Algebra II. Released Test Questions. What is the complete solution to the equation. What is the solution to the system of equations shown below?

Transcription

1 LIFORNI STNRS TEST lgebra II What is the complete solution to the equation =? What is the solution to the system of equations shown below? = ; = = ; = = ; = = ; = ST0007 ( 0,, ) y+ z = 8 y z = 0 + y 9z = What are the possible values of in =? 0,, no solution =. 0or = < < 0. infinitely many solutions. > >. =. 0or= 0. ST000 For a wedding, Shereda bought several dozen roses and several dozen carnations. The roses cost $ per dozen, and the carnations cost $8 per dozen. Shereda bought a total of 7 dozen flowers and paid a total of $9. How many roses did she buy? dozen 7 dozen restaurant manager bought 0 packages of bagels. Some packages contained bagels each, and the rest contained bagels each. There were 8 bagels in all. How many packages of bagels did the manager buy? 8 9 ST008 8 dozen ST009 9 dozen ST00099 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

2 LIFORNI STNRS TEST lgebra II What system of inequalities best represents the graph shown below? 8 Which system of linear inequalities is represented by this graph? y y y> and y> + y> and y< y< and y> + y< and y< + ST0000 y + y 7 Which point lies in the solution set for the y system? y < y + y y + y (, ) (, ) ( 0, ) (, ) + y y ST0079 ST009 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

3 LIFORNI STNRS TEST lgebra II 9 What is the solution to the following system of equations? (, ) (, ) (, ) (, ) y = + y = ( + +) ( +)= ST00 ST0078 Which epression is equivalent to ( y )( y + )? ) y y y +y +y y +y y ST What is the volume of the figure below? ST0009 Which polynomial represents ( + )( )? ST ST08 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

4 LIFORNI STNRS TEST lgebra II What is ( )( )? ST09 9 Which epression shows the complete factorization of 7? ( 7)( + ) ( )( + 7) ( 7 )( + 7 ) ( 7)( + 7 ) ST07 8a + c = ( a+ c)( a+ c)( a+ c ) ( a c)( a + ac + c ) ( a c)( a + ac + c ) ( a+ c)( a ac + c ) 0 0y + y = ( y ) ( +0 y) ( y ( ) y ) ST008 ST008 7 The total area of a rectangle is 9 y. Which factors could represent the length times width? ( y)( + y) ( + y)( + y) ( y)( y) ( + y)( y ) ST = Which product of factors is equivalent to ( + ) y? ST009 ( + + y) ( + y) ( + y)( y) ( + + y)( + y) ST000 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

5 LIFORNI STNRS TEST lgebra II c a b Which is a simplified form of? (a b c ) + 9 i = + + a bc ab c bc + ab c + ST007 ST What is? 7 y y y 8 8y 7 y 8 What is the simplest form of y+ 0 y + 0 y? y ( + ) ( + y) + y + y ST009 8y 7 ST i = Which product is equivalent to? ( ) ( + ) ( ) ( + ) ST00 8 ( + )( ) + ( + )( + ) 8 ( + )( + ) ST007 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

6 LIFORNI STNRS TEST lgebra II 8 y y (+ y) y ( y) ( + y ) y ( + y ) y = y 0 0 If i =, what is the value of i? i i ST008 Which of the following comple numbers is represented by the point on the graph below? ST008 9 If i =, which point shows the location of i on the plane? Imaginary Real Imaginary i i i + i Real ST0 point point point point ST000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

7 LIFORNI STNRS TEST lgebra II If i =, then i( i) = 8 8 What is an equivalent form of? + i i ST00 If i = and a and b are non-zero real numbers, what is? a+ bi a+ b i a + b a bi a + b a+ b i a b a b i a b i i i ST000 What is the product of the comple numbers ( + i) and ( i)? i 0 i ST008 Which epression represents ( i) ( + i)? 8 i 8 i i i 7 What is the sum of the comple numbers ( i) and ( + i)? 9 i 9i + i 9 9 i ST07 ST00 ST00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

8 LIFORNI STNRS TEST lgebra II 8 What are the solutions to the equation + + = 0? 0 There are two numbers with the following properties. = 0; = = 0; = i = + i; = i = + ; = ST00 ) The second number is more than the first number. ) The product of the two numbers is 9 more than their sum. Which of the following represents possible values of these two numbers? 9 What are the solutions to the equation + =? = + ; =,,,, ST009 = + ; = = + ; = = + ; = ST0097 Jenny is solving the equation 8 = 9 by completing the square. What number should be added to both sides of the equation to complete the square? 8 ST0008 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

