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Algebra 2 ---- 1st Semester Final Exam Review 1st Semester Final Exam Review Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. To which sets of numbers does the number belong? ____ ____ ____ 1. a. irrational numbers, real numbers b. integers, rational numbers, real numbers c. rational numbers, irrational numbers d. whole numbers, integers, rational numbers, real numbers 2. –17 a. integers, rational numbers, real numbers b. whole numbers, integers, rational numbers, real numbers c. whole numbers, integers, real numbers d. rational numbers, real numbers 3. An irrational number can ________ be expressed as a quotient of integers. a. always b. sometimes c. never Insert <, >, or = to make the sentence true. ____ 4. a. < b. > c. = Name the property of real numbers illustrated by the equation. ____ ____ ____ 5. a. Distributive Property b. Associative Property of Multiplication c. Commutative Property of Multiplication d. Associative Property of Addition 6. –6 + 6 = 0 a. Identity Property of Multiplication b. Inverse Property of Multiplication c. Associative Property of Addition d. Inverse Property of Addition 7. –2.5 + 0 = –2.5 a. Inverse Property of Multiplication b. Identity Property of Addition c. Inverse Property of Addition d. Identity Property of Multiplication Evaluate the expression for the given value of the variable(s). ____ 8. ;b=2 a. 19 b. 17 c. –11 d. 21 Algebra 2 ---- 1st Semester Final Exam Review ____ 9. ; x = –3 a. 3 b. –1 c. 11 d. –17 c. d. Simplify by combining like terms. ____ 10. a. b. ____ 11. Find the perimeter of the figure. Simplify the answer. x+y 2x 4x y 2x x a. 9x + 2y b. 10x + y c. 10x + 2y d. 9x + 3y b. c. d. Solve the equation. ____ 12. a. ____ 13. a. c. 8 2 or x = − 9 9 b. 2 x = 0 or x = −2 3 8 2 or x = −2 9 3 d. 8 x = or x = 0 9 x= x= Solve the equation or formula for the indicated variable. ____ 14. , for t a. b. c. ____ 15. The formula for the time a traffic light remains yellow is d. , where t is the time in seconds and s is the speed limit in miles per hour. a. Solve the equation for s. b. What is the speed limit at a traffic light that remains yellow for 4.5 seconds? a. b. ; s = 28 mi/h ; s = 36 mi/h c. d. ; s = 35 ; s = 28 mi/h Algebra 2 ---- 1st Semester Final Exam Review Solve for x. State any restrictions on the variables. ____ 16. a. c. ; b. ; d. ; ; ____ 17. A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary. a. 7.5 cm by 22.5 cm c. 20 cm by 60 cm b. 7.5 cm by 52.5 cm d. 15 cm by 22.5 cm ____ 18. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm? a. 10.5 cm, 11.5 cm, and 12.5 cm c. 7.5 cm, 11.5 cm, and 32.1 cm b. 22.5 cm, 30 cm, and 37.5 cm d. 19.3 cm, 25.7 cm, and 32.1 cm ____ 19. Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than the other car. The cars are 500 mi apart in 5 h. How fast is each car traveling? a. 35 mi/h and 45 mi/h c. 45 mi/h and 55 mi/h b. 55 mi/h and 35 mi/h d. 55 mi/h and 65 mi/h Solve the inequality. Graph the solution set. ____ 20. –4k + 5 ≤ 21 a. k ≥ –4 –8 –6 –4 –2 b. k ≥ −6 c. k ≤ –4 0 2 4 6 8 d. 1 2 –8 –6 –4 –2 0 2 4 6 8 ____ 21. 26 + 6b ≥ 2(3b + 4) a. all real numbers –8 –6 –4 –2 –8 –6 –4 –2 2 4 6 b≥1 b≤1 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 8 d. no solutions 1 2 –8 –6 –4 –2 –8 –6 –4 –2 4 1 2 –8 –6 –4 –2 b. 2 1 2 –8 –6 –4 –2 c. 0 k ≤ −6 0 0 2 4 6 8 Algebra 2 ---- 1st Semester Final Exam Review Solve the compound inequality. Graph the solution set. ____ 22. 4x – 5 < –17 or 5x + 6 > 31 a. x < –3 or x > 5 –8 –6 –4 –2 0 c. 2 4 6 x < –3 or x > 7 2 5 8 –8 –6 –4 –2 b. d. 1 2 x < −5 or x > 7 2 5 –8 –6 –4 –2 0 2 4 6 0 2 4 6 8 0 2 4 6 8 1 x < −5 or x > 5 2 8 –8 –6 –4 –2 ____ 23. a. c. –8 –6 –4 –2 0 2 4 6 8 b. –8 –6 –4 –2 0 2 4 6 8 –8 –6 –4 –2 0 2 4 6 8 d. –8 –6 –4 –2 0 2 4 6 8 Solve the inequality. Graph the solution. ____ 24. a. c. –40 –30 –20 –10 0 10 20 30 40 b. –20 –15 –10 –5 0 5 10 15 20 –20 –15 –10 –5 0 5 10 15 20 d. –20 –15 –10 –5 0 5 10 15 20 ____ 25. a. –18 > x > 8 –20 –15 –10 –5 c. –36 < x < 16 0 5 10 15 20 b. –18 < x < 8 –20 –15 –10 –5 –40 –30 –20 –10 0 10 20 30 40 –20 –15 –10 –5 5 d. 0 5 10 15 20 Short Answer 26. Name the property used in each step of simplification. 