review test4 (math1650:500) instructor: koshal...

Name: ________________________ Rec/Sec: ____________

1

Review Test4

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Find the equivalent expression.

tan4x sec4xa. cot2x csc2xb. csc2x cot2xc. csc2x tan2xd. tan2x sec2xe. sec2x tan2x

____ 2. Simplify the following trigonometric expression.

sec2x 1

sec2xa. 1b. sin xc. sin 2 xd. sec 2 x

____ 3. Simplify the following trigonometric expression.

sin(z) + cos(–z) + sin(–z)a. sin zb. cos zc. 2sin z – cos zd. 2sin z

____ 4. Simplify the following trigonometric expression as much as possible.

csc x sinxcsc x

a. sin xb. cos 2 xc. sin 2 xd. csc x


sin 2 t + cos 2 t + tan 2 ta. tan xb. sec 2 xc. sec xd. tan 2 x

Instructor: Koshal Dahal Test 4 date: Fri, May 1(Math1650:500)

Name: ________________________ ID: A

2


1 cos xsinx

sinx1 cos x

a. 2 sin xb. cos xc. sin xd. 2 csc x


sec2y tan2y

csc2y

a. csc xb. tan xc. sin 2 xd. sec 2 x


1 tanx1 tanx

a.sec x csc xsinx cos x

b.cos x sinxcos x sinx

c.cos x sinxcos x sinx

d.sinx cos xsinx cos x

e.sinx cos xsinx cos x


1csc x cotx

1csc x cotx

a. 2 csc xb. cot xc. cot 2 xd. csc x

Name: ________________________ ID: A

3


1 sinx1 sinx

1 sinx1 sinx

a. 4tanx sec xb. 4cotx sec xc. 4cotx csc xd. 4cotx csc xe. 4tanx sec x

____ 11. Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume

0 1 2

.

x

1 x2, x sin t

a. sin tb. 1c. tan td. cos t

____ 12. Use an addition or subtraction formula to find the exact value of the expression.

sin 705( )

a. 6 2

4

b.6 2

4

c.6 2

4


tan 255( )

a. 1 3

b. 2 1

3

c. 2 3

d. 1 1

3

Name: ________________________ ID: A

4


sin1112

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a.6 2

4

b. 3 6

4

c. 6 3

4

d. 6 2

4


cos12

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. 6 2

4

b.6 2

4

c.6 2

4

d.2 6

4

____ 16. Use an addition or subtraction formula to write the expression as a trigonometric function of one number.

sin34cos 56 cos 34 sin56a. sin 90( )b. cos 180( )c. cos 90( )d. sin 90( )

Name: ________________________ ID: A

5

____ 17. Use an addition or subtraction formula to write the expression as a trigonometric function of one number.

cos34

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ cos

8

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ sin

34

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ sin

8

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. cos78

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

b. sin78

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

c. sin78

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

d. cos78

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

____ 18. Simplify the following expression as much as possible.

tan92

xÊ

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. tan(x)b. –tan(x)c. cot(x)d. –cot(x)

____ 19. Simplify the following expression.

sin u 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a. sin ub. –cos uc. cos ud. –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)

Name: ________________________ ID: A

6

____ 22. Simplify the expression.

tan p – tan x

a.sin(p x)cos p cos x

b.cos(p x)cos p cos x

c.sin(p x)cos p cos x

____ 23. Write the following expression in terms of sine only.

sin z + cos z

a. 3 sin6 z

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

b. 2 sin4 z

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

c. 3 sin6 z

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

d. 2 sin z 4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

____ 24. Write the following expression in terms of sine only.

5sinx 5 3 cosx

a. 5sin x 3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

b. 5sin x 3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

c. 10sin x 3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

d. 10sin x 3

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

Name: ________________________ ID: A

7

____ 25. Rewrite the expression as an algebraic expression in x.

tan (sin – 1 x)

