Algebra II H Semester 2 Practice Exam A DRAFT. B. 2 2x 3 A. 47 B. 92 C. 139 D. 407 B. C.

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1 Algebra II H Semester Practice Eam A. Find the solution set of 5 5 +, , , 6 =.. Let f ( ) = and g( ) =. Which epression is equivalent to f g? ( ) ( ) + ( 6) 9 9 +,. What is the simplified form of the epression a 6 + a 08a? a a a + a + 6 a a a. Simplif b 5 b b b b. 5. If h( ) = 0 and j( ) h( ) + j ( )? = +, what is 6. Let f ( ) = and g( ) =. Which epression is equivalent to f g? ( )( ) GO ON Clark Count School District Revised 08/0/0

2 Algebra II H Semester Practice Eam A 7. Which is the inverse of the function k = 6 for 0? ( ) k ( ) k ( ) = + + ( ) = k = + k ( ) 6 = + 8. What function is represented b this graph? 9. Solve for : 5 = = 5 = 5 = 5 = You are tring to determine the height of a regular truncated pramid that cannot be measured directl. The height h and slant height s of a truncated pramid are related b the formula s = h + ( b ) b where b and b are the lengths of the upper and lower bases of the pramid, respectivel. If s = 5, b =, and b =, what is the height of the pramid? 6 = + + = + + = + = +. Simplif the epression ( i) + ( + i) ( + i) where i = i 7 i 5 + 5i 5 5i GO ON Clark Count School District Revised 08/0/0

3 Algebra II H Semester Practice Eam A. What function is represented b the graph?. Which graph represents f ( ) =? = + = + = + = GO ON Clark Count School District Revised 08/0/0

4 Algebra II H Semester Practice Eam A. Which epression is equivalent to log 6? log6 6log log log 6 log 6 log 7. Which is a solution for the equation 0 n =? n = log 5 n = log8 0 n = log n = log 5. Which epression is equivalent to log+ log6 log8? log 8 log78 log log 8. Solve for : = = 7 = no solution = Solve the equation for : ln( ) = + e = e + = e + = e + = 9. In the ear 995, about 0 million people used the Internet. Between 995 and 00, the number of people who used the internet grew b about 75% each ear. Which function best models the relationship between p, the number of people using the internet (in millions), and t, the number of ears since 995?.75 pt ( ) = 0 t pt ( ) = ( 0.75) 0 t pt () = 0(.75) t p( t) = t GO ON Clark Count School District Revised 08/0/0

5 Algebra II H Semester Practice Eam A 0. What is the minimum or maimum of the quadratic function q = 8 +? ( ). What function is represented b the graph? q = ( ) q = ( ) ( ) q = 5 q( ) = 8. The value of w varies directl with and inversel with. If w = 5 when = and =, what is the value of w when = and =? f ( ) f ( ) f ( ) f ( ) = = + = =. Which of the following functions have an asmptote at =? I. II. III. = = = II onl I and II onl I and III onl I, II, and III GO ON Clark Count School District Revised 08/0/0

6 Algebra II H Semester Practice Eam A. Simplif the epression 5 9 ( + ) ( ) 5 5. What is the solution set of =? {, } {0, } { } 6. What is the solution set of = +? { 8, } { 8} {, } { } The harmonic mean h of a set of n numbers {,,,, n} is given b the formula = h n What is the harmonic mean of two positive numbers that differ b one if the smaller number is k? h = k + h = k ( + ) k k h = k + k + h = k + k 8. Given the sstem of linear equations: + = 5 + = 6 Which epression below shows the solution to the sstem using matrices? 5 = 6 5 = = 6 5 = GO ON Clark Count School District Revised 08/0/0

7 Algebra II H Semester Practice Eam A 9. What is the equation of the graph below? 0. Which graph best represents the equation ( ) = +? ( ) ( + ) = 9 ( + ) ( ) = 9 ( + ) ( ) = 9 ( + ) ( ) = GO ON Clark Count School District Revised 08/0/0

8 Algebra II H Semester Practice Eam A. What is the equation for the graph below?. Which graph best represents the graph of 6 + = 8? ( ) ( ) = ( ) ( ) + = ( ) ( ) = 6 ( ) ( ) + = GO ON Clark Count School District Revised 08/0/0

