ALGEBRA II SEMESTER EXAMS PRACTICE MATERIALS SEMESTER (1.2-1) What is the inverse of f ( x) 2x 9? (A) (B) x x (C) (D) 2. (1.

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1 04-05 SEMESTER EXAMS. (.-) What is the inverse of f ( ) 9? f f f f ( ) 9 ( ) 9 9 ( ) ( ) 9. (.-) If 4 f ( ) 8, what is f ( )? f( ) ( 8) 4 f ( ) f( ) 6 4 f( ) ( 8). (.4-) Which statement must be true if f and g are inverses of one another? ( f g)( ) ( g f)( ) ( f g)( ) f( ) g( ) ( g f)( ) g( ) f( ) ( f g)( ) f( g( )) ( g f)( ) g( f( )) ( f g)( ) ( g f)( ) Page of Revised October 04

2 04-05 SEMESTER EXAMS 4. (.4-) Simplify( 4i) (5 6i). 8 0i 9 8i 8 0i 6 0i 5. (.4-) Simplify( i) ( 7i). 4 0i 4 4i 8 6i 4i 6. (.6-) (.) Solve the quadratic equation by taking the square root i Page of Revised October 04

3 04-05 SEMESTER EXAMS 7. (.7-) A student has learned that test scores in math are determined by this quadratic function: st () ( t 6) 99 In the function, s is the score and t is the number of hours that a student spends on homework each week. a) How many hours must a student spend on homework to achieve maimum score? b) What is the maimum score? c) Based on the function, what will be the score if a student does no homework? 8. (.7-) Show that ( i) is a root of (.7-) Solve 5 0 over the set of comple numbers. 5i 5 5i 5 0. (.7-4) Function A and Function B are continuous quadratic functions. Function A f( ) 6 Function B y Which function has a greater positive -intercept? -7 Function A Function B Page of Revised October 04

4 04-05 SEMESTER EXAMS. (.7-5) What is the equation of the parabola shown? y y 4 y y y 4. (.7-6) Factor 9. ( )( ) ( )( ) ( i)( i) ( i)( i). (.7-7) Solve the equation by factoring. 7 or 7 or Page 4 of Revised October 04

5 04-05 SEMESTER EXAMS 4. (.7-8) What is the solution set of y y y 4? y 7 y or y 7 7 y y 7 5. (.7-9) Which of the following is a factor of( a ) b? a b a b a a b 6. (.8-) Which of the following quadratic equation has no real roots? (.8-) Find the verte of y and state if it is a maimum or a minimum. (-, -4); maimum (-, -4); minimum (-4, -); maimum (-4, -); minimum Page 5 of Revised October 04

6 04-05 SEMESTER EXAMS 8. (.8-) Consider the function f( ) 48. a) Determine the roots of the function. Show your work. b) The verte of g is the point (, 0). Write the function rule for g in verte form. c) Eplain how f transformed to become g. 9. (.8-4) For what values of c will c 0 have eactly one distinct real root? 0. (.9-) Solve the equation by using the quadratic formula. 5 0 or 6 or or. (.9-) Given the general form of a quadratic equation b c 0, determine the effect of each condition on the solutions. a) b 0 b) c 0 c) c 0 d) What is needed for the solutions to have imaginary parts? Page 6 of Revised October 04

7 04-05 SEMESTER EXAMS. (.-) Use the graph provided to choose the best description of what the graph represents. Height (ft) Time (s) A ball I dropped from a height of 4 feet and lands on the ground after seconds. A ball is dropped from a height of 4 feet and lands on the ground after.5 seconds. A ball is shot up in the air and reaches a height of 4 feet after second. A ball is shot up in the air, reaches a height of 4 feet, and lands on the ground after.5 seconds.. (.4-) The height of Carl, the human cannonball, is given by ht ( ) 6t 56t 40 where h is in feet and t is in seconds after the launch. a) What was his height at the launch? b) What is his maimum height? c) How long before he lands in the safety net, 8 feet above the ground? Page 7 of Revised October 04

