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Math 2
Final Exam Review
Name:
Period:
MM2A3. Students will analyze quadratic functions in the forms f ( x)  ax 2  bx  c and
f ( x)  a( x  h)2  k .
1. The domain of the given function is:
a) 3  x  1
c) 1  x  
b) all real numbers
d) 1  x  
2. The range of the given function is:
a) 1  y  
c)   y  1
b) all real numbers
d)   y  1
3. The vertex form of the equation y  x 2  6 x  9 is:
a) y  ( x  3)2
b) y  ( x  81)2
c) y  ( x  3)2
d) y  ( x  6)2  9
4. Find the solution(s) to the given function:
b) 5
d) 5, 0
a) 0, 5
c) 2, 2
MM2A4. Students will solve quadratic equations and inequalities in one variable.
5. Solve  x 2  6 x  40  0 algebraically.
a) x  4 or x  10
b) 5  x  11
c) x  5 or x  11
6. Find the average rate of change for the function on the given interval.
f  x   2x2  5x  7; 2  x  1
a) 3
b) 1
c) 4
10
7. Find the sum.
a) 285
k
2
d) no real solutions
d) 7
3
k 1
b) 415
c) 412
d) 455
MM2N1. Students will represent and operate with complex numbers.
8. Find the product: (3  3i )( 4  9i)
a) 12  42i
b) 33 17i
9. Simplify: (3  5i)2
a) 28  21i
c) 44  45i
b) 13  84i
10. Find the difference (15  11i )  (14  13i)
a) 32  28i
b) 29  6i
d) 39 15i
c) 16  30i
d) 21  20i
c) 1  24i
d) 1  6i
MM2A4. Students will solve quadratic equations and inequalities in one variable.
11. Describe the nature of the roots of the equation:
3x 2  2 x  2  0
a) 1 real root
c) 2 real irrational roots
b) 2 real rational roots
d) 2 imaginary roots
12. Solve 3( x  2)2  75
a) x  3, x  7
b) x  3, x  7
c) x  2, x  8
d) No Real Solutions
13. Solve x 2  2  4 x
a) 2  6, 2  6 b) 4  24, 4  24 c) 2  6, 2  2 6 d) No Real Solutions
MM2G1. Students will identify and use special right triangles.
14. In a 30-60-90 right triangle, the length of the short leg is 7. Find the length of the hypotenuse.
3
a)
b) 7 3
c) 7 2
d) 14
7
15. The side of an equilateral triangle is 10 meters. What is the height of the triangle?
a) 5 3 m
b) 5 2 m
c) 100 m
d) 5 m
c) 16 2
d) 32
16. Find the diagonal of the rectangle:
a) 160
b) 16 3
16
30
17. The length of a diagonal of a square is 14 inches. What is its perimeter?
a) 28 2
b) 7 2
c) 7
d) 14 2
18. A leg of an isosceles right triangle is 12 cm. What is the hypotenuse?
a) 6 2
b) 6 3
c) 6
d) 12 2
19. Find X and Y
a) x  9.5 3, y  9.5
b) x  9.5, y  9.5 3
c) x  9.5, y  9.5 2
d) x  9.5, y  9.5
MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.
B
5
20. Given ABC to the right, what is sin B = __?
3
C
a)
3
4
b)
4
3
c)
3
5
8
. What is sin A = __?
10
b) 0.8
c) 1.67
d)
4
4
5
21. In a right triangle, cos A =
a) 1.25
22. In right ABC ,  A and  B are the acute angles. If sin B =
a)
13
8
b)
12
13
c)
8
13
d) 0.6
8
, what is cos A = __?
13
d) Cannot be determined
A
23. A ladder is leaning against a house so that the top of the ladder is 14 feet above the ground. The
angle with the ground is 46. How far is the base of the ladder from the house?
a) 14.5 feet
b) 13.52 feet
c) 9.73 feet
d) 20.15 feet
24. A man that is 6 ft tall casts a shadow 18 ft long. Find the angle of elevation of the sun.
6 ft
???
18 ft
a) 18.43 degrees
b) 19.47 degrees
c) 71.57 degrees
d) 70.53 degrees
25. Find the height in feet of the Eiffel Tower if the angle of elevation from the base is 82.34 and
the distance from the center to the outside of each leg is 72 feet. Round your answer to the
nearest tenth.
a) 448.22 feet
b) 633.89 feet
c) 553.83 feet
d) 535.38 feet
26. Given right triangle ABC. If tan A =0.53, find AC. Round your answer to the nearest tenth.
B
a) 4.2
b) 8.9
c) 15.1
8
d) 18.2
A
C
MM2G3. Students will understand the properties of circles.
27. In circle R, mSRV  74 , mTRU  41 , and ST is a diameter. Find mVRT .
a)
b)
c)
d)
116
139
115
106
28. In circle D, the diameter is 26 units and BD=5. Find the measure of AC . If necessary, round to the
nearest tenth.
