Download Test4 Review

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
page
8
page
9
page
10
page
11
page
12
page
13
page
14
page
15
page
16
page
17
page
18
page
19
page
20
page
21
page
22
page
23
Document related concepts
no text concepts found
Transcript 
Name: ________________________ Rec/Sec: ____________
Review Test4 (Math1650:500)
Instructor: Koshal Dahal
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the equivalent expression.
tan 4 x  sec 4 x
a. cot 2 x  csc 2 x
b. csc 2 x  cot 2 x
c. csc 2 x  tan 2 x
d. tan 2 x  sec 2 x
e. sec 2 x  tan 2 x
____
2. Simplify the following trigonometric expression.
sec 2 x  1
sec 2 x
a. 1
b. sin x
c. sin 2 x
d. sec 2 x
____
3. Simplify the following trigonometric expression.
sin(z) + cos(–z) + sin(–z)
a. sin z
b. cos z
c. 2sin z – cos z
d. 2sin z
____
4. Simplify the following trigonometric expression as much as possible.
csc x  sin x
csc x
a. sin x
b. cos 2 x
c. sin 2 x
d. csc x
____
5. Simplify the following trigonometric expression as much as possible.
sin 2 t + cos 2 t + tan 2 t
a. tan x
b. sec 2 x
c. sec x
d. tan 2 x
1
Test 4 date: Fri, May 1
Name: ________________________
____
ID: A
6. Simplify the following trigonometric expression as much as possible.
sin x
1  cos x

1  cos x
sin x
a. 2 sin x
b. cos x
c. sin x
d. 2 csc x
____
7. Simplify the following trigonometric expression as much as possible.
sec 2 y  tan 2 y
a.
b.
c.
d.
____
csc 2 y
csc x
tan x
sin 2 x
sec 2 x
8. Find the equivalent expression.
1  tan x
1  tan x
sec x  csc x
a.
sinx  cos x
cos x  sin x
b.
cos x  sin x
cos x  sin x
c.
cos x  sin x
sinx  cos x
d.
sinx  cos x
sinx  cos x
e.
sinx  cos x
____
9. Simplify the following trigonometric expression as much as possible.
1
1

csc x  cot x csc x  cot x
a. 2 csc x
b. cot x
c. cot 2 x
d. csc x
2
Name: ________________________
ID: A
____ 10. Find the equivalent expression.
1  sin x 1  sin x

1  sin x 1  sin x
a. 4tanx sec x
b. 4cot x sec x
c. 4 cot x csc x
d. 4cot x csc x
e. 4 tanx sec x
____ 11. Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume

01
2
x
1x
sin t
1
tan t
cos t
.
, x  sin t
2
a.
b.
c.
d.
____ 12. Use an addition or subtraction formula to find the exact value of the expression.
sin (705)
a.
 6
4
b.
6
4
2
c.
6
4
2
2
____ 13. Use an addition or subtraction formula to find the exact value of the expression.
tan (255)
a. 1  3
1
b. 2 
3
c.
d.
2
3
1
1 
3
3
Name: ________________________
ID: A
____ 14. Use an addition or subtraction formula to find the exact value of the expression.
ÊÁ 11 ˆ˜
˜˜
sin ÁÁÁ
ÁË 12 ˜˜¯
6
a.
4
2
b.
 3
4
6
c.
 6
4
3
d.
 6
4
2
____ 15. Use an addition or subtraction formula to find the exact value of the expression.
ÊÁ  ˆ˜
cos ÁÁÁ ˜˜˜˜
ÁË 12 ¯
 6
a.
4
2
b.
6
4
2
c.
6
4
2
d.
2
4
6
____ 16. Use an addition or subtraction formula to write the expression as a trigonometric function of one number.
sin34 cos 56  cos 34 sin56
a. sin (90)
b. cos (180)
c. cos (90)
d. sin (90)
4
Name: ________________________
ID: A
____ 17. Use an addition or subtraction formula to write the expression as a trigonometric function of one number.
ÊÁ 3
cos ÁÁÁ
ÁË 4
a.
b.
c.
d.
ˆ˜
Ê ˆ
Ê
˜˜ cos ÁÁÁ  ˜˜˜  sin ÁÁÁ 3
˜˜
ÁÁ 8 ˜˜
ÁÁ 4
¯
Ë ¯
Ë
ÊÁ 7 ˆ˜
˜˜
cos ÁÁÁÁ
˜˜
Ë 8 ¯
ÊÁ 7 ˆ˜
˜˜
sin ÁÁÁÁ
˜˜
8
Ë
¯
ÊÁ 7 ˆ˜
˜˜
sin ÁÁÁÁ
˜˜
8
Ë
¯
ÊÁ 7 ˆ˜
˜˜
cos ÁÁÁÁ
˜˜
8
Ë
¯
ˆ˜ ÊÁ  ˆ˜
˜˜ sin ÁÁ ˜˜
˜˜ ÁÁ 8 ˜˜
¯ Ë ¯
____ 18. Simplify the following expression as much as possible.
ÊÁ 9
ˆ˜
tan ÁÁÁ
 x ˜˜˜˜
ÁË 2
¯
a. tan(x)
b. –tan(x)
c. cot(x)
d. –cot(x)
____ 19. Simplify the following expression.
ÁÊ
 ˜ˆ
sinÁÁÁÁ u  ˜˜˜˜
2¯
Ë
a. sin u
b. –cos u
c. cos u
d. –sin u
____ 20. Simplify the following expression.
sin(v + x) – sin(v – x)
a. 2cos(v)cos(x)
b. 2sin(x)sin(v)
c. 2cos(v)sin(x)
d. 2cos(x)sin(v)
____ 21. Simplify the following expression
cos(p + z) – cos(p – z)
a. –2cos(p)cos(z)
b. 2cos(p)cos(z)
c. 2sin(p)sin(z)
d. –2sin(p)sin(z)
5
Name: ________________________
ID: A
____ 22. Simplify the expression.
tan p – tan x
sin(p  x)
a.
cos p cos x
cos(p  x)
b.
cos p cos x
sin(p  x)
c.
cos p cos x
____ 23. Write the following expression in terms of sine only.
sin z + cos z
ÊÁ 
ˆ˜
3 sin ÁÁÁÁ  z ˜˜˜˜
a.
Ë6
¯
ÊÁ 
ˆ˜
2 sin ÁÁÁÁ  z ˜˜˜˜
b.
Ë4
¯
ÊÁ 
ˆ˜
3 sin ÁÁÁÁ  z ˜˜˜˜
c.
Ë6
¯
ÊÁ
ˆ˜

2 sin ÁÁÁ z  ˜˜˜˜
d.
ÁË
4¯
____ 24. Write the following expression in terms of sine only.
5 sin  x  5 3 cos  x
ÊÁ
 ˆ˜
a. 5 sin ÁÁÁÁ  x  ˜˜˜˜
3¯
Ë
ÊÁ
 ˆ˜
b. 5 sin ÁÁÁÁ  x  ˜˜˜˜
3¯
Ë
ÊÁ
 ˆ˜
c. 10sin ÁÁÁÁ  x  ˜˜˜˜
3¯
Ë
ÁÊ
 ˜ˆ
d. 10sin ÁÁÁÁ  x  ˜˜˜˜
3¯
Ë
6
Name: ________________________
ID: A
____ 25. Rewrite the expression as an algebraic expression in x.
tan (sin – 1 x)
1
a.
x2  1
x
b.
1  x2
c.
1  x2
d.
x2  1
____ 26. Rewrite the expression as an algebraic expression in x.
sin (cos – 1 x)
a.
b.
x2  1
x–1
c.
d.
e.
1  x2
1–x
x
____ 27. Find the exact value of the expression.
ÊÁ
ˆ
ÁÁ 1 3 ˜˜˜
Á
˜˜
cos ÁÁ sin
ÁÁ
2 ˜˜˜
Ë
¯
a.
b.

2
1
2
c.
2
2
d.
3
2
7
Name: ________________________
ID: A
____ 28. Simplify the expression.
sin 14x
sin13x  sin x
sin6x
a.
sin7x
cos 6x
b.
cos 7x
sin 13x
c.
sin6x
sin7x
d.
sin6x
cos 7x
e.
cos 6x
____ 29. Find all solutions of the equation.
2 cos x 
2 0
Select the correct answer, where k is any integer:
4

 2k  ,
 2k 
a.
5
5
7

b.
 2k  ,
 2k 
4
4
7

c.
 k ,
 k
4
4
9

d.
 2k  ,
 2k 
5
5
____ 30. Find all solutions of the equation.
2 sin x  1  0
Select the correct answer, where k is any integer:
11

 k ,
 k
a.
6
6
5

b.
 k ,
 k
6
6
5

c.
 2k  ,
 2k 
6
6
11

d.
 2k  ,
 2k 
6
6
8
Name: ________________________
ID: A
____ 31. Find all solutions of the following equation.
4 cos 2 x  3  0
Select the correct answer, where k is any integer:
5
7
11

