. II, III, and IV
D. I, II, and IV
Points of Concurrency
16. Roger, Sarah, Tony are looking for a place to meet and decide on at a cafe at point P, as
shown in the picture below. Which point of concurrency describes point P?
17.
18.
19.
20.
The angle bisectors meet at the ______________________________
The circumcenter is where the _______________________ meet.
The point of concurrency for medians is the __________________.
The point where the altitudes meet is the ____________________.
Standard MM1G1
Distance/Midpoint Formula
21. What is the distance between ( 3, 2) and ( 4,3) ?
22. What is the distance between (5, 6) and ( 10,7) ?
23. Find the midpoint of a segment with endpoints A( 7,3) and B(3, 3)
24. Find the midpoint of a segment with endpoints A( 10,2) and B( 12,6)
25. The vertices of a right triangle are (5, 2) , (0,6) and (0, 2) . What is the length of the
hypotenuse?
26. Use the diagram to find the length of MP . M is the midpoint of PQ .
(A) 25
(B) 50
(C) 40
(D) 30
27. Use points A(5,1) , B(5,6) , C(1,4) and D(4, 2) to determine which of the following
is true.
(A)
AB  BC
(B)
AB  CD
(C)
AB  BD
(D)
AC  AB
28. What special type of quadrilateral has the vertices A( 2,1) , B(2, 3) , C(2,1) , and
D( 2, 3) ?
29. A helicopter flies 9 miles west and then 6 miles south. How far is the helicopter
from the starting point?
30. If points A and B below are two vertices of an equilateral triangle, what is the
perimeter of the triangle?
31. What is the perimeter of CAR in the figure below?
Standard MM2D1
Statistics
31. The standard deviation of 16 measurements of people’s weights (in pounds) is
computed to be 5.4. What is the variance?
32. Joe’s 8 test scores in his calculus class are: 81, 85, 99, 90, 79, 83, 87, 96.
What is the standard deviation of his scores?
33. The five-number summary of a set of data is
A.
B.
C.
D.
the mean, standard deviation, first quartile, median, and third quartile
the mean, median, mode, variance, and standard deviation
the minimum, first quartile, median, third quartile, and maximum
the minimum, first quartile, mean, third quartile, and maximum
34. The scores on a university examination are normally distributed with a mean
of 62 and a standard deviation of 11. If the middle 68% of students will get
a “C”, what is the lowest mark that a student can have and still be awarded a C?
35. The height of adult males are normally distributed with a mean of 70 inches and a standard
deviation of 2.3 inches. Out of 1400 adult males, how many would you expect to be
less than 67.7 inches tall?
36. Mr. Jones’ math class had an average of 86 on the first test with a standard
deviation of 3.4. Mrs. Smith’s math class had an average of 86 on the first test
with a standard deviation of 6.2. Which class did better and why?
37. What is the median of the following set of data?
12, 13, 5, 8, 9, 20, 16, 14, 14, 6, 12, 12, 9
38. The following scenario is an example of which type of sampling method?
The manager of a movie theater is trying to determine which snacks he would
like to provide at the concession stands. He decides to survey his customers,
and does so choosing every 9th person that exits the theater.
39. The following scenario is an example of which type of sampling method?
A statistics class is doing a project on normal distribution, and decides to
collect data from students throughout the school. To do so, they first group
the student body by grade level, put all of the names in a hat according to grade level, and then pick
100 names out of each hat to be surveyed.
Standard MM2G1
Special Right Triangles
40. In a 45-45-90 triangle, the length of one of the sides is 6. What is the length of the hypotenuse?
41. In a 45-45-90 triangle, the length of one of the sides is 8. What is the length of the hypotenuse?
42. In a 30-60-90 triangle, the length of the side opposite the 30o angle is 9. What is the length of the
side opposite the 60o angle.
43. In a 30-60-90 triangle, the length of the side opposite the 30o angle is 5. What is the length of the
side opposite the 60o angle.
44. In a 45-45-90 triangle, the length of the hypotenuse is 12. Find the length of one of the legs.
45. In a 45-45-90 triangle, the length of the hypotenuse is 15. Find the length of one of the legs.
46. . In a 30-60-90 triangle, the length of the hypotenuse is 15. Find the length of the side opposite
the 30o angle.
47. What is the perimeter of a 45-45-90 triangle with a hypotenuse length of 28 ft.?
48. What is the length of an altitude of an equilateral triangle with sides of length 24?
Standard MM2G2
Right Triangle Trig
49. What is the definition of the tangent ratio of an acute angle of a triangle?
50. What is the definition of the sine ratio of an acute angle of a triangle?
51. What is the definition of the cosine ration of an acute angle of a triangle?
52. In the triangle to the right, cosA 
A.
C.
8
15
15
8
15
. Find sinA.
17
A
B.
D.
8
17
17
15
53. A and B are the acute angles of a right triangle. If tanA 
A.
C.
5
13
12
13
54. What is the equivalent trig ratio for sin30?
55. What is the equivalent trig ratio for cos 21?
56. What is the equivalent trig ratio for tan 25?
B.
D.
C
5
, then find tanB.
12
12
5
7
12
B
57. In any right triangle, which of the following statements is always true?
A.
C.
sinA  cosB
1
tanA 
tanA
B.
sinA  cosA
D.
None of the above
58. A water slide rises from the ground at an angle of 28o. If the slide extends horizontally for 78.4
meters, then estimate the height of the slide.
59. Find x in the following triangle.
60. Find x in the following triangle.