Polynomials Practice Test

Transcription

1 Name: Class: Date: Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. From the list, which terms are like 7x? 7x 2, 6x, 5, 8x, 7x, 8x 2, 7 a. 7x 2, 6x, 8x, 7x, 8x 2 c. 7x b. 6x, 8x, 7x d. 7x 2, 7x, 7 2. Add. 8a 2 6 5a 2 4 a. 3a 2 10 b. 3a 4 10 c. 7 d. 7a 2 3. Subtract. ( 3n 2 8) (5 7n 2 ) a. 10n 2 15 c. 10n 2 3 b. 8n 2 15 d. 4n Subtract. ( 4b 6b 2 2) (8b 8 7b 2 ) a. 12b 13b 2 10 c. b 14b 2 5 b. 12b 13b 2 6 d. 12b b In the term 4s 2 t 2, the number 4 is best described as being the a. coefficient c. polynomial b. exponent d. variable 1

2 Name: 6. In the term 7p 3 q 4, the letter p is best described as being a(n) a. binomial c. exponent b. coefficient d. variable 7. The expression 3s 2 4s 2 can be described as a(n) a. binomial c. polynomial b. equation d. term 8. The expression 3a 3 3a can be described as a(n) a. binomial c. term b. equation d. trinomial 9. How many terms are there in the polynomial 4x 2 3x 5? a. 2 b. 3 c. 4 d What is the degree of the term 3p 2? a. 1 b. 2 c. 3 d The degree of the term 3p 4 q 3 r 2 is a. 2 b. 3 c. 7 d What is the degree of the polynomial 5g 2 2gh h 2 7? a. 1 b. 2 c. 4 d. 7 2

3 Name: 13. Which polynomial is represented by the following model? a. 2n 2 5n 3 c. 5n 2n 2 3 b. 2n 2 5n 3 d In the expression 2y 3 4y 5, the 2 is a(n) a. coefficient c. term b. exponent d. variable 15. The opposite expression for 2g 2 4gh 3h 2 6 is a. 2g 2 4gh 3h 2 6 c. 2g 2 4gh 3h 2 6 b. 2g 2 4gh 3h 2 6 d. 2g 2 4gh 3h What is the volume of this rectangular prism? a. 24 c. 24x 2 b. 24x d. 24x Multiply: 4(5x) a. 3 b. 7x c. 20x d. 9x 3

4 Name: 18. Multiply: 9(5x 2 4x) a. 45x 2 5x b. 45x 2 4x c. 14x 2 5x d. 45x 2 36x 19. How many terms are in the polynomial below? 4a 4 a. 4 b. 3 c. 2 d Name the coefficients of the variable in the polynomial 3x 2 7x 9. a. 3 b. 3, 7 c. 3, 7 d. 3, 9 4

5 Name: Completion Complete each statement. 1. Simplify the following by combining like terms. 4y 3y 2 y 3y 2 2y 2 2y 2. Simplify the following by combining like terms. 5d 4 7d 2 3. Subtract the following polynomials. (2n 5) ( 3n 2) 4. The quotient of 4.8t2 7.2t is _. 5. The total area of the figure, in simplified form, is _. 5

6 Name: Matching Match the correct term to each of the following descriptions. A term may be used more than once or not at all. a. binomial d. polynomial b. monomial e. trinomial c. opposite expressions 1. two expressions that add to zero 2. the specific name for an expression with one term 3. the specific name for an expression with three terms 4. an algebraic expression made up of terms connected by operations of addition and/or subtraction 6

7 Name: Short Answer 1. What is the total surface area of this rectangular prism? 2. Write a simplified expression for the area of this figure. What is the area of the figure? 7

8 Name: 3. Combine like terms. 6x 5x 2 4x 2x 2 4. What is the constant term in the polynomial below? 9m Expand. 5(q 3) 6. Expand. 7(5 t) 7. Is the polynomial below a monomial, binomial, or trinomial? 2p 8. Determine the product of ( 2x) ( 3x). 8

9 Name: 9. Determine the area of a square with side length 2x. 10. Identify the like terms in the following list of terms. 3c 2, 5c 2 d, 2d 2, 4c 2, 2cd 2 9

10 Name: Problem 1. Write a polynomial for the perimeter of this trapezoid. Simplify the polynomial. 10

11 Name: 2. a) Write a simplified expression representing the perimeter of the figure. b) If s = 5 cm, what is the perimeter of the figure? 11

12 Name: 3. The diagram below shows one rectangle inside another. a) Determine the area of each rectangle. b) Determine the area of the shaded region. 12

13 Polynomials Practice Test Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Easy REF: Adding and Subtracting Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding MSC: ANS: A PTS: 1 DIF: Easy REF: Adding and Subtracting Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Procedural Knowledge MSC: ANS: D PTS: 1 DIF: Easy REF: Adding and Subtracting Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Procedural Knowledge MSC: ANS: D PTS: 1 DIF: Easy REF: Adding and Subtracting Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Procedural Knowledge MSC: ANS: A PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: coefficient term 6. ANS: D PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: variable term 7. ANS: C PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: polynomial 8. ANS: A PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: polynomial 9. ANS: B PTS: 1 DIF: Average OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: polynomial term 10. ANS: B PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: term degree 11. ANS: D PTS: 1 DIF: Average OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: term degree 12. ANS: B PTS: 1 DIF: Average OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: polynomial degree 13. ANS: A PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR6 TOP: The Language of Mathematics KEY: polynomial model 14. ANS: A PTS: 1 DIF: Easy OBJ: Section 5.2 NAT: PR5 TOP: Equivalent Expressions KEY: expression coefficient 15. ANS: C PTS: 1 DIF: Average OBJ: Section 5.3 NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: opposite expression 16. ANS: D PTS: 1 DIF: Difficult+ OBJ: Section 7.1 NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: multiplying monomials volume 1

