MATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 1) 5x + 5 + 3 = 12 1) 2) 3 5x + 4 + 5 = 0 2) 3) 16x - 16 = x + 3 3) 4) x 2-2 = 7 4) 5) 3 11x - 6 = 3 x + 10 5) 6) 5x + 4 = 3x - 3-3 6) 7) 2x + 3 = 1 + x + 1 7) Use the Pythagorean theorem to find the unknown side of the right triangle. 8) 8) 4 114 9) 9) 9 12 Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 10) ( 3x - 5-5) 2 10) 11) ( 3 x + -3)( 3 x + 2 x + 9) 11) 12) (4 + 3 3)(4-3 3) 12) Graph the inequality. 13) -7x - 6y > 0 13) 1
List the elements of the set. 14) If A = {-5, -4, -3, 0} and B = {-7, -5, -4, -2}, list the elements of A B. 14) Graph the solution set of the system of inequalities or indicate that the system has no solution. 15) x + y 9 y 9x - 3 x 0 y 0 15) Graph the solution of the system of linear inequalities. 16) y < 1x + 4 y > 1x - 1 16) Graph the solution set of the system of inequalities or indicate that the system has no solution. 17) 2x + 3y 6 x - y 3 y 2 17) Graph the inequality. 18) 1 5 x - 1 y -1 18) 7 Solve the compound inequality. Graph the solution set. 19) -5x + 1 11 or 6x + 3-21 19) 20) -2 3 5 x - 5 < 1 20) Solve and graph. Write the solution set in interval notation. 21) 4x - 10 18 and 2x - 1 13 21) Solve the absolute value inequality. Write the solution set using interval notation. 22) 20-3 x + 1 11 22) For the compound inequality, give the solution set in both interval and graph forms. 23) 2x + 9 8 or 2x + 9 20 23) 2
Solve the absolute value inequality. Write the solution set using interval notation. 5-4x 24) 3 24) 7 Solve the equation. 1 25) 2 n + 2 = 3 4 n - 2 25) 26) 8 + 1 5 x = 2 26) Write the domain of f in interval notation. 27) f(x) = 8-7x 27) Solve the inequality. Graph the solution set. 7y + 21 28) < 7 28) 3 Graph the solution of the system of linear inequalities. 29) y + 4x 9 3x - 4y 16 29) Solve the compound inequality. Graph the solution set. 30) -4x > 8 and x + 4 > 1 30) Determine whether the ordered pair given is a solution of the linear inequality in two variables. 31) x + 2y > -6; (6, -5) 31) List the elements of the set. 32) If A = {29, 30, 31, 34} and B = {27, 29, 30, 32}, list the elements of A B. 32) Solve the inequality. Graph the solution set. 9y + 36 33) > 9 33) 4 Use rational exponents to write as a single radical expression. 34) 3 y 2 5 y 34) 3
Solve the inequality. Graph the solution set. 35) 4k + 2 5 35) Use rational exponents to write as a single radical expression. 36) 12 x 3 x 2 36) Factor the given factor from the expression. 37) s-6/7; 14s5/7-14s-6/7 37) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 38) 2 7 + 14 38) 6 7-14 Use the properties of exponents to simplify the expression. Write with positive exponents. 39) (5x3/2 ) 2 x 1/6 39) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. a 40) 40) a + t Identify the domain and then graph the function. 41) f(x) = 3 x - 5; use the following table. x f(x) 4 5 6 13 41) Use the properties of exponents to simplify the expression. Write with positive exponents. 42) y 5/9 (y 2/9-9y 3/9 ) 42) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 2x 43) 43) 5 1331x 17 y 13 Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 44) (5 3 + 9)(7 3 + 8) 44) 4
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 7 45) 45) 3 25x 2 46) 4 81 25x 11 46) Use the Pythagorean theorem to find the unknown side of the right triangle. 47) 47) 7 2 Add or subtract. Assume all variables represent positive real numbers. 48) 2x 2 + 7 50x 2-3 50x 2 48) Solve. 49) Find the perimeter of the trapezoid. Simplify. 49) 2 27 in. 4 3 in. 27 in. 2 75 in. Add or subtract. Assume all variables represent positive real numbers. 50) 6 3 x 3 y 7-2xy 3 8y 4 50) Simplify the radical expression. Assume that all variables represent positive real numbers. 51) 5 243 x 3 y 17 51) Add or subtract. Assume all variables represent positive real numbers. 52) 162 + 3 128-8 72 52) Simplify the radical expression. Assume that all variables represent positive real numbers. 56x5y6 53) 2y4 53) 5
Solve. 54) Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 11 feet from the bottom of the pole. To the nearest tenth of a foot, find the length of the rope. 54) 55) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 50 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 120 feet long. 55) 6
Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING2018 1) 76 5 2) - 129 5 3) 5 4) 51, - 51 5) 8 5 6) 7) -1, 3 8) 7 2 9) 15 10) 3x - 10 3x - 5 + 20 11) 2 6 x 5 + 3 x 2 + 6 3 x - 6 x - 27 12) 16-3 9 13) 14) {-5, -4} 15) 7
Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING2018 16) 17) 18) 19) (-, ) 20) [5, 10) 8
Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING2018 21) {7} 22) [-4, 2] 23) (-, -0.5] [5.5, ) 24) - 4, 13 2 25) {16, 0} 26) {-50, -30} 27) -, 8 7 28) (-6, 0) 29) 30) (-3, -2) 31) Yes 32) {27, 29, 30, 31, 32, 34} 33) (-, -8) (0, ) 34) 15 y 7 35) -, - 7 4 3 4, 9
Answer Key Testname: MATH125TEST2REVIEWSHEETSPRING2018 36) 4 x 3 37) s-6/7(14s11/7-14) 38) 7 + 4 2 17 39) 25x 17/6 40) a - at a - t 41) (-, ) 42) y 7/9-9y 8/9 43) 2 5 121x 3 y 2 11x 4 y 3 44) 177 + 103 3 45) 7 3 5x 5x 46) 3 4 25x 3 5x 3 47) 5 48) 21x 2 49) 23 3 in. 50) 2 xy 2 3 y 51) 3y 3 5 x 3 y 2 52) -15 2 53) 2x2y 7x 54) 12.5 ft 55) 10 119 ft 10