f 1 x 5 4,whatis f 5 2 100 n expansionof have? n 2 Sem 2...Name: Per: Page 1 - 5/22/15 Moreno©2013...

Name: Per:

Page 1 - 5/22/15Moreno©2013

77

Sem 2 Practice

Algebra 2Sem 2 PracticeA2 2015

How many terms does the binomial

expansion of x5 + 3y2( )100 have?

(1606) A2-20.0 Ch06-8

1

If f −1 x( ) = x − 5 + 4, what is f ?

x2 − 8x + 21

(3002) A2-24.0 Ch07-7

2

2n + 5( )n=1

12

∑ =

(3271) A2-22.0 Ch11-4

3

Rationalize the denominator4 − 2 63

43

(3254) A2-8.0 Ch07-3

4

What is the value of log3 27?

3

(3261) A2-14.0 Ch08-4

5Simplify. Assume all variables are positive

a12b−13

a34b

12

(3256) A2-8.0 Ch07-4

6

If f x( ) = 5x − 6 and g x( ) = 3x + 10,what is f + g( ) x( )?

8x + 4

(2990) A2-24.0 Ch07-6

7Given f x( ) = x2 + 3x − 7 and g x( ) = 2x − 3( )2 .Find g x( ) − f x( ) .

3x2 − 15x + 16

(2987) A2-24.0 Ch07-6

8Change log2 65 into a logarithmwith base e.

(3031) A2-13.0 Ch08-5

9

Name: Per:

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77

Sem 2 Practice


A box contains 7 large red marbles,5 large yellow marbles, 3 small redmarbles, and 5 small yellow marbles.If a marble is drawn at random, whatis the probability that it is red, giventhat it is one of the small marbles?

38

(2926) PS-2.0 Ch12-2

10

Solve 3 x + 3( )34 = 81

(3258) A2-8.0 Ch07-5

11Write log4 64 = x as an exponent.

(3034) A2-13.0 Ch08-5

12

2x2 + 3y2 + 4x +12y+ 8 = 0Write in standard form and identifythe conic given above. x + 1( )2

3 +y + 2( )22 = 1

Ellipse

(3058) A2-17.0 Ch10-6

13Write as a single logarithmlog z − log3

4 − 5 log x2

(3263) A2-14.0 Ch08-4

14Write y = x2 + 8x − 7, in standard form.vertex form( )

y = x + 4( )2 − 23

(2946) A2-9.0 Ch05-2

15

What is the nth term in thearithmetic series below?

3+ 7 +11+15 +19… 4n −1

(2769) A2-22.0 Ch11-5

16

Abelardo wants to create several different 7 – character screen names. He wants touse arrangements of the first 3 letters of his first name (abe), followed by arrangements of 4 digits in 1984, the year of his birth. How many different screen names can he create in this way?

144

(2764) A2-18.0 Ch06-7

17Find the 15th term of the sequence8, 17, 26, 35,…

a15 = 8 + 14 • 9= 134

(3044) A2-22.0 Ch11-3

18

Name: Per:

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77

Sem 2 Practice


If the log2 ≈ 0.301 and log 3 ≈ 0.477,what is the approximate value of log 36?

1.556

(2892) A2-14.0 Ch08-4

19Given f x( ) = x2 − 2, and g x( ) = 3x + 2.Find f g x( )( )

9x2 + 12x + 2

(2985) A2-24.0 Ch07-6

20

Bacteria in a culture are growingexponentially with time, as shownin the table below.

Bacteria GrowthDay Bacteria

0 50

1 100

2 200

What equations expresses the numberof bacteria, y, present at any time, t?

(2882) A2-12.0 Ch08-1

21

Expand the logarithm

log 2 x5

⎛⎝⎜

⎞⎠⎟3

(3264) A2-14.0 Ch08-4

22


3

(2890) A2-14.0 Ch08-4

23

Find the solutions to x − 3( )23 + 7 = 11

(2984) A2-8.0 Ch07-5

24

Solve 2 x −1( )43 + 4 = 36

(3260) A2-8.0 Ch07-5

25Find the sum of the infinite geometric series

4 +1+ 14 +116 + ....

(3037) A2-22.0 Ch11-5

26

Solve x + 5( )23 −1= 3

(2983) A2-8.0 Ch07-5

27

Name: Per:

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77

Sem 2 Practice



log x2 − 4x + 3( )2

(3265) A2-14.0 Ch08-4

28

Graph y = x − 2( )2+ 4

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

(3020) A2-9.0 Ch05-3

29

Solve 4x + 3( )23 = 16x + 44( )13

(3259) A2-8.0 Ch07-5

30

A certain radioactive element decaysover time according to the equation

y = A 12( )

t300

, where A = the number

of grams present initially and t = timein years. If 1000 grams were presentinitially how many grams will remainafter 900 years?

