ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY

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1 ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Constructed Response # Objective Sllabus Objective NV State Standard 1 Graph a polnomial function Analze graphs of polnomial functions to determine characteristics Graph quadratic functions. Identif the domain and range of linear, quadratic, or polnomial functions. Develop a mathematical model to solve real world problems. Organize data using matrices. Simplif matri epressions. Multiple Choice # Objective Sllabus Objective NV State Standard Practice Ke A/B 1 Differentiate among subsets of real number sstems C / Evaluate algebraic epressions A / 3 Simplif algebraic epressions D / 4 Solve linear equations C / 5 Solve for a given variable in a given equation with more than one variable D / Solve for a given variable in a given equation with more than one variable B / 7 Solve an absolute value equation or inequalit C / 8 Solve a compound inequalit A / 9 Applications of linear models B / 10 Differentiate between a relation and a function C / 11 Identif the domain and range of functions A / 1 Write the equation of a line C / 13 Write the equation of a line D / 14 Calculate the slope of a line D / 15 Recognize slope as a rate of change of one variable in terms of another C / 1 Use slopes to classif lines as parallel, perpendicular, or neither A / 17 Graph linear and absolute value equations and inequalities D / 18 Solve application problems using linear models and appling direct variation.1.1. A / 19 Define, graph, or evaluate piecewise functions B / 0 Solve sstem of equations D / 1 Solve sstem of equations C / Solve sstem of equations B / 3 Graph solution set of a sstem of inequalities A / 4 Solve application problems involving sstems of equations or inequalities B / 5 Solve application problems using linear programming C / Organize data using matrices B / Final Ke Page 1 of 3 Revised: 8/18/08 Clark Count School District

2 ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Multiple Choice # Objective Sllabus Objective NV State Standard Practice Ke A / B 7 Simplif matri epressions A /.1. 8 Simplif matri epressions B / Find the determinant of a matri C / Solve sstems using matrices D / Graph quadratic functions D / Solve quadratic equations C / Solve quadratic equations D / Solve quadratic equations C / Solve quadratic equations D / Analze the nature of the roots of a quadratic equation B / Solve quadratic equation with comple solutions A / 38 Perform operations with comple numbers B / Graph and solve quadratic inequalities D / Develop models involving quadratic equations to solve realworld problems B / 41 Graph a polnomial function D / 4 Graph a polnomial function A / 43 Simplif polnomial epressions B / Solve polnomial equations b factoring and graphing C / Solve polnomial equations b factoring and graphing C / Find rational zeros of a polnomial A / Final Ke Page of 3 Revised: 8/18/08 Clark Count School District

3 ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Multiple Choice # Objective Sllabus Objective 47 Use the Fundamental Theorem of Algebra to determine the number of zeros. NV State Standard Practice Ke A / B D / 48 Divide polnomials A / 49 Analze graphs of polnomial functions to determine characteristics B / 50 Analze graphs of polnomial functions to determine characteristics B / Final Ke Page 3 of 3 Revised: 8/18/08 Clark Count School District

4 1. To which sets of numbers does 5 belong? I. integers II. natural numbers III. rational numbers IV. real numbers V. whole numbers II and IV onl III and IV onl I, III, and IV onl III, IV, and V onl. Evaluate b c = ac for a = 3, b = 1, and 3. Which is a simplified form of the epression 1( 1) ( 18)? What is the value of n if 9 n + = 5? n = 4 39 n = n = n = Below is the formula for the surface area of a right circular clinder. A = π rh + π r Which is a correct formula for the height, h, epressed in terms of radius, r, and surface area, A? π r A h = π r A h = π r π r h= A π r π r A h= r π r. Which represents in terms of for the equation 3 + = 5 +? = + = = 8 = GO ON

5 7. Rewrite the absolute value inequalit as a compound inequalit: + > < < 1 > 13 or < 1 < 13 or > 1 no solution 8. Which epresses all of the solutions for the compound inequalit below? ( z + 4) and z 3 z 8 z = 3 and z = 8 z 3 and z 8 no solution 9. In 000 the average price of a home in West Count was $95,000. B 007 the average price of a home was $13,000. Which of the following is a linear model for the price of a home, P, in West Count in terms of the ear, t? Let t = 0 correspond to 000. P= 13,000 4,000t P= 95, ,000t P= 13,000 8,000t P= 8, ,000t 10. Which relation is a function? = = {( 1, ), (3, ), ( 5, )} {(, 5), (, ), (, 1)} 11. What is the range of the following relation? {(,0),(1, 3),(5, )}? { 3,, 0} {, 1, 5} {0,, 3} { 5, 1, } 1. Write the standard form of the equation of the line that passes through the point (,) and is parallel to the line 5+ = 1. 5 = 8 5 = 1 5+ = 5+ = GO ON

6 13. Which equation describes the pattern in the table? = 3 4 = 3+ 4 = 4 3 = Use the graph below. 15. William is hiking in the hills. He began the hike at 10:00 a.m. at an elevation of,000 ft. He reached a peak of 4,000 ft. at :00 p.m. What is the average rate of change in Bill s elevation? 00 ft. per hour 50 ft. per hour 500 ft. per hour 1000 ft. per hour 1. Write an equation in standard form that is perpendicular to = 5 and goes through ( 10,3). + 5 = 5 5 = 5 5 = = 4 What is the slope of the line? GO ON

