ExamView - Chapter 5 Practice Test - Ms Jeong W 5 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Factor the binomial 15y2 - 48y.

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  • Name: ________________________ Class: ___________________ Date: __________ ID: A

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    Chapter 5 Practice Test

    Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

    ____ 1. Factor the binomial 15y 2 48y.a. 3(5y 2 16y) c. y(15y 48)b. 3y(5y 16y) d. 3y(5y 16)

    ____ 2. Factor the trinomial 4 8n + 12n 2 .a. 4(2n + 3n 2) c. 2(2 4n + 6n 2)b. 4(1 2n + 3n 2) d. 4(1 + 2n + 3n 2)

    ____ 3. Factor the trinomial 24c 3d 40c2 d 2 32cd 3 .a. 8cd(3c2 5cd 4d 2) c. 8cd(3c2 + 5cd + 4d 2)b. 8cd(3c 2 + 5cd + 4d 2) d. 8cd(3c2 + 5cd + 4d 2)

    ____ 4. Factor the binomial 10m2 40m4 .a. 10m2(1 + 4m2 ) c. 10(m2 + 4m4)b. 10m2(4m2) d. 5m2 (2 + 8m2)

    ____ 5. Identify the greatest common factor of the terms in the trinomial 6s3 t4 + 12s4 t2 15s2 t3 .a. 6s2 t2 c. 3s2 t3

    b. 3s2 t2 d. 3s3 t2

    ____ 6. Factor the trinomial 20a 2 b 25ab + 45ab 2 .a. 5ab(4a 5 + 9b) c. ab(20a 25 + 45b)b. 5ab(4a 5ab + 9b) d. 5(4a 2 b 5ab + 9ab 2)

    ____ 7. Which expression represents the area of the shaded region?

    a. 2r(2r ) b. r2(1 ) c. r2(4 ) d. r(r 2)

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    ____ 8. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.a. y 2 + 3y + 12 c. y 2 + 8y + 15b. y 2 + 12y + 5 d. y 2 + 14y + 3

    ____ 9. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.a. 2a 2 + 29a + 12 c. 2a 2 + 14a + 63b. 2a 2 + 19a + 9 d. 2a 2 + 9a + 2

    ____ 10. Expand and simplify: (4 r)(7 r) a. 28 11r + r2 c. 28 + 3r + r2

    b. 28 3r + r2 d. 28 + 11r + r2

    ____ 11. Factor: v 2 13v + 36a. (v + 3)(v + 12) c. (v 4)(v 9)b. (v 3)(v 12) d. (v + 4)(v + 9)

    ____ 12. Factor: 24 2x + x 2a. (6 + x)(4 + x) c. (3 + x)(8 + x)b. (3 + x)(8 + x) d. (6 + x)(4 + x)

    ____ 13. Factor: 3b 2 + 15b + 18a. 3(b 2)(b + 3) c. 3(b 1)(b + 6)b. 3(b + 2)(b 3) d. 3(b + 1)(b 6)

    ____ 14. Factor: 4d 2 28d + 240a. 4(d + 3)(d 20) c. 4(d 3)(d + 20)b. 4(d + 5)(d 12) d. 4(d 5)(d + 12)

    ____ 15. Complete: (a + 6)(a ) = a 2 + a 12 a. (a + 6)(a 4) = a 2 + 4a 12 c. (a + 6)(a 2) = a 2 + 2a 12b. (a + 6)(a 2) = a 2 + 4a 12 d. (a + 6)(a 4) = a 2 + 2a 12

    ____ 16. Factor: c 2 4c 117a. (c 9)(c + 13) c. (c + 9)(c 13)b. (c 3)(c + 39) d. (c + 3)(c 39)

    ____ 17. Factor: 12 4g g 2

    a. (4 g)(3 + g) c. (6 g)(2 + g)b. (6 + g)(2 g) d. (4 + g)(3 g)