(2760) A2-12.0 Ch08-1

31

A train is made up of a two locomotivesand 7 different cars. If each of thelocomotives must be at each end, how manydifferent ways can the train be ordered? 5040

(2898) A2-18.0 Ch06-7

32Rationalize the denominator3+ 82 − 2 8

(3252) A2-8.0 Ch07-3

33

Find the standard form of the conic sectionx2 + y2 + 4x − 6y − 3= 0.

(2936) A2-17.0 Ch10-6

34

What is the sum of the infinitegeometric series

12 +

14 + 18 +

116 +…? 1

(2768) A2-22.0 Ch11-5

35

A certain radioactive element decaysover time according to the equation

y = A 15( )

t150

, where A is the number

of grams present initially and t is timein years. If 1000 grams were presentinitially, how many grams will remainafter 300 years?

(2879) A2-12.0 Ch08-1

36

Name: Per:

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77

Sem 2 Practice


Given f x( ) = x2 + 1 and g x( ) = x2 − 2.Find g f( ) −2( ) .

23

(2995) A2-24.0 Ch07-6

37

The graph ofy216 −

x29 = 1 is a

hyperbola. What are theequations that represent theaysmptotes of the hyperbola'sgraph?

(2865) A2-16.0 Ch10-5

38log2 32 =

(3030) A2-11.0 Ch08-3

39

Find the standard form of the conicequation and identify it by name.

4x2 − 5y2 −16x − 30y − 9 = 0

(2757) A2-17.0 Ch10-6

40

Given f x( ) = 2x2 − 3 and g x( ) = 7x − 4.What is g f( ) −2( )?

31

(2986) A2-24.0 Ch07-6

41Rationalize the denominator3− 2 710 − 7

(3253) A2-8.0 Ch07-3

42

log10 n x1 02 0.3013 0.4774 0.6025 0.6996 0.7787 0.8458 0.9039 0.95410 1

Do not use a calcuator

What is the solution to theequation 5x = 20?

(2758) A2-11.0 Ch08-5

43

If f x( ) = 3x + 4, what is f −1 ?

x − 43

(3001) A2-24.0 Ch07-7

44

Evaluate 2 5C4( )−3 C2

(3250) A2-18.0 Ch06-7

45

Name: Per:

Page 6 - 5/22/15Moreno©2013

77

Sem 2 Practice


log 100,000 =

5

(3029) A2-11.0 Ch08-3

46log10 n x

1 0

2 0.301

3 0.477

4 0.602

5 0.699

6 0.778

7 0.845

8 0.903

9 0.954

10 1

Use the table to evaluate.

Solve 4x= 12

(2871) A2-11.0 Ch08-5

47Write as a single logarithm2 logb x3 + 3logb y4

⎛⎝⎜

⎞⎠⎟ − 5 logb z

(3262) A2-14.0 Ch08-4

48


log xy( )13 ÷ z2⎡⎣⎢

⎤⎦⎥3

(3266) A2-14.0 Ch08-4

49

8C4 =

70

(3051) A2-18.0 Ch06-7

50What is the summation formulafor the infinite geometric series:S = 2 + 2

5 + 225 + 2

125 + 2625 + ...

(3038) A2-22.0 Ch11-5

51

If log10 x = −2, what is the value of x ?

(2759) A2-11.0 Ch08-3

52Simplify. Assume all variables are positive

a23b−14

a12b−12

(3255) A2-8.0 Ch07-4

53

Expand 3a −1( )4

81a4 −108a3 + 54a2 −12a +1

(2767) A2-20.0 Ch06-8

54

Name: Per:

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77

Sem 2 Practice


Identify the vertex of the parabola.y = −3 x − 5( )2 − 6

5, − 6( )

(3019) A2-9.0 Ch05-3

55

Graph y = −3 x − 2( )2+ 2

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

(2945) A2-10.0 Ch05-2

56

Simplify 23 log6 216

(3033) A2-13.0 Ch08-5

57

Solve log4 x = 5

(3035) A2-13.0 Ch08-5

58


(2889) A2-14.0 Ch08-4

59If f x( ) = −x2 + 2x and g x( ) = x2 + 4,what is f − g( ) x( )?

−2x2 + 2x − 4

(2991) A2-24.0 Ch07-6

60


3

(2762) A2-14.0 Ch08-4

61What is the nth term in the arithmeticseries : 6 + 2 − 2 − 6 −10... ?

(2912) A2-22.0 Ch11-5

62

Do not use a calculator

If the log 2 ≈ 0.301 and log 3 ≈ 0.477,what is the approximate value of log 72 ?