7 17. Graph the linear equation 9 7 = Joe s pa (P) varies directl with the square of the number of widgets (w) he produces. When he produces widgets, he is paid $1. How man widgets would he have to produce to make $144? Evaluate f ( 3) for the piecewise function f( ) = f ( 3) = 18 f ( 3) = 3 f ( 3) = 0 f ( 3) = 18, 0. 3, > 0 0. Solve the following linear sstem. (0, 4) (, 8) 5 = 8 5 = + 3 infinitel man solutions no solution GO ON

8 1. Find the -coordinate of the solution to the linear sstem. 3 4 = 1 + = no solution 3. Graph the sstem of inequalities What is the -coordinate of the solution to the following sstem of equations? z = 5 + 3z = z = GO ON

9 4. For one month of internet access, Southern Nevada Web charges $4.00 per hour with a base fee of $0.00. Silver State Internet does not charge a base fee, but charges $.00 per hour for internet access. How man hours of use will the costs for the two companies be the same? hours 10 hours 1 hours 4 hours 5. Using linear programming procedures, the equation C = 4+ 7 is to be maimized subject to the following constraints: The grid ma be used to sketch the feasible region What is the minimum value for the objective function? GO ON

10 . A school fundraiser sells different sizes of gift baskets with a varing assortment of books and pencils. A basic basket contains 3 books and 4 pencils. A big basket contains 7 books and 8 pencils. Books cost $5, and pencils cost $. Which of the following shows the use of matrices to find the total cost for each size of basket? = = = = 3 7. Which is the sum A + B, given that 9 3 A = and B = 4 3 7? Given A 0 1 = and find the product A not possible 9. Calculate the determinant Solve for and : ( 8,1) 3, , 3 4 ( 5,3 ) 1 4 B = 0 1, = GO ON

11 31. Which graph from a graphing calculator represents the function = 4( )? (Assume the scale on each graph is one unit per tick mark.) 3. Solve the equation factoring. = ± 9 = 9 = 9 no solution = 0 b 33. Which is the solution set for = 0, using the quadratic formula? , , , , Which are solutions for + 40= 0 when solved b completing the square? = 10 or = 4 = 10 or = 4 = 10 or = 4 = 10 or = GO ON

12 35. Which is the solution set of ( + 4) = 77? , , , , 38. Write the epression i 3+ 9i number in standard form i i i i as a comple 3. Use the discriminant to determine the number and tpes of solutions of the equation = 0. no real solutions, imaginar solutions 1 real solution, no imaginar solutions 1 real solution, 1 imaginar solution real solutions 37. What are the solutions of the quadratic equation = 4? 5+ i 3 =, 5+ i 73 =, = = 5 i 3 5 i i 3 =, 5+ i 73 =, = = 5 i 3 5 i GO ON

13 39. Which of the following screens from a graphing calculator represents 4? (Assume the scale on each graph is one unit per tick mark.) 40. For the scenario below, use the model h= 1t + v0t+ h0, where h = height (in feet), h 0 = initial height (in feet), v 0 = initial velocit (in feet per second), and t = time (in seconds). A cheerleading squad performs a stunt called a basket toss where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is thrown upward leaving her teammates hands feet above the ground with an initial vertical velocit of 15 feet per second. When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air? 1 1 second 1 second seconds seconds GO ON

14 41. Which graph represents the factored function f ( ) = ( 3)( + )? (Assume the scale on each graph is one unit per tick mark.) 4. Graph the polnomial function: 4 f( ) = GO ON

15 43. Multipl the following polnomials. ( + 4)( + + 4) 4. Which of the following represents the solution set of the polnomial equation below? Factor the polnomial completel. + + ( 1)( 1)( 9) ( 8) ( 3)( 3)( 1) ( + 1) ( 3)( + 3) f 3 ( ) = ,, 1 1,, { 0, 1, } 1,, 47. According to the Fundamental Theorem of Algebra, how man solutions does the 3 5 polnomial f ( ) = have? 45. Factor the polnomial equation ( + 3) ( )( + ) ( + 3)( 4 + 9) ( 3)( ) What is 3 divided b 5? GO ON

16 49. State the end behavior of the graph of f = as. ( ) 3 f( ) f( ) + f( ) 4 f( ) Which best represents the polnomial 4 3 function = 5? (Assume the scale on each graph is one unit per tick mark.)

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18 Free Response 1. Let p( ) ( 3) ( 1) = +. Sketch the graph of p( ). Label all intercepts. Find another polnomial function, q( ), that has the same zeros as ( ) point ( 1,1). p and goes through the Eplain how to determine the end behaviors of a polnomial function GO ON

19 Free Response. Let ( ) f = Find the verte and the ais of smmetr. ( 0, 15) is a point on f ( ) parabola to find another point on = f ( ). =. Eplain how ou can use the smmetric properties of a Sketch the graph of = f ( ). Include and label at least 5 points on our graph including the verte and intercepts. Find the domain and range of f ( ) GO ON

20 Free Response 3. A baker chain displas prices in a 1 3matri and dail sales at its three stores in a 3 3 matri as shown below: Prices Cupcakes Cookies Cakes [ $ $1 $10 ] Number of Items Sold Store A Store B Store C Cupcakes Cookies Cakes 4 1 Find the product of the two matrices. Eplain what the product represents. How would ou find the total gross revenue from all three stores?