9 Algebra II H Semester Practice Eam A. What equation represents the graph below? 5. The charge for parking at an airport is $5 for time up to one hour, plus $ for each additional hour (or portion of an hour) up to a maimum of $5. What graph represents this situation? = = = =. Which is the equation of a parabola? ( ) ( ) = 6 6= 0 ( ) + = 8 = GO ON Clark Count School District Revised 08/0/0

10 Algebra II H Semester Practice Eam A 6. Epand the epression n + n= What is the series when written in summation notation? 9. Figure shows a square with an area of 9 square units. In Figure, the first square has been divided into nine smaller congruent squares and the middle one removed. In Figure, each of the squares is again subdivided and the middle square removed. If the pattern continues, what is the area of Figure 6? Figure i i= i + i= i + i + 6 i i= i i= i i Figure Figure 8. What equation is the sum of the 8 terms in the series ? S8 = + 87 S S 8 8 = = + S 8 = GO ON Clark Count School District Revised 08/0/0

11 Algebra II H Semester Practice Eam A 0. What is the sum of the geometric series n n=? 9. Which is a formula of a geometric sequence when g = and g 6 = 96? ( ) g = ( ) g n n n = g n n = n ( ) ( ) g n = n. Which is a formula of the arithmetic sequence,, 7, 9,?. Which is a recursive rule for the sequence,, 7,, 6,? t =, t = t n n t =, t = t + n n, n n t = t = t + n t =, t = t n n n. In the 980 s, the standard configuration for a Woming license plate was a small number between and, inclusive, followed b four digits with repetition allowed. For eample: WYOMING How man license plates were possible for the entire state of Woming in the 980 s? an an a n a n 5 = + n = + n = 8 n n 9 = + 6,000 0,000 00,000,000, GO ON Clark Count School District Revised 08/0/0

12 Algebra II H Semester Practice Eam A 5. A student will randoml choose four digits from the set {,,,, 5, 6}, without replacement, and arrange them in the order the were chosen. How man different four-digit numbers can be made in this wa? Which is a term of the epanded form of ( 5 a)? 000a 600a 0a 6a 7. What is the coefficient of epansion of ( + )? 8 in the 8. A cooler contains 8 cans of cola, 6 cans of ginger ale, cans of root beer, and cans of orange soda. If a person reaches in the cooler and pulls out two cans at random, what is the probabilit that both cans will be ginger ale? Which of these measures are greatl influenced b etreme values? I. mean II. median III. interquartile range IV. range IV onl I and IV onl II and III onl I, III, and IV onl GO ON Clark Count School District Revised 08/0/0

13 Algebra II H Semester Practice Eam A 50. The graph below shows the number of home runs hit b the teams in a baseball league. 0 Home Runs b Teams in a Baseball League Number of Teams Home Runs Which value could be the median number of home runs? What is the range of the function f = +? ( ) 8 f ( ) 8 f ( ) f ( ) 0 all real numbers 5. What is the domain of the function f ( ) = 7 +? { } { 5} { 0} { } GO ON Clark Count School District Revised 08/0/0

14 Algebra II H Semester Practice Eam A 5. What are the domain and range of the function f ( ) = +? 56. Which equation is represented in the graph below? Domain: 0 Range: > 0 Domain: 0 Range: Domain: all real numbers Range: > Domain: all real numbers Range: all real numbers 5. What are the domain and range of the f = ln? function ( ) ( ) Domain: > 0 Range: < Domain: > Range: < 0 Domain: > 0 Range: all real numbers Domain: > Range: all real numbers = + 5 f ( ) f ( ) f e = 5 + e = + ( ) 5 e f ( ) = + e 55. What are the horizontal asmptotes of the logistic growth function 6 f ( ) =? + e = 0, = = 0, = 6 =, = =, = GO ON Clark Count School District Revised 08/0/0