(2763) A2-14.0 Ch08-4

63

Name: Per:

Page 8 - 5/22/15Moreno©2013

77

Sem 2 Practice


Solve x − 2( )23 = 9

(3257) A2-8.0 Ch07-5

64

Add 324 + 484

(3251) A2-8.0 Ch07-3

65Write in standard form and identify the conic section :

x2 + y2 + 8x +16y − 32 = 0

(3054) A2-16.0 Ch10-3

66

log10 n x

1 0

2 0.301

3 0.477

4 0.602

5 0.699

6 0.778

7 0.845

8 0.903

9 0.954

10 1

log5 15 =

(2886) A2-13.0 Ch08-5

67

Graph y = x2 + 10x + 19

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

(3021) A2-9.0 Ch05-2

68

Which ordered pair is the vertex off x( ) = −2x2 + 4x − 7?

1, − 5( )

(2944) A2-10.0 Ch05-2

69

Evaluate 8P46!

(3210) A2-18.0 Ch06-7

70

Write in exponentional form :

log5 23 = x5x = 23

(2877) A2-11.0 Ch08-3

71

Evaluate 7C5

5P3

(3249) A2-18.0 Ch06-7

72

Page 1 - 5/22/15Moreno@2013

77

AnswersAlgebra 2Sem 2 PracticeA2 2015

101[1]

(1606) A2-20.0 Ch06-8

x2 − 8x + 21[2]

(3002) A2-24.0 Ch07-7

216[3]

(3271) A2-22.0 Ch11-4

2 23 − 123[4]

(3254) A2-8.0 Ch07-3

3[5]

(3261) A2-14.0 Ch08-4

1a14b

56

[6]

(3256) A2-8.0 Ch07-4

8x + 4[7]

(2990) A2-24.0 Ch07-6

3x2 − 15x + 16[8]

(2987) A2-24.0 Ch07-6

logm n =logb nlogb m

log2 65 =loge 65log3 2

= ln65ln2

[9]

(3031) A2-13.0 Ch08-5

38

[10]

(2926) PS-2.0 Ch12-2

78[11]

(3258) A2-8.0 Ch07-5

bx = y⇔ logb y = x

log4 64 = x⇒ 4 x = 64

[12]

(3034) A2-13.0 Ch08-5

x + 1( )23 +

y + 2( )22 = 1

Ellipse

[13]

(3058) A2-17.0 Ch10-6

logbz4

34 • 2 x⎛⎝⎜

⎞⎠⎟

[14]

(3263) A2-14.0 Ch08-4

y = x + 4( )2 − 23[15]

(2946) A2-9.0 Ch05-2

Page 2 - 5/22/15Moreno@2013

77


4n −1[16]

(2769) A2-22.0 Ch11-5

144[17]

(2764) A2-18.0 Ch06-7

a15 = 8 + 14 • 9= 134

[18]

(3044) A2-22.0 Ch11-3

1.556[19]

(2892) A2-14.0 Ch08-4

9x2 + 12x + 2[20]

(2985) A2-24.0 Ch07-6

y = abx b > 1, growthb < 1, decay{

0, 50( ), x = 0, y = 50⇒ 50 = ab0, a = 50

1,100( ), x = 1, y = 100⇒100 = 50b1

2 = b

y = 50 2( )x

[21]

(2882) A2-12.0 Ch08-1

3 log2 + 12 log x − log5( )[22]

(3264) A2-14.0 Ch08-4

3[23]

(2890) A2-14.0 Ch08-4

−5,11[24]

(2984) A2-8.0 Ch07-5

−7, 9[25]

(3260) A2-8.0 Ch07-5

S∞ =a11− r ; r <1

No Sum; r >1

⎧⎨⎪

⎩⎪r = 1

4

S∞ = a11− r =

41− 1

4

= 444 − 1

4= 43

4

= 4 • 43 = 163

[26]

(3037) A2-22.0 Ch11-5

−13, 3[27]

(2983) A2-8.0 Ch07-5

12 log x2 − 4( )− 2 log x + 3( )[28]

(3265) A2-14.0 Ch08-4

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

2, 4( )

[29]

(3020) A2-9.0 Ch05-3

− 74 ,54

[30]

(3259) A2-8.0 Ch07-5

Page 3 - 5/22/15Moreno@2013

77


A = 1000, t = 900y = 1000 1

2( )900300y = 1000 1

2( )3y = 1000 1

8( ) = 125125 grams

[31]

(2760) A2-12.0 Ch08-1

5040[32]

(2898) A2-18.0 Ch06-7

11+ 8 2−14

[33]

(3252) A2-8.0 Ch07-3

x2 + 4x + y2 − 6y = 3+ 4 + 9 + 4 + 9

x2 + 4x + 4( )+ y2 − 6y + 9( ) = 16x + 2( )2 + y − 3( )2 = 16

circlecenter : −2, 3( )radius : r = 4

[34]

(2936) A2-17.0 Ch10-6

1[35]