 2k  ,
 2k  ,
 2k  ,
 2k 
a.
6
6
6
6
11

b.
 k ,
 k
6
6
5
7
11

c.
 k ,
 k ,
 k ,
 k
6
6
6
6
5

d.
 2k  ,
 2k 
6
6
____ 32. Find all solutions of the following equation.
4 cos 2 x – 4 cos x + 1 = 0
Select the correct answer, where k is any integer:
7

 2k  ,
 2k 
a.
4
4
5

b.
 2k  ,
 2k 
3
3
5

c.
 2k  ,
 2k 
6
6
3

d.
 2k  ,
 2k 
4
4
____ 33. Use an addition or subtraction formula to simplify the following equation. Then find all the solutions in the
ÈÍ
Í  ˆ˜
interval ÍÍÍÍ 0, ˜˜˜˜ .
ÍÎ 4 ¯
cos x cos 7 x – sin x sin 7 x = 0
a.
b.
c.
d.

16

8
,
3
8
,
3
16

8

16
9
Name: ________________________
ID: A
ÁÊ 
____ 34. Plot the point that has the polar coordinates ÁÁÁÁ 5,
Ë 4
a.
d.
b.
e.
˜ˆ˜
˜˜ .
˜
¯
c.
10
Name: ________________________
ID: A
ÁÊ
7
____ 35. Plot the point that has the polar coordinates ÁÁÁÁ 3, 
6
Ë
a.
d.
b.
e.
c.
____ 36. Find the third term of the sequence.
a n = 2n + 1
a.
b.
c.
d.
e.
a3
a3
a3
a3
a3
=7
=6
=5
=1
=2
11
˜ˆ˜
˜˜ .
˜
¯
Name: ________________________
ID: A
____ 37. Find the fourth term of the sequence.
an =
a.
b.
c.
d.
e.
1
n+1
a4 = 5
1
a4 =
5
4
a4 =
5
1
a4 =
4
1
a4 =
1
____ 38. Find the 200th term of the sequence.
an = 10
a. a 200 = 1
b. a 200 = 10
c. a 200 = 200
d. a 200 = 210
e. a 200 = 2000
____ 39. Find the nth term of the sequence.
2, 4, 8, 16, ...
a. an = 2 n – 1
b. an = 2n
c. an = 2 n
d. an = 2 n + 1
e. an = 2 + 2n
____ 40. Find the partial sum S 7 of the sequence.
5, 10, 15, 20, ...
a. S 7 = 140
b. S 7 = 50
c. S 7 = 280
d. S 7 = 141
e. S 7 = 20
12
Name: ________________________
ID: A
____ 41. Find the partial sum S 5 of the sequence.
1, –1, 1, –1, ...
a. S 5 = 0
b. S 5 = 2
c. S 5 = –2
d. S 5 = –1
e. S 5 = 1
____ 42. Find the sum.
18
4
i4
18
a.
 4  13
i4
18
b.
 4  60
i4
18
c.
 4  72
i4
18
d.
 4  56
i4
18
e.
4  4
i4
____ 43. Find the sum.
4
 k2
k
k1
4
a.
 k2
k
 99
k
 64
k
 91
k
 10
k
 98
k1
4
b.
 k2
k1
4
c.
 k2
k1
4
d.
 k2
k1
4
e.
 k2
k1
13
Name: ________________________
ID: A
____ 44. Write the following sum.
7
 k (k  9)
k5
7
a.
 k(k  9)  5(5  9)  7(7  9)
k5
7
b.
 k(k  9)  6(6  9)  7(7  9)
k5
7
c.
 k(k  9)  6(6  9)  7(7  9)  8(8  9)
k5
7
d.
 k(k  9)  5(5  9)  6(6  9)  7(7  9)
k5
7
e.
 k(k  9)  5(5  9)  6(6  9)  8(8  9)
k5
____ 45. Write the following sum using sigma notation.
5 + 10 + 15 + 20 + ... + 50
50
a.
5
k0
10
b.
k
5
k0
10
c.
 5k
k1
10
d.
5
k
k0
50
e.
k
k5
____ 46. The first term of the arithmetic sequence a is 4 and common difference d is 6. Find the nth term and the 10th
term.
a. a n  1  6(n  4), a 10  62