0 10 15 20 Algebra 2 ---- 1st Semester Final Exam Review 1st Semester Final Exam Review Chapter 2 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Find the domain and range of the relation and determine whether it is a function. y 4 2 –4 O –2 2 4 x –2 –4 ____ a. Domain: all real numbers; range: all real numbers; yes, it is a function b. Domain: x > 0; range: y > 0; yes, it is a function. c. Domain: positive integers; range: positive integers; no, it is not a function. d. Domain: x ≥ 0; range: y ≤ 0; no, it is not a function. 2. Use the vertical-line test to determine which graph represents a function. y y a. c. –4 –2 4 4 2 2 O x –2 , –4 –2 O –2 –4 –4 d. y –4 3. For 4 –2 b. ____ 2 4 2 2 2 4 x –4 –2 O –2 –2 –4 –4 . 4 x 2 4 x y 4 O 2 Algebra 2 ---- 1st Semester Final Exam Review ____ a. –19 4. Suppose b. 1 and Find the value of . a. b. 1 5 9 2 c. –21 d. 21 c. −2 d. 2 . 4 7 Find the slope of the line through the pair of points. ____ 1 1 1 5. (− , 0) and (− , − ) 3 2 2 a. −3 b. c. 1 3 − 1 3 d. 3 Write in standard form an equation of the line passing through the given point with the given slope. ____ ____ 6. slope = –8; (–2, –2) a. 8x + y = –18 b. –8x + y = –18 c. 8x – y = –18 d. 8x + y = 18 7. Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5). a. c. 1 1 y + 4 = (x – 2) y + 5 = − (x + 6) 8 8 b. d. 1 1 y + 4 = − (x + 6) y + 4 = (x + 6) 8 8 Find the slope of the line. ____ 8. a. − b. 5 3 c. 5 3 − 3 5 d. 3 5 Find the slope of the line. ____ 9. y 4 2 –4 –2 O 2 4 x –2 –4 a. undefined ____ 10. x = a a. a b. 2 c. 1 d. 0 b. 0 c. undefined d. 1 Algebra 2 ---- 1st Semester Final Exam Review Find an equation for the line: 5 ____ 11. through (2, 6) and perpendicular to y = − x + 1. 4 a. b. c. 5 7 4 38 y= x+ y=− x+ y= 4 2 5 5 ____ 12. through (–4, 6) and parallel to y = −3x + 4. a. y = −3x − 6 b. y = 3x + 18 c. y= 4 22 x+ 5 5 d. 5 17 y=− x+ 4 2 1 22 x+ 3 3 d. 1 14 y=− x+ 3 3 Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. ____ 13. x y 6 24 18 72 54 216 162 648 a. yes; k = 4; y =4x b. yes; k = 3; y =3x c. yes; k = 6; y =6x d. no Determine whether y varies directly with x. If so, find the constant of variation k. ____ 14. –6y = –5x a. 5 yes; 6 b. yes; 6 5 c. yes; –5 d. no ____ 15. A leaky valve on the water meter overcharges the residents for one gallon of water in every months. The overcharged amount w varies directly with time t. a. Find the equation that models this direct variation. b. How many months it will take for the residents to be overcharged for 8 gallons of water? a. b. ; 20 months ; 20 months c. d. ; months ; months ____ 16. A 3-mi cab ride costs $3.00. A 6-mi cab ride costs $4.80. Find a linear equation that models cost c as a function of distance d. a. c = 0.80d + 1.20 c. d = 0.60c + 1.80 b. c = 1.00d + 1.80 d. c = 0.60d + 1.20 ____ 17. What is the vertex of the function ? a. b. 2 c. 2 d. 2 2 (− , –4) ( , –4) ( , 4) (− , 4) 3 3 3 3 Algebra 2 ---- 1st Semester Final Exam Review ____ 18. Write two linear equations you can use to graph a. c. b. . d. ____ 19. Write an equation for the horizontal translation of . y 8 4 –8 –4 O 4 8 x –4 –8 a. b. c. ____ 20. Write the equation that is the translation of a. b. d. left 1 unit and up 2 units. c. d. Short Answer 21. An electronics store makes a profit of $20 for every portable DVD player sold and $45 for every DVD recorder sold. The manager’s target is to make at least $180 a day on sales of the portable DVD players and DVD recorders. Write and graph an inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target. Let p represent the number of portable DVD players and r represent the number of DVD recorders. 22. Graph the equation . 23. Graph the absolute value inequality y < |x + 2| – 2 24. Graph the absolute value equation 25. Graph the absolute value equation 26. Graph the inequality 4x – 2y < –3 27. Graph the function . 28. A new candle is 8 inches tall and burns at a rate of 2 inches per hour. a. Write an equation that models the height h after t hours. b. Sketch the graph of the equation. 29. Graph the equation by finding the intercepts. Algebra 2 ---- 1st Semester Final Exam Review 1st Semester Final Exam Review Chapter 3 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. A Month Jan Feb Mar Apr May 1 2 3 4 5 6 a. b. B Revenue 4000 9000 13,000 16,000 21,000 C Expenses 22,000 24,000 25,000 27,000 30,000 The spreadsheet shows the monthly revenue and expenses for a new business. Use your graphing calculator to find a linear model for monthly revenue and a linear model for monthly expenses. Use the models to predict the month in which revenue will equal expenses. a. c. a. a. b. October b. August b. d. a. a. b. September b. September Without graphing, classify each system as independent, dependent, or inconsistent. ____ ____ ____ 2. a. dependent b. inconsistent c. independent a. independent b. inconsistent c. dependent a. independent b. inconsistent c. dependent 3. 