INTERMEDIATE ALGEBRA REVIEW FOR TEST 3 Evaluate the epression. ) a) 73 (-4)2-44 d) 4-3 e) (-)0 f) -90 g) 23 2-4 h) (-2)4 80 i) (-2)5 (-2)-7 j) 5-6 k) 3-2 l) 5-2 Simplify the epression. Write your answer with positive integer eponents only. 2) a) 54 59 5 9 (6p4) (-9p8) d) c 5 e) 9 8 35 32 c f) -49 3 72 g) (-5) 9 h) (-2) -6 Simplify the epression. Write your answer with positive integer eponents only. 3) a) (-4y5)-3 (5-9y4z-6) -2 (42y3) - (24y) 3 d) (-4) 32(yz)3-64y-3z Find the requested value of the given polynomial function. 4) f() = -42 + 9-3 a) f(-2) f(0) f( + h) - f() Solve the problem. 6) An object is thrown upward with an initial velocity of 29 feet per second from the top of a 573-foot building. The height of the object at any time t can be described by the polynomial function P(t) = -6t2 + 29t + 573. Find the height of the object at t = 5 seconds. 7) The total cost in dollars for a certain company to produce empty jars to be used by a jelly producer is given by the polynomial equation C() = 0.6 + 40,000. Find the cost of producing 70,000 jars. 8) The revenue R, in dollars, from selling hundred tetbooks is R() = -.22 + 274. The cost C, in dollars, from selling hundred tetbooks is C() = 0.063-32 + 30 + 800. a) Find the profit function, P() = R() - C(). Find the profit if = 5 hundred tetbooks are sold. The graph of two functions, f and g, is shown below. Use the graph to find the value. 0 5 y f -5 5 0 g For the given functions f and g, find the requested function. 5) f() = 32 + 5-4; g() = 6 + 6 a) Find (f + g)() Find (f + g)(-2). 9) a) (f + g)(8) (f + g)(0) (f- g)(5) d) (g- f)(-3)
Review for Test 3 Page 2 Find the product. 0) a) (67y)(-35y2) 8y(4y2-7y) 5a6(9a6 + 3 + 0a) d) (4-8)( + ) e) (-5-2)(3 - ) f) (5 + 8y)(2 + 9y) g) ( + 4)(32 + 7 + 8) h) ( + 3)(2-3 + 9) Find the special product. ) a) ( + 6)( - 6) (2p + )(2p - ) (