Determine whether the equation is a conditional equation, an identity, or a contradiction.

Transcription

1 Test Review-chap.4-.7,.,.4, 6., 6., 6. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the equation is a conditional equation, an identity, or a contradiction. ) 4(z + ) - z = -4 - z + + ) Conditional Identity C) Contradiction Solve the problem. ) The JUST-SAY-MOW lawn mowing company consists of two people: Lucy and David. If Lucy cuts the lawn by herself, she can do it in hours. If David cuts the same lawn himself, it takes him an hour longer than Lucy. How long would it take them if they worked together? Round to the nearest hundredth of an hour..00 hours.0 hours C).00 hour.0 hours ) A nurse mixes 90 cc of a 4% saline solution with a 0% saline solution to produce a 0% saline solution. How much of the 0% solution should he use? 7. cc cc C) 0 cc 40 cc 4) The plans for a rectangular deck call for the width to be 8 feet less than the length. Sam wants the deck to have an overall perimeter of 60 feet. What should the length of the deck be? 4 feet 8 feet C) 7 feet 9 feet Solve the equation. ) w (w + 6) = -64 ) ) 4) ) - 8, - 8 0, - 6 C) - 8, 8 8, 8 Solve the quadratic equation by completing the square and applying the square root property. 6) x + 6 = 9x {9-87, } -9 -, C) {-9-87, } 9 -, ) Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. 7) j - 8j + n n = 8; (j - 9) n = 9; (j - 9) C) n = 9; (j + 9) n = 8; (j - 9) 7)

2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide the missing information. 8) A equation is a second degree equation of the form ax + bx + c = 0 where a 0. 8) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation by using the square root property. 9) (z - 8) + 8 = 40 {40 +, } { - 40} C) {6 + i, 6 - i } { + 40} Solve the equation by using the quadratic formula. 0) - 4 = 6 x - x 9) 0) 0 ± 6 0-8, 9 0 C) 6 ± 99 6 i -, 8 Use the discriminant to determine the type and number of solutions. ) 4x + x + = 0 Two rational solutions One rational solution C) Two irrational solutions Two imaginary solutions Solve for the indicated variable. ) nt + ry = h for t t = ± n(h - ry) t = ± C) t = n(h - ry) n or t = n(h + ry) n t = h - ry n n(h - ry) n ) ) List the elements of. ) A = {-8, 4, -, -, -4, 9} and B = {, -, -, -4} {-8, 4, -, -, -4, 9,, -} {-, -4} C) { } {-} ) Solve the inequality. Write the solution set in interval notation. 4) -(8y - 7) + y y - (- + y) 8, -, 4 C) -, 4 4, 4) Solve and express your solution in simplified form. ) x 4-4x - =0 {6, i} {±4, ± } C) {6, } {±4, ±i } )

3 Solve the inequality. Write the solution set in interval notation. 6) 6 > x and 6 + x -, - 6, { } 6) C) - 6, -, 6 Determine the intersection X Y. Express the answer in interval notation. 7) X = {x x 8} and Y = {x x < 7} (-, 7] (8, ) [7, 8) C) { } (7, 8] Solve the equation by using substitution. 8) (t + 8) - (t + 8) - = 0 {4, -} {4, } C) {-, -} {-4, -} Solve the equation. 9) 8 - p p = - {-} {±7} C) {-, -7} {-7} 0) + x + = 7) 8) 9) 0) 0 C) - ) x + = x - x - 8 x - 8 ) {} { } C) {8, } -, Solve the problem. ) Sparky has scores of 74, 6, and 69 on his first three Sociology tests. If he needs to keep an average of 70 to stay eligible for lacrosse, what scores on the fourth exam will accomplish this? He must score more than 76 He must score 7 or higher. C) He must score 76 or higher. He must score more than 7 Solve the absolute value equation. ) - w + 4 = 6 { } {, -} C) {} {, -} Solve the absolute value inequality. Write the solution in interval notation. 4) b - 0 > -6 (-, 7] [, ) (-, ) C) { } [7, ] ) ) 4)

4 ) x + 4 < 8 (-,-) (4, ) (-4, ) C) (-, 4) (-4, 4) ) Solve the absolute value equation. 6) r + = r - 6), 6-6, 6 C) 6 7) v = -9 - v 9, 0 -, - 9 C) {-} {0, 0} 7) Solve the compound inequality. Write the answer in interval notation. 8) 7 < x or 0 + x 8) (-, ) - 9, 7 C) - 7, 9 -, - 9 7, Find the x- and y-intercepts. (x - ) 9) + (y + ) = 6 x-intercept: (9, 0); y-intercept: (0, -) x-intercepts: (-4, 0) and (4, 0); y-intercepts: (0, -) and (0, ) C) x-intercept: none; y-intercept: none x-intercept: (4, 0); y-intercept: (0, ) Find the midpoint of the line segment whose endpoints are the given points. 0) (,- 7) and (6, 7) (, 6 7) (7, 4 7) C) 7, 7, 7 Solve the problem. ) A skydiving company insists that its customers weigh at least 0 pounds, but no more than 80 pounds, including parachute and other gear. If the total weight of all gear is pounds, write and solve a compound inequality that represents the weight range without gear that is acceptable. 0 w 0 w 0 C) 0 w w 9) 0) ) 4

5 Determine whether the ordered pair is a solution of the system. ) (4, ); 6x - y = 0-8x + y = -6 No Yes Solve the system by substitution. x + y= 0 ) x - 7y= - {(4, -)} {(6, )} C) (x, y) y = - x + ; The equations are dependent ) ) {(, 4)} Solve the system of equations by using the substitution method. 4) (x + y) = -7 - y 9x - = 8 + y - 7, -, - C) 0, - - 7, 0 4) Solve the system of equations by using the addition method. ) (x - y) = y - -x + = -y {(0, -6)} {(8, 6)} C) {(8, 9)} {(-6, 0)} Solve the problem. 6) Camille and Sasha each make an ice cream sundae. Camille gets scoops of Cherry ice cream and scoop of Mint Chocolate Chunk ice cream for a total of 46 g of fat. Sasha has scoops of Cherry ice cream and scoop of Mint Chocolate Chunk ice cream for a total of 77 g of fat. How many grams of fat does scoop of each type of ice cream have? Cherry has 4 g of fat and Mint Chocolate Chunk has 7 g of fat. Cherry has 6 g of fat and Mint Chocolate Chunk has g of fat. C) Cherry has 7 g of fat and Mint Chocolate Chunk has 4 g of fat. Cherry has g of fat and Mint Chocolate Chunk has 6 g of fat. 7) A fishing boat travels 6 mi with the current in hr. It travels 4 mi against the current in hr. Find the speed of the boat in still water. The boat travels 4 mph in still water. The boat travels 6 mph in still water. C) The boat travels 8 mph in still water. The boat travels mph in still water. ) 6) 7)

6 a. Graph the equations in the system. b. Solve the system by using the substitution method. 8) x + y = 4x + y = 0 {(-, 4), (, -4)} 4 y {(-4, ), (4, -)} 4 y 8) x C) {(-, -4), (, 4)} y x x {(-4, -), (4, )} y x Solve the system by the substitution method. 9) y = 9x - 8x y = 9x {(, 7)} {(0, 0)} C) { } {(0,0), (, 7)} Solve the system of equations by using the addition method. 40) x - xy = - x + xy = 4 {(-, -4), (, 4)} {(, 4), (, -4), (-, 4), (-, -4)} C) {(, 4), (, -4)} { } 9) 40) 6

7 Solve the system. 4) x + y = 0 y - x = 4 {(, 6), (-, - 6)} { } C) {(, 6)} {(, 6), (, - 6), (-, 6), (-, - 6)} Solve the problem. 4) Abram and Fred leave opposite ends of a bike trail 8. miles apart and travel toward each other. Abram is traveling mph faster than Fred. Find each of their speeds if they meet after 0 minutes. Abram: 0 mph; Fred: 7 mph Abram: 7 mph; Fred: 0 mph C) Abram: 0 mph; Fred: 7 mph Abram: 7 mph; Fred: 0 mph 4) 4) Write the augmented matrix for the given system. 4) -x - 6y + 9z= -x + y= -0 x - 8z= ) C) Write a system of linear equations represented by the augmented matrix. 44) x= 6 8x - y= x + 8y= 6 -y= Perform the elementary row operation on the given matrix. 4) - R R C) x + 8y= 6 x - y= x + 8y= 6 -x= 44) 4) C)