(2768) A2-22.0 Ch11-5

A = 1000, t = 300y = 1000 1

5( )300150y = 1000 1

5( )2y = 1000 1

25( ) = 4040 grams

[36]

(2879) A2-12.0 Ch08-1

23[37]

(2995) A2-24.0 Ch07-6

y = ± 43 x[38]

(2865) A2-16.0 Ch10-5

5[39]

(3030) A2-11.0 Ch08-3

4x2 −16x − 5y2 − 30y = 94 x2 − 4x( )− 5 y2 + 6y( ) = 9

+ 4 + 9 +16 − 454 x2 − 4x + 4( )− 5 y2 + 6y + 9( ) = −20

−x − 2( )25 +

y + 3( )24 = 1

y + 3( )24 −

x − 2( )25 = 1

Hyperbolacenter : 2, − 3( )

[40]

(2757) A2-17.0 Ch10-6

31[41]

(2986) A2-24.0 Ch07-6

16 −17 793

[42]

(3253) A2-8.0 Ch07-3

5x = 20log5x = log20x log5 = log20

x = log20log5

x = log10+log2log5

x = 1+.301.699

x ≈1.861

[43]

(2758) A2-11.0 Ch08-5

x − 43

[44]

(3001) A2-24.0 Ch07-7

7[45]

(3250) A2-18.0 Ch06-7

Page 4 - 5/22/15Moreno@2013

77


5[46]

(3029) A2-11.0 Ch08-3

4 x = 12log4 x = log12x log4 = log12

x = log12log4

x = log4+log3log4

x = .602+.477.602

x ≈1.792

[47]

(2871) A2-11.0 Ch08-5

logbx23 y34

z5⎛

⎝⎜

⎞

⎠⎟

[48]

(3262) A2-14.0 Ch08-4

log x + log y − 6 log z[49]

(3266) A2-14.0 Ch08-4

70[50]

(3051) A2-18.0 Ch06-7

S∞ =a11− r ; r <1

No Sum; r >1

⎧⎨⎪

⎩⎪

r = 15S∞ = a1

1− r =21− 1

5

[51]

(3038) A2-22.0 Ch11-5


log10 x = −2⇒10−2 = x

1100 = x

[52]

(2759) A2-11.0 Ch08-3

a16b

14

[53]

(3255) A2-8.0 Ch07-4

81a4 −108a3 + 54a2 −12a +1[54]

(2767) A2-20.0 Ch06-8

5, − 6( )[55]

(3019) A2-9.0 Ch05-3

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

[56]

(2945) A2-10.0 Ch05-2

23 log6 21623 log6 6

3

23 • 3log6 623 • 3= 1

[57]

(3033) A2-13.0 Ch08-5

log4 x = 54log4 x = 45

x = 45

[58]

(3035) A2-13.0 Ch08-5


log4 4 = 1...4 x = 41

x = 1

[59]

(2889) A2-14.0 Ch08-4

−2x2 + 2x − 4[60]

(2991) A2-24.0 Ch07-6

Page 5 - 5/22/15Moreno@2013

77


3[61]

(2762) A2-14.0 Ch08-4

d = −4an = a1 + n −1( )dan = 6 + n −1( ) −4( )an = 6 + −4n + 4an = −4n +10

[62]

(2912) A2-22.0 Ch11-5

log72 = log 8 • 9( )= log8 + log9= log23 + log32

= 3log2 + 2 log3= 3 .301( )+ 2 .477( )= 1.857

[63]

(2763) A2-14.0 Ch08-4

−25, 29[64]

(3257) A2-8.0 Ch07-5

2 24 + 2 34[65]

(3251) A2-8.0 Ch07-3

x2 + 8x + y2 +16y = 32+16 + 64 +16 + 64

x2 + 8x +16( )+ y2 +16y + 64( ) = 112x + 4( )2 + y + 8( )2 = 112

Circlecenter : −4, − 8( ), radius 112

[66]

(3054) A2-16.0 Ch10-3

log15log5

=log 5 • 3( )log5 = log5 + log3log5

= .699 + .477.699 ≈1.683

[67]

(2886) A2-13.0 Ch08-5

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

−5, − 6( )

[68]

(3021) A2-9.0 Ch05-2

1, − 5( )[69]

(2944) A2-10.0 Ch05-2

8P46! = 8 • 7 • 6 • 5

6 • 5 • 4 • 3• 2 •1= 73

[70]

(3210) A2-18.0 Ch06-7

5x = 23

[71]

(2877) A2-11.0 Ch08-3

720

[72]

(3249) A2-18.0 Ch06-7

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f 1 x 5 4,whatis f 5 2 100 n expansionof have? n 2 Sem 2...Name: Per: Page 1 - 5/22/15 Moreno©2013...

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