4. The length of a rectangle is 10 units greater than the width, x. Which of the following expressions gives the area, A, of the rectangle?

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1 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal. Which of the following is an algebraic expression for twice the sum of a number and 5? ( n - 5) ( n + 5) n n + 5. The length of a rectangle is 0 units greater than the width, x. Which of the following expressions gives the area,, of the rectangle? = x( 0 + x) = x + ( x + 0) = x( 0 - x) = 0x. Henry opened a savings account by depositing $50. He also signed an automatic draft agreement to have $5 deposited directly from his pay check each month. If x is the number of months that have passed since Henry opened the account, which of the following shows how much Henry has deposited into his savings account? f ( x) = x f ( x) = 50x + 5 f ( x) = (50 + 5) x f ( x) = ( x). Three less than four times a number is 7. Which equation could be used to find the number? x - = 7 - x = 7 ( x - ) = 7 ( x ) = 7 Page Published October 00. May reproduce for instructional and

2 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 5. There are yards of rope with which to enclose a rectangular area. If w is the width of the rectangle, what is the area function for the roped-off rectangle? = w + w = w = w + w = w - w 6. Local scientists have been asked to study the population of gnats around a lake. fter five days, the scientists generated these results: ay Gnats ,0 How can the data best be described? The population doubles daily. The population quadruples daily. The population increases by daily. The population increases daily by squaring. Page Published October 00. May reproduce for instructional and

3 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 7. Which of the following equations describes the data in the table below? x (% reduction (or increase) in dietary fat) 6 5 y (weight loss (or gain) in pounds) x + y = 7 x - y = x + y = x - y = Page Published October 00. May reproduce for instructional and

4 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 8. What is the relationship between the input (x) and output (y)? y x The output is twice the input. The output is seven less than four times the input. The output is two more than the input. The output is four less than three times the input. Page Published October 00. May reproduce for instructional and

5 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 9. Shirley used data to find an equation relating the number of hours that students spent per day working at a part-time job and their grade point average (GP). She found that the top GP was.90 if the student did not work at all, and for every hour a student worked, 0.0 points were lost. Which of the following best describes the relationship Shirley found between the number of hours a student worked and the student s GP? s the number of hours worked decreased, the GP decreased. s the number hours worked increased, the GP increased. s the number of hours worked decreased, the GP increased. no apparent relationship between the number of hours worked and the GP 0. The function h(t ) = 6t + 00 can be used to study the relationship between the height, ht ( ), of a falling object that is dropped from an altitude of 00 feet and the time, t, it takes to hit the ground. What is the independent variable for the function? ht () 6 t 00. Mailing a letter costs 7 for the first ounce and for each additional ounce. Suppose that we want to write a cost function to describe this situation. Which of the following is an independent variable?. 7 the letter s weight the mailing cost the number of stamps needed Jill uses data to find an equation relating the number of hours ( h) that students spent working per day at after-school jobs with their last math test grade ( G). If her equation is G = 5.5h + 95, what is the dependent variable in this relationship? the test grade the student after-school jobs the hours worked Given f x = x + 5, what is the range of the function?. ( ) all real numbers less than or equal to 5 all integers less than or equal to 5 all nonnegative real numbers all nonnegative integers Page 5 Published October 00. May reproduce for instructional and

6 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal. In the equation x + y =, if an x-value is increased by, what would be the effect on the corresponding y-value? The value of y will be times as large. The value of y be as large. will decrease to The value of y will increase by 6. The value of y will decrease by 6. Page 6 Published October 00. May reproduce for instructional and

7 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 5. n object is shot upward from ground level with an initial velocity of 6 feet per second. Its height after t seconds is given by h = 6t - 6 t. Which graph best represents this function? h h t t h h t t Page 7 Published October 00. May reproduce for instructional and

8 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 6. chemist presented this graph to local government officials who needed to know the rate at which trash decays inside a landfill. Rate of ecay of Trash in Landfill 8,000, Years Which is the correct interpretation of the rate of decay? Half of the trash will decay every year. Half of the trash will decay every two years. Half of the trash will decay every three years. Half of the trash will decay every six months. Page 8 Published October 00. May reproduce for instructional and

9 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 7. enisha bought a car for $5,000. The value depreciates linearly. fter years the value is $,50. What is the amount of yearly depreciation? $, This graph represents how much Juan charges to take care of one child. y $,500 0 $, $ Mark burns calories when he plays volleyball for 0 minutes. If he plays for 5 minutes, he burns 5 calories. How fast is Mark burning calories? calories per minute calories per minute calories per minute Time (hours) x 7 5 calories per minute How much does Juan charge per hour? $5.00 $8.00 $0.00 $.00 Page 9 Published October 00. May reproduce for instructional and

