Algebra II Honors Test Review 6-1 to 6-4

Transcription

1 Name: Class: Date: Algebra II Honors Test Review 6-1 to 6-4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use a graphing calculator to determine which type of model best fits the values in the table. x y a. quadratic model c. linear model b. cubic model d. none of these 2. Determine which binomial is not a factor of 4x 4 21x 3 46x x a. x + 4 c. x 5 b. x + 3 d. 4x The volume of a shipping box in cubic feet can be expressed as the polynomial 2x x x + 6. Each dimension of the box can be expressed as a linear expression with integer coefficients. Which expression could represent one of the three dimensions of the box? a. x + 6 c. 2x + 3 b. x + 1 d. 2x + 1 Short Answer 4. Zach wrote the formula w(w 1)(5w + 4) for the volume of a rectangular prism he is designing, with width w, which is always has a positive value greater than 1. Find the product and then classify this polynomial by degree and by number of terms. 5. Write the polynomial 6x 2 9x in standard form. 6. Write 4x 2 ( 2x 2 + 5x 3 ) in standard form. Then classify it by degree and number of terms. 1

2 Name: 7. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in Years since Trees planted (in thousands) Write the expression (x + 6)(x 4) as a polynomial in standard form. 9. Write 4x 3 + 8x 2 96x in factored form. 10. Miguel is designing shipping boxes that are rectangular prisms. One shape of box with height h in feet, has a volume defined by the function V(h) = h(h 10)(h 8). Graph the function. What is the maximum volume for the domain 0 < h < 10? Round to the nearest cubic foot. 11. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of y = 3x x 2 12x 60. If necessary, round to the nearest hundredth. 12. Find the zeros of y = x(x 3)(x 2). Then graph the equation. 13. Write a polynomial function in standard form with zeros at 5, 4, and 1. 2

3 Name: 14. Find the zeros of f(x) = (x + 3) 2 (x 5) 6 and state the multiplicity. 15. Divide 3x 3 3x 2 4x + 3 by x + 3. Divide using synthetic division. 16. (x x 3 77x x 36) (x 4) Solve the equation by graphing. 17. x 2 + 7x + 19 = The dimensions in inches of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x 1. The volume is about 7.6 ft 3. Find the dimensions of the box in inches. Round to the nearest inch. 19. Over two summers, Ray saved $1000 and $600. The polynomial 1000x x represents her savings after three years, where x is the growth factor. (The interest rate r is x 1.) What is the interest rate she needs to save $1850 after three years? Factor the expression. 20. x x 4 20x

4 Name: 22. Solve 125x = 0. Find all complex roots. 23. Ian designed a child s tent in the shape of a cube. The volume of the tent in cubic feet can be modeled by the equation s 3 64 = 0, where s is the side length. What is the side length of the tent? 24. Solve x 4 34x 2 = The volume in cubic feet of a workshop s storage chest can be expressed as the product of its three dimensions: V(x) = x 3 3x 2 x + 3. The depth is x + 1. a. Find linear expressions with integer coefficients for the other dimensions. b. If the depth of the chest is 6 feet, what are the other dimensions? 4

5 Algebra II Honors Test Review 6-1 to 6-4 Answer Section MULTIPLE CHOICE 1. C 2. A 3. D SHORT ANSWER 4. 5w 3 w 2 4w; cubic trinomial 5. 2x 2 3x x 5 8x 4 ; quintic binomial 7. T(x) = 0.4x x x; thousand trees 8. x 2 + 2x x(x 4)(x + 6) ft relative minimum: (0.36, 62.24), relative maximum: ( 3.69, 37.79), zeros: x = 5, 2, , 3, f(x) = x 3 2x 2 19x , multiplicity 2; 5, multiplicity x 2 12x + 32, R x x 2 x no solution in. by 20 in. by 44 in % 20. (x + 6)(x 2 6x + 36) 21. (x 2)(x + 2)(x 4)(x + 4) 1

6 , 35 ± 35i feet 24. 3, 3, 5, a. height, x 1; width, x 3 b. height, 4 ft; width, 2 ft 2