Download Use the triangle at the right to answer questions 1 and 2

Algebra II/Trig Semester 2 Review
15.0 Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing
the square to put the equation into standard form and can recognize whether the graph of the equation is a
circle, ellipse, parabola, or hyperbola. Students can then graph the equation.
equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.
Identify each of the following as a parabola, a circle, an ellipse or an hyperbola.
1. 25x2 + y2 + 100x – 2y + 76 = 0
3.
2. x2 + y2 + 2x – 6y + 6 = 0
32y – 50 + 11x + 10y2 + 6x2 = 0
4. 5x + 7x2 + 7y2 – 11y – 61 = 0
5. y2 – x2 – 6x – 7y – 10 = 0
6. 8(y + 3)2 = x + 8
Rewrite each equation in center-vertex form.
7. x2 – 4x – 8y + 32 = 0?
8. x2 + 25y2 – 100y – 2x + 76 = 0
9. x2 + y2 + 4x – 8y + 11 = 0
10. x2 – y2 – 2x + 4y + 4 = 0
Write the equation of each conic section.
11.
12.
14.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci,
eccentricity) depends on the coefficients of the quadratic equation representing it.
13.
What is the foci of the conic section 49x2 – 16y2 = 784?
14.
What is the center and radius of this conic equation x2 + y2 + 12x – 10y + 45 = 0?
15.
If a parabola has an equation y  ( x  1) 2  2 , the focus and directrix are:
1
8
1
Algebra II/Trig Semester 2 Review
Sequences and Series
22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric
series.
20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive
integer powers.
16. Find the 20th term of the arithmetic sequence in which a1 = -4 and d = 5.
17. What is Sn for the arithmetic series in which 15 + 11 + 7 +… +-17?
18. What is Sn for the arithmetic series

10
n 1
(3n  1)
19. What is the indicated term for the geometric sequence?
a1 = 2
r=2
n = 10
20. What is the formula for the sum of a geometric series?
21. What is the sum of the first 6 terms of the geometric series 2 + 4 + 8 + …?
22. What is the sum of the infinite geometric sequence in which a1 = 10 and r = 
23. Expand (3x – 4)3 ?
24. What is the 5th term of (x – 2y)10?
25. Expand (a – 3b)5.
26. Find the 5th term of (2a – 3b)7.
2
1
?
2
Algebra II/Trig Semester 2 Review
Statistics & Probability
18.0 Students use fundamental counting principles to compute combinations and permutations.
19.0 Students use combinations and permutations to compute probabilities.
27. How many license plates of 6 symbols can be made using non repeating letters for the
1st two symbols and numbers that can repeat for the last 4 symbols?
28. How many different batting line-ups on a baseball team can there be if 3rd baseman bats first,
shortstop bats 2nd, and second baseman bats third?
29. In a class of 36 students, a president, vice president, and secretary are to be chosen. In how many
ways can this be done?
30. Find the number of ways 6 history, 5 math, and 3 science books can be placed on a shelf if the books
are arranged according to subject.
31. Most credit cards have 16 digits and digits can repeat. The first digit is never a 0. How many possible
credit card account numbers are there?
32. In how many ways can 8 runners finish a race first, second, or third?
33. A group has 8 men and 7 women. How many ways can a committee be formed consisting of 3 men
and 4 women?
How many ways can the letters of each word be arranged?
34. Cocoon
35. Elephant
36. At Pacific Pizza, you can order pizzas with cheese, mushroom, sausage, pepperoni, green peppers,
onions, pineapple, eggplant, zucchini, shrimp, and anchovies. How many three topping pizzas can be
made with these ingredients?
37. A pizza place has 10 toppings and 3 sizes to choose from. If the customer picks one topping, the size
of the pizza, and whether it has thick or thin crust, how many different pizzas can be ordered?
38. A drawer has 8 blue socks, 4 white socks, 7 red socks, and 5 green socks. If a sock is selected at
random from the drawer, what is the probability that it is white or green?
39. You have an equally likely chance of choosing any number from 1 to 10. What is the probability that
you choose a number less than 4?
40. A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10
or a diamond?
41. When two fair coins are tossed, there are four possible outcomes. What is the probability that at least
one tail is tossed?
3
Algebra II/Trig Semester 2 Review
Chapter 6
1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert
between degrees and radians.
2.0 Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are
familiar with the graphs of the sine and cosine functions.
9.0 Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at
various standard points.
12.0 Students use trigonometry to determine unknown sides or angles in right triangles
19.0 Students are adept at using trigonometry in a variety of applications and word problems
Change each degree measure to radians.
42. 390 °
43. 40 °
44. 48 °
Change each radian measure to degrees.
45.
9
2
46. 
7
4
47. 
17
30
Find one positive angle and one negative angle that is co-terminal with each angle
48. 750
49. 1350
50. 2450
51. What is the smallest possible value for cosine? sine?
52. If cos  = 5/13, and
53. Find sec  if sin  =
3
   2 , find the other 5 trig functions.
2
4
3
and    
.
7
2
54. Graph the function y = 5 cos 2x. Find the period and amplitude.