4. Solve the system by the method of substitution. ____ 5. a. (0, –5) b. (–5, 0) c. (5, 1) d. (1, 5) Algebra 2 ---- 1st Semester Final Exam Review Solve the system by the method of substitution. ____ ____ 6. a. (–1, –6, –1) b. (1, –6, 1) c. (–1, –6, 1) d. (–1, 6, 1) 7. A group of 52 people attended a ball game. There were three times as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. a. c. ; 39 adults; 25 children ; 25 adults; 39 children b. d. ; 39 adults, 13 children ; 13 adults, 39 children Use the elimination method to solve the system. ____ 8. a. (0, –2) ____ b. (–2, 0) c. (–2, 2) d. (2, –2) 9. a. (1, –3, 1) b. (1, 3, 1) c. (–1, 3, 1) d. (1, 3, –1) ____ 10. Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value? a. maximum value at (5, 4); 32 b. maximum value at (0, 8); 16 c. maximum value at (9, 0); 27 d. maximum value at (0, 0); 0 Algebra 2 ---- 1st Semester Final Exam Review ____ 11. Given the system of constraints, name all vertices. Then find the maximum value of the given objective function. Maximum for a. (0, 2), (2, 0), (4, 6); maximum value of –6 b. (0, 2), (2, 0), (6, 4); maximum value of 12 c. (0, 2), (2, 0), (4, 2); maximum value of 10 d. (0, 2), (2, 0), (4, 6); maximum value of 8 Solve the system using either method of substitution or elimination. ____ 12. a. (–3, 6, –2) b. (–3, 8, 0) c. (–3, 6, –8) d. no solution ____ 13. a. no solution b. (2, –5, –2) Short Answer Solve the system by graphing. 14. 15. Solve the system of inequalities by graphing. 16. 17. 18. c. (–2, –5, 2) d. (2, 5, 2) Algebra 2 ---- 1st Semester Final Exam Review 1st Semester Final Exam Review Chapter 4 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ 1. State the dimensions of the matrix. Identify the indicated element. a. 3 × 2, 0 b. 2 × 3, –7 2. How many elements are in an m × n matrix? a. m + n b. c. 2 × 3, 4 d. 3 × 2, –7 c. d. mn Find the sum or difference. ____ ____ ____ 3. a. c. b. d. a. c. b. d. 4. 5. Suppose A and B are 2 × 5 matrices. Which of the following are the dimensions of the matrix A + B? a. 2 × 5 b. 10 × 10 c. 7 × 1 d. 7 × 7 Find the values of the variables. ____ 6. a. f = 4, k = 4, w = 11 b. f = 4, k = 4, w = 11 or –11 c. f = 4, k = –4, w = 11 or –11 d. f = 4, k = 4, w = 121 or –121 Algebra 2 ---- 1st Semester Final Exam Review Solve the matrix equation. ____ ____ 7. a. c. b. d. 8. a. b. c. Find the product. ____ 9. a. c. b. d. [12] a. c. b. d. ____ 10. d. Algebra 2 ---- 1st Semester Final Exam Review ____ 11.Which of the following is the multiplicative inverse of the given matrix? a. b. c. d. ____ 12. Which of the following is the multiplicative inverse of the given matrix? a. c. b. d. Evaluate the determinant of the matrix. ____ 13. a. 17 b. 1 c. –1 d. –17 a. –24 b. 40 c. –32 d. –40 ____ 14. Determine whether the matrix has an inverse. If an inverse exists, find it. ____ 15. a. c. does not exist b. d. Algebra 2 ---- 1st Semester Final Exam Review Determine whether the matrix has an inverse. If an inverse exists, find it. ____ 16. a. c. does not exist b. d. ____ 17. Write an augmented matrix to represent the system. a. c. b. d. ____ 18. Use an augmented matrix to solve the system a. ____ 19. b. no solution . c. d. Use Cramer’s Rule to solve the system. a. b. no solution ____ 20. Use Cramer’s Rule to solve the system. a. (3, 5, 4) b. (3, –5, –4) c. d. . c. (–2, –25, 10) d. (–3, –5, –4) Algebra 2 ---- 1st Semester Final Exam Review Solve the system. ____ 21. Use an augmented matrix: a. (7, 13, –13) b. (–4, –1, 3) c. (–4, 1, –3) d. (4, 1, –3) ____ 22. Use an augmented matrix: a. no unique solution b. (2, 0, –5) c. (2, 1, 5) d. (–2, 0, –5) Algebra 2 ---- 1st Semester Final Exam Review Chapter 5 Review Questions Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Consider the quadratic function of symmetry. a. The y-intercept is –2. . Find the y-intercept and the equation of the axis 1 2 The equation of the axis of symmetry is x = − . b. 1 2 The y-intercept is . The equation of the axis of symmetry is x = 2. c. The y-intercept is + 2. 