b. a n  4  6(n  1), a 10  58
c. a n  4  6(n  4), a 10  56
d. a n  6  4(n  1), a 10  59
e. a n  6  4(n  6), a 10  55
14
Name: ________________________
ID: A
____ 47. Find the common difference d of the arithmetic sequence.
5, 7, 9, 11, ...
a.
b.
c.
d.
e.
2
2n
n
7
5
____ 48. Find the first five terms and determine if the sequence is arithmetic.
an
a.
b.
c.
d.
e.
 2  6n
a 1  8, a 2
a 1  8, a 2
a 1  8, a 2
a 1  8, a 2
a 1  8, a 2
 14, a 3
 14, a 3
 14, a 3
 14, a 3
 14, a 3
 20, a 4
 20, a 4
 20, a 4
 20, a 4
 20, a 4
 23, a 5
 30, a 5
 24, a 5
 26, a 5
 27, a 5
 35 The sequence is not arithmetic.
 28 The sequence is not arithmetic.
 34 The sequence is arithmetic.
 32 The sequence is arithmetic.
 33 The sequence is arithmetic.
____ 49. If it is arithmetic, express the nth term of the sequence in the standard form a n  a  d(n  1) and find the
common difference.
an
a.
b.
c.
d.
e.
 8n  1
a n  3  7(n  1), d  7
a n  3  6(n  1), d  6
Not an arithmetic sequence.
a n  3  5(n  1), d  5
a n  3  8(n  1), d  8
____ 50. Find the fifth term of the arithmetic sequence.
2, 10, 18, 26, ...
a. 26
b. 27
c. 34
d. 44
e. 5
____ 51. Find the fifth term of the arithmetic sequence.
5, 9, 13, 17, ...
a.
b.
c.
d.
e.
21
17
30
5
18
15
Name: ________________________
ID: A
____ 52. Find the nth term of the arithmetic sequence.
2, 2 + s, 2 + 2s, 2 + 3s, ...
a. s  2n
b. 2  sn
c. s  2 (n  1)
d. 2  s (n  1)
1
e. 2n  sn (n  1)
2
____ 53. The 12th term of an arithmetic sequence is 13 and the 5th term is 6. Find the 22th term.
a. 24
b. 43
c. 21
d. 10
e. 23
____ 54. The 20th term of an arithmetic sequence is 97, and the common difference is 5. Find a formula for the nth
term.
a. 20 + 5(n – 1)
b. 2 + 5(n)
c. 5 + 2(n – 1)
d. 2 + 5(n – 1)
e. 5 + 2(n + 1)
____ 55. Which term of the arithmetic sequence 3, 8, 13,... is 73?
a. 15
b. 17
c. 14
d. 16
e. 13
____ 56. Find the partial sum S n of the arithmetic sequence that satisfies the following conditions.
a = 1, d = 4, n = 15
a.
b.
c.
d.
e.
57
435
465
870
61
16
Name: ________________________
ID: A
____ 57. Find the product of the numbers.
1
10
2
10
10 ,10 ,10
a. 380
b. 10 380
c.
d.
e.
3
10
,10
4
10
, ... , 10
19
10
19
10
10
190
10 19
____ 58. Find the nth term of the geometric sequence with given first term a and common ratio r. What is the fifth
term?
a
a.
7
1
,r
3
3
n
Ê
7 ÁÁÁ 1 ˆ˜˜˜
1
a n  ÁÁ  ˜˜ , a 5 
3 Ë 3¯
243
b.
n1
7 ÊÁÁÁ 1 ˆ˜˜˜
7
a n  ÁÁ  ˜˜ , a 5 
3 Ë 3¯
81
c.
an 
d.
an 
e.
n1
7 ÊÁÁÁ 1 ˆ˜˜˜
7
a n  ÁÁ  ˜˜ , a 5 
3 Ë 3¯
243
n1
1 ÁÊÁÁ 1 ˜ˆ˜˜
7

