Algebra 2 Chapter 5 Practice Test (Review)

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1 Name: Class: Date: Algebra 2 Chapter 5 Practice Test (Review) Multiple Choice Identify the choice that best completes the statement or answers the question. Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.. y = (x + )(6x 6) 6x 2 a. linear function linear term: 35x constant term: 6 b. quadratic function quadratic term: 6x 2 linear term: 35x constant term: 6 c. linear function linear term: 0x constant term: 6 d. quadratic function quadratic term: 6x 2 linear term: 0x constant term: 6 2. Find a quadratic function to model the values in the table. Predict the value of y for x = 6. x y a. y = 2x 2 + 2x 2; 58 c. y = 2x 2 2x 2; 58 b. y = 2x 2 2x 2; 60 d. y = 2x 2 + 2x + 2; A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake s population of waterfowl on each of the next six weeks. Week Population ,070,37 a. Find a quadratic function that models the data as a function of x, the number of weeks. b. Use the model to estimate the number of waterfowl at the lake on week 8. a. P(x) = 25x 2 28x + 585;,64 waterfowl b. P(x) = 30x x + 535; 2,679 waterfowl c. P(x) = 25x 2 28x + 585;,96 waterfowl d. P(x) = 30x x + 535; 2,20 waterfowl

2 Name: 4. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = 3x 2 + 6x + 0, where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit. a.,000 units; $300 c.,000 units; $600 b. 3,000 units; $00 d. 2,000 units; $00 5. Use vertex form to write the equation of the parabola. a. y = 3(x 2) c. y = 3(x + 2) b. y = 3(x 2) 2 2 d. y = (x + 2) Use vertex form to write the equation of the parabola. a. y = (x 2) 2 2 c. y = (x 2) 2 2 b. y = (x + 2) d. y = (x + 2) 2 2 2

3 Name: 7. Write y = 2x 2 + 2x + 4 in vertex form. a. y = 2(x + 2) c. y = (x + 3) b. y = 6(x + 9) 2 4 d. y = 2(x + 3) 2 4 Write the equation of the parabola in vertex form. 8. vertex (4, 2), point (0, 50) a. y = (x + 4) 2 2 c. y = 50(x 4) b. y = 3(x 4) 2 2 d. y = 3(x + 4) vertex ( 3, 2), point ( 2, 6) a. y = 4(x + 3) 2 2 c. y = 4(x 3) 2 2 b. y = 2(x 3) 2 2 d. y = 6(x + 3) Factor the expression. 0. 5x 2 2x a. x( 5x 2) c. 3x(5x + 7) b. 5x(x + 7) d. 5x(x 3 + 7). 8x 2 + 2x 6 a. 2( 4x 2 + 2x 6) c. 8x( 2x 3) b. 8x 2 + 2x 6 d. 4( 2x 2 3x + 4) 2. x 2 + 4x + 48 a. (x + 6)(x 8) c. (x 8)(x 6) b. (x + 8)(x 6) d. (x + 6)(x + 8) 3. x 2 6x + 8 a. (x + 4)(x + 2) c. (x 4)(x + 2) b. (x 2)(x 4) d. (x 2)(x + 4) 4. x 2 2x 63 a. (x 9)(x + 7) c. (x 9)(x 7) b. (x + 7)(x + 9) d. (x 7)(x + 9) 5. 3x x + 35 a. (x + 5)(3x + 7) c. (3x + 5)(x 7) b. (3x + 7)(x 5) d. (3x + 5)(x + 7) 6. 5x 2 22x 5 a. (5x + 3)(x + 5) c. (5x + 3)(x 5) b. (x + 3)(5x 5) d. (5x 5)(x 3) 7. 6x x + 25 a. (4x 5) 2 c. (4x + 5) 2 b. (4x + 5)( 4x 5) d. ( 4x + 5) 2 3

