algebra 2 second semester exam...

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Algebra 2 – Second Semester Exam Review

1) Simplify. Write using positive exponents only.

a) 32( 16) (Section 6.1 and 6.2)

b) 43( 64) (Section 6.1 and 6.2)

c) 8 54 16x y (Section 6.2)

d) 3 33 6 9 6 (Section 6.2)

2) For the functions 2( ) 3 5 2f x x x and 2( ) 2 8g x x , (a) evaluate ( ) ( )f x g x and

(b) evaluate ( ) ( )f x g x . (Section 6.3)

3) For the functions 3( ) 18f x x and

4

3( )g x x , evaluate ( ( ))f g x (Section 6.4)

4) Given the relation below: (a) write the inverse relation and (b) determine )0(1f ? (Section 6.4)

5) Determine the inverse of the function: (Section 6.4)

x 0 1 2 3

)(xf 8 4 0 -4

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6) Graph 2)( 2 xxf for 0x and )(1 xf on the same graph.

(Section 6.4)

7) Evaluate: 4

1log

64

(Section 7.4)

8) Evaluate: 3log 243 (Section 7.4)

9) Write the equation log10,000 4 in exponent form. (Section 7.4)

10) Write the equation 4log 64 3 in exponent form. (Section 7.4)

11) Write the equation ln 1e in exponent form. (Section 7.4)

12) Expand: 2

3

4ln

x

y

(Section 7.5)

13) Condense: log9 2log 3log3y x (Section 7.5)

14) Solve: ln(2 1) 5x (round to the nearest hundredth) (Section 7.6)

15) Solve for x: 23log ( 2) 6x (Section 7.6)

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16) Solve for x: log 243 5x (Section 7.6)

17) Solve for x: 34log 3 28x (Section 7.6)

18) Determine the value of x: 10 4 10x (round to 3 decimal places) (Section 7.6)

19) Solve: 42 14

3 3

xe (round to 3 decimal places) (Section 7.6)

20) Solve: 2 15 30x (round to 3 decimal places) (Section 7.5 and 7.6)

21) For each of the graphs below, name the type of function shown in the graph and answer the question:

“Does that family of functions have asymptotic behavior?” If yes, give the equation of the asymptote(s).

(Sections 4.2, 6.5, 7.1, 8.2)

a) b)

c) d)

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22) Graph. Include the equation of the asymptote when necessary. Name the type of function shown in your

graph (i.e. exponential, logarithmic, rational, etc.). (Sections 6.5, 7.1, 7.4, 8.2)

a) 32)( xxf b) 2)3()( xxf

c) 42

1)(

xxf d) )1(log2)( 2 xxf

23) Describe the domain of the function: 2

1 1( )

5 3 2

xf x

x x x

(Section 8.2)

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24) Graph: 1

43

yx

(Section 8.2)

25) Simplify the following rational expression: 2

2

2 8

x

x x

(Section 8.4)

26) Simplify the following rational expression: 2

2

4

6

x

x x

(Section 8.4)

27) Add: 2 4

1 2

x

x x

(Section 8.5)

28) Add: 2

3

5 6 2

x

x x x

(Section 8.5)

29) Multiply: 2

2

7 12( 3)

2 15

x xx

x x

(Section 8.4)

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30) Multiply: 2

2

2

( 6)( 4 4)

4

x xx x

x

(Section 8.4)

31) Subtract: 2

6 3

25 5x x

(Section 8.5)

32) Subtract: 2

2 5

3 6 9

x x

x x x

(Section 8.5)

33) Simplify: 4

2

16

4

4

x

x

x

(Section 8.5)

34) Simplify:

23

3

9 2

x

x

(Section 8.5)

35) Solve: 2 3

3

x

x x

(Section 8.6)

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36) What is the radius of the circle whose equation is: 2 2( 3) ( 4) 150x y (Section 9.3)

37) Write the equation of the specific conic in standard form: (Sections 9.3, 9.5)

a) b)

38) A plane intersects a cone as shown. What type of conic section is formed by each intersection shown

below? (Ch 9—Conics)

39) Graph: 2

2 19

yx (Section 9.5)

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40) Graph: 2 2( 3)

116 9

x y (Section 9.4)

41) Graph: 24( 3)x y (Section 9.2)

42) A data set includes the following numbers: 4, 8, 12, 12, 13, 17, 18, 21. Determine the mean, median,

mode, range and standard deviation for the data. (Section 11.1)

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43) The IQ (intelligence quotient) scores for people in the United States are thought to be approximately

normally distributed with a mean of 100 and a standard deviation of 15. What is the approximate

probability of the following: (Section 11.3)

a) A randomly selected U.S. person’s IQ is higher than 130?

b) A randomly selected U.S. person’s IQ is between 85 and 115?

44) If a U.S. person has an IQ of 127, what is their z-score? (Section 11.3)

45) Using the Standard Normal Table above, what is the probability that a randomly selected

U.S. person would have at least an IQ of 127? What is the probability that the randomly selected person

would have at most an IQ of 127? (Section 11.3)

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46) Fill in the first quadrant of the unit circle. (Section 13.2)

47) Determine the exact value of each trigonometric function. (Section 13.3)

a) sin 120 b) cos4

c) 5

tan6

d) cos0

e) cos 210 f) 4

tan3

g) sin 300 h) tan

2

48) Which is the graph of 2 cos2

y x

(Section 14.2)

A. B.

C. D.

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49) State the amplitude and period of the following functions. (Section 14.1)

a) b)

c) d)

e) 5 2sin3y x f) 2cosy x

50) State the domain and range of the following functions. (Section 14.1)

a) 2 siny x b) 2cosy x c) 3 4siny x d) 4 3cosy x

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MULTIPLE CHOICE PRACTICE

Choose the best answer.

51) Solve: 6

3 3

x

x x

(Section 8.6)

a) 3, 6

b) 0, 6

c) 3

d) 6

52) Given the graphs below, determine which of the following has an inverse that is also a function. (Section 6.4)

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53) Which of these is the graph of 2 2( 3) ( 1) 4x y ? (Section 9.3)

54) Write the equation of the graph. (Section 8.2)

a) ( ) ( 2)( 3)f x x x

b) ( 3)

( )( 2)

xf x

x

c) 1

( ) 32

f xx

d) 1

( ) 23

f xx

55) Given ( ) 2 5g x x and 2( ) 4f x x , find ( ( ))g f x . (Section 6.3)

a) 9 16x

b) 3 23 12 4x x

c) 24 20 21x x

d) 22 13x

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56) Condense the expression: 9 92log 6loga b (Section 7.5)

a) 2 3

9log ( )b a

b) 2

9 6log

a

b

c) 3

9log ( )b a

d) 2 6

9log ( )b a

57) Expand the expression: 4 5

4log ( )x y (Section 7.5)

a) 4 4

14log log

2y x

b) 4 420log 20logx y

c) 4 420log 5logx y

d) 4 44log 5logx y

58) Which function can be obtained by translating the graph of logy x right 2 units and down one unit?

(Section 7.4)

a) log( 1) 2y x

b) log( 2) 1y x

c) log( 2) 1y x

d) log( 2) 1y x

algebra 2 second semester exam...

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