Final Exam Review for DMAT 010 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polynomial completely. What is one of the factors? 1) x 2 + 2x - 8 1) A) (x - 2) B) (x - 4) C) (x + 4) D) (x + 2) 2) 15z2 + 14z - 8 2) A) prime B) (z - 4) C) (z - 2) D) (5z - 2) ) 121 - w 2 ) A) prime B) (11 - w) C) 11 - w 2 D) 121 - w 4) t + 1000 4) A) (t - 10) B) (t2 + 100) C) (t2 + 10t + 100) D) (t2-10t + 100) Solve the equation. 5) x(4x + 18) = 10 5) A) 2, 5 B) 0, 9 2 C) 1 2, -5 D) 0, - 9 2 6) 49x - x = 0 6) A) - 1 7 B) 1 7 C) 1 7, 0 D) 1 7, - 1 7, 0 Simplify the expression. 7) a2 - ab + 8a - 8b a + 8 7) A) a2 - ab + 8a - 8b a + 8 B) a - 2b + 1 C) a - b D) 1 a + 8 Solve the problem. 8) If f(x) = x2-8 x, find f(-5). 8) - 8x A) - 5 17 B) - 1 5 C) - 17 1 D) - 17 125 Find the quotient and simplify. 9) z2 + 10z + 16 z 2 + 11z + 24 z 2 + 2z z 2 + 1z + 0 9) A) z + 10 B) z + 10 z 2 + z C) z z 2 + 11z + 24 D) z + 10 z
Find the product and simplify. 10) x + 1 7x x - x 2 + x -56x - 56 10) A) - x + 1 8(x + 1) B) - x2 + 1 8 C) - 1 8 D) x + 1 8(-x - 1) Find the least common denominator (LCD). 7 7 11) x 2, - 6x + 5 x 2 + x - 4 A) (x + 5)(x + 1)(x + 4) B) (x - 1)(x + 4) C) (x - 5)(x - 1)(x + 4) D) (x - 5)(x - 1) 11) Perform the indicated operation. Simplify if possible. 10x - 2 9x - 6 12) x 2 - + 12x + 2 x 2 + 12x + 2 12) A) 1 x + 8 B) 1 x + 4 C) x - 4 x 2 + 12x + 2 D) 1 x 2 + 12x + 2 1) -6x + 8 x + 7x - 7 6x 1) A) -4x + 41 6x B) -29x + 41-29x + 41 6x 2 C) 6x D) -29x - 55 6x 14) x2 - x + 2 + 7 x2-1 14) A) 42x - 11 (x - 1)(x + 1)(x - 2) B) 10x - 11 (x - 1)(x - 2) C) 10x - 11 (x - 1)(x + 1)(x - 2) D) 11x - 10 (x - 1)(x + 1)(x - 2) Solve the equation. x 15) 2x + 2 = -2x 4x + 4 + 2x - x + 1 15) A) no solution B) - C) 2 D) 16) x+8 x+2 + 12 x 2 = 2 +2x x A) -2 B) -4 C) -2,-4 D) 2 16) Solve the equation for the indicated variable. 17) x a + y b = 1 a for a 17) A) a = y b - x B) a = 1 by - y C) a = by - 1 y D) a = b - bx y 2
Solve. 18) There are 0.5 milligrams of iron in a.5 ounce serving of cod. How much iron is in 5 ounces of cod? Round the answer to one decimal place. A) 1.4 mg B) 0.7 mg C) 1.7 mg D) 0.4 mg 19) A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job. How long would it take for them to complete the job if they were working together? A) 16 15 hr B) hr C) 8 hr D) 6 hr 6 16 18) 19) 20) A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on mountainous terrain. If the rate of the car is 0 miles per hour less in the mountains than on level ground, find its rate in the mountains. A) 80 mph B) 20 mph C) 50 mph D) 40 mph 20) Determine whether the graph is the graph of a function and find the domain. 21) 21) A) yes; Domain = [-6,2] B) no; Domain = [-6,2] C) yes; Domain = [2,4] D) no; Domain = [2,4] Find the domain and range of the function graphed. 22) 22) A) domain: (-, ); range: (-, ] B) domain: (-, ); range: (-, ) C) domain: (-, -2) (-2, ); range: (-, ) (, ) D) domain: (-5, 1]; range: (-, ]