1 2 The equation of the axis of symmetry is x = . d. 1 2 The y-intercept is − . The equation of the axis of symmetry is x = –2. ____ 2. Graph the quadratic function f( x) a. –5 –4 –3 –2 . f( x) c. 6 6 5 5 4 4 3 3 2 2 1 1 –1 –1 1 2 3 4 5 6 7 8 9 10 11 x –5 –4 –3 –2 –1 –1 –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 1 2 3 4 5 6 7 8 9 10 11 x Algebra 2 ---- 1st Semester Final Exam Review f( x) b. –5 –4 –3 –2 f( x) d. 6 6 5 5 4 4 3 3 2 2 1 1 –1 –1 1 2 3 4 5 6 7 8 9 10 11 x –5 –4 –3 –2 –1 –1 –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 1 2 3 4 5 6 7 8 9 10 11 x Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function. ____ 3. a. b. c. d. The function has a maximum value. The maximum value of the function is 1. The function has a maximum value. The maximum value of the function is 5. The function has a minimum value. The minimum value of the function is 1. The function has a minimum value. The minimum value of the function is 5. Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. ____ a. 4. One c. f( x) –4 f( x) 6 6 4 4 2 2 –2 2 4 6 8 10 x –4 –2 2 –2 –2 –4 –4 –6 –6 solution is between 3 and 4, while the other solution is between 0 and 1. 4 6 8 10 solution is between –3 and 0, while the other solution between –4 and –1. Algebra 2 ---- 1st Semester Final Exam Review b. One d. f( x) –4 6 6 4 4 2 2 –2 2 4 6 8 10 x –4 –6 –6 5. c. d. 6. a. {–4, − } b. {− , 2} 7 2 7 2 c. {–4, 7} d. {2, 7} Simplify. ____ ____ 2 –4 a. b. ____ –2 –2 Solve the equation by factoring. ____ –4 –2 solution is between –3 and –1, while the other solution is between 0 and –4. ____ f( x) 7. a. b. c. d. a. b. c. d. a. b. c. d. a. b. c. d. a. c. 8. 9. ____ 10. ____ 11. 4 6 8 10 solution is between –3 and –4, while the other solutio between 0 and –1. Algebra 2 ---- 1st Semester Final Exam Review b. d. Solve the equation by completing the square. ____ 12. a. b. c. d. a. b. c. d. ____ 13. Find the exact solution of the following quadratic equation by using the Quadratic Formula. ____ 14. a. c. b. d. Find the value of the discriminant. Then describe the number and type of roots for the equation. ____ 15. a. The discriminant is 196. Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational. b. The discriminant is –204. Because the discriminant is less than 0, the two roots are complex. c. The discriminant is 204. Because the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational. d. The discriminant is –188. Because the discriminant is less than 0, the two roots are complex. ____ 16. a. The discriminant is –29. Because the discriminant is less than 0, the two roots are complex. b. The discriminant is 1. Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational. c. The discriminant is –27. Because the discriminant is less than 0, the two roots are complex. d. The discriminant is 27. Because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational. Write the following quadratic function in vertex form. Then, identify the axis of symmetry. ____ 17. Algebra 2 ---- 1st Semester Final Exam Review a. The vertex form of the function is The equation of the axis of symmetry is b. The vertex form of the function is The equation of the axis of symmetry is c. The vertex form of the function is The equation of the axis of symmetry is d. The vertex form of the function is The equation of the axis of symmetry is . . . . ____ 18. a. The vertex form of the function is . The equation of the axis of symmetry is . b. The vertex form of the function is . The equation of the axis of symmetry is . c. The vertex form of the function is . The equation of the axis of symmetry is . d. The vertex form of the function is . The equation of the axis of symmetry is . ____ 19. Write an equation for the parabola whose vertex is at and which passes through a. c. b. d. . Short Answer where 25. The path of the water from a sprinkler is modeled by a quadratic function h(d) is the height of water, in feet, at a distance of d feet from the jet. Find how far from the sprinkler the water hits the ground. 