Name: Class: Date: ID: A Honors Algebra Quarterly #3 Review Mr. Barr Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the expression. 1. (3 + i) + ( + i) a. 4 + 3i c. 7i b. 5 i d. 5 + i. ( 3 + i) (1 + i) a. 4 i c. + 3i b. 4 + i d. 5i 3. (5i)( 5i) a. 5 c. 5 b. 5i d. 5i 4. ( 3 6i)( 6 i) a. 6(18 + 7i) c. 30 + 4i b. 6(3 + 7i) d. 6(1 + 7i) 5. 5 + i 3i a. 1 5 + 3 4 i c. 1 1 5 13 i 7 b. 13 i d. 7 13 1 4 13 i 6. Classify 8x 5 + 5x 4 5x 3 by degree. a. quintic c. cubic b. quadratic d. quartic 7. Classify 9x 5 + x 4 6x 3 + 7 by number of terms. a. polynomial of 5 terms c. polynomial of 4 terms b. binomial d. trinomial 1
Name: ID: A Consider the leading term of each polynomial function. What is the end behavior of the graph? 8. 5x 5 + 3x a. The leading term is 5x 5. Since n is odd and a is negative, the end behavior is up and up. b. The leading term is 5x 5. Since n is odd and a is negative, the end behavior is down and up. c. The leading term is 5x 5. Since n is odd and a is negative, the end behavior is up and down. d. The leading term is 5x 5. Since n is odd and a is negative, the end behavior is down and down. What are the zeros of the function? Graph the function. 9. y = x(x 3)(x + 5) a. 3, 5 c. 3, 5, 3 b. 0, 3, 5 d. 0, 3, 5
Name: ID: A 10. What is a cubic polynomial function in standard form with zeros 4, 5, and 5? a. f(x) = x 3 + 6x 19x + 100 c. f(x) = x 3 + 6x 15x 0 b. f(x) = x 3 6x 15x + 100 d. f(x) = x 3 + 6x + 15x + 100 What are the real or imaginary solutions of each polynomial equation? 11. x 4 34x = 5 a. 5, 5, 3, 3 c. 5, 3 b. 5, 5 d. no solution 1. Divide 3x 3 4x + x 3 by x + 3. a. 3x + 5x 38 c. 3x 13x + 40, R 13 b. 3x + 5x 38, R 117 d. 3x 13x + 40 13. Use synthetic division to find P( ) for P(x) = x 4 + 7x 3 10x 4x + 4. a. 100 b. 16 c. d. 68 Find the roots of the polynomial equation. 14. x 3 + x 19x + 0 = 0. One Root is x = -4 a. 3 + i, 3 i, 4 c. b. 3 + i 3 i,, 4 d. 3 + i 3 + i, 3 i, 3 i, 4, 4 Find all of the roots of the equation. 15. x 4 6x + 8 = 0 a. ±1, c. 1, ± b. d. 1, Find all the zeros of the equation. 16. 7x 144 = x 4 a. 4, 3i c. 4, 4, 3i, 0 b. 4, 4, 3i, 3i d. 4, 3i What is the equation of y = x 3 with the given transformations? 17. vertical stretch by a factor of 3, horizontal shift 4 units to the right, vertical shift 7 units down a. y = 3(x 4) 3 + 7 c. y = 1 3 (x 4) 3 7 b. y = 3(x 4) 3 7 d. y = 3(x + 4) 3 7 3
Name: ID: A Multiply and simplify if possible. 18. 10 a. 0 b. 5 c. 5 d. not possible 19. Write 3x ( 3x + 5x 3 ) in standard form. a. 15x 5 + 9x 4 c. 15x 5 15x 4 b. 6x 5 9x 4 d. 6x + x 4 Write the polynomial in factored form. 0. x 3 + 0x + 48x a. x(x + 6)(x 4) c. x(x + 4)(x + 6) b. 6x(x + )(x + 4) d. 4x(x + 6)(x + ) 1. x 3 = 16 What are the real or imaginary solutions of the polynomial equation? a. 6, 3 + 3i 7, and 3 3i 7 c. 6, 3 + 3i 7, and 3 3i 7 b. 6, 3 + 3i 3, and 3 3i 3 d. 6, 3 + 3i 3, and 3 3i 3 4
ID: A Honors Algebra Quarterly #3 Review Answer Section Mr. Barr MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: L REF: 4-8 Complex Numbers NAT: CC N.CN.1 CC N.CN. CC N.CN.7 CC N.CN.8 N.5.f A.4.g TOP: 4-8 Problem 3 Adding and Subtracting Complex Numbers KEY: complex number. ANS: A PTS: 1 DIF: L3 REF: 4-8 Complex Numbers NAT: CC N.CN.1 CC N.CN. CC N.CN.7 CC N.CN.8 N.5.f A.4.g TOP: 4-8 Problem 3 Adding and Subtracting Complex Numbers KEY: complex number 3. ANS: A PTS: 1 DIF: L REF: 4-8 Complex Numbers NAT: CC N.CN.1 CC N.CN. CC N.CN.7 CC N.CN.8 N.5.f A.4.g TOP: 4-8 Problem 4 Multiplying Complex Numbers KEY: complex number 4. ANS: D PTS: 1 DIF: L3 REF: 4-8 Complex Numbers NAT: CC N.CN.1 CC N.CN. CC N.CN.7 CC N.CN.8 N.5.f A.4.g TOP: 4-8 Problem 4 Multiplying Complex Numbers KEY: complex number 5. ANS: D PTS: 1 DIF: L3 REF: 4-8 Complex Numbers NAT: CC N.CN.1 CC N.CN. CC N.CN.7 CC N.CN.8 N.5.f A.4.g TOP: 4-8 Problem 5 Dividing Complex Numbers KEY: complex number complex conjugates 6. ANS: A PTS: 1 DIF: L REF: 5-1 Polynomial Functions OBJ: 5-1.1 