9 LIFORNI STNRS TEST lgebra II Two consecutive positive integers have the property that one integer times twice the other equals. What is the sum of these two integers? 7 9 What are the solutions to the equation + = 8? and i and i + i and i + i and i Which of the following most accurately describes the translation of the graph y = ( + ) to the graph of y = ( ) +? up and to the right down and to the right down and to the left up and to the left ST000 ST0 Which of the following sentences is true about the graphs of y = ( ) + and y = ( + ) +? Their vertices are maimums. The graphs have the same shape with different vertices. The graphs have different shapes with different vertices. One graph has a verte that is a maimum, while the other graph has a verte that is a minimum. What are the -intercepts of the graph of y =? and and and ST09 and ST0097 ST007 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

10 LIFORNI STNRS TEST lgebra II 7 Which is the graph of y = ( ) +? y y y y ST09 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

11 LIFORNI STNRS TEST lgebra II 8 Which ordered pair is the verte of f( ) = + +? (, ) (, ) (, 0) (, 0 ) 0 Which of the following represents a parabola? + y = r y + = a b p = y y = a b ST00 ST008 9 The graph of y = is a hyperbola. Which set of equations represents the asymptotes of the hyperbola s graph? y =, y = y =, y = y =, y = y =, y = y 0 y 9 = 0 What is the standard form of the equation of the conic given above? ( ) (y ) = (y + ) ( ) = (y ) ( + ) = 9 ( ) (y ) + = ST00 ST00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

12 LIFORNI STNRS TEST Which statement describes the graph of the equation + y + y = 0? a hyperbola with center (, ) and vertices (, ) and (, ) a hyperbola with center (, ) and vertices (, ) and (, ) a circle with center (, ) and radius 8 a circle with center (, ) and radius ST07 What is the solution to the equation = 7? lgebra II Which equation is equivalent to log =? 9 = 9 = 9 = 9 9 = ST0 = If log y =, which of the following is true? y = = log 0 y = = y = log log 0 = y ST00 log 7 = 0 log 0 If log 0 ST00 7 Which is the first incorrect step in simplifying log? = 0 = =, what is the value of? 0 = 00 Step : log = log log Step : = Step : = Step Step Step Each step is correct. =00 ST007 ST0 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

13 LIFORNI STNRS TEST lgebra II 8 Jeremy, Michael, Shanan, and renda each worked the same math problem at the chalkboard. Each student s work is shown below. Their teacher said that while two of them had the correct answer, only one of them had arrived at the correct conclusion using correct steps. Jeremy s work Shanan s work 7 7 = = 7 7 = 0, 0 =, 0 Michael s work renda s work 7 7 = = 7 7 =, 0 =, 0 Which is a completely correct solution? Jeremy s work Michael s work Shanan s work renda s work ST student showed the following steps in his solution of the equation below, but his answer was not correct. log ( + ) log ( ) + log = Step : log ( )( ) log ( ) + = Step : log ( )( ) log ( ) = Step : log ( ) = Step : = Step : = In which step did he make his first error? Step Step Step Step ST0 Which is the first incorrect step in simplifying ( ) ( )? Step : ( ) ( ) = Step : = Step : = Ste p : = Step Step Step Step ST009 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

14 LIFORNI STNRS TEST certain radioactive element decays over time according to the equation y = 00, where = the number of grams present initially and t = time in years. If 000 grams were present initially, how many grams will remain after 900 years? t lgebra II If the equation y = is graphed, which of the following values of would produce a point closest to the -ais? 00 grams 0 grams 8 grams ST0. grams ST007 acteria in a culture are growing eponentially with time, as shown in the table below. acteria Growth Which table below correctly describes points of the eponential function f( )=? 0 f() 8 ay acteria Which of the following equations epresses the number of bacteria, y, present at any time, t? y = 00 + t y =( 00) i ( ) t y = t t y =( 00) i () ST0 0 f() 0 8 f() 9 0 f() 7 ST09 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

15 LIFORNI STNRS TEST lgebra II In 997 the population of a small town was 700. If the annual rate of increase is about 0.8%, which value below epresses the population five years later? ( 700 )(0.008) (700)(.008) ( 700)(0.008) (700)(.008 ) 8 What is the value of log 7? 9 ST009 ST0 9 If log 0.0 and log 0.77, what is the approimate value of log 7? log 0 = log 0 + log log 0 log 0 0 ST0 (log 0 )(log 0 0 ) log 0 0 log 0 ST Jonathan wrote the equation log ( ) = 0 on the board. He needs one clue for problem solving. Which fact provides the correct information that he needs to solve the equation? 0 = = =0 = ST Which of the following is a simplified form of the epression log + log log? log 0 log 0 log 7 log 7 ST00 If is a real number, for what values of is the 9 equation = true? all values of some values of no values of impossible to determine ST000 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