10 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 0. The cost of a large pizza is given by the formula t () =.5t , where t () is the cost of the pizza and t is the number of toppings. What does the slope represent? number of toppings. bank has a checking account plan that charges a $.5 monthly service fee plus $0.5 per check written during that month. If n is the number of checks written, which equation represents the bank s monthly charges () for its checking account plan? cost per slice cost of each topping cost of the pizza with no toppings =.5n = 0.5n +.5 = 0.05n +.5 = 0.05n -.5. line has a slope of and a y-intercept of. Which of the following is the equation of the line? x - y = x - y = x - y = x - y = Page 0 Published October 00. May reproduce for instructional and

11 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal. Which line has a slope of and passes through (, )? y y x x y y x x Page Published October 00. May reproduce for instructional and

12 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal. In planning a summer trip for his family, Jill s dad made up a mileage and cost table. Mileage 50 miles 50 miles 75 miles ost $67.5 $0.5 $.0 6. If the slope of a line changes from to and the y-intercept changes from to 0, then the graph of the line will be affected in what ways? less steep; up units less steep; down units If the relationship between mileage and cost is linear, what equation would apply? steeper; up units steeper; down units = 50m + 50 = 0.5m = 0.5m - 50 = 0.50m Smith s Video Store charges $.0 for each video rented plus a $.00 surcharge. The store decided to lower the surcharge to $0.50. Which equation represents the new fee for renting m videos? 7. The drama club is selling tickets to a play for $0 each. The cost to rent the theater and costumes is $500. In addition the printers are charging $ per ticket to print the tickets. How many tickets must the drama club sell to make a profit? P =.90m +.00 P =.90m P =.0m P =.0m The length of a rectangle is one inch longer than twice the width. What is the maximum width of the rectangle when the perimeter is no more than 9 inches? inches 5 inches 8 inches inches Page Published October 00. May reproduce for instructional and

13 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 9. Solve: x + > x if x Œ,,, { 0,,, }. Solve: x + y = x + 5y = 7 (,) {,, } {,, 0,,, } {,,, 0,,, } (, ) (, ) (, ) 0. Janie s outique had a sale in which sweaters were marked 5% off. If ridget paid $9.08 for a sweater (after a 6% sales tax was added), what was the original price of the sweater? $.55 $.00 $7.00 $7.06. Solve: y = x + x - y = (, ) (, ) (, ) (, ). region is defined by the following system. y > x + y x - In which quadrants of the coordinate plane is the region located? I, II, III II, III III, IV I, II, III, IV. store received $8 from the sale of 5 tape recorders and 7 radios. If the receipts from the tape recorders exceeded the receipts from the radios by $7, what is the cost of a tape recorder? $9 $68 $8 $96 Page Published October 00. May reproduce for instructional and

14 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 5. What are the vertex and y-intercept of the quadratic function fx () = + x- x? 7. Which of the following statements best describes the solution(s) of x + x =? 6 ( ) vertex:, y-intercept: no solution ( ) vertex:, y-intercept: ( ) y vertex:, -intercept: negative solution positive solution and negative solution positive solutions ( ) y vertex:, -intercept: 8. What are the solutions for x - = 0? {0, } 6. Which of the following is an x-intercept of y = 8x - 0x +? {,} {,} {0,} 9. Which is an x-intercept of y = x - 7x +? 7 Page Published October 00. May reproduce for instructional and

15 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 0. Twelve less than twice the square of a number is equal to the product of 5 and the number. What are the solutions? { },. The height of an object dropped from a hot-air balloon can be determined by the formula 6, where is the height h = t + s h of the object in feet, t is the elapsed time in seconds, and s is the height of the balloon. { }, { }, If the balloon is 00 feet from the ground, how long will it take for an object dropped from the balloon to hit the ground?.5 seconds { }, 5 seconds 7.5 seconds 0 seconds. Solve: ( x - ) = 6 { 9, } {, 9} { 7, } { 7, } Page 5 Published October 00. May reproduce for instructional and

16 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal. new automobile is purchased for x $0,000. If V = 0, 000(0. 8) gives the car s value after x years, then about how long will it take for the car to be worth half its purchase price?. The population of a town is 5,000. t The function ft ( ) = 5,000(. ) gives the predicted population of the town in t years. pproximately what will the population be in years? years years 5 years 6 years 50, , ,000,50,000 Page 6 Published October 00. May reproduce for instructional and

17 North arolina Testing Program EO Mathematics lgebra I Sample Items Goal 5. lan won $,000 in an essay contest. He invested the money in a savings account which pays 6% interest compounded annually. onsider the formula: ( ) = 0( + ) () t t r, where t is the accumulated amount at time t, 0 is the amount invested at time t = 0, r is the interest rate, and t is time in years. What is lan s investment worth after two years? $0 $7 $,0 $,7 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, sex, religion, color, national or ethnic origin, age, disability, or military service in its policies, programs, activities, admissions or employment. Page 7 Published October 00. May reproduce for instructional and