a.1

x2 1

b.x

1 x2

c. 1 x2

d. x2 1

____ 26. Rewrite the expression as an algebraic expression in x.

sin (cos – 1 x)

a. x2 1b. x – 1

c. 1 x2

d. 1 – x

e. x

____ 27. Find the exact value of the expression.

cos sin1 32

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃

a.2

b.12

c.2

2

d.3

2

Name: ________________________ ID: A

8

____ 28. Simplify the expression.

sin14xsin13x sinx

a.sin6xsin7x

b.cos 6xcos 7x

c.sin13xsin6x

d.sin7xsin6x

e.cos 7xcos 6x

____ 29. Find all solutions of the equation.

2cos x 2 0

Select the correct answer, where k is any integer:

a.5 2k,

45

2k

b.4 2k,

74

2k

c.4 k,

74

k

d.5 2k,

95

2k

____ 30. Find all solutions of the equation.

2sinx 1 0


a.6 k,

116

k

b.6 k,

56

k

c.6 2k,

56

2k

d.6 2k,

116

2k

Name: ________________________ ID: A

9

____ 31. Find all solutions of the following equation.

4cos2x 3 0


a.6 2k,

56

2k,76

2k,11

6 2k

b.6 k,

116

k

c.6 k,

56

k,76

k,11

6 k

d.6 2k,

56

2k

____ 32. Find all solutions of the following equation.

4 cos 2 x – 4 cos x + 1 = 0


a.4 2k,

74

2k

b.3 2k,

53

2k

c.6 2k,

56

2k

d.4 2k,

34

2k

____ 33. Use an addition or subtraction formula to simplify the following equation. Then find all the solutions in the

interval 0,4

È

Î

ÍÍÍÍÍÍÍÍ

ˆ

¯

˜̃̃˜̃̃ .

cos x cos 7 x – sin x sin 7 x = 0

a.16

b.8

,38

c.8

d.16

,316

Name: ________________________ ID: A

10

____ 34. Plot the point that has the polar coordinates 5,4

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ .

a. d.

b. e.

c.

Name: ________________________ ID: A

11

____ 35. Plot the point that has the polar coordinates 3,76

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃ .

a. d.

b. e.

c.

____ 36. Find the third term of the sequence.

an = 2n + 1

a. a 3 = 7b. a 3 = 6c. a 3 = 5d. a 3 = 1e. a 3 = 2

Name: ________________________ ID: A

12

____ 37. Find the fourth term of the sequence.

an =1

n + 1

a. a4 = 5

b. a4 =15

c. a4 =45

d. a4 =14

e. a4 =11

____ 38. Find the 200th term of the sequence.

an = 10a. a 200 = 1b. a 200 = 10c. a 200 = 200d. a 200 = 210e. a 200 = 2000

____ 39. Find the nth term of the sequence.

2, 4, 8, 16, ...a. an = 2 n – 1

b. an = 2nc. 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 = 140b. S 7 = 50c. S 7 = 280d. S 7 = 141e. S 7 = 20

Name: ________________________ ID: A

13

____ 41. Find the partial sum S 5 of the sequence.

1, –1, 1, –1, ...a. S 5 = 0b. S 5 = 2c. S 5 = –2d. S 5 = –1e. S 5 = 1

____ 42. Find the sum.

4i 4

18

a. 4 13i 4

18

b. 4 60i 4

18

c. 4 72i 4

18

d. 4 56i 4

18

e. 4 4i 4

18


k2k

k 1

4

a. k2k 99k 1

4

b. k2k 64k 1

4

c. k2k 91k 1

4

d. k2k 10k 1

4

e. k2k 98k 1

4

Name: ________________________ ID: A

14

____ 44. Write the following sum.

kk 5

7

(k 9)

a. k(k 9)k 5

7

5(5 9) 7(7 9)

b. k(k 9)k 5

7

6(6 9) 7(7 9)

c. k(k 9)k 5

7

6(6 9) 7(7 9) 8(8 9)

d. k(k 9)k 5

7

5(5 9) 6(6 9) 7(7 9)

e. k(k 9)k 5

7

5(5 9) 6(6 9) 8(8 9)