a)
b)
c)
d)
12
5
24
13.9
29. JK is tangent to circle L at K and JM is tangent to circle L at M. Find the value of x.
a)
b)
c)
d)
7
5
9
3
30. MN is tangent to LM . Find LN. If necessary, round to the nearest tenth.
a)
b)
c)
d)
8.2
6.0
8.1
6.1
31. Find the value of x.
a)
b)
c)
d)
7
2
7
2
2
7
7
2
32. Find the value of x. Round to the nearest tenth if necessary.
a)
b)
c)
d)
20
9
16
11
33. Find the value of x. Round to the nearest tenth if necessary.
a)
b)
c)
d)
18
18.3
13.8
13.9
34. Find the perimeter of the shaded region.
a)
b)
c)
d)
58.27
30.4
28.27
43.27
35. Find the area of the shaded region.
a)
b)
c)
d)
21.46 cm2
78.54cm2
115.7 cm2
58.54 cm2
36. Find the surface area of a sphere whose diameter is 12.6 cm.
a) 1995.04 cm2
b) 158.34 cm2
c) 79.17 cm2
d) 498.76 cm2
37. Find the volume of a sphere whose radius is 12 in.
a) 150.80 in2
38. Find the value of x and y.
a)
b)
c)
d)
x=68; y=104
x=76; y=112
x=112; y=76
x=104; y=68
39. Find m1 .
a)
b)
c)
d)
68
74
37
62
b) 904.78in2
.
c) 7238.23 in2
d) 603.19 in2
40. Find m1 .
a)
b)
c)
d)
24
66
34
56
MM2D1: Using sample data, students will make informal inferences about population means and
standard deviations
41. In the accompanying display, which has the larger mean and which has the larger standard
deviation?
a) Larger mean, A; larger standard deviation, A
b) Larger mean, A; larger standard deviation, B
c) Larger mean, B; larger standard deviation, B
d) Larger mean, B; larger standard deviation, A
42. Salaries of professional football players take on a left-skewed distribution. If we were to take both
the mean and mode of this distribution, what would be true about the relationship between these two
measures?
a) Mean salary is equal to mode salary
b) Mean salary is less than mode salary
c) Mean salary is greater than mode salary
d) There is not enough information provided to answer.
43. The standard deviation of 16 measurements of people’s weights (in pounds) is computed to be 8.70.
What is the variance of these measurements?
a) 17.4
b) 2.95
c) 34.8
d) 75.69
44. There are five children in a room, ages ten, eleven, twelve, thirteen, and fourteen. If a twelve-yearold child enters the room the
a)
b)
c)
d)
mean and standard deviation will stay the same
mean and standard deviation will increase
mean will stay the same, and standard deviation will increase
mean will stay the same and standard deviation will decrease
45. Find the standard deviation for the following data set: {4, 5, 7, 8, 5, 4}
a) 2.25
b) 1.5
c) 3
d) 5.5
46. The scores on a university examination are normally distributed with a mean of 80 and a
standard deviation of 5. 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?
a) 85
b) 70
c) 75
d) 73
MM2A1. Students will investigate step and piecewise functions, including greatest integer and
absolute value functions.
3x  2, x  3
47. Evaluate f (3) if f  x   
.
 x  1, x  3
a) 2
b) 11
c) -4
d) 8
3, x  0
48. What is the range of the following function f  x   
?
3, x  0
a) 3
b) -3
c) 3, -3
d) All real numbers
49. What function is represented by the graph.
 x  3, x  3
a) f  x   
 x  1, x  1
y
 x  3, x  0
b) f  x   
 x  1, x  0
x
 x  3, x  0
c) f  x   
 x  1, x  0
 x  3, x  0
d) f  x   
 x  1, x  0
50. Solve for x: 10  x  4
a) 6
b) -6
c) 6, -6
d) 2.5, -2.5
b) x  12
c) x  .5 or x  12
d) x  2 or x  12
51. Solve: 4 x  7  3  23
a) x  2
MM2A2. Students will explore exponential functions.
52. Solve for x: 22 x  2  64
a) 1
b) 2
c) 3
d) none of these
53. A certain population increases according to the model P (t )  250e0.47t . Use the model to
determine the population when t = 5. Round your answer to the nearest integer.
a) 400
b) 2621
c) 1998
d) 1597
b) 16a 2b8c10
c) 16a 2b8c10
d) 4a 3b6c 7
54. Simplify: (4ab4c5 )2
a) 4a 2b8c10
55. Which of these describes the graph of f(x) = 2x + 1?
a) It has a vertical asymptote at x = 1.
c) It has a vertical asymptote at x = 2.
b) It has a horizontal asymptote at y = 1.
d) It has a horizontal asymptote at y = 0.
56. How would you translate the graph of f(x) = 3x to produce the graph of
a)
b)
c)
d)
f(x) = 3x-1 + 2?
Translate the graph up one unit, and right 2 units
Translate the graph up 2 units, and left 1 unit
Translate the graph up 2 units, and right 1 unit
Translate the graph down one unit and right 2 units
MM2A5. Students will explore inverses of functions.
57. Which is an equation for the inverse of the function y = 2x - 3?
a) y 
2x  3
2
b) y  3x  2
c) y 
x3
2
d) y 
x 3
2
1
2
58. Which of the following is an equation for the inverse of the function f ( x)  x  ?
3
3
3x  2
2
1
c. f 1 ( x)  x  2
3
b. f 1 ( x)  3x  2
d. f 1 ( x)  3x  2
a. f 1 ( x) 
MM2D2. Students will determine an algebraic model to quantify the association between two
quantitative variables.
59. Name the type of model suggested by the graph.
a)
b)
c)
d)
linear
quadratic
exponential
cubic
60. For which graph of a set of data is a linear function the best model?
a)
b)
c)
61. This graph plots the number of wins in the 2006 and 2007 seasons for a sample of professional
football teams. What is the equation of the median-median line for these data?
a) y = x 
1
3
b) y = 2x - 9
c) y = x + 1
d) y = x – 1
62. The graph above graph plots the number of wins in the 2006 and 2007 seasons for a sample of
professional football teams. The linear regression model for this data is y =1.10x−2.29. Based on this
model, what is the predicted number of 2007 wins for a team that won 5 games in 2006?
a) 3.2
b) 4.5
c) 5.5
d) 6.6