APPLIED ALGEBRA II SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY Constructed Response # Objective Sllabus Objective NV State Standard 1 Graph a polnomial function. 1.1.7.1 Analze graphs of polnomial functions to determine.1.4.8 characteristics 4.1.9 3 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. 1.1 1.1.8 C / Evaluate algebraic epressions. 1..1.3 A / 3 Simplif algebraic epressions. 1..1.3 D / 4 Solve linear equations. 1.4.1. C / 5 Solve for a given variable in a given equation with more than one variable. 1.5.1.4 D / Solve for a given variable in a given equation with more than one variable. 1.5.1.4 B / 7 Solve an absolute value equation or inequalit. 1..1. C / 8 Solve a compound inequalit. 1..1. A / 9 Applications of linear models. 1.7.1. B / 10 Differentiate between a relation and a function..1.1.4 C / 11 Identif the domain and range of functions...1.4 A / 1 Write the equation of a line..5 4.1.5 C / 13 Write the equation of a line..5 4.1.5 D / 14 Calculate the slope of a line.. 4.1.5 D / 15 Recognize slope as a rate of change of one variable in terms of another..7 4.1.5 C / 1 Use slopes to classif lines as parallel, perpendicular, or neither..8 4.1.5 A / 17 Graph linear and absolute value equations and inequalities..10 4.1.5 D / 18 Solve application problems using linear models and appling direct variation.1.1. A / 19 Define, graph, or evaluate piecewise functions..13 4.1.5 B / 0 Solve sstem of equations. 3.1.1.5 4.1.5 D / 1 Solve sstem of equations. 3.1.1.5 4.1.5 C / Solve sstem of equations. 3.1.1.5 4.1.5 B / 3 Graph solution set of a sstem of inequalities. 3. 4.1.5 A / 4 Solve application problems involving sstems of equations or inequalities. 3.3.1. B / 5 Solve application problems using linear programming. 3.4 5.1.1 C / Organize data using matrices. 4.1 1.1.7 B /. 5.1 1.7 4.1 4..1.3.1.4 1.1.7.1. Final Ke 008 009 Page 1 of 3 Revised: 8/18/08 Clark Count School District
APPLIED 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. 4. 1.1.7 A /.1. 8 Simplif matri epressions. 4..1.5 B / 4.1.5 9 Find the determinant of a matri. 4.3.1. C /.1. 30 Solve sstems using matrices. 4.5.1.5 D / 4.1.5 31 Graph quadratic functions. 5.1.1.3.1.4 D / 1.1. 3 Solve quadratic equations. 5. 1.1.7 C /.1.3 1.1. 33 Solve quadratic equations. 5. 1.1.7 D /.1.3 1.1. 34 Solve quadratic equations. 5. 1.1.7 C /.1.3 1.1. 35 Solve quadratic equations. 5. 1.1.7 D /.1.3 1.1. 3 Analze the nature of the roots of a quadratic equation. 5.3 1.1.7 B /.1.4 37 Solve quadratic equation with comple solutions. 5.4 1.1.7 A / 38 Perform operations with comple numbers. 5.5.1.3.1.4 B / 1.1. 39 Graph and solve quadratic inequalities. 5. 1.1.7.1.3 D / 4.1.5 1.1. 40 Solve quadratic equations. 5. 1.1.7 B /.1.3 41 Graph a polnomial function..1.1.4 D / 4 Graph a polnomial function..1.1.4 A / 43 Simplif polnomial epressions.. 1.1.7.1.4 B / 1.1.7 44 Solve polnomial equations b factoring and graphing..3.1.3 C /.1.4 1.1.7 45 Solve polnomial equations b factoring and graphing..3.1.3 C /.1.4 4 Find rational zeros of a polnomial..4.1.3.1.4 A / Final Ke 008 009 Page of 3 Revised: 8/18/08 Clark Count School District
APPLIED 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.5 1.1.7 D / 48 Divide polnomials.. 1.1.7 A / 49 Analze graphs of polnomial functions to determine 1.1.7.8 characteristics. 4.1.9 B / 50 Analze graphs of polnomial functions to determine 1.1.7.8 characteristics. 4.1.9 B / Final Ke 008 009 Page 3 of 3 Revised: 8/18/08 Clark Count School District
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 =. 3 17 17 5 4ac for a = 3, b = 1, and 3. Which is a simplified form of the epression 1( 1) ( 18)? 3 1 4 8 4 + 8 4. What is the value of n if 9 n + = 5? 7 3 14 7 n = 4 39 n = 98 13 n = 54 43 n = 54 5. 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 = 8+ 008 009 1 GO ON
7. Rewrite the absolute value inequalit as a compound inequalit: + > 7. 13 < < 1 > 13 or < 1 < 13 or > 1 no solution 8. Which epresses all of the solutions for the compound inequalit below? ( z + 4) and 15 9 + 3z 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= 95,000 + 4,000t P= 13,000 8,000t P= 8,000 + 95,000t 10. Which relation is a function? = + 4 + = 3 5 1 {( 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+ = 1 008 009 GO ON
13. Which equation describes the pattern in the table? 1 3 4 5 7 11 15 19 3 = 3 4 = 3+ 4 = 4 3 = 4 + 3 14. 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 = 5 + 5 = 4 What is the slope of the line? 5 1 1 5 5 1 1 5 008 009 3 GO ON
17. Graph the linear equation 9 7 = 3. 18. 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? 8 1 3 19. 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 008 009 4 GO ON
1. Find the -coordinate of the solution to the linear sstem. 3 4 = 1 + = 5 5 3 no solution 3. Graph the sstem of inequalities. + 1 + 3 10 10 10. What is the -coordinate of the solution to the following sstem of equations? 14 5 1 + z = 5 + 3z = 14 3 + z = 10 10 10 10 10 10 10 10 10 10 10 10 10 008 009 5 GO ON
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: 0 0 + 3+ 4 8 5 10 The grid ma be used to sketch the feasible region. 51 14 8 0 What is the minimum value for the objective function? 008 009 GO ON
. 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 4 7 8 = 5 54 3 4 5 3 7 8 = 51 3 7 41 4 8 = 5 48 3 7 5 9 4 8 = 3 7. Which is the sum A + B, given that 9 3 A = 1 5 8 and 5 4 0 B = 4 3 7? 14 3 3 1 14 3 3 1 4 3 3 8 1 14 3 5 8 15 8. Given A 0 1 = 5 1 0 and find the product A 0 8 5 1 5 1 5 19 7 3 1 not possible 9. Calculate the determinant 50 30 0 30. Solve for and : ( 8,1) 3, 3 11 5, 3 4 ( 5,3 ) 1 4 B = 0 1, 5 1 3 0 4 1 3. 0 5 5 11 = 3 7 5 008 009 7 GO ON
31. Which graph from a graphing calculator represents the function = 4( + 8+ 15)? (Assume the scale on each graph is one unit per tick mark.) 3. Solve the equation factoring. = ± 9 = 9 = 9 no solution 18+ 81 = 0 b 33. Which is the solution set for + 7+ 1= 0, using the quadratic formula? 7+ 41 7 41, 4 4 7+ 57 7 57, 4 4 7+ 57 7 57, 4 4 7+ 41 7 41, 4 4 34. Which are solutions for + 40= 0 when solved b completing the square? = 10 or = 4 = 10 or = 4 = 10 or = 4 = 10 or = 4 008 009 8 GO ON
35. Which is the solution set of ( + 4) = 77? 4 77 4+ 77, 1 1 4 77 4+ 77, 4 77 4+ 77, 1 1 4 77 4+ 77, 38. Write the epression 7 + 3 i 3+ 9i number in standard form. 1 3 1 4 i 8 3 15 5 i 8 4 15 + 5 i 1 1 + i as a comple 3. Use the discriminant to determine the number and tpes of solutions of the equation 9 30+ 5= 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 3 + 5 = 4? 5+ i 3 =, 5+ i 73 =, = = 5 i 3 5 i 73 5+ i 3 =, 5+ i 73 =, = = 5 i 3 5 i 73 008 009 9 GO ON
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. In the model h= 1t + v0t+ h0, h = height (in feet), h 0 = initial height (in feet), v 0 = initial velocit (in feet per second), and t = time (in seconds). If v 0 = 15 feet per second and h 0 = feet, what is the value of t (in seconds) when h = 5 feet? 1 1 second 1 second 9 1 1 seconds seconds 008 009 10 GO ON
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( ) = + 1. 008 009 11 GO ON
43. Multipl the following polnomials. ( + 4)( + + 4) 4. Which of the following represents the solution set of the polnomial equation below? 3 + + 1 3 + 5 + 8 + 1 3 + 3 + 8 + 1 3 + 5 + 1 44. Factor the polnomial completel. + + ( 1)( 1)( 9) ( 8) 9 + + ( 3)( 3)( 1) ( + 1) ( 3)( + 3) 8 9 4 f 3 ( ) = 4 8 + 1 1,, 1 1,, { 0, 1, } 1,, 47. According to the Fundamental Theorem of Algebra, how man solutions does the 3 5 polnomial f ( ) = 10 + 3+ 4 have? 45. Factor the polnomial equation ( + 3) 3 3 3 ( )( + ) ( + 3)( 4 + 9) ( 3)( 4 + + 9) 3 8 + 7 3 4 5 48. What is 3 divided b 5? 3 44 + + 10+ 5 0 8+ 40 5 4 8 5 + + 5 4 008 009 1 GO ON
49. State the end behavior of the graph of f = + 7+ 4 as. ( ) 3 f( ) f( ) + f( ) 4 f( ) 0 50. Which best represents the polnomial 4 3 function = 5? (Assume the scale on each graph is one unit per tick mark.) 008 009 13
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. 008 009 14 GO ON
Free Response. Let ( ) f = + 15. 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 ( ). 008 009 15 GO ON
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 1 10 0 Cookies 5 40 80 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? 008 009 1