4 Name: 8. 9x 2 6 a. (3x + 4)( 3x 4) c. ( 3x + 4)(3x 4) b. (3x + 4)(3x 4) d. (3x 4) 2 9. Solve by factoring. 4x x 32 = 0 a. 8, 2 b. 8, 4 c. 8, d., x 2 = 2 Solve the equation by finding square roots. 2 2 a. 7 c., 3 3 b. 7, 7 d. 7, x 2 = 47 a , b. 7 6, 7 6 c. 6 7, 6 7 d , The function y = 6t models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second. a seconds c seconds b..02 seconds d. 5.5 seconds 23. Use a graphing calculator to solve the equation 5x 2 + 6x 9 = 0. If necessary, round to the nearest hundredth. a..47,.47 c. 0.87, 2.07 b..74, 4.4 d. 2.07, Simplify 75 using the imaginary number i. a. i 75 b. 5i 7 c. 5 7 d. 5 7 Write the number in the form a + bi a i c i b. 0 + i 4 d i a. 6 + i 48 c. 6 4i 3 b. 6 4i 3 d i Find the additive inverse of 7 + 5i. a. 7 5i c. 7 5i b i d i 4

5 Name: Simplify the expression. 28. ( + 6i) + ( 4 + 2i) a. 5 8i c i b. 5 2i d. 3i 29. (2 5i) (3 + 4i) a. + 9i c. 9i b. 5 i d. 0i 30. ( 6i)( 6i) a. 36 b. 36 c. 36i d. 36i 3. (2 + 5i)( + 5i) a i c i b i d i Solve the equation x = 0 a. 4 3 i, 4 3 i c. 3 4 i, 3 4 i b. 6 9 i, 6 9 i d. 4 3, x 2 + 8x + 8 = 25 a. 4, 4 c. 4, 4 b. 4, 4 d. 4, 4 Solve the quadratic equation by completing the square. 34. x 2 + 0x + 4 = 0 a. 0 ± 6 c. 5 ± 6 b. 00 ± d. 5 ± 35. x 2 + 0x + 35 = 0 a. 0 ± 5 c. 00 ± i 0 b. 5 ± i 5 d. 5 ± i x 2 + 6x + 66 = 0 a. 256 ± i 2 c. 8 ± i 2 b. 8 ± i 62 d. 6 ± x 2 + 2x + 4 = 0 a. 6 ± i 3 c. 44 ± i 5 b. 6 ± i 5 d. 2 ± 3 5

6 Name: Use the Quadratic Formula to solve the equation x 2 + 9x 2 = 0 a. 2 5, 4 b. 5, 2 c. 56 5, 3 d. 2, x 2 + x + 8 = 0 a. b. 4 ± 4 ± x 2 x + 3 = 0 a. 8 ± 47 8 b. 8 ± i 94 8 c. d. c. d. 2 ± ± ± i ± i x 2 5x 0 = 0 a..6,.6 c. 2.95,.7 b..47, 0.85 d. 0.85,.47 Short Answer 42. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again. a. Find a quadratic model for the data in the table. b. Use the model to estimate the population of bacteria at 9 hours. Time (hours) Population (000s)

7 Name: 43. Graph y = x 2 + 3x + 2. Identify the vertex and the axis of symmetry. 44. Graph y = 3x 2 2x + 3. What is the minimum value of the function? 45. Graph y = 3x 2 + 6x + 5. Does the function have a maximum or minimum value? What is this value? 7

8 Name: 46. A science museum is going to put an outdoor restaurant along one wall of the museum. The restaurant space will be rectangular. Assume the museum would prefer to maximize the area for the restaurant. a. Suppose there is 20 feet of fencing available for the three sides that require fencing. How long will the longest side of the restaurant be? b. What is the maximum area? 47. Graph y = (x 7) Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. 49. The Sears Tower in Chicago is 454 feet tall. The function y = 6t models the height y in feet of an object t seconds after it is dropped from the top of the building. a. After how many seconds will the object hit the ground? Round your answer to the nearest tenth of a second. b. What is the height of the object 5 seconds after it is dropped from the top of the Sears Tower? 8