, a5 
3 ÁÁË 3 ˜˜¯
81
n1
7 ÁÊÁÁ 1 ˜ˆ˜˜
7

, a5 
3 ÁÁË 3 ˜˜¯
81
____ 59. Determine whether the sequence
6, 24, 96, 384...
is geometric. If it is geometric, find the common ratio.
a. Geometric sequence, r = 6
1
b. Geometric sequence, r 
4
c. Not a geometric sequence.
d. Geometric sequence, r = 4
1
e. Geometric sequence, r 
5
17
Name: ________________________
ID: A
____ 60. Determine whether the sequence is geometric.
8, –4, 2, –1,...
If it is geometric, find the common ratio.
1
a. Geometric,
2
b. Not geometric.
1
c. Geometric, 
2
d. Geometric, 2
e. Geometric, –2
____ 61. Determine whether the sequence is geometric. If it is geometric, find the common ratio.
e 4 , e 7 , e 10 , e 13 , ...
a. Geometric, r = e 3
b. Not geometric.
c. Geometric, r = 3
1
d. Geometric, r = 3
e
e. Geometric, r = e 4
____ 62. Find the first five terms of the sequence and determine if it is geometric. If it is geometric express the nth term
of the sequence in the standard form a n  ar n  1 .
a n  (1) 3 n
a. –3, 9, –27, 81, –243; ; it is not geometric.
b. –3, 9, –27, 81, –243; a n  3(4) n  1
n
c.
–3, 9, –27, 84, –243; a n  3(4) n  1
d.
–3, 9, –27, 81, –243; a n  3(3) n  1
e.
–3, 9, –27, 84, –243; a n  3(3) n  1
____ 63. Determine the common ratio, the 6th term, and the nth term of the geometric sequence.
5, 20, 80, 320, ...
a.
b.
c.
d.
e.
Common ratio 5, the 6th term 5,120, and the nth term 4 n  1
Common ratio 4, the 6th term 5,120, and the nth term 54 n  1
Common ratio 4, the 6th term 12,500, and the nth term 5 n  1
Common ratio 5, the 6th term 12,500, and the nth term 54 n  1
Common ratio 4, the 6th term 5,120, and the nth term 4 n  1
18
Name: ________________________
ID: A
____ 64. Determine the nth term of the geometric sequence.
1,
a.
b.
c.
d.
e.
11 ,11,11 11, ...
11 n  1
n1
ÁÊÁ 1 ˜ˆ˜
˜˜
ÁÁ
˜˜
ÁÁ
Ë 11 ¯
ÊÁ 1 ˆ˜ n  1
ÁÁÁ ˜˜˜
Á 11 ˜
Ë ¯
Not a geometric series.
ÊÁ
ˆn1
ÁÁ 11 ˜˜˜
Ë
¯
____ 65. Determine the nth term of the geometric sequence.
x2 x3 x4
, ,
, ...
5 25 125
xn
a.
5
xn
b.
5n
c. x n  1
xn  1
d.
5n  1
xn
e.
5n  1
x,
____ 66. The first term of a geometric sequence is 6, and the second term is 3. Find the fifth term.
3
a.
2
3
b.
8
6
c.
8
19
Name: ________________________
____ 67. The common ratio in a geometric sequence is
a.
b.
c.
d.
e.
ID: A
4
7
, and the fourth term is . Find the third term.
3
3
3
4
4
7
6
3
14
4
7
4
____ 68. Which term of the geometric sequence 5, 20, 80, . . . is 20480?
a. 7th
b. 13th
c. 6th
d. 8th
e. 9th
____ 69. Find the partial sum Sn of the geometric sequence that satisfies the given conditions.
a = 3, r = 4, n = 6
a. Sn = 4,092
b. Sn = 16,383
c. Sn = 8,190
d. Sn = 4,094
e. Sn = 4,095
____ 70. Find the partial sum Sn of the geometric sequence that satisfies the given conditions.
a4
a.
b.
c.
d.
e.
 16, a 6  64, n  4
Sn = 60
Sn = 62
Sn = 28
Sn = 29
Sn = 30
____ 71. Find the sum.
1 + 4 + 16 + ... + 4096
a. Sn = 1,365
b. Sn = 10,922
c. Sn = 21,845
d. Sn = 5,460
e. Sn = 5,461
20
Name: ________________________
ID: A
____ 72. Find the sum of the infinite geometric series.
1
a.
b.
c.
d.
e.
1 1 1
 
 ...
3 9 27
4
2
5
4
1
2
3
3
2
____ 73. Find the sum of the infinite geometric series.
1
a.
b.
c.
d.
e.
1 1
1


 ...
5 25 125
5
6
11
12
6
5
1
6
4
5
21
ID: A
Review Test4
Answer Section
MULTIPLE CHOICE
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.
35.
36.
37.
38.
39.
40.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
D
C
B
B
B
D
C
B
A
E
C
C
C
A
B
A
A
C
B
C
D
C
B
D
B
C
B
E
B
C
A
B
D
A
C
A
B
B
C
A
1
ID: A
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
E
B
E
D
C
B
A
D
E
C
A
D
E
D
A
B
E
E
D
C
A
D
B
E
E
B
E
A
E
E
E
E
A
2
Related documents