16 LIFORNI STNRS TEST lgebra II 7 On a recent test, Jeremy wrote the equation = +. Which of the following statements is correct about the equation he wrote? The equation is always true. The equation is always true, ecept when =. The equation is never true. The equation is sometimes true when =. 7 Given the equation y = n where >0 and n <0, which statement is valid for real values of y? y > 0 y = 0 y < 0 y 0 ST00 ST00 7 If is a real number, which best describes the values of for which the inequality >0 is true? all > 0 all 0 all values of no values of Which of the following conclusions is true about the statement below? = The statement is always true. The statement is true when is negative. The statement is true when = 0. The statement is never true. ST0 If is a real number, for what values of is the equation log = true? all values of some values of no values of impossible to determine ST0000 belardo wants to create several different 7-character screen names. He wants to use arrangements of the first letters of his first name (abe), followed by arrangements of digits in 98, the year of his birth. How many different screen names can he create in this way? ST00 ST009 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

17 LIFORNI STNRS TEST lgebra II 78 train is made up of a locomotive, 7 different cars, and a caboose. If the locomotive must be first, and the caboose must be last, how many different ways can the train be ordered? 00 8,0,880 8, ST09 80 Teresa and Julia are among 0 students who have applied for a trip to Washington,.. Two students from the group will be selected at random for the trip. What is the probability that Teresa and Julia will be the students selected? 79 There are candidates in a city election. The winner will be the mayor, and the runner-up will be the vice-mayor. How many different combinations of mayor and vice-mayor are possible? ST0007 ST009 8 ( y ) = 8y 08y + y y + 8y +08y y y + 8y y 08y y + 8y + y 08y y + ST How many terms does the binomial epansion 0 of ( + y ) contain? ST0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

18 LIFORNI STNRS TEST 8 What are the first terms in the epansion of ( + )? What is ( + y ) in epanded form? + y + y + y + y + y + y + y + y + y +0 y + y + y ST00 + y +0 y +0 y + y + y ST What is the sum of the infinite geometric series ? 8 ST What is the nth term in the arithmetic series below? n + n n + n Which epression represents f( g( )) if f( )= and g( )= +? lgebra II ST078 ST00 Given that f( ) = and g( ) =, what is g( f( ))? 8 0 ST009 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

19 LIFORNI STNRS TEST lgebra II 89 If f ( )= + + and g( )= ( + ), which is an equivalent form of f( )+ g( )? One bag contains green marbles and white marbles, and a second bag contains green marbles and white marble. If Trent randomly draws one marble from each bag, what is the probability that they are both green? ST00 90 math teacher is randomly distributing rulers with centimeter labels and 0 rulers without centimeter labels. What is the probability that the first ruler she hands out will have centimeter labels and the second ruler will not have labels? ST08 ST0 9 bo contains 7 large red marbles, large yellow marbles, small red marbles, and small yellow marbles. If a marble is drawn at random, what is the probability that it is yellow, given that it is one of the large marbles? On a certain day the chance of rain is 80% in San Francisco and 0%in Sydney. ssume that the chance of rain in the two cities is independent. What is the probability that it will not rain in either city? 8 SN00 7% % % 0% ST080 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

20 LIFORNI STNRS TEST lgebra II 9 The probabilities that Jamie will try out for various sports and team positions are shown in the chart below. Jamie Try out for basketball team Try out for baseball team Try out for guard 80% Try out for forward 0% Try out for catcher 70% Try out for pitcher 0% Jamie will definitely try out for either basketball or baseball, but not both. The probability that Jamie will try out for baseball and try out for catcher is %. What is the probability that Jamie will try out for basketball? 0% 0% 80% 90% ST00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.

21 LIFORNI STNRS TEST lgebra II 9 small-business owner must hire seasonal workers as the need arises. The following list shows the number of employees hired monthly for a -month period.,,,, 9 If the mean of these data is approimately 7, what is the population standard deviation for these data? (Round the answer to the nearest tenth.) ,,,, 7, James found the mean and standard deviation of the set of numbers given above. If he adds to each number, which of the following will result? The mean will be multiplied by. The standard deviation will increase by. The mean will not change. The standard deviation will not change. SN007 ST00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 009 alifornia epartment of Education.