    ____ 18. Expand and simplify: (h 6)(h + 11) a. h 2 5h 66 c. h 2 + 17h 66b. h 2 + 5h 66 d. h 2 17h 66

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    ____ 19. Complete. (k )(k 5) = k 2 k + 135 a. (k 27)(k 22) = k 2 5k + 135 c. (k 27)(k 32) = k 2 5k + 135b. (k 27)(k 5) = k 2 32k + 135 d. (k 27)(k 5) = k 2 22k + 135

    ____ 20. Factor: 5m2 + 20m + 60a. 5(m + 2)(m 6) c. 5(m 4)(m + 3)b. 5(m 2)(m + 6) d. 5(m + 4)(m 3)

    ____ 21. Which multiplication sentence does this set of algebra tiles represent?

    a. (2x 2)(2x + 2) c. (2x 2 + 2x)(2x2 + 2x)b. (2x 2 + 2)(2x 2 + 2) d. (2x + 2)(2x + 2)

    ____ 22. Which set of algebra tiles represents 3x 2 + x + 4?

    a. c.

    b. d.

    ____ 23. Factor: 24b 2 + 50b 14a. 2(4b 1)(3b + 7) c. 2(4b 7)(3b + 1)b. 2(4b + 7)(3b + 1) d. 2(4b + 1)(3b 7)

    ____ 24. Expand and simplify: 3(1 2t)(9 + 4t) a. 24t2 + 42t + 27 c. 72t2 126t + 81b. 24t2 + 66t + 27 d. 24t2 42t + 27

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    ____ 25. Factor: 4 9z 13z2

    a. (2 13z)(2 + z) c. (2 + 13z)(2 z)b. (4 13z)(1 + z) d. (4 + 13z)(1 z)

    ____ 26. Which polynomial, written in simplified form, represents the area of this rectangle?

    a. 8x2 36xy 20y2 c. 16x 2 + 72xy 40y 2

    b. 8x2 + 22xy 20y2 d. 8x2 + 36xy 20y2

    ____ 27. Expand and simplify: (6x y)(3x + 8y) (2x 3y)2 a. 14x 2 + 51xy 17y 2 c. 14x 2 + 57xy + 1y2

    b. 14x 2 + 33xy + 1y2 d. 14x 2 + 57xy 17y 2

    ____ 28. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region.

    a. 5x2 + 31x + 66 c. 5x2 + 31x + 30b. 5x2 + 37x + 30 d. 5x2 + 37x + 66

    ____ 29. Factor: 16p 2 81q 2

    a. (4p 9q)2 c. (16p 9q)(p 9q)b. (4p + 9q)2 d. (4p + 9q)(4p 9q)

    ____ 30. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither.9a 2 + 9a + 36a. Difference of squares c. Neitherb. Perfect square trinomial

    ____ 31. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither.25g 2 9h 2

    a. Perfect square trinomial c. Neitherb. Difference of squares

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    ____ 32. Factor: 3z4 768z2

    a. 3z2 (z + 16)(z 16) c. z2(z + 48)(z 16)b. 3z2 (z + 16)2 d. 3z2 (z 16)2

    ____ 33. Factor: 162 2w4

    a. (9 w2)(18 w2 ) c. 2(9 w2)2

    b. 2(9 + w2)(3 + w)(3 w) d. 2(9 + w2)2

    ____ 34. Determine the area of the shaded region in factored form.

    a. 4(x + 12) c. (3x + 12)(x + 2)b. (3x + 2)(x + 12) d. (3x 2)(x 12)

    Short Answer

    35. Factor the binomial 85x 3 20x.

    36. Factor the trinomial 8m2 n 18n 2 2mn.

    37. Write an expression for the width of this rectangle.

    38. Identify the greatest common factor of the terms in this set. 8x2 y, 24y 2 , 18xy

    39. Factor: s2 33s + 32

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    40. Find and correct the errors in this factorization.w2 2w 80 = w 8 w + 10

    41. Find and correct the error(s) in this solution of factoring by decomposition.90y 2 + 77y 52 = 90y 2 + 117y 40y 52 = 9y(10y + 13) + 4(10y + 13) = (10y + 13)(9y + 4)

    42. Copy and complete this statement.

    (60a 25)(a 385) = + 9625

    43. Find and correct the errors in this solution.(11a + b)(2a 13b + 4)= 13a 2 143ab + 44a 2ab 13b 2 + 4b= 13a 2 145ab 13b 2 44a + 4b

    44. Expand and simplify. (5r 6s + s2)(13r + 3s 5s2)

    45. Factor: 49s2 64t2

    46. Find an integer to replace so that the trinomial is a perfect square.121x 2 308xy + y 2

    47. The area of a square is represented by the trinomial 36m2 + 84mn + 49n 2 . Determine an expression for the perimeter of the square.

    Problem

    48. A square is drawn inside a circle with radius 11x. a) Write an expression for the area of the shaded region.b) Factor the expression.

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    49. Find the area of the rectangle.

    50. Use decomposition to factor 81y 2 + 36y + 4. Explain your steps.

    51. A rectangle has length 14x and width y. Strips of width x 8 are cut from the rectangle as shown. Write an expression that represents the area of the rectangle that remains.

    52. Factor. Explain your steps.196x 2 16y 2

    53. A picture and its frame have dimensions as shown. a) Find an expression for the area of the frame, in factored form. b) Determine the area of the frame when s = 15 cm.

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    Chapter 5 Practice TestAnswer Section

    MULTIPLE CHOICE

    1. ANS: D PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    2. ANS: B PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    3. ANS: D PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    4. ANS: A PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    5. ANS: B PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    6. ANS: A PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    7. ANS: C PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    8. ANS: C PTS: 1 DIF: Easy REF: 3.4 Modelling Trinomials as Binomial Products LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    9. ANS: B PTS: 1 DIF: Easy REF: 3.4 Modelling Trinomials as Binomial Products LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    10. ANS: A PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

    11. ANS: C PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    12. ANS: D PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    13. ANS: D PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    14. ANS: D PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

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    15. ANS: B PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

    16. ANS: C PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    17. ANS: B PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    18. ANS: B PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

    19. ANS: B PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

    20. ANS: A PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    21. ANS: D PTS: 1 DIF: Easy REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    22. ANS: B PTS: 1 DIF: Easy REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    23. ANS: A PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    24. ANS: D PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

    25. ANS: B PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

    26. ANS: D PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

    27. ANS: D PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

    28. ANS: A PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

    29. ANS: D PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    30. ANS: C PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    31. ANS: B PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    32. ANS: A PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

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    33. ANS: B PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    34. ANS: B PTS: 1 DIF: Difficult REF: 3.8 Factoring Special PolynomialsLOC: 10.AN4 | 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    SHORT ANSWER

    35. ANS: 5x(17x2 4)

    PTS: 1 DIF: Easy REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    36. ANS: 2n(4m2 9n m)

    PTS: 1 DIF: Easy REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    37. ANS: a + 6b

    PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    38. ANS: 2y

    PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    39. ANS: s 32 s 1

    PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    40. ANS: w2 2w 80 = w + 8 w 10

    PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    41. ANS: 90y 2 + 77y 52 = 90y 2 + 117y 40y 52 = 9y(10y + 13) 4(10y + 13) = (10y + 13)(9y 4)

    PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

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    42. ANS: (60a 25)(a 385) = 60a 2 23 125a + 9625

    PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    43. ANS: (11a + b)(2a 13b + 4)= 22a 2 143ab + 44a + 2ab 13b 2 + 4b= 22a 2 141ab + 44a 13b 2 + 4b

    PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

    44. ANS: 65r2 63rs 12rs2 18s2 + 33s3 5s4

    PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

    45. ANS: 7s + 8t 7s 8t

    PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    46. ANS: 196

    PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

    47. ANS: 4 6m + 7n

    PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

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    PROBLEM

    48. ANS: a) The area of the shaded region is the area of the circle minus the area of the square.

    Use the formula for the area of a circle.A = r2

    A = (11x)2

    A = 121x 2

    To determine the area of the square, first determine the side length, s, of the square.Use the Pythagorean Theorem in right ABC.s2 = AB2 + BC2

    s2 = (11x)2 + (11x)2

    s2 = 121x2 + 121x 2

    s2 = 242x2

    s = 242x 2

    Use the formula for the area, A, of a square.A = s2

    A = 242x 2

    2

    A = 242x2

    The area, A, of the shaded region is:.A = 121x 2 242x 2

    b) 121x 2 242x 2 = 121x 2( 2)