9 Algebra 2 Chapter 5 Practice Test (Review) Answer Section MULTIPLE CHOICE. ANS: C PTS: DIF: L2 REF: 5- Modeling Data With Quadratic Functions OBJ: 5-. Quadratic Functions and Their Graphs STA: CO 2. CO 2.2 CO 2.6 CO 2.4 TOP: 5- Example KEY: quadratic function quadratic term linear term constant term 2. ANS: C PTS: DIF: L3 REF: 5- Modeling Data With Quadratic Functions OBJ: 5-.2 Using Quadratic Models STA: CO 2. CO 2.2 CO 2.6 CO 2.4 TOP: 5- Example 3 KEY: quadratic function quadratic model 3. ANS: C PTS: DIF: L2 REF: 5- Modeling Data With Quadratic Functions OBJ: 5-.2 Using Quadratic Models STA: CO 2. CO 2.2 CO 2.6 CO 2.4 TOP: 5- Example 4 KEY: quadratic model quadratic function word problem problem solving multi-part question 4. ANS: A PTS: DIF: L3 REF: 5-2 Properties of Parabolas OBJ: Finding Maximum and Minimum Values STA: CO 2.4 CO 2.5 TOP: 5-2 Example 4 KEY: maximum value word problem problem solving multi-part question 5. ANS: C PTS: DIF: L2 REF: 5-3 Translating Parabolas OBJ: 5-3. Using Vertex Form STA: CO 2.4 CO 2.5 CO 4. TOP: 5-3 Example 2 KEY: parabola equation of a parabola vertex form 6. ANS: C PTS: DIF: L2 REF: 5-3 Translating Parabolas OBJ: 5-3. Using Vertex Form STA: CO 2.4 CO 2.5 CO 4. TOP: 5-3 Example 2 KEY: parabola equation of a parabola vertex form 7. ANS: D PTS: DIF: L2 REF: 5-3 Translating Parabolas OBJ: 5-3. Using Vertex Form STA: CO 2.4 CO 2.5 CO 4. TOP: 5-3 Example 4 KEY: parabola vertex form 8. ANS: B PTS: DIF: L3 REF: 5-3 Translating Parabolas OBJ: 5-3. Using Vertex Form STA: CO 2.4 CO 2.5 CO 4. TOP: 5-3 Example 2 KEY: parabola equation of a parabola vertex form 9. ANS: A PTS: DIF: L3 REF: 5-3 Translating Parabolas OBJ: 5-3. Using Vertex Form STA: CO 2.4 CO 2.5 CO 4. TOP: 5-3 Example 2 KEY: parabola equation of a parabola vertex form