Find an equation of the line. Write the equation using function notation. 2) Through (-2, -2); perpendicular to 4x + 7y = -14 2) A) f(x) = - 7 4 x + 2 B) f(x) = 7 4 x + 2 C) f(x) = - 4 7 x - 2 D) f(x) = - 4 7 x - 14 24) (6, -16), (8, -22) 24) A) f(x) = -x + 2 B) y = - 1 x - 14 C) y = -x + 2 D) f(x) = x - 4 Write an equation of the line using function notation. 25) Horizontal; through (-6, -) 25) A) x = - B) x = -6 C) f(x) = - D) f(x) = -6 Use the given graph of the function. 26) Find f(-). 26) A) B) 4 C) 5 D) -4 27) If f(x) = 1, what is the value of x? 27) A) x = 6 B) x= -5 C) x =-5 D) x = -2 4
Graph the function. 28) h(x) = 4x - 28) A) B) C) D) Solve the compound inequality. Graph the solution set. 29) x 1 and x - 29) A) (-, 1) B) (-, -] [1, ) C) D) [-, 1] Solve the compound inequality. Write the solution set in interval notation. 0) -17 -c + 1 < -8 0) A) [-6, -) B) [, 6) C) (, 6] D) (-6, -] 1) 6x - 4 < 2x or -2x -6 1) A) [1, ] B) C) (-, 1) [, ) D) (1, ) 5
Solve the absolute value equation. x + 1 2) = 2) 9 A) B) - 26 C) 28 D) 26, - 28 ) -x + 9 = 8-4x ) A) B) - 1, - 17 C) - 1, 17 D) - 1 7 7 Solve the inequality. Write the solution set in interval notation. 4) 8k - 2 < - 4) A) - 5 8, 1 8 B) C) - 1 8, 5 8 D) -, - 1 8 5 8, 5) k - 2 + 8 > 17 5) A) - 7, 11 B) -, - 7 11, C) 11, D) -, - 7 11, 6
Graph the solution of the system of linear inequalities. 6) y < 2x + 7 y x - 8 6) A) B) C) D) 7
7) x x + 2y -4 A) B) 7) C) D) Find the cube root. 8) - -8x 0 y 24 8) A) 2x 10 y 8 B) 4x 10 y 8 C) 2x 10 y 12 D) -2x 0 y 8 Simplify the radical expression. Assume that all variables represent positive real numbers. 9) 16x 4 y 11 9) A) 4x 2 y 5 y B) 2xy 2xy 2 C) 4xy xy D) 2xy 2 2xy 5 8
Identify the domain and then graph the function. 40) f(x) = x + 5; 40) A) [0, ) B) [0, ) C) [-5, ) D) [5, ) Write with positive exponents. Simplify if possible. 41) 6 -/2 41) A) - 1 1 B) -216 C) 216 D) 216 216 Use the properties of exponents to simplify the expression. Write with positive exponents. 42) (5x/2 ) 2 x 1/6 42) A) 25x 19/6 B) 5x 19/6 C) 25x 17/6 D) 5x 17/6 Use rational exponents to simplify the following. 4) 25 y 10 z 25 4) A) y 2/5 z B) y 5/5 z 5/2 C) y 5/2 z D) y 2/5 Simplify the radical expression. Assume that all variables represent positive real numbers. 44) 128 44) A) 8 B) 4 C) 4 2 D) 4 8 9
45) 100 5 45) A) 5 B) 100 5 C) 500 5 D) 2 5 Find the midpoint of the line segment whose endpoints are given. 46) (6, -8), (-2, 7) 46) A) 4, - 15 B) (4, -1) C) (8, -15) D) 2, - 1 2 2 Add or subtract. Assume all variables represent positive real numbers. 47) 2x 2 + 7 50x 2-50x 2 47) A) 4x 7 B) 4x 2 C) 21x 7 D) 21x 2 Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 48) 7( + 5) 48) A) 8 7 B) 21 + 5 C) 7 + 7 5 D) 56 49) ( x - 1 + 4) 2 49) A) x + 8 x - 1 + 16 B) x + 8 x - 1 + 25 C) x + 8 x - 1 + 15 D) x + 8 x - 1 + 17 Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 1 50) 6 A) 6 B) 1 C) 6 6 D) 6 6 50) 51) 11 17 + 4 51) A) 11 17 + 44 B) 11 17-44 C) 11 17 + 44 4 D) 11 17-4 Solve. 52) 10x - 9-9 = 0 52) A) 81 B) 9 C) 6 D) 5 5) 4x - 4 = 4 - x 5) A) B) 10 C) 2 D) 2, 10 54) 5x + 4 = x + 1 + 54) A) 0, B) 0, 5 C) D) Perform the indicated operation. Write the result in the form a + bi. 55) ( + 8i) - (-2 + i) 55) A) -5-7i B) 5 + 7i C) 1 + 9i D) 5-7i 10