8 04-05 SEMESTER EXAMS 4. (.4-) Several values of the quadratic function f ( ) are given in the table. f( ) The function gis ( ) given by g ( ) ( ). Which function has the greater maimum for which value of? f( ); for 0 f( ); for 6 g ( ); for g ( ); for 5. (.4-) Which statement best describes these two functions? f 4 g 7 The maimum of f ( ) is less than the minimum of g. ( ) The minimum of f ( ) is less than the maimum of g. ( ) The maimum of f ( ) is greater than the minimum of g. ( ) The minimum of f ( ) is greater than the maimum of g. ( ) Page 8 of Revised October 04

9 04-05 SEMESTER EXAMS 6. (.4-4) The amount of fuel F (in billions of gallons) used by trucks from 990 through 009 can be approimated by the function F f( t) t where t 0 represents 990. a) Describe the transformation of the common function f () t t. Then sketch the graph over the interval 0 t 9. f (9) f (0) b) Find and interpret. 9 0 c) Rewrite the function so that t 0 represents 000. Eplain how you got your answer. d) Use the model from part (c) to predict the amount of fuel used by trucks in 05. Does your answer seem reasonable? Eplain. 7. (4.-) What is the 4 th term of the epanded binomial ( )? (4.-) Suppose y and ( y). What is y? Page 9 of Revised October 04

10 04-05 SEMESTER EXAMS 9. (4.-) The table lists all the real roots of a 5 th degree polynomial p( ) and the multiplicity of each root. Multiplicity Which general factorization correctly represents p( )? a ( )( ) ( ) a ( )( ) ( ) a ( )( )( ) ( ) a ( )( ) ( ) 0. (4.-) A 4 th degree polynomial with real coefficients is found to have eactly two distinct real roots. What must be true about the other two roots? One root is real and the other is imaginary. Both roots must be real. Both roots are imaginary roots that are comple conjugates. All the roots have been found.. (4.4-) Divide 4 ( 7) ( ) using long division Page 0 of Revised October

11 04-05 SEMESTER EXAMS. (4.4-) The volume V( ) and height ( h ) of the prism is given. Find a polynomial epression for the area of the base ( B ) in terms of. (Hint: V Bh) h V( ) 5 4. (4.4-) Write an epression that represents the width of a rectangle with length 5 and area Page of Revised October 04

12 04-05 SEMESTER EXAMS 4. (4.6-) Use the graph of p( ) to answer questions a) True or False: The leading term of p( ), when written in standard form, is positive. b) True or False: From the graph, p( ) 0. The multiplicity of the factor ( ) is even. Eplain your answer Page of Revised October 04

13 04-05 SEMESTER EXAMS 5. (4.6 ) Which graph represents 5 f ( ) 6 9? Page of Revised October 04

14 04-05 SEMESTER EXAMS 6. (4.7-) Use the information in the table. a) What are the three real zeros of the polynomial function f? b) What can be said about the behavior of the graph of f at 0? c) What is the least possible degree of f? Eplain. Can the degree of f ever be even? Eplain. 7. (4.8-) According to the Fundamental Theorem of Algebra, how many roots does the following equation have? Interval Value of f() (, ) Negative (,) Positive (,4) Negative (4, ) Positive Page 4 of Revised October 04

15 04-05 SEMESTER EXAMS 8. (4.9-) Consider the graph of p( ) below. Which general factorization correctly represents p( ). Which general factorization correctly represents p( )? a ( )( )( 4) a ( )( )( 4) a ( )( )( 4) a ( )( )( 4) 9. (4.9-) The graph of p( ) is shown below. Which general factorization correctly represents p( )? 4( )( )( 4) 6( )( )( 4) ( )( )( 4) 4 4( )( )( 4) Page 5 of Revised October 04

16 04-05 SEMESTER EXAMS 40. (4.9-) If 4 f( ) 7 8 4, find the possible rational roots of f ( )., 4, 4,,,,, 4 4. (4.9-4) Given polynomial q, ( ) q(4) 6. Which statement is correct? 4 is not a root 4 is a root ( 4) is a factor ( 4) is not a factor 4. (4.9-5) 5 4 p( ) a) Show that p( ) is a root. b) Factor p( ) completely c) If f( ) p( ), what are the real roots of f ( )? 4 4. (4.9-6) Given the polynomial p ( ) 6: a) Show that p( i) is a root. b) What other root must also be a root of p( )? Eplain. c) Factor p( ) completely Page 6 of Revised October 04

17 04-05 SEMESTER EXAMS 44. (4.9-7) Write a cubic function that passes through the following points: (-, 0) (, 0) (-, 0) and (, ). y 7 6 y y y (4.9-8) How many possible rational zeros eist for the polynomial function 6 y 9 4? (4.9-9) This polynomial function has at least one rational root. 4 p ( ) k 9 a) What are all the possible integer values of k? Show your work or eplain how you know. b) What are all the possible real roots of the function? Show your work or eplain how you know (4.-) Consider p( ) 5 5. a) Show that 5 and 5 are zeros of p( ). b) Completely factor p( ) where all the coefficients are rational numbers. c) h ( ) is p( ) translated 4 units right and units up. What is the equation of h ( )? Page 7 of Revised October 04

18 04-05 SEMESTER EXAMS (4.-) Consider p( ) a) Show that 6 are roots of p( ), then write p( ) as the appropriate factorizations at this point. b) Factor p( ) completely. c) Let q ( ) p(4 ). List out the roots of q. ( ) d) Let f ( ) be p( ) vertically stretched by, translated units to the right and 4 units up. Write out the algebraic relationship between f ( ) and p( ). 49. (4.-) Consider the function f ( ) 9 9. a) Use the leading coefficient and degree of f ( ) to describe the end behavior. b) Write the rule for the function g ( ) f( ), and describe the transformation. c) Describe the end behavior of g. ( ) How does the end behavior of grelate ( ) to the transformation of f ( )? 50. (4.-) The town of Frostburg eperienced a bit of a heat wave during January of this year. The graph to the right shows the curve of best fit that represents the low temperature of every day in January. A newspaper journalist is writing a story on the weather and needs to report some information. He needs a bit of guidance with interpreting the graph. ) Write a few sentences describing the key characteristics of the graphs as it relates to the contet of the problem. Be sure to include domain, range, intervals where the function increases and decreases, and y intercepts, and any other important information Page 8 of Revised October 04

19 04-05 SEMESTER EXAMS The graph below shows the curve of best fit that represents the low temperature of every day in February. ) Three different models have been proposed that could be used to determine the temperature for a particular date in February. The models are given below: Model : y a b c Model : y a( )( 9)( 0) Model : y a( )( 9)( 0) Which model would best describe the low temperatures for February? Eplain why you chose that model. The weather in July showed a related pattern to the weather in February. The curve of best fit for July is shown below: ) Eplain the relationship between the graph for February and the graph for July. Use that relationship to create an equation for the temperatures in July Page 9 of Revised October 04

20 04-05 SEMESTER EXAMS 5. (5.-) If f () and g(), which epression represents f () g() for? 5. (5.-) Identify the and y intercepts of the function f( ) 8. (8,0) and (0,-) (,0) and (0,) (8,0) and (0,8) (-,0) and (0,8) 5. (5.-) Which is the domain of the function f( ) 5 4? { 4} { } { 0} { } 54. (5.4-) Compare the graph of f ( ). y 6 with the graph of its parent function Shifts 6 units down Reflects across the -ais and shifts 6 units down Reflects across the -ais and shifts 6 units up Reflects across the y-ais and shifts 6 units up Page 0 of Revised October 04

21 04-05 SEMESTER EXAMS 55. (5.5-) Which value of makes this equation true? 4 9( 7) (5.5-) Solve for : No real solution 57. (5.5-) Solve for. 7 5 and No real solutions 58. (5.5-4) Solve for No real solutions Page of Revised October 04

22 04-05 SEMESTER EXAMS 59. (5.5-5) If 8 4, what is the value of -8 7? 60. (5.6-) Which is the inverse of f( ) ( ) 4? a ( ) 4 4 b ( ) a ( ) 4 a ( ) Page of Revised October 04

1. A student has learned that test scores in math are determined by this quadratic function:

01 014 SEMESTER EXAMS 1. A student has learned that test scores in math are determined by this quadratic function: s( t) ( t 6) 99 In the function, s is the score and t is the number of hours that a student