Solve algebraically. 1) 7 - a -4 1) Solve algebraically. Write answer in set builder or interval notation. 2) 4m m - 7 2)

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Ralph Bishop
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1 Chapter 9 & 10 Practice. The following is an aid to study for the Chapter 9 & 10 eam. Disclaimer: The actual eam is different. You do need to show work on the actual eam and will not be given credit for questions where work is incorrect. Solve algebraically. 1) 7 - a - 1) Solve algebraically. Write answer in set builder or interval notation. 2) m m - 7 2) ) -( + ) - 22 < -6( - 9) - ) Find the domain of the function. Write answer in set builder or interval notation. ) f() = 6 - ) Find the domain of the function. 5) f() = 5-9 5) Find the indicated intersection or union. 6) Let A = {q, s, u, v, w,, y, z}, B = {q, s, y, z}, C = {v, w,, y, z}, and D = {s}. List the elements in the set A B. 6) 7) Let A = {q, s, u, v, w,, y, z}, B = {q, s, y, z}, C = {v, w,, y, z}, and D = {s}. List the elements in the set A D. 7) 8) Let A = {q, s, u, v, w,, y, z}, B = {q, s, y, z}, C = {v, w,, y, z}, and D = {s}. List the elements in the set C B. 8) Graph and write interval notation for the compound inequality. 9) -1 < < 9) ) 2 and - 10) Solve the inequality and graph the solution set. 11) 6 - < 2 or ) ) or )

2 1) 7 2t + 1 1) Solve the equation. 1) m = 10 1) 15) b = ) 16) 7m + 5 = 9 16) 17) Let f() = 2 -. Find all for which f() = -. 17) 18) Let f() = Find all for which f() =. 18) 19) 1 2 n + 2 = n ) 20) n + 8 = - n 20) Solve the absolute-value inequality. Write solution in set builder or interval notation. 21) ) 22) 8k < 10 22) Solve the absolute-value inequality. 2) 2y < -11 2) 2) b - - > 1 2) Solve and graph. 25) 7k ) 26) ) 27) - > 15 27) 2

3 28) 7k > -2 28) 29) 2-5 > 0 29) Find the requested solution. 0) Let f() = Find all for which f() -. 0) 1) Let f() = Find all for which f() < 18. 1) Choose the ordered pair which is a solution of the inequality. 2) 2 + y 5 A) (1, 1) B) (, 2) C) (1, 2) D) (0, 2) 2) ) 2 + y > 8 A) (2, 2) B) (2, 1) C) (0, 0) D) (0, 1) ) Graph on a plane. ) - y > y )

4 Graph the system of linear inequalities. 5) 2 + y and - 1 > 0 5) 2 1 y ) 2 + y and y - 1 < 0 6) 2 1 y Find all square roots of the number. 7) 289 7) Simplify. 8) ) 9) ) Simplify. Assume that variables can represent any value. 0) 25y2 0) 1) - 1 1)

5 Simplify. Unless otherwise specified, assume that variables can represent any number. 2) ) ) 11 ( - 6)11 ) Simplify. Assume all variables represent nonnegative values. ) 81a ) 5) ) 6) 256 6) Use the laws of eponents to simplify. Do not use negative eponents in the answer. Assume that even roots are of nonnegative quantities and that all denominators are nonzero. 7) y/ y 1/ 7) 8) 7 11/1 7-6/1 8) 9) z -2/7 z /7 9) 50) (9k 2 m - ) 1/2 50) 51) (8a 1/7 b 5/7 ) 51) Multiply. 52) 10p 12q 52) Simplify by factoring. 5) 112 5) 5) 8 k 7 q 8 5) Simplify. Assume that no radicands were formed by raising negative numbers to even powers. 55) 512 y 5 55) 5

6 56) -8a 8 b 5 56) Multiply and simplify. Assume all variables represent nonnegative real numbers. Write your answer in radical notation. 57) 1m5 7m11 57) 58) y5 7y17 58) Simplify by taking the roots of the numerator and the denominator. Assume all variables represent positive numbers. 59) ) 60) ) Rationalize the denominator. Assume all variables represent positive numbers. 61) 61) ) 62) 6) 98 6) 6) - 98 y5 6) Add or subtract. Simplify by combining like radical terms, if possible. Assume all variables and radicands represent nonnegative numbers. 65) ) 66) ) 67) ) 6