56) 8-6i 6 + 4i A) 10-17 18 i B) 20 5-17 20 i C) 6 1-17 1 i D) 72 1 + 4 1 i 56) 57) (9-6i) 2 57) A) 45 + 0i B) 45-108i C) 117-108i D) 81-108i + 6i 2 Represent each given condition using a single variable, x. 58) Three consecutive odd integers 58) A) x, x + 2, and x + 4, if x is an odd integer B) x, x + 1, and x + 2, if x is an odd integer C) x + 2, x + 4, and x + 6, if x is an odd integer D) x and x + 2, if x is an odd integer Solve. 59) An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadratic equation h = -16t 2 + 48t + 160. When will the object hit the ground? A) 2 sec B) 160 sec C) -2 sec D) 5 sec 60) Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg. A) 18 m B) 17 m C) 10 m D) 9 m 59) 60) Use the square root property to solve the equation. 61) x 2 + 6 = 0 61) A) 1296 B) -6i, 6i C) 6 D) -6, 6 62) (x + 5)2 = 20 62) A) -5-2 5, -5 + 2 5 B) 2 5-5, 2 5 + 5 C) -2 5, 2 5 D) -5-2 10, -5 + 2 10 Solve the equation by completing the square. 6) 4x2 + 8x + = 0 6) A) - 1 2, - 2 B) 1 2, 2 C) - 2, 2 D) - 1 4, - 4 Use the quadratic formula to solve the equation. 64) x2 + 14x + 5 = 0 64) A) 7-5, 7 + 5 B) -7-14, -7 + 14 C) -14 + 5 D) 7 + 14 65) (x - 9)(x - 1) = 20 65) A) -11, 1 B) -5-14, -5 + 14 C) -1, 11 D) 5-14, 5 + 14 11
66) x2 10 + x + 11 10 = 0 66) A) -10 + 11 B) 5-11, 5 + 11 C) 5 + 14 D) -5-14, -5 + 14 Solve. 67) The product of a number and 8 less than the number is. Find the number. 67) A) -2 or 12 B) -11 or C) - or 11 D) -12 or 2 Solve the inequality. Write the solution set in interval notation. 68) x 2-7x + 10 > 0 68) A) (-, 2) B) (5, ) C) (2, 5) D) (-, 2) (5, ) 69) x 2 + 4x - 69) A) (-, -] [-1, ) B) (-, -] C) [-1, ) D) [-, -1] 70) (x - 1)( - x) (x - 2) 2 0 70) A) (-, -] (-2, -1) [1, ) B) (-, 1) (, ) C) (-, -) (-1, ) D) (-, 1] [, ) 12
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. 71) f(x) = x2-5 71) A) vertex (0, -5); axis x = 0 B) vertex (0, 5); axis x = 0 C) vertex (5, 0); axis x = 5 D) vertex (-5, 0); axis x = -5 1
72) f(x) = (x - 5)2 + 2 72) A) vertex (2, 5); axis x = 2 B) vertex (-5, 2); axis x = -5 C) vertex (-2, -5 ); axis x = -2 D) vertex (5, 2); axis x = 5 Provide an appropriate response. 7) Given a parabola opens upward and the vertex is located in quadrant III, determine the number of x-intercept(s). A) cannot be determined B) 0 C) 1 D) 2 7) Find the vertex of the graph of the quadratic function. 74) f(x) = x 2-12x + 9 74) A) (-12, 297) B) (6, -99) C) (6, -27) D) (-6, 117) Fine the x-intercepts and y-intercept: 75) f(x) = x 2 + 8x +7 75) A) x-intercepts: (-7,0),(-1,0) y-intercept (0,7) C) x-intercepts: (-7,0),(-1,0) y-intercept (0,-7) B) x-intercepts: (7,0,(1,0) y-intercept (0,7) D) x-intercepts: (-8,0),(-1,0) y-intercept (0,-7) 14
10 Final Exam Review 1 B 26 B 51 B 2 D 27 A 52 B B 28 D 5 C 4 D 29 D 54 D 5 C 0 C 55 B 6 D 1 C 56 C 7 C 2 D 57 B 8 B C 58 A 9 D 4 B 59 D 10 C 5 D 60 C 11 C 6 B 61 B 12 A 7 C 62 A 1 C 8 A 6 A 14 C 9 B 64 B 15 D 40 C 65 C 16 B 41 D 66 D 17 D 42 C 67 C 18 B 4 A 68 D 19 B 44 C 69 A 20 B 45 D 70 D 21 B 46 D 71 A 22 A 47 D 72 D 2 B 48 B 7 D 24 A 49 C 74 C 25 C 50 C 75 A 15
76) 76) A) B) C) 16