18 Goal nswers to EO Mathematics lgebra I Sample Items. Objective.0 Translate word phrases and sentences into expressions and equations and vice versa. Thinking Skill: nalyzing orrect nswer:. Objective.0 Translate word phrases and sentences into expressions and equations and vice versa. Thinking Skill: nalyzing orrect nswer:. Objective.0 Translate word phrases and sentences into expressions and equations and vice versa. Thinking Skill: nalyzing orrect nswer:. Objective.0 Translate word phrases and sentences into expressions and equations and vice versa. Thinking Skill: nalyzing orrect nswer: 5. Objective.0 Translate word phrases and sentences into expressions and equations and vice versa. Thinking Skill: Generating orrect nswer: 6. Objective.0 Identify properties and relationships of data in tables, graphs, and equations. Thinking Skill: nalyzing orrect nswer: 7. Objective.0 Identify properties and relationships of data in tables, graphs, and equations. Thinking Skill: pplying orrect nswer: 8. Objective.0 Identify properties and relationships of data in tables, graphs, and equations. Thinking Skill: nalyzing orrect nswer: 9. Objective.0 Identify properties and relationships of data in tables, graphs, and equations. Thinking Skill: nalyzing orrect nswer: North arolina Testing Program Published October 00. May reproduce for instructional and educational purposes only; not for personal or financial gain.

19 Goal nswers to EO Mathematics lgebra I Sample Items 0. Objective.0 efine and distinguish between relations and functions, dependent and independent variables, domain and range. Thinking Skill: Knowledge orrect nswer:. Objective.0 efine and distinguish between relations and functions, dependent and independent variables, domain and range. Thinking Skill: Organizing orrect nswer:. Objective.0 efine and distinguish between relations and functions, dependent and independent variables, domain and range. Thinking Skill: Knowledge orrect nswer:. Objective.0 efine and distinguish between relations and functions, dependent and independent variables, domain and range. Thinking Skill: nalyzing orrect nswer:. Objective.0 Graph and interpret in the context of the problem, relations and functions on the coordinate plane. Include linear equations and inequalities, quadratics and exponentials. Thinking Skill: nalyzing orrect nswer: 5. Objective.0 Graph and interpret in the context of the problem, relations and functions on the coordinate plane. Include linear equations and inequalities, quadratics and exponentials. Thinking Skill: nalyzing orrect nswer: 6. Objective.0 Graph and interpret in the context of the problem, relations and functions on the coordinate plane. Include linear equations and inequalities, quadratics and exponentials. Thinking Skill: nalyzing orrect nswer: 7. Objective.05 etermine and use slopes of linear relationships to solve problems. a) Find the slope of a line given the graph of the line, an equation of the line, or two points on the line. b) escribe the slope of the line in the context of a problem situation. Thinking Skill: Integrating orrect nswer: North arolina Testing Program Published October 00. May reproduce for instructional and educational purposes only; not for personal or financial gain.

20 Goal nswers to EO Mathematics lgebra I Sample Items 8. Objective.05 etermine and use slopes of linear relationships to solve problems. a) Find the slope of a line given the graph of the line, an equation of the line, or two points on the line. b) escribe the slope of the line in the context of a problem situation. Thinking Skill: Integrating orrect nswer: 9. Objective.05 etermine and use slopes of linear relationships to solve problems. a) Find the slope of a line given the graph of the line, an equation of the line, or two points on the line. b) escribe the slope of the line in the context of a problem situation. Thinking Skill: nalyzing orrect nswer: 0. Objective.05 etermine and use slopes of linear relationships to solve problems. a) Find the slope of a line given the graph of the line, an equation of the line, or two points on the line. b) escribe the slope of the line in the context of a problem situation. Thinking Skill: nalyzing orrect nswer:. Objective.06 Write the equation of and graph linear relationships given the following information: a) Slope and y-intercept. b) Slope and one point on the line. c) Two points on the line. Thinking Skill: Integrating orrect nswer:. Objective.06 Write the equation of and graph linear relationships given the following information: a) Slope and y-intercept. b) Slope and one point on the line. c) Two points on the line. Thinking Skill: nalyzing orrect nswer:. Objective.06 Write the equation of and graph linear relationships given the following information: a) Slope and y-intercept. b) Slope and one point on the line. c) Two points on the line. Thinking Skill: nalyzing orrect nswer:. Objective.06 Write the equation of and graph linear relationships given the following information: a) Slope and y-intercept. b) Slope and one point on the line. c) Two points on the line. Thinking Skill: Integrating orrect nswer: North arolina Testing Program Published October 00. May reproduce for instructional and educational purposes only; not for personal or financial gain.