55. What is the value of tan 1  
3
?
3 
Find the EXACT value of each function
0
56. sin 60 + sin 30
0
cos 2100  sin 2400
57.
2
58. From the top of a cliff, a geologist spots a dry riverbed. The measurement of the angle of depression
to the riverbed is 500. The cliff is 300 meters high. How far is it to the riverbed from the base of the
cliff?
4
Algebra II/Trig Semester 2 Review
Chapter 6
10.0 Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs
and can use those formulas to prove and/ or simplify other trigonometric identities.
11.0 Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines
and can use those formulas to prove and/ or simplify other trigonometric identities.
59. Using sum or difference formulas, solve sin 195o.
60. What is the exact value of cos
61. If sin u  
62. If sin u 

?
12
4
3
u
with   u 
, what does cos equal?
5
2
2
8

12
3
with 0  u  and cos v  
with   v 
, what is sin(u + v)?
17
2
13
2
63. If cos  = -3/5 and 90o    180o , find sin 2, cos 2, sin


, and cos .
2
2
Chapter 6
13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems.
14.0 Students determine the area of a triangle, given one angle and the two adjacent sides.
19.0 Students are adept at using trigonometry in a variety of applications and word problems
Solve each triangle using the Law of Sines or Law of Cosines.
64. A = 510, b = 40, c = 45
65. a = 10, b = 16, c = 19
66. A = 400, B = 450, c = 4
67. a = 20, c = 24, B = 470
68. A = 30o, a = 2, b = 4
Find the area of each triangle
69. a = 11, b = 13, C = 310
70. b = 4, c = 19, A = 730
71. Given a triangle with a = 3, b = 4, and A = 30o, what is (are) possible lengths of c?
72. Find the area of
ABC if A = 72o, b = 9 feet and c = 10 feet.
5
Algebra II/Trig Semester 2 Review
73. Two streets meet at a 650 angle. The two sides of the vacant triangular lot on the corner of these
streets have sides of 140 ft. each. What is the perimeter of the lot?
11.0 Students prove simple laws of logarithms.
11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship to
solve problems involving logarithms and exponents.
11.2 Students judge the validity of an argument according to whether the properties of real numbers, exponents, and
logarithms have been applied correctly at each step.
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in
problems involving exponential growth and decay.
13.0 Students use the definition of logarithms to translate between logarithms in any base.
14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to
identify their approximate values.
74.
Write the equation 7 4  2401 in logarithmic form.
75.
Write in exponential form : a  log17 b
76.
Write in expanded log form  1 
77.
Solve : log 4
78.
Find the solution : 5x = 3x – 3
79.
Evaluate : ln 35
80.
Solve :
81.
If the value of log b 2  0.1234, and the value of logb 5  0.4567 find the value of logb 80.
82.
If the value of log b 2  0.1234, logb 3  0.3456, and logb 5  0.4567 find the value of logb 120 .
83.
Solve: log5 (x - 4) – log5 x = 2
84.
Write as a single logarithm : 3 logb x - 5 logb y
85.
$5000 is put into an account earning 5.75% interest compounded continuously. In how many years,
to the nearest hundredth, will the value be doubled ?


27 
.
x3 
1
x.
64
1
 82 x 3
64
6
Algebra II/Trig Semester 2 Review
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
36.
38.
40.

6
57.
- 3
2
58.
251.1 m
59.
61.
63.
91
-9
155
1024
126
20/3
2 6
4
62. –171/221
67. b = 17.92; A = 54.7C = 78.3
35.
37.
39.
41.
20160
60
3/10
3/4
43. 2/9
45. 810
46. -315
47. -102
48. 435, -285
49. 495, -225
51. –1, 1
68.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
B=90o, C=60o, c=3.569. 36.83
36.34
5.7, 1.2
42.8 ft2
430.4 ft
log 72401 = 4
17a = b
log (x – 3) + log (x2 + 3x + 9) – 3log x
x = -3
-6.4519
3.5553
x = -15/6
0.9503
1.1725
x = -1/6
84.
x3
logb 5
y
85. 12.05 years
52. sin=-12/13,sec=13/5,csc=-13/12, tan=-12/5,cot=-5/12
7 33
33
60.
66. C = 95a = 2.58; b = 2.84
44. 4/15
50. 605, -115
3 1
2
65. A = 31.8; B = 57.3; C = 90.9
3360x6y4
a5 – 15a4b + 90a3b2 – 270a2b3 + 405ab4 – 243b5
22,680a3b4
6,500,000
720
42,840
3,110,400
9 x 1015
336
1,960
60
165
3/8
4/13
2 6
4
5

5
24 7 2 5 5
, ,
,
25 25 5
5
56.
64. a = 36.87; B = 57.5; C = 71.5
42. 13/6
53.
55.
54. P = , A = 5
7