26. The height of a pebble dropped from a cliff 604 feet high is described by the formula . How long will the pebble take to reach a height of 348 feet? 27. A rectangular frame has length is the value of ? units and width units. If the area is 7 square units, what 28. The volume of a box is 400 cubic meters. If the width of the box is 2 meters and its length is 10 meters more than its height, find the length and height of the box. 29. The window of a building is in the shape of a parabola that can be modeled by the equation where h(w) is the height of the window and w is the width in feet. Find the width of the window at a height of 8 feet. 30. The trajectory of a rocket launched from the top of a cliff can be modeled by a quadratic equation. The rocket reaches a maximum height of 250 feet at a horizontal distance of 4 feet from the cliff. The rocket touches the ground at a horizontal distance of 9 feet from the cliff. Determine a quadratic function that models the height h(d) of the rocket at any given distance d feet from the cliff. 31. The figure below shows the trajectory followed by a tennis ball on the first volley. Assuming that the ball was served at the origin, write an equation of the parabola that models the trajectory of the ball. Algebra 2 ---- 1st Semester Final Exam Review Algebra 2 ---- 1st Semester Final Exam Review Algebra 2 ---- 1st Semester Final Exam Review Chapter 1 Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. A A C B B D B D B B C C B D A D A B C A A A B C B SHORT ANSWER 26. Distributive Property Commutative Property of Addition Associative Property of Addition Distributive Property Definition of Addition Commutative Property of Multiplication Commutative Property of Addition Algebra 2 ---- 1st Semester Final Exam Review 1st Semester Final Exam Review Chapter 2 Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. B C A B D A B C D C C A A A A D B C B B SHORT ANSWER 20p + 45r ≥ 180 21. 22. y r 4 6 2 4 –4 –2 O 2 4 –2 2 –4 0 2 4 23. 6 p 24. y y 16 6 12 3 8 –6 –3 O 3 6 x 4 –3 –6 –8 –4 O –4 4 8 x x Algebra 2 ---- 1st Semester Final Exam Review 25. 26. 4 y y 6 –8 O –4 4 8 x 4 –4 2 –8 –6 –4 –2 O –2 2 4 6 x –12 –4 –16 –6 27. y 6 3 –6 –3 O 3 6 x –3 –6 28. 29. t 16 15 y 12 10 8 4 5 –4 0 5 10 15 h O –4 4 8 12 16 x Algebra 2 ---- 1st Semester Final Exam Review 1st Semester Final Exam Review Chapter 3 Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. SHORT ANSWER 14. B C C B A C D A B C D A A –4 15. y –2 y 4 4 2 2 O 2 4 x –4 –2 O –2 –2 –4 –4 2 4 (3, 1) 16. x No solutions 17. 18. y y y 6 4 4 4 2 2 2 –4 –2 O 2 4 x –6 –4 –2 O 2 –2 –2 1st Semester Final Exam Review Chapter 4 Answer Section MULTIPLE CHOICE D D B A A B B B D 10. 11. 12. 13. 14. 15. 16. 17. 18. B B B C D D C B A 19. 20. 21. 22. x –4 –2 O –4 –6 1. 2. 3. 4. 5. 6. 7. 8. 9. 6 –2 –4 –4 4 D B C A 2 4 x Algebra 2 ---- 1st Semester Final Exam Review Chapter 5 Review Questions Answer Section MULTIPLE CHOICE 1. ANS: C For the quadratic equation symmetry is , the y-intercept is c and the equation of axis of . Feedback A B C D Did you check the signs? Did you interchange the y-intercept and the x-coordinate of the vertex? Correct! Did you use the correct formulas for the y-intercept and the x-coordinate of the vertex? PTS: 1 DIF: Average REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions. NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 STA: IL J 8B.2 | IL J 8B TOP: Graph quadratic functions. KEY: Quadratic Functions | Graph Quadratic Functions 2. ANS: B First, choose integer values for x. Then evaluate the function for each x value. Graph the resulting coordinate pairs and connect the points with a smooth curve. Feedback A B C D Graph ordered pairs that satisfy the function. Correct! Did you plot the graph correctly? When the coefficient of x2 is less than 0, the graphs opens down. PTS: 1 DIF: Advanced REF: Lesson 5-1 OBJ: 5-1.1 Graph quadratic functions. NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 STA: IL J 8B.2 | IL J 8B TOP: Graph quadratic functions. KEY: Quadratic Functions | Graph Quadratic Functions 3. ANS: C The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the function. Feedback A B C D The coefficient of x2 is greater than zero. The graph of this function opens up. Correct! What is the value of the y-coordinate of the vertex? PTS: OBJ: NAT: TOP: KEY: 4. ANS: 1 DIF: Average REF: Lesson 5-1 5-1.2 Find and interpret the maximum and minimum values of a quadratic function. NA 2 | NA 6 | NA 8 | NA 10 | NA 3 STA: IL J 8B.4 | IL J 8B Find and interpret the maximum and minimum values of a quadratic function. Maximum Values | Minimum Values | Quadratic Functions D Algebra 2 ---- 1st Semester Final Exam Review When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers between which the roots are located. Feedback A B C D Is the coefficient of x2 less than zero? Did