21 Goal nswers to EO Mathematics lgebra I Sample Items 5. Objective.07 Investigate and determine the effects of changes in slope and intercepts on the graph and equation of a line. a) hange only slope. b) hange only the x- or y- intercept. c) hange the slope and an intercept. Thinking Skill: nalyzing orrect nswer: 6. Objective.07 Investigate and determine the effects of changes in slope and intercepts on the graph and equation of a line. a) hange only slope. b) hange only the x- or y- intercept. c) hange the slope and an intercept. Thinking Skill: nalyzing orrect nswer: 7. Objective.08 Use linear equations or inequalities to solve problems. Solve by: a) Graphing. b) Using properties of equality; justify steps used. Thinking Skill: Integrating orrect nswer: 8. Objective.08 Use linear equations or inequalities to solve problems. Solve by: a) Graphing. b) Using properties of equality; justify steps used. Thinking Skill: pplying orrect nswer: 9. Objective.08 Use linear equations or inequalities to solve problems. Solve by: a) Graphing. b) Using properties of equality; justify steps used. Thinking Skill: pplying orrect nswer: 0. Objective.08 Use linear equations or inequalities to solve problems. Solve by: a) Graphing. b) Using properties of equality; justify steps used. Thinking Skill: pplying orrect nswer:. Objective.09 Use systems of linear equations or inequalities in two variables to solve problems. etermine the solution by: a) Graphing. b) Substitution. c) Elimination. Thinking Skill: pplying orrect nswer:. Objective.09 Use systems of linear equations or inequalities in two variables to solve problems. etermine the solution by: a) Graphing. b) Substitution. c) Elimination. Thinking Skill: pplying orrect nswer:. Objective.09 Use systems of linear equations or inequalities in two variables to solve problems. etermine the solution by: a) Graphing. b) Substitution. c) Elimination. Thinking Skill: pplying orrect nswer: North arolina Testing Program Published October 00. May reproduce for instructional and educational purposes only; not for personal or financial gain.

22 Goal nswers to EO Mathematics lgebra I Sample Items. Objective.09 Use systems of linear equations or inequalities in two variables to solve problems. etermine the solution by: a) Graphing. b) Substitution. c) Elimination. Thinking Skill: pplying orrect nswer: 5. Objective.0 Graph quadratic functions. a) Locate the intercepts and the vertex. b) Recognize the x- intercepts of the function as the solutions of the equation. Thinking Skill: Integrating orrect nswer: 6. Objective.0 Graph quadratic functions. a) Locate the intercepts and the vertex. b) Recognize the x- intercepts of the function as the solutions of the equation. Thinking Skill: Integrating orrect nswer: 7. Objective.0 Graph quadratic functions. a) Locate the intercepts and the vertex. b) Recognize the x- intercepts of the function as the solutions of the equation. Thinking Skill: Integrating orrect nswer: 8. Objective.0 Graph quadratic functions. a) Locate the intercepts and the vertex. b) Recognize the x- intercepts of the function as the solutions of the equation. Thinking Skill: pplying orrect nswer: 9. Objective. Use quadratic equations to solve problems. Solve by: a) Factoring. b) Locating points on the graph. Thinking Skill: pplying orrect nswer: 0. Objective. Use quadratic equations to solve problems. Solve by: a) Factoring. b) Locating points on the graph. Thinking Skill: pplying orrect nswer:. Objective. Use quadratic equations to solve problems. Solve by: a) Factoring. b) Locating points on the graph. Thinking Skill: pplying orrect nswer:. Objective. Use quadratic equations to solve problems. Solve by: a) Factoring. b) Locating points on the graph. Thinking Skill: pplying orrect nswer: North arolina Testing Program Published October 00. May reproduce for instructional and educational purposes only; not for personal or financial gain.

23 Goal nswers to EO Mathematics lgebra I Sample Items. Objective. Use formulas and graphs to solve problems involving exponential functions. Solve a problem by: a) Locating points on the graph. b) Evaluating an exponential expression. Thinking Skill: pplying orrect nswer:. Objective. Use formulas and graphs to solve problems involving exponential functions. Solve a problem by: a) Locating points on the graph. b) Evaluating an exponential expression. Thinking Skill: pplying orrect nswer: 5. Objective. Use formulas and graphs to solve problems involving exponential functions. Solve a problem by: a) Locating points on the graph. b) Evaluating an exponential expression. Thinking Skill: pplying orrect nswer: North arolina Testing Program Published October 00. May reproduce for instructional and educational purposes only; not for personal or financial gain.