7 68) ) Multiply. Assume that all variables represent nonnegative real numbers. 69) ( 5 + )( 5 - ) 69) 70) ( )( - 5 ) 70) Rationalize the denominator. Assume all variables represent positive numbers. 71) ) 72) ) Multiply and simplify. Assume all variables represent nonnegative real numbers. Write your answer in radical notation. 7) m m1 7) Divide and, if possible, simplify. Assume all variables represent positive real numbers. 7) 2 5 7) Solve. 75) + = 7 75) 76) + 5 = 2 76) 77) 8 y = y 77) 78) = ) 79) z = 0 79) 80) + 1 = ) 81) y1/ - 2 = 81) 7

8 Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. The legs of the right triangle are represented by a and b, and the hypotenuse is represented by c. 82) a = 10, b = 2 82) Solve the problem. If necessary, round to the nearest tenth. 8) On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 m long and the tree is 0 m tall, how long is the shadow? 8) Find the distance between the pair of points. Give your answer in eact form and where appropriate find an approimation to three decimal places. 8) (-2, -) and (6, 1) 8) 85) (-1, -) and (5, -2) 85) Find the midpoint of the segment with the given endpoints. 86) (0, -6) and (-9, 2) 86) 87) - 2, and 7 2, ) Epress in terms of i. 88) -6 88) Perform the indicated operation and simplify. Write the answer in the form a + bi. 89) (-6 + i) + (9 + i) 89) 90) (12-9i) - ( - i) 90) 91) (9 + i) - (- + i) 91) 92) ) 9) (6-2i)( + 8i) 9) 9) ( - 7i)(7 - i) 9) 95) ( - 2i)2 95) 96) i 96) 97) -1i -5 + i 97) 8

9 98) + 7i 9 + i 98) Find the power of i. 99) i 8 99) 100) (-i)2 100) 9

10 Answer Key Testname: 125CH9&10P 1) {a a 11} or [11, ) 2) m m or -, ) { < 70} or (-, 70) ) { 6} or (-, 6] 5) 5 9 or -, 5 9 6) {q, s, y, z} 7) {s} 8) {q, s, v, w,, y, z} 9) (-1, ) 10) [2, ) ) ) ) ) 1, ) 16) 7, ) 18) , ) {16, 0} 20) ) (-, -1] [11, ) 22) - 9 8, 5 8 2) 2) (-, -1) (21, ) 10

11 Answer Key Testname: 125CH9&10P 25) - 1 7, ) [, 11] ) (-, -12) (18, ) ) -, , ) -, , 0) R 1) - 1 7, 9 7 2) A ) A ) y

12 Answer Key Testname: 125CH9&10P 5) (0, ) y 2 1 (2, 0) (1, 0) ) y (0, ) 2 (0, 1) 1 (2, 0) ) 17, ) ) ) 5 y 1) - 7 2) - 5 ) - 6 ) a 5) ) 7) y 1/2 8) 717/1 9) z 1/7 50) k m 2 51) 512a /7 b 15/7 12

13 Answer Key Testname: 125CH9&10P 52) 120pq 5) 7 5) ( 2 k q ) 2 k 55) 8y( y 2) 56) -2a 2 b( a 2 b 2) 57) 7m8 2 58) 2y7 2y 59) 6 60) 2 61) 62) ) 7 2 6) - 65) 2 7 2y y 66) ) ) ) - 70) ) ) ) m m 7) ) 76) 77) 0, 6 78) 12 1

14 Answer Key Testname: 125CH9&10P 79) No solution 80) 5, 8 81) ) c = 26 8) 0 m 8) ) ) - 9 2, ) 1, ) 8i 89) + 7i 90) 8-5i 91) 1 + 2i 92) - 8 9) + 2i 9) -7-61i 95) 12-16i 96) i 97) i 98) i 99) 1 100) -1 1

Final Exam REVIEW- Intermediate Algebra

Final Exam REVIEW- Intermediate Algebra Final Eam REVIEW- Intermediate Algebra Solve the inequalit. Write the solution set in interval notation and graph the solution set. 1) 7z - 7 6z - 7 1) Solve the compound inequalit. Graph the solution