( ) A company found that its monthly profit, P, is given by 1. ( ) ( )

Transcription

1 If f = and g =, what. ( ) ( ) is f g( )? B ( ) car insurance company has a special plan for safe drivers. For each year that a driver has no tickets or violations, the premium is reduced by 0%, and a credit of $5.00 is awarded. Which equation shows the amount a driver with no tickets or violations owes in the ( n + ) th year as a function of the amount owed in the nth year? f( n ) f( n) f( n) + = B f( n ) f( n) f( n) + = f( n ) f( n) f( n) + = f( n ) f( n) f( n) + = company found that its monthly profit, P, is given by P = where is the selling price for each unit of product. Which of the following is the best estimate of the maimum price per unit that the company can charge without losing money? $300 B $0 $ $6 If 3 + i is a solution for + m + n = 0, where m and n are real numbers, what is the value of m? 3 B Page Published November 006. May reproduce for instructional and

2 5. James purchased a truck for $5,900. The value of the truck decreases by % per year. What will the approimate value be 8 years after the purchase? $3,00 B $7,00 $9,300 $, The Wongs bought a new house three years ago for $9,000. The house is now worth $3,000. ssuming a steady annual percentage growth rate, approimately what was the yearly rate of appreciation? 7.% B 8.6%.8% 7. The equation c = 53,430(.93) t models the pounds of U.S. copper produced from 987 to 99. Which statement best interprets the coefficient and base of this equation? The copper production in 987 was 53,430 pounds, and it increased at a rate of.93% per year during that period. B The copper production in 987 was 53,430 pounds, and it increased at a rate of 9.3% per year during that period. The copper production increased by a factor of 53, pounds per year during that period. The copper production at the beginning of 987 was at.93 pounds, and it increased by a factor of 53,430 pounds per year during that period. 6% Page Published November 006. May reproduce for instructional and

3 8. The table shows the growth of a certain bacteria. Time in Hours, Number of ells, N If N represents the number of cells at time, which equation best models this set of data? N = B N = N = (.4)( 50.06) N = ( 50.06)(.4) 9. The chart below shows the weight of fish (in thousands of pounds) caught in area lakes for si consecutive years. Elapsed Time, t (in years) Weight (in thousands of pounds) Based on the best-fit quadratic model, at which value of t will the amount of fish caught be approimately 6,700 pounds? 6 B Page 3 Published November 006. May reproduce for instructional and

4 0. Solve: = { 3 } 3 3. The graph of g () = is translated up 5 units to produce the graph of the function h (). Which of the following could be h ()? B { 5 } {} {} 5 B h 3 () = h 3 () = h 3 () = h 3 () = In which direction must the graph of y = be shifted to produce the graph of y =? + up B down right left 4. Mr. Greene has 8.5 in. by in. cardboard sheets. s a class project, Mr. Greene asked each of his students to make an open-top bo under these conditions: I) Each bo must be made by cutting small squares from each corner of a cardboard sheet. II) The bo must have a 3 volume of 48 in.. Which of the following is a horizontal asymptote of f ( ) =? 6 = 4 B y = 4 = y = 0 III) The amount of cardboard waste must be minimized. What is the approimate side length for the small squares that would be cut from the cardboard sheet? B 3.65 in..66 in. 0.7 in in. Page 4 Published November 006. May reproduce for instructional and

5 5. Solve: = 4 { 4 } B { 4,} {, 4 } 7. survey at a local high school shows 8.6% of the students read the newspaper. Results of surveys of this size can be off by as much as.5 percentage points. Which inequality describes the results compared to the actual percentage of students that read the newspaper,? no solution B 0.86 > The point ( 3, 4 ) lies on the graph of f () = + a. Which ordered pair below lies on the graph of g () = + a? 3 ( ), B ( 5, 3 ) ( 3, ) ( 7, 8) > For y= , which set describes when y< 8? { 3< < 4} B { 3< < 0} { < 3 or > 4} { < 3 or > 0} Page 5 Published November 006. May reproduce for instructional and

6 9. Which is the graph of a circle with equation + 4+ y 6y = 3? y B y y y Page 6 Published November 006. May reproduce for instructional and