15 Algebra II H Semester Practice Eam A 57. What is the approimate local maimum of the function below? 58. Which interval contains the local + minimum of f ( ) =? 6 < < < < The function has no local minimum. 59. What is assumed in the second step in a proof b mathematical induction? (, 8) ( 0.67,.8) (., 0 ) (.77, 0 ) The statement is true for k = 0. The statement is true for n =. The statement is true for n = k. The statement is true for n = k In a proof b mathematical induction that i( i ) ( + )( i+ ) n i i + = for all positive integers i n, what should be proven in the second step of the proof? = ( ) ( + )( + ) + = k k = k( k ) ( k )( k ) = ( + )( k+ ) ( k+ )( k+ )( k+ ) Clark Count School District Revised 08/0/0

16 Applied Algebra II Semester Practice Eam B Free Response. This question obsolete as of 0 0. See new test specifications and practice questions.. This question obsolete as of 0 0. See new test specifications and practice questions.. This question obsolete as of 0 0. See new test specifications and practice questions Clark Count School District Revised 08/0/0

17 Algebra II Honors 0 0 Semester Free Response Practice Eam A OK Calculators allowed. Use the function g( ) 5 below. = + to answer the questions (a) State the domain and range of g( ). (b) Find g ( ) g( ) using composition of functions. (c) State the domain and range of g ( ). (d) The graph of a function h( ) graph of = h ( ) on the same aes. and verif our answer is the inverse of = is shown. Sketch the. A species of deep water fish has an etremel long lifespan and rarel has offspring. There are currentl 8 fish of this tpe, and their growth rate is % each month. (a) Write an eponential growth function to model the population of the fish species in terms of time t in ears. (b) Using the model, how man fish will there be in half of a ear? In 0 ears? (c) Use the model to predict when the population will reach 5,000 fish. + 7 = 9. Use the functions ( ) f and g( ) 8 =. + (a) Graph the function f ( ) on the grid provided, labeling the asmptotes and intercepts on the graph. (b) Find the local maimum of f ( ). (c) Find the local minimum of f ( ). (d) Solve for if f ( ) = g( ). (e) Simplif f ( ) + g( ). 0 0 Clark Count School District Revised 0/05/0

18 Algebra II Honors 0 0 Semester Free Response Practice Eam B OK Calculators allowed. Use the function h( ) 5 questions below. = + + to answer the (a) State the domain and range of h( ). (b) Find h ( ) h( ) using composition of functions. (c) State the domain and range of h ( ). (d) Sketch and label the graphs of h( ) = h ( ) on the grid provided. and verif our answer is the inverse of = and r. Use the formula for compound interest A= P +, where A is the amount in an account, n beginning with principal P, after time t with interest rate r compounded n times annuall. (a) Suppose $,000 is invested in a savings account. If the interest rate is % compounded quarterl, how much mone will be in the account after8 ears? (b) Eplain wh the same $,000 in an account earning 8% interest compounded quarterl will be worth more than twice the amount in part (a). (c) At what interest rate, compounded quarterl, would the $,000 need to be invested in order to have $6,000 after 8 ears? nt. Use the functions f ( ) = and g( ) 6 =. + (a) Graph the function f ( ) on the grid provided. Label the asmptotes and intercepts on the graph. (b) Identif the domain and range of functions f ( ) and g( ). (c) Find the local minimum and maimum of f ( ). (d) Solve for if f ( ) = g( ). 0 0 Clark Count School District Revised 0/05/0

19 Algebra II Honors 0 0 Semester Free Response Practice Eam C OK Calculators allowed. Use the function f ( ) = + to answer the questions below. (a) State the domain and range of f ( ). (b) Find f ( ) f ( ) and verif our answer is the inverse of using composition of functions. (c) State the domain and range of f ( ). (d) Sketch and label the graphs of = f ( ) and = f ( ) on the grid provided.. The approimate diameter of a wound in millimeters t das after it begins to heal is given b the function W() t = W0e 0.5t, where W 0 is the initial diameter of the wound. (a) If a wound s diameter is initiall 5 millimeters, write a function to determine the diameter of the wound. (b) Does the function indicate growth or deca of the wound s diameter? Eplain. (c) What is the diameter of the wound after das? (d) When will the diameter of the wound be 0.5 millimeters (almost completel healed)?. Use the functions to answer the questions below. f + 6 ( ) = g( ) = ( ) = h 9 5 = 7+ 0 ( ) s (a) Identif the horizontal and vertical asmptotes of s( ). (b) Graph s( ). Label an asmptotes and intercepts. (c) Find the local maimum of s( ), if it eists. (d) Simplif g( ) h( ) s( ). (e) Solve for if f ( ) = g( ) Clark Count School District Revised 0/05/0