8 46) R R 46) C) Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these ) 47), column matrix, row matrix C), none of these, none of these Determine the value of the given element of the matrix. 48) a A = ) - C) -7 4 For what values of x, y, and z will A = B? 49) A = - x z 9 B = y ) x = 9, y = -, z = 8 x =, y = -, z = 8 C) x = 8, y = -, z = 9 x =, y = 9, z = Solve the system using Gaussian elimination or Gauss-Jordan elimination. 0) x - 7y =- -6x + y =7 0) {(-, -)} {(, )} C) {(-, )} {(-, -)} Find the additive inverse of A. ) A = 9-4 ) C)

9 Find A + B. ) A = , B = ) Undefined C) Perform the indicated operations. ) Find -A - 4B. ) A = and B = C) Given the matrices A and B, solve for X. 4) X - B = A. 4) A = and B = C) Find AB, if possible ) A = 9 and B = ) C) Not possible 7 7 9

10 Solve the problem. 6) A street vendor at a parade sells fresh lemonade, soda, bottled water, and iced-tea, and the unit price for each item is given in matrix P. The number of units sold of each item is given in matrix N. Compute NP and interpret the result. 6) Lemonade Soda Water Tea N = P = $.00 Lemonade $.00 Soda $.00 Water $.0 Tea [$,40]; The value $,40 represents the total revenue from the sale of these four items [$900]; The value $900 represents the total revenue from the sale of these four items C) [$6,00]; The value $6,00 represents the total revenue from the sale of these four items [$,9]; The value $,9 represents the total revenue from the sale of these four items 7) The labor costs per hour for an electrician, plumber, and air-conditioning/heating expert are given in matrix L. The time required from each specialist for three new model homes is given in matrix T. Cost/hr L = $40 $8 $4 Electrician Plumber AC/heating 7) Time(hr) Electrician Plumber AC/heating Model T = 9 Model 7 8 Model Find a matrix that gives the total cost for these three services for each model. [$,604] [$,600] C) $7,676 $,48 $,446 $8,8 $,88 $,64 0

11 8) y (, ) 8) 4 (-, ) (4, ) x - - (-, -) a. Write a matrix A that represents the coordinates of the quadrilateral. Place the x-coordinate of each point in the first row of A and the corresponding y-coordinate in the second row of A. b. What operation on A will shift the graph of the quadrilateral units upward? a. A = b. A C) a. A = b. A a. A = b. A a. A = b. A Evaluate the determinant of the given matrix. 9) A = ) - - C) 60) A = u - 9 u 60) -u - 4 -u + 4 C) u - 4 u + 4

12 Find the cofactor of the given element. 6) a 7 - A = [a ij ] = ) -8 C) - -8 Evaluate the determinant of the given matrix and state whether the matrix is invertible ) A = ) -6, Yes -, No C) -6, No -, Yes Find the measure of angles x and y. 6) (The figure is not necessarily drawn to scale.) 6) y + 6 x - 6 y x x = 86 ; y = 8 x = 6 ; y = 84 C) x = 84 ; y = 6 x = 8 ; y = 86

13 Answer Key Testname: TEST- REVIEW-4 ) B ) B ) B 4) D ) A 6) D 7) D 8) quadratic 9) C 0) D ) D ) B ) B 4) B ) D 6) D 7) C 8) D 9) A 0) D ) A ) B ) A 4) B ) C 6) A 7) B 8) D 9) C 0) C ) C ) B ) B 4) B ) B 6) D 7) B 8) A 9) D 40) A 4) D 4) A 4) D 44) B 4) A 46) D 47) D 48) B 49) B

14 Answer Key Testname: TEST- REVIEW-4 0) A ) B ) B ) D 4) D ) A 6) D 7) C 8) C 9) B 60) D 6) C 6) D 6) B 4