    PTS: 1 DIF: Difficult REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Problem-Solving Skills

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    49. ANS: Use the formula for the area, A, of a rectangle. A = l w

    A = 5b 6 3b 2

    Use the distributive property. A = 5b(3b 2) + (6)(3b 2)

    A = 15b 2 10b 18b + 12

    A = 15b 2 28b + 12

    The area of the rectangle is 15b 2 28b + 12 square units.

    PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Problem-Solving Skills

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    50. ANS: 81y 2 + 36y + 4

    Check for common factors; there are none.

    The product of the coefficient of y2 and the constant term is: 81(4) = 324

    Write 36y as the sum of two terms whose coefficients have a product of 324.

    Factors of 324 Sum of Factors

    1, 324 1 + 324 = 325

    2, 162 2 + 162 = 164

    3, 108 3 + 108 = 111

    4, 81 4 + 81 = 85

    6, 54 6 + 54 = 60

    9, 36 9 + 36 = 45

    12, 27 12 + 27 = 39

    18, 18 18 + 18 = 36

    The two coefficients are 18 and 18, so write the trinomial 81y 2 + 36y + 4 as 81y 2 + 18y + 18y + 4.

    Remove a common factor from the 1st pair of terms, and from the 2nd pair of terms.81y 2 + 18y + 18y + 4 = 9y(9y + 2) + 2(9y + 2)

    Each product has a common binomial factor.81y 2 + 18y + 18y + 4 = (9y + 2)(9y + 2)

    So, 81y 2 + 36y + 4 = (9y + 2)(9y + 2)

    PTS: 1 DIF: Difficult REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Communication | Problem-Solving Skills

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    51. ANS: The length of the rectangle that remains is:14x (x 8) = 14x x + 8 = 13x + 8

    The width of the rectangle that remains is: y (x 8) = y x + 8

    Use the formula for the area, A, of a rectangle:A = lw

    A = (13x + 8)(y x + 8)

    A = 13x(y) + 13x(x) + 13x(8) + 8(y) + 8(x) + 8(8)

    A = 13xy 13x 2 + 104x + 8y 8x + 64

    A = 13xy 13x 2 + 96x + 8y + 64

    The expression 13xy 13x 2 + 96x + 8y + 64 represents the area of the rectangle that remains.

    PTS: 1 DIF: Difficult REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Problem-Solving Skills

    52. ANS: 196x 2 16y 2

    As written, each term of the binomial is not a perfect square. But the terms have a common factor 4. Remove this common factor.

    196x 2 16y 2

    = 4(49x 2 4y 2)

    Write each term in the binomial as a perfect square.

    4(49x 2 4y 2) = 4 (7x)2 (2y)2

    Write these terms in binomial factors.

    = 4(7x 2y)(7x + 2y)

    PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Communication | Problem-Solving Skills

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    53. ANS: a) The area, A, of the larger square is: 8s 2 = 64s2

    The area, A, of the smaller square is: (8s 4 4)2 = 8s 8 2

    = 64s2 128s + 64

    The area, A, of the frame is: A = 64s2 (64s2 128s + 64)

    A = 64s2 64s2 + 128s 64

    A = 128s 64

    A = 64(2s 1)

    b) When s = 15 cm, the area, A square centimetres, of the frame is:A = 64(2s 1)

    A = 64 2 15 1

    A = 1856The area of the frame is 1856 cm2 .

    PTS: 1 DIF: Difficult REF: 3.8 Factoring Special PolynomialsLOC: 10.AN4 | 10.AN5 TOP: Algebra and Number KEY: Problem-Solving Skills

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