20 ALGEBRA II HONORS SEMESTER EXAM ITEM SPECIFICATION SHEET & KEY Free Response # Course Concepts / Objectives Sllabus Objectives Radical functions, arithmetic of functions, and composition of functions Eponential functions and applications Rational equations and functions NV State Standards # Objective Sllabus Objective NV State Standard Ke Solve quadratic equations and inequalities B Simplif radical epressions b appling properties of radicals A Use properties of rational eponents to simplif epressions B Perform arithmetic operations of functions D 5 Perform arithmetic operations of functions A 6 Find a composition of functions D 7 Derive and verif inverses of functions A 8 Graph square root/cube root equations C 9 Solve equations with radicals or rational eponents... D 0 Solve application problems using roots, rational eponents, powers, and radicals... D Perform operations with comple numbers C Graph eponential and logarithmic functions A Graph eponential and logarithmic functions B Evaluate and simplif epressions using properties of logarithms D 5 Evaluate and simplif epressions using properties of logarithms A 6 Solve eponential and logarithmic equations D 7 Solve eponential and logarithmic equations D 8 Solve eponential and logarithmic equations B 0 0 Page of Revised: 09/9/0 Clark Count School District

21 ALGEBRA II HONORS SEMESTER EXAM ITEM SPECIFICATION SHEET & KEY Sllabus NV State # Objective Objective Standard Ke 9 Develop and solve real world models using eponential and logarithmic equations C 0 Analze graphs of polnomial functions to determine characteristics...9 B Solve problems using direct, inverse, or joint variation A Graph rational functions C Identif domain, range, and asmptotes of rational functions A Simplif rational epressions B 5 Solve rational equations A 6 Solve rational equations D 7 Develop and solve real world models using rational equations C.. 8 Solve sstems using matrices A Graph or write the equation of a conic section A Graph or write the equation of a conic section D..5.. Graph or write the equation of a conic section C..5.. Graph or write the equation of a conic section D..5 Classif a conic section B Classif a conic section B 5 Define, graph, or evaluate piecewise functions....5 D 6 Write a series in epanded form given summation notation.... B 7 Write a series in summation notation given the epanded form.... A 8 Determine the n th term of an arithmetic or geometric sequence or series.... B 9 Develop and solve real world models using sequences or series.... C 0 Find the sum of a convergent infinite geometric series..5.. D Determine the n th term of an arithmetic or geometric sequence or series.... D Determine the n th term of an arithmetic or geometric sequence or series.... A 0 0 Page of Revised: 09/9/0 Clark Count School District

22 ALGEBRA II HONORS SEMESTER EXAM ITEM SPECIFICATION SHEET & KEY Sllabus Objective NV State Standard # Objective Ke Determine a recursive formula for a given sequence..7.. C Calculate the number of was an event ma occur using the Fundamental Counting Principle B 5 Calculate the permutations or combinations of a set of n objects taken r at a time C 6 Epand a binomial epression B 7 Calculate the r th term of a binomial epression D 8 Find the theoretical and/or eperimental probabilit of a simple/compound event C 9 Distinguish among the various measures of tendenc and variabilit B 50 Organize data using statistical methods C 5 Find the domain and range of square root and cube root equations A 5 Find the domain and range of square root and cube root equations D 5 Find the domain and range of logarithmic and eponential equations C 5 Find the domain and range of logarithmic and eponential equations C 55 Evaluate and graph logistic growth functions Evaluate and graph logistic growth functions Find local minimum and local maimum values of functions. Find local minimum and local maimum values of functions. Use mathematical induction to prove statements about all positive integers. Use mathematical induction to prove statements about all positive integers B A B A.8.. C.8.. D 0 0 Page of Revised: 09/9/0 Clark Count School District