14 17. ANS: C PTS: 1 DIF: Easy REF: Multiplying a Polynomial by a Monomial LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations) KEY: Procedural Knowledge MSC: ANS: D PTS: 1 DIF: Moderate REF: Multiplying a Polynomial by a Monomial LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations) KEY: Procedural Knowledge MSC: ANS: C PTS: 1 DIF: Easy REF: Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding MSC: ANS: C PTS: 1 DIF: Easy REF: Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding MSC: COMPLETION 1. ANS: 4y 2 7y PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6 TOP: Equivalent Expressions KEY: simplify expression like terms 2. ANS: 2d 2 PTS: 1 DIF: Easy OBJ: Section 5.2 NAT: PR6 TOP: Equivalent Expressions KEY: simplify expression like terms 3. ANS: 5n 7 PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6 TOP: Equivalent Expressions KEY: subtraction polynomial 4. ANS: 2t 2 3t 10 PTS: 1 DIF: Difficult OBJ: Section 7.3 NAT: PR7 TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a monomial simplify 5. ANS: 2x 2 5x PTS: 1 DIF: Difficult OBJ: Section 7.2 NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a polynomial by a monomial area model MATCHING 1. ANS: C PTS: 1 DIF: Average OBJ: Section 5.3 NAT: PR6 TOP: Adding and Subtracting Polynomials KEY: opposite expression 2. ANS: B PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: monomial expression 2

15 3. ANS: E PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: trinomial expression 4. ANS: D PTS: 1 DIF: Average OBJ: Section 5.1 NAT: PR5 TOP: The Language of Mathematics KEY: expression term addition subtraction polynomial SHORT ANSWER 1. ANS: SA 22a ( a) 23a ( a) 22a ( 3a) 4a 2 6a 2 12a 2 22a 2 The surface area of the rectangular prism is 22a 2. PTS: 1 DIF: Difficult OBJ: Section 7.1 NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: multiplying monomials like terms 2. ANS: (5y)(7y 4) 35y 2 20y The perimeter is 35y 2 20y. PTS: 1 DIF: Easy OBJ: Section 7.2 NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial area model 3. ANS: 2x 7x 2 PTS: 1 DIF: Easy REF: Adding and Subtracting Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Procedural Knowledge MSC: ANS: 4 PTS: 1 DIF: Easy REF: Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding MSC: ANS: 5q 15 PTS: 1 DIF: Easy REF: The Distributive Property LOC: 8.PR2 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding MSC:

16 6. ANS: 35 7t PTS: 1 DIF: Easy REF: The Distributive Property LOC: 8.PR2 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding MSC: ANS: Monomial PTS: 1 DIF: Easy REF: Polynomials LOC: 9.PR5 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding MSC: ANS: 6x 2 PTS: 1 DIF: Easy OBJ: Section 7.1 NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: multiplying monomials simplify 9. ANS: 4x 2 PTS: 1 DIF: Easy OBJ: Section 7.1 NAT: PR7 TOP: Multiplying and Dividing Monomials KEY: multiplying monomials area model area of a square 10. ANS: 3c 2 and 4c 2 PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR5 TOP: Equivalent Expressions KEY: like terms PROBLEM 1. ANS: The perimeter is the sum of the measures of the sides of the trapezoid. 2x 4 2x 3 2x 4 5x 1 11x 12 The perimeter of the trapezoid is 11x 12. PTS: 1 DIF: Moderate REF: Adding and Subtracting Polynomials LOC: 9.PR6 TOP: Patterns and Relations (Variables and Equations) KEY: Problem-Solving Skills Communication MSC:

17 2. ANS: a) s 2 (5s 2) 4s s (3s 4) (3s 2) s 2 5s 4s s 3s 3s s 2 16s 4 b) s 2 16s 4 (5) 2 16(5) If s = 5 cm, the perimeter of the figure is 101 cm. PTS: 1 DIF: Average OBJ: Section 5.2 Section 5.3 NAT: PR6 TOP: Equivalent Expressions Adding and Subtracting Polynomials KEY: perimeter expression simplify 3. ANS: a) The outer rectangle has dimensions 9y and 6y. Its area is: (9y)(6y) 54y 2 The inner rectangle has dimensions 5y and 3y. Its area is: (5y)(3y) 15y 2 b) The total area of the shaded region is the difference in the areas of the rectangles: 54y 2 15y 2 39y 2 PTS: 1 DIF: Moderate REF: Multiplying a Polynomial by a Monomial LOC: 9.PR7 TOP: Patterns and Relations (Variables and Equations) KEY: Problem-Solving Skills MSC: