Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question.
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1 Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers is not both a perfect square and a perfect cube? a b c d Factor the trinomial. 3. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check. 4. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check. 5. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check. 6. Factor: 7. Factor: 8. Which polynomial, written in simplified form, represents the area of this rectangle? 8 x 4y x + 5y 9. Expand and simplify: 10. Expand and simplify:
2 Short Answer 11. Identify the greatest common factor of the terms in this set. 12. Copy and complete this statement. 13. Expand and simplify. 14. Factor: 15. The area of a square is represented by the trinomial. Determine an expression for the perimeter of the square. Problem 16. Use factoring to determine whether 4913 is a perfect square, a perfect cube, or neither. 17. Calculate the volume of the largest possible sphere that can fit in a cube with volume cm 3. Give the volume to the nearest tenth of a cubic centimetre. Explain your steps. 18. A student is asked to find an integer to replace so that can be factored. The student said the only possible integer is. Is the student correct? Explain. 19. Find the area of the rectangle. 5 b 6 3 b Factor. Explain your steps.
3 Review Unit Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Moderate REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots LOC: 10.AN1 2. ANS: B PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5 3. ANS: B PTS: 1 DIF: Easy REF: 3.4 Modelling Trinomials as Binomial Products LOC: 10.AN5 4. ANS: A PTS: 1 DIF: Easy REF: 3.4 Modelling Trinomials as Binomial Products LOC: 10.AN5 5. ANS: B PTS: 1 DIF: Easy REF: 3.4 Modelling Trinomials as Binomial Products LOC: 10.AN5 6. ANS: C PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5 7. ANS: B PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5 8. ANS: D PTS: 1 DIF: Moderate REF: 3.7 Multiplying Polynomials LOC: 10.AN4 9. ANS: A PTS: 1 DIF: Moderate REF: 3.7 Multiplying Polynomials LOC: 10.AN4 10. ANS: A PTS: 1 DIF: Moderate REF: 3.7 Multiplying Polynomials LOC: 10.AN4 SHORT ANSWER 11. ANS: PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5 12. ANS: PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5 13. ANS:
4 PTS: 1 DIF: Moderate REF: 3.7 Multiplying Polynomials LOC: 10.AN4 14. ANS: PTS: 1 DIF: Easy REF: 3.8 Factoring Special Polynomials LOC: 10.AN5 15. ANS: PTS: 1 DIF: Moderate REF: 3.8 Factoring Special Polynomials LOC: 10.AN5 PROBLEM 16. ANS: Write 4913 as a product of its prime factors. PTS: 1 DIF: Moderate REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots LOC: 10.AN1 17. ANS: To determine the volume of the sphere, first determine the edge length of the cube. The edge length, e, of a cube is equal to the cube root of its volume. The radius, r, of the largest sphere that will fit in the cube is one-half of the edge length of the cube. Use the formula for the volume of a sphere.
5 he volume of the largest possible sphere that can fit in the cube is approximately cm 3. PTS: 1 DIF: Difficult REF: 3.2 Perfect Squares, Perfect Cubes, and Their Roots LOC: 10.AN1 18. ANS: Replace with : Find two integers whose product is and whose sum is. The integers are 7 and. So, The student is not correct because is not the only possible integer. The product of any pair of integers whose sum is will allow to be factored. For example, replace with : Find two integers whose product is and whose sum is. The integers are 8 and. So, There are an infinite number of integers that could replace so that... can be factored: PTS: 1 DIF: Difficult REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4 10.AN5 19. ANS: Use the formula for the area, A, of a rectangle. Use the distributive property. The area of the rectangle is square units. PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5 KEY: Problem-Solving Skills
6 20. ANS: As written, each term of the binomial is not a perfect square. But the terms have a common factor 4. Remove this common factor. Write each term in the binomial as a perfect square. PTS: 1 DIF: Moderate REF: 3.8 Factoring Special Polynomials LOC: 10.AN5
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