7 0. Which is an equation for the parabola that has verte ( ) ( ) through the point, 5? B y = y = y = + 8, 3 and passes. pizza parlor charges price for a slice of pizza and price y for a drink. Two slices of pizza and one drink cost Mary nn $4.50. Three slices and two drinks cost Elmo $7.5. Which matri could be multiplied by È4.50 Í to find and y? Î7.5 y = È Í Î. Solve: y = y = 5 5, 0 {( ), (,5) 3 3 } B, 0 {( ), (,5) 3 3 } {(, ) ( )} 0,, {(, ) ( )} 0,, B È Í Î È Í Î 3 3 È Í Î End of Goal Sample Items In compliance with federal law, including the provisions of Title IX of the Education mendments of 97, the epartment of Public Instruction does not discriminate on the basis of race, se, religion, color, national or ethnic origin, age, disability, or military service in its policies, programs, activities, admissions or employment. Page 7 Published November 006. May reproduce for instructional and

8 Goal nswers to EO lgebra II Sample Items. Objective.0 Use the composition and inverse of functions to model and solve problems; justify results. Thinking Skill: pplying orrect nswer:. Objective.0 Use the composition and inverse of functions to model and solve problems; justify results. Thinking Skill: nalyzing orrect nswer: 3. Objective.0 Use quadratic functions and inequalities to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. Thinking Skill: Integrating orrect nswer: 4. Objective.0 Use quadratic functions and inequalities to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. Thinking Skill: pplying orrect nswer: B 5. Objective.03 Use eponential functions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants, coefficients, and bases in the contet of the problem. Thinking Skill: nalyzing orrect nswer: 6. Objective.03 Use eponential functions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants, coefficients, and bases in the contet of the problem. Thinking Skill: Integrating orrect nswer: 7. Objective.03 Use eponential functions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants, coefficients, and bases in the contet of the problem. Thinking Skill: nalyzing orrect nswer: B North arolina Testing Program Published November 006. May reproduce for instructional and educational purposes only; not for personal or financial gain.

9 Goal nswers to EO lgebra II Sample Items 8. Objective.04 reate and use best-fit mathematical models of linear, eponential, and quadratic functions to solve problems involving sets of data. a) Interpret the constants, coefficients, and bases in the contet of the data. b) heck the model for goodnessof-fit and use the model, where appropriate, to draw conclusions or make Thinking Skill: Generating orrect nswer: 9. Objective.04 reate and use best-fit mathematical models of linear, eponential, and quadratic functions to solve problems involving sets of data. a) Interpret the constants, coefficients, and bases in the contet of the data. b) heck the model for goodnessof-fit and use the model, where appropriate, to draw conclusions or make Thinking Skill: Generating orrect nswer: B 0. Objective.05 Use rational equations to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. c) Identify the asymptotes and intercepts graphically and algebraically. Thinking Skill: pplying orrect nswer: B. Objective.05 Use rational equations to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. c) Identify the asymptotes and intercepts graphically and algebraically. Thinking Skill: nalyzing orrect nswer:. Objective.05 Use rational equations to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. c) Identify the asymptotes and intercepts graphically and algebraically. Thinking Skill: nalyzing orrect nswer: 3. Objective.06 Use cubic equations to model and solve problems. a) Solve using tables and graphs. b) Interpret constants and coefficients in the contet of the problem. Thinking Skill: pplying orrect nswer: North arolina Testing Program Published November 006. May reproduce for instructional and educational purposes only; not for personal or financial gain.

10 Goal nswers to EO lgebra II Sample Items 4. Objective.06 Use cubic equations to model and solve problems. a) Solve using tables and graphs. b) Interpret constants and coefficients in the contet of the problem. Thinking Skill: Integrating orrect nswer: 5. Objective.07 Use equations with radical epressions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the degree, constants, and coefficients in the contet of the problem. Thinking Skill: pplying orrect nswer: 6. Objective.07 Use equations with radical epressions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the degree, constants, and coefficients in the contet of the problem. Thinking Skill: nalyzing orrect nswer: 7. Objective.08 Use equations and inequalities with absolute value to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. Thinking Skill: nalyzing orrect nswer: 8. Objective.08 Use equations and inequalities with absolute value to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. Thinking Skill: pplying orrect nswer: 9. Objective.09 Use the equations of parabolas and circles to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. Thinking Skill: pplying orrect nswer: 0. Objective.09 Use the equations of parabolas and circles to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the contet of the problem. Thinking Skill: pplying orrect nswer: North arolina Testing Program Published November 006. May reproduce for instructional and educational purposes only; not for personal or financial gain.

11 Goal nswers to EO lgebra II Sample Items. Objective.0 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matri operations, and algebraic properties. Thinking Skill: pplying orrect nswer: B. Objective.0 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matri operations, and algebraic properties. Thinking Skill: Generating orrect nswer: B North arolina Testing Program Published November 006. May reproduce for instructional and educational purposes only; not for personal or financial gain.