To classify polynomials NAT: CC A.SSE.1.a CC F.IF.4 CC F.IF.7 CC F.IF.7.c TOP: 5-1 Problem 1 Classifying Polynomials KEY: degree of a polynomial polynomial function standard form of a polynomial function 7. ANS: C PTS: 1 DIF: L REF: 5-1 Polynomial Functions OBJ: 5-1.1 To classify polynomials NAT: CC A.SSE.1.a CC F.IF.4 CC F.IF.7 CC F.IF.7.c TOP: 5-1 Problem 1 Classifying Polynomials KEY: degree of a polynomial polynomial function standard form of a polynomial function 8. ANS: C PTS: 1 DIF: L REF: 5-1 Polynomial Functions OBJ: 5-1. To graph polynomial functions and describe end behavior NAT: CC A.SSE.1.a CC F.IF.4 CC F.IF.7 CC F.IF.7.c TOP: 5-1 Problem Describing End Behavior of Polynomial Functions KEY: polynomial end behavior turning point 9. ANS: B PTS: 1 DIF: L3 REF: 5- Polynomials, Linear Factors, and Zeros OBJ: 5-.1 To analyze the factored form of a polynomial NAT: CC A.SSE.1 CC A.APR.3 CC F.IF.7 CC F.IF.7.c CC F.BF.1 TOP: 5- Problem Finding Zeros of a Polynomial Function 1
ID: A 10. ANS: B PTS: 1 DIF: L3 REF: 5- Polynomials, Linear Factors, and Zeros OBJ: 5-. To write a polynomial function from its zeros NAT: CC A.SSE.1 CC A.APR.3 CC F.IF.7 CC F.IF.7.c CC F.BF.1 TOP: 5- Problem 3 Writing a polynomial function from its zeros KEY: factor theorem 11. ANS: A PTS: 1 DIF: L3 REF: 5-3 Solving Polynomial Equations OBJ: 5-3.1 To solve polynomial equations by factoring NAT: CC A.SSE. CC A.REI.11 A..a TOP: 5-3 Problem 1 Solving Polynomial Equations Using Factors 1. ANS: C PTS: 1 DIF: L REF: 5-4 Dividing Polynomials OBJ: 5-4.1 To divide polynomials using long division NAT: CC A.APR.1 CC A.APR. CC A.APR.6 N.1.d A.3.c A.3.e TOP: 5-4 Problem 1 Using Polynomial Long Division 13. ANS: D PTS: 1 DIF: L3 REF: 5-4 Dividing Polynomials OBJ: 5-4. To divide polynomials using synthetic division NAT: CC A.APR.1 CC A.APR. CC A.APR.6 N.1.d A.3.c A.3.e TOP: 5-4 Problem 5 Evaluating a Polynomial KEY: synthetic division remainder theorem 14. ANS: A PTS: 1 DIF: L3 REF: 5-5 Theorems About Roots of Polynomial Equations OBJ: 5-5.1 To solve equations using the Rational Root Theorem NAT: CC N.CN.7 CC N.CN.8 TOP: 5-5 Problem Using the Rational Root Theorem KEY: Rational Root Theorem 15. ANS: B PTS: 1 DIF: L3 REF: 5-6 The Fundamental Theorem of Algebra OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions NAT: CC N.CN.7 CC N.CN.8 CC N.CN.9 CC A.APR.3 TOP: 5-6 Problem Finding All the Roots of a Polynomial Function KEY: Fundamental Theorem of Algebra roots 16. ANS: B PTS: 1 DIF: L3 REF: 5-6 The Fundamental Theorem of Algebra OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions NAT: CC N.CN.7 CC N.CN.8 CC N.CN.9 CC A.APR.3 TOP: 5-6 Problem Finding All the Zeros of a Polynomial Function KEY: Fundamental Theorem of Algebra 17. ANS: B PTS: 1 DIF: L3 REF: 5-9 Transforming Polynomial Functions OBJ: 5-9.1 To apply transformations to graphs of polynomials NAT: CC F.IF.7.c CC F.IF.8 CC F.IF.9 CC F.BF.3 G..c TOP: 5-9 Problem 1 Transforming y = x^3 18. ANS: B PTS: 1 DIF: L REF: 6- Multiplying and Dividing Radical Expressions OBJ: 6-.1 To multiply and divide radical expressions NAT: CC A.SSE. N.5.e A.3.c A.3.e TOP: 6- Problem 1 Multiplying Radical Expressions 19. ANS: A PTS: 1 DIF: L3 REF: 5-1 Polynomial Functions OBJ: 5-1.1 To classify polynomials NAT: CC A.SSE.1.a CC F.IF.4 CC F.IF.7 CC F.IF.7.c TOP: 5-1 Problem 1 Classifying Polynomials KEY: degree of a polynomial polynomial function standard form of a polynomial
ID: A 0. ANS: C PTS: 1 DIF: L3 REF: 5- Polynomials, Linear Factors, and Zeros OBJ: 5-.1 To analyze the factored form of a polynomial NAT: CC A.SSE.1 CC A.APR.3 CC F.IF.7 CC F.IF.7.c CC F.BF.1 TOP: 5- Problem 1 Writing a Polynomial in Factored Form 1. ANS: D PTS: 1 DIF: L3 REF: 5-3 Solving Polynomial Equations OBJ: 5-3.1 To solve polynomial equations by factoring NAT: CC A.SSE. CC A.REI.11 A..a TOP: 5-3 Problem Solving Polynomial Equations by Factoring KEY: sum of cubes difference of cubes 3