____ 45. Write the following sum using sigma notation.

5 + 10 + 15 + 20 + ... + 50

a. 5k 0

50

b. k 5

k 0

10

c. 5kk 1

10

d. 5k

k 0

10

e. kk 5

50

____ 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

Name: ________________________ ID: A

15

____ 47. Find the common difference d of the arithmetic sequence.

5, 7, 9, 11, ...

a. 2b. 2nc. nd. 7e. 5

____ 48. Find the first five terms and determine if the sequence is arithmetic.

a n 2 6n

a. a 1 8, a 2 14, a 3 20, a 4 23, a 5 35 The sequence is not arithmetic.

b. a 1 8, a 2 14, a 3 20, a 4 30, a 5 28 The sequence is not arithmetic.

c. a 1 8, a 2 14, a 3 20, a 4 24, a 5 34 The sequence is arithmetic.

d. a 1 8, a 2 14, a 3 20, a 4 26, a 5 32 The sequence is arithmetic.

e. a 1 8, a 2 14, a 3 20, a 4 27, a 5 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.

a n 8n 1

a. a n 3 7(n 1), d 7

b. a n 3 6(n 1), d 6

c. Not an arithmetic sequence.d. a n 3 5(n 1), d 5

e. a n 3 8(n 1), d 8

____ 50. Find the fifth term of the arithmetic sequence.

2, 10, 18, 26, ...a. 26b. 27c. 34d. 44e. 5

____ 51. Find the fifth term of the arithmetic sequence.

5, 9, 13, 17, ...

a. 21b. 17c. 30d. 5e. 18

Name: ________________________ ID: A

16

____ 52. Find the nth term of the arithmetic sequence.

2, 2 + s, 2 + 2s, 2 + 3s, ...a. s 2nb. 2 snc. s 2 n 1( )d. 2 s n 1( )

e. 2n 12

sn n 1( )

____ 53. The 12th term of an arithmetic sequence is 13 and the 5th term is 6. Find the 22th term.a. 24b. 43c. 21d. 10e. 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. 15b. 17c. 14d. 16e. 13

____ 56. Find the partial sum S n of the arithmetic sequence that satisfies the following conditions.

a = 1, d = 4, n = 15

a. 57b. 435c. 465d. 870e. 61

Name: ________________________ ID: A

17

____ 57. Find the product of the numbers.

10

1

10,10

2

10,10

3

10,10

4

10, ... , 10

19

10

a. 380

b. 10380

c. 10

19

10

d. 190

e. 1019

____ 58. Find the nth term of the geometric sequence with given first term a and common ratio r. What is the fifth term?

a 73

, r 13

a. a n 73

13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n

, a 5 1

243

b. an 73

13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n 1

, a 5 781

c. an 13

13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n 1

, a 5 781

d. an 73

13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n 1

, a 5 781

e. a n 73

13

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n 1

, a 5 7

243

____ 59. Determine whether the sequence

6, 24, 96, 384...

is geometric. If it is geometric, find the common ratio.a. Geometric sequence, r = 6

b. Geometric sequence, r 14

c. Not a geometric sequence.d. Geometric sequence, r = 4

e. Geometric sequence, r 15

Name: ________________________ ID: A

18

____ 60. Determine whether the sequence is geometric.

8, –4, 2, –1,...