you graph the function correctly? When the coefficient of x2 is greater than 0, the graph opens up. Correct! PTS: 1 DIF: Advanced REF: Lesson 5-2 OBJ: 5-2.2 Estimate solutions of quadratic equations by graphing. NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2 STA: IL J 8B.4 | IL J 8B TOP: Estimate solutions of quadratic equations by graphing. KEY: Quadratic Equations | Solve Quadratic Equations 5. ANS: B , then either , , or both a and b are equal to zero. For any real numbers a and b, if Feedback A B C D Did you use the Zero Product Property correctly? Correct! Did you verify the answer by substituting the values? Did you factor the binomial correctly? PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2 STA: IL J 8D TOP: Solve quadratic equations by factoring. KEY: Quadratic Equations | Solve Quadratic Equations | Factoring 6. ANS: B For any real numbers a and b, if , then either , , or both a and b are equal to zero. Feedback A B C D Did you use the Zero Product Property correctly? Correct! Did you factor the binomial correctly? Did you verify the answer by substituting the values? PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.2 Solve quadratic equations by factoring. NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2 STA: IL J 8D TOP: Solve quadratic equations by factoring. KEY: Quadratic Equations | Solve Quadratic Equations | Factoring 7. ANS: C Multiply the real numbers and imaginary numbers separately. Feedback A B C D Check your calculation. Check the sign. Correct! Multiply the imaginary numbers again. Algebra 2 ---- 1st Semester Final Exam Review PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.2 Perform operations with pure imaginary numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: IL J 6B.1 | IL J 6B TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers 8. ANS: A Multiply the real numbers and imaginary numbers separately. Feedback A B C D Check your calculation. Check the sign. Correct! Compute again. PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.2 Perform operations with pure imaginary numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: IL J 6B.1 | IL J 6B TOP: Perform operations with pure imaginary numbers. KEY: Imaginary Numbers 9. ANS: A Combine the real and imaginary parts of the complex numbers to add them. Feedback A B C D Correct! Combine the real parts and then combine the imaginary parts. Add the real and imaginary parts of the two numbers separately. Did you combine the similar terms correctly? PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.3 Perform addition and subtraction operations with complex numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: IL J 6B.3 | IL J 6B.7 | IL J 6B TOP: Perform addition and subtraction operations with complex numbers. KEY: Complex Numbers | Add Complex Numbers | Subtract Complex Numbers 10. ANS: B . Combine the Use the FOIL method to multiply the complex numbers and use the formula real parts and then the imaginary parts of the two numbers. Feedback A B C D Did you combine the real parts? Correct! Use the value of i2. Did you use the FOIL method to find the product? PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.4 Perform multiplication operations with complex numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: IL J 6B.3 | IL J 6B.7 | IL J 6B Algebra 2 ---- 1st Semester Final Exam Review TOP: Perform multiplication operations with complex numbers. KEY: Complex Numbers | Multiply Complex Numbers 11. ANS: D Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression. Feedback A B C D Multiply the numerator with the conjugate of the denominator. Have you multiplied the constant in the numerator with its conjugate of the denominator? Did you multiply the conjugates correctly in the denominator? Correct! PTS: 1 DIF: Average REF: Lesson 5-4 OBJ: 5-4.5 Perform division operations with complex numbers. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 6B TOP: Perform division operations with complex numbers. KEY: Complex Numbers | Divide Complex Numbers 12. ANS: A To complete the square for any quadratic expression of the form . the result. Then, add the result to STA: IL J 6B.3 | IL J 6B.7 | IL J , find half of b, and square Feedback A B C D Correct! Did you make the quadratic expression a perfect square? Did you verify the answer by substituting the values? Did you check the signs of the roots? PTS: 1 DIF: Average REF: Lesson 5-5 OBJ: 5-5.2 Solve quadratic equations by completing the square. NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: IL J 8D TOP: Solve quadratic equations by completing the square. KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square 13. ANS: D To complete the square for any quadratic expression of the form , find half of b, and square the result. Then, add the result to . Feedback A B C D Did you make the quadratic expression a perfect square? Did you check the signs of the roots? Find both the solutions. Correct! PTS: OBJ: NAT: TOP: KEY: 1 DIF: Average REF: Lesson 5-5 5-5.2 Solve quadratic equations by completing the square. NA 1 | NA 3 | NA 7 | NA 10 | NA 2 STA: IL J 8D Solve quadratic equations by completing the square. Quadratic Equations | Solve Quadratic Equations | Completing the Square Algebra 2 ---- 1st Semester Final Exam Review 14. ANS: D The solution of a quadratic equation of the form the formula , where , is obtained by using . Feedback A B C D Did you substitute the values of a, b, and c correctly in the formula? Did you evaluate the discriminant correctly? Did you use the correct formula? Correct! PTS: OBJ: NAT: TOP: KEY: 15. ANS: If If 1 DIF: Average REF: Lesson 5-6 5-6.1 Solve quadratic equations by using the Quadratic Formula. NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 8D Solve quadratic equations by using the Quadratic Formula. Quadratic Equations | Solve Quadratic Equations | Quadratic Formula C and is a perfect square, then the roots are rational. and is not a perfect square, then the roots are real and irrational. Feedback A B C D Did you use the correct formula for the discriminant? Did you check the sign of the answer? Correct! Did you use the correct order of operations while evaluating the discriminant? PTS: OBJ: NAT: TOP: KEY: 16. ANS: If 1 DIF: Basic REF: Lesson 5-6 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation. NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 8D Use the discriminant to determine the number and types of roots of a quadratic equation. Quadratic Equations | Roots of Quadratic Equations | Discriminates C , then the roots are complex. Feedback A B C D Did you use the correct order of operations while evaluating the discriminant? Did you use the correct formula for the discriminant? Correct! Did you check the sign of the answer? PTS: 1 DIF: Basic REF: Lesson 5-6 OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: IL J 8D TOP: Use the discriminant to determine the number and types of roots of a quadratic equation. KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates 17. ANS: A The vertex form of a quadratic function is . . The equation of the axis of symmetry of a parabola is Algebra 2 ---- 1st Semester Final Exam Review Feedback A B C D Correct! Did you check the x-coordinate of the vertex? Did you identify the coordinates of the vertex correctly? Did you use the correct equation of the axis of symmetry of a parabola? PTS: 1 DIF: Basic REF: Lesson 5-7 OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k. NAT: NA 2 | NA 7 | NA 8 | NA 10 | NA 6 STA: IL J 8B.4 | IL J 8B TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k. KEY: Quadratic Functions | Axis of Symmetry 18. ANS: C The vertex form of a quadratic function is . The equation of the axis of symmetry of a parabola is . Feedback A B C D Did you use the correct equation of the axis of symmetry? Did you check the x-coordinate of the vertex? Correct! Did you identify the coordinates of the vertex correctly? PTS: 1 DIF: Basic REF: Lesson 5-7 OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k. NAT: NA 2 | NA 7 | NA 8 | NA 10 | NA 6 STA: IL J 8B.4 | IL J 8B TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k. KEY: Quadratic Functions | Axis of Symmetry 19. ANS: C If the vertex and another point on the graph of a parabola are known, the equation of the parabola can be written in vertex form. Feedback A B C D Did you substitute correctly in the vertex form of the equation? Did you find the correct coefficient values? Correct! Did you check the signs of the coefficients? PTS: OBJ: NAT: TOP: KEY: 20. ANS: If 1 DIF: Average REF: Lesson 5-7 5-7.2 Write a quadratic function in the form y = a(x - h)^2 + k. NA 2 | NA 7 | NA 8 | NA 10 | NA 6 STA: IL J 8B Write a quadratic function in the form y = a(x – h)^2 + k. Quadratic Functions B are the coordinates of a point on a circle, is the center, and r is the radius, then the equation of this circle is . Feedback A Did you subtract the y-coordinate of the center from y? Algebra 2 ---- 1st Semester Final Exam Review B C D Correct! Take the square of the radius on the right side of the equation. Did you subtract the x-coordinate of the center from x? PTS: 1 DIF: Average REF: Lesson 10-3 OBJ: 10-3.1 Write equations of circles. NAT: NA 2 | NA 6 | NA 9 | NA 10 | NA 3 STA: IL J 8B.9 | IL J 8B TOP: Write equations of circles. KEY: Circles | Equations of Circles 21. ANS: A If is the equation of a circle in standard form, then circle and r is the radius. is the center of the Feedback A B C D Correct! Did you calculate the radius correctly? The y-coordinate of the center of the circle is incorrect. How do you determine the coordinates of the center of a circle? PTS: NAT: TOP: 22. ANS: 1 DIF: Advanced REF: Lesson 10-3 OBJ: 10-3.2 Graph circles. NA 2 | NA 6 | NA 9 | NA 10 | NA 3 STA: IL J 8B.5 | IL J 8B Graph circles. KEY: Circles | Graph Circles C If is the equation of a circle in standard form, then circle and r is the radius. is the center of the Feedback A B C D How do you determine the coordinates of the center? The y-coordinate of the center of the circle is incorrect. Correct! Did you calculate the radius correctly? PTS: NAT: TOP: 23. ANS: 1 DIF: Advanced REF: Lesson 10-3 OBJ: 10-3.2 Graph circles. NA 2 | NA 6 | NA 9 | NA 10 | NA 3 STA: IL J 8B.5 | IL J 8B Graph circles. KEY: Circles | Graph Circles B The equation of an ellipse is , where is the center of the ellipse, 2a is the length of the major axis, and 2b is the length of the minor axis. Feedback A B C D Did you use the correct expression for the length of the two axes? Correct! The center of the ellipse is not at the origin. Take the squares of the values of a and b for the ellipse. PTS: 1 DIF: Advanced REF: Lesson 10-4 OBJ: 10-4.1 Write equations of ellipses. NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3 STA: IL J 8B.9 | IL J 8B Algebra 2 ---- 1st Semester Final Exam Review TOP: Write equations of ellipses. KEY: Ellipses | Equations of Ellipses 24. ANS: C You can determine the type of conic section represented by the equation , where , by checking the relationship between A and C. Feedback A B C D The coefficients of neither x2 nor y2 is zero. The coefficients of x2 and y2 are equal. Correct! The coefficients of x2 and y2 are equal and have the same signs. PTS: OBJ: NA 3 STA: KEY: 1 DIF: Basic REF: Lesson 10-6 10-6.2 Identify conic sections from their equations. NAT: NA 2 | NA 6 | NA 9 | NA 10 | IL J 8B.5 | IL J 8B TOP: Identify conic sections from their equations. Conic Sections | Equations of Conic Sections | Identify Conic Sections SHORT ANSWER 25. ANS: 3.6 ft When the water hits the ground, its height will be zero. Replace h(d) by 0 in the given quadratic function and solve for d. PTS: 1 DIF: Basic TOP: Solve multi-step problems. 26. ANS: 4s Replace REF: Lesson 5-2 OBJ: 5-2.3 Solve multi-step problems. KEY: Solve multi-step problems. in the given quadratic function and solve for t. PTS: 1 DIF: Average TOP: Solve multi-step problems. 27. ANS: x=5 REF: Lesson 5-2 OBJ: 5-2.3 Solve multi-step problems. KEY: Solve multi-step problems. Solve the quadratic equation PTS: 1 DIF: Average REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems. TOP: Solve multi-step problems. KEY: Solve multi-step problems. 28. ANS: Length is 20 meters and height is 10 meters. Solve the quadratic equation PTS: 1 DIF: Average TOP: Solve multi-step problems. 29. ANS: REF: Lesson 5-3 OBJ: 5-3.3 Solve multi-step problems. KEY: Solve multi-step problems. Algebra 2 ---- 1st Semester Final Exam Review 1.4 ft Repalce in the quadratic equation and solve for w. PTS: 1 DIF: Advanced TOP: Solve multi-step problems. 30. ANS: REF: Lesson 5-5 OBJ: 5-5.3 Solve multi-step problems. KEY: Solve multi-step problems. Use the vertex form of the quadratic equation PTS: 1 DIF: Basic TOP: Solve multi-step problems. 31. ANS: REF: Lesson 5-7 OBJ: 5-7.3 Solve multi-step problems. KEY: Solve multi-step problems. Find an equation of the parabola of the form PTS: 1 DIF: Average problems. TOP: Solve multi-step problems. to model the trajectory of the rocket. with vertex and focus REF: Lesson 10-2 OBJ: 10-2.3 Solve multi-step KEY: Solve multi-step problems. Algebra 2 ---- 1st Semester Final Exam Review