10 0. ANS: C PTS: DIF: L2 OBJ: 5-4. Finding Common and Binomial Factors TOP: 5-4 Example KEY: factor a quadratic expression quadratic expression greatest common factor of an expression. ANS: D PTS: DIF: L2 OBJ: 5-4. Finding Common and Binomial Factors TOP: 5-4 Example KEY: factor a quadratic expression quadratic expression greatest common factor of an expression 2. ANS: D PTS: DIF: L2 OBJ: 5-4. Finding Common and Binomial Factors TOP: 5-4 Example 2 KEY: factor a quadratic expression quadratic expression 3. ANS: B PTS: DIF: L2 OBJ: 5-4. Finding Common and Binomial Factors TOP: 5-4 Example 3 KEY: factor a quadratic expression quadratic expression 4. ANS: A PTS: DIF: L2 OBJ: 5-4. Finding Common and Binomial Factors TOP: 5-4 Example 4 KEY: factor a quadratic expression quadratic expression 5. ANS: D PTS: DIF: L2 OBJ: 5-4. Finding Common and Binomial Factors TOP: 5-4 Example 5 KEY: factor a quadratic expression quadratic expression 6. ANS: C PTS: DIF: L2 OBJ: 5-4. Finding Common and Binomial Factors TOP: 5-4 Example 6 KEY: factor a quadratic expression quadratic expression 7. ANS: C PTS: DIF: L2 OBJ: Factoring Special Expressions TOP: 5-4 Example 7 KEY: factor a quadratic expression factor a trinomial perfect square trinomial 8. ANS: B PTS: DIF: L2 OBJ: Factoring Special Expressions TOP: 5-4 Example 8 KEY: difference of two squares factoring a difference of two squares 9. ANS: C PTS: DIF: L2 REF: 5-5 Quadratic Equations OBJ: 5-5. Solving by Factoring and Finding Square Roots STA: CO 2.4 CO 2.5 TOP: 5-5 Example KEY: factor a quadratic expression 20. ANS: B PTS: DIF: L2 REF: 5-5 Quadratic Equations OBJ: 5-5. Solving by Factoring and Finding Square Roots STA: CO 2.4 CO 2.5 TOP: 5-5 Example 2 KEY: square root 2. ANS: B PTS: DIF: L2 REF: 5-5 Quadratic Equations OBJ: 5-5. Solving by Factoring and Finding Square Roots STA: CO 2.4 CO 2.5 TOP: 5-5 Example 2 KEY: square root 2

11 22. ANS: D PTS: DIF: L2 REF: 5-5 Quadratic Equations OBJ: 5-5. Solving by Factoring and Finding Square Roots STA: CO 2.4 CO 2.5 TOP: 5-5 Example 3 KEY: round a number word problem problem solving 23. ANS: C PTS: DIF: L2 REF: 5-5 Quadratic Equations OBJ: Solving by Graphing STA: CO 2.4 CO 2.5 TOP: 5-5 Example 5 KEY: graphing calculator round a number 24. ANS: B PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: 5-6. Identifying Complex Numbers TOP: 5-6 Example KEY: i imaginary number 25. ANS: C PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: 5-6. Identifying Complex Numbers TOP: 5-6 Example 2 KEY: i imaginary number complex number 26. ANS: B PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: 5-6. Identifying Complex Numbers TOP: 5-6 Example 2 KEY: i imaginary number complex number 27. ANS: C PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: Operations With Complex Numbers TOP: 5-6 Example 4 KEY: additive inverse complex number 28. ANS: C PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: Operations With Complex Numbers TOP: 5-6 Example 5 KEY: simplifying a complex number complex number 29. ANS: C PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: Operations With Complex Numbers TOP: 5-6 Example 5 KEY: simplifying a complex number complex number 30. ANS: B PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: Operations With Complex Numbers TOP: 5-6 Example 6 KEY: simplifying a complex number complex number multiplying complex numbers 3. ANS: A PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: Operations With Complex Numbers TOP: 5-6 Example 6 KEY: simplifying a complex number complex number multiplying complex numbers 32. ANS: A PTS: DIF: L2 REF: 5-6 Complex Numbers OBJ: Operations With Complex Numbers TOP: 5-6 Example 7 KEY: complex number imaginary number 33. ANS: B PTS: DIF: L2 REF: 5-7 Completing the Square OBJ: 5-7. Solving Equations by Completing the Square STA: CO 2. CO 2.2 CO 2.3 CO 2.4 TOP: 5-7 Example KEY: perfect square trinomial 34. ANS: D PTS: DIF: L2 REF: 5-7 Completing the Square OBJ: 5-7. Solving Equations by Completing the Square STA: CO 2. CO 2.2 CO 2.3 CO 2.4 TOP: 5-7 Example 3 KEY: completing the square 3

12 35. ANS: D PTS: DIF: L2 REF: 5-7 Completing the Square OBJ: 5-7. Solving Equations by Completing the Square STA: CO 2. CO 2.2 CO 2.3 CO 2.4 TOP: 5-7 Example 4 KEY: completing the square 36. ANS: C PTS: DIF: L2 REF: 5-7 Completing the Square OBJ: 5-7. Solving Equations by Completing the Square STA: CO 2. CO 2.2 CO 2.3 CO 2.4 TOP: 5-7 Example 4 KEY: completing the square 37. ANS: B PTS: DIF: L2 REF: 5-7 Completing the Square OBJ: 5-7. Solving Equations by Completing the Square STA: CO 2. CO 2.2 CO 2.3 CO 2.4 TOP: 5-7 Example 4 KEY: completing the square 38. ANS: B PTS: DIF: L2 REF: 5-8 The Quadratic Formula OBJ: 5-8. Using the Quadratic Formula TOP: 5-8 Example KEY: Quadratic Formula 39. ANS: A PTS: DIF: L2 REF: 5-8 The Quadratic Formula OBJ: 5-8. Using the Quadratic Formula TOP: 5-8 Example KEY: Quadratic Formula 40. ANS: C PTS: DIF: L2 REF: 5-8 The Quadratic Formula OBJ: 5-8. Using the Quadratic Formula TOP: 5-8 Example 2 KEY: Quadratic Formula 4. ANS: B PTS: DIF: L2 REF: 5-5 Quadratic Equations OBJ: Solving by Graphing STA: CO 2.4 CO 2.5 TOP: 5-5 Example 4 KEY: graphing calculator round a number SHORT ANSWER 42. ANS: a. P = 0.38x x b. 3,830 bacteria PTS: DIF: L2 REF: 5- Modeling Data With Quadratic Functions OBJ: 5-.2 Using Quadratic Models STA: CO 2. CO 2.2 CO 2.6 CO 2.4 TOP: 5- Example 4 KEY: quadratic model quadratic function problem solving word problem multi-part question 4

13 43. ANS: Ê vertex: 3 2, ˆ Ë Á 4, axis of symmetry: x = 3 2 PTS: DIF: L2 REF: 5-2 Properties of Parabolas OBJ: 5-2. Graphing Parabolas STA: CO 2.4 CO 2.5 TOP: 5-2 Example 2 KEY: quadratic function vertex of a parabola axis of symmetry 44. ANS: minimum: PTS: DIF: L2 REF: 5-2 Properties of Parabolas OBJ: Finding Maximum and Minimum Values STA: CO 2.4 CO 2.5 TOP: 5-2 Example 3 KEY: quadratic function minimum value 5

14 45. ANS: maximum value; 8 PTS: DIF: L2 REF: 5-2 Properties of Parabolas OBJ: Finding Maximum and Minimum Values STA: CO 2.4 CO 2.5 TOP: 5-2 Example 3 KEY: quadratic function minimum value maximum value 46. ANS: a. 40 ft b.,600 ft 2 PTS: DIF: L3 REF: 5-2 Properties of Parabolas OBJ: Finding Maximum and Minimum Values STA: CO 2.4 CO 2.5 TOP: 5-2 Example 3 KEY: maximum value quadratic function area problem solving word problem multi-part question 6

15 47. ANS: PTS: DIF: L2 REF: 5-3 Translating Parabolas OBJ: 5-3. Using Vertex Form STA: CO 2.4 CO 2.5 CO 4. TOP: 5-3 Example KEY: graphing translation parabola 48. ANS: x 2 9; (x 3)(x + 3) PTS: DIF: L2 OBJ: Factoring Special Expressions TOP: 5-4 Example 8 KEY: difference of two squares factoring a difference of two squares 49. ANS: a. 9.5 seconds b.,054 ft PTS: DIF: L3 REF: 5-5 Quadratic Equations OBJ: 5-5. Solving by Factoring and Finding Square Roots STA: CO 2.4 CO 2.5 TOP: 5-5 Example 3 KEY: round a number word problem problem solving multi-part question 7

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