If it is geometric, find the common ratio.

a. Geometric, 12

b. Not geometric.

c. Geometric, 12

d. Geometric, 2e. Geometric, –2

____ 61. Determine whether the sequence is geometric. If it is geometric, find the common ratio.

e4 , e7 , e10 , e13 , ...a. Geometric, r = e 3

b. Not geometric.c. Geometric, r = 3

d. Geometric, r = 1

e3

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 arn 1 .

an 1( ) n3n

a. –3, 9, –27, 81, –243; ; it is not geometric.

b. –3, 9, –27, 81, –243; a n 3(4)n 1

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. Common ratio 5, the 6th term 5,120, and the nth term 4n 1

b. Common ratio 4, the 6th term 5,120, and the nth term 5 4n 1

c. Common ratio 4, the 6th term 12,500, and the nth term 5n 1

d. Common ratio 5, the 6th term 12,500, and the nth term 5 4n 1

e. Common ratio 4, the 6th term 5,120, and the nth term 4n 1

Name: ________________________ ID: A

19

____ 64. Determine the nth term of the geometric sequence.

1, 11,11,11 11, ...

a. 11n 1

b.1

11

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

n 1

c.111

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n 1

d. Not a geometric series.

e. 11ÊËÁÁÁ

ˆ¯˜̃̃

n 1

____ 65. Determine the nth term of the geometric sequence.

x,x2

5,x3

25,

x4

125, ...

a.xn

5

b.xn

5n

c. xn 1

d.xn 1

5n 1

e.xn

5n 1

____ 66. The first term of a geometric sequence is 6, and the second term is 3. Find the fifth term.

a.32

b.38

c.68

Name: ________________________ ID: A

20

____ 67. The common ratio in a geometric sequence is 43

, and the fourth term is 73

. Find the third term.

a.34

b.47

c.63

d.144

e.74

____ 68. Which term of the geometric sequence 5, 20, 80, . . . is 20480?a. 7thb. 13thc. 6thd. 8the. 9th

____ 69. Find the partial sum Sn of the geometric sequence that satisfies the given conditions.

a = 3, r = 4, n = 6a. Sn = 4,092b. Sn = 16,383c. Sn = 8,190d. Sn = 4,094e. Sn = 4,095

____ 70. Find the partial sum Sn of the geometric sequence that satisfies the given conditions.

a 4 16, a 6 64, n 4

a. Sn = 60b. Sn = 62c. Sn = 28d. Sn = 29e. Sn = 30


1 + 4 + 16 + ... + 4096a. Sn = 1,365b. Sn = 10,922c. Sn = 21,845d. Sn = 5,460e. Sn = 5,461

Name: ________________________ ID: A

21

____ 72. Find the sum of the infinite geometric series.

1 13 1

9 1

27 ...

a.42

b.54

c. 1

d.23

e.32

____ 73. Find the sum of the infinite geometric series.

1 15 1

25 1

125 ...

a.56

b.1112

c.65

d.16

e.45

ID: A

1

Review Test4Answer Section

MULTIPLE CHOICE

1. ANS: D2. ANS: C3. ANS: B4. ANS: B5. ANS: B6. ANS: D7. ANS: C8. ANS: B9. ANS: A

10. ANS: E11. ANS: C12. ANS: C13. ANS: C14. ANS: A15. ANS: B16. ANS: A17. ANS: A18. ANS: C19. ANS: B20. ANS: C21. ANS: D22. ANS: C23. ANS: B24. ANS: D25. ANS: B26. ANS: C27. ANS: B28. ANS: E29. ANS: B30. ANS: C31. ANS: A32. ANS: B33. ANS: D34. ANS: A35. ANS: C36. ANS: A37. ANS: B38. ANS: B39. ANS: C40. ANS: A

ID: A

2

41. ANS: E42. ANS: B43. ANS: E44. ANS: D45. ANS: C46. ANS: B47. ANS: A48. ANS: D49. ANS: E50. ANS: C51. ANS: A52. ANS: D53. ANS: E54. ANS: D55. ANS: A56. ANS: B57. ANS: E58. ANS: E59. ANS: D60. ANS: C61. ANS: A62. ANS: D63. ANS: B64. ANS: E65. ANS: E66. ANS: B67. ANS: E68. ANS: A69. ANS: E70. ANS: E71. ANS: E72. ANS: E73. ANS: A

review test4 (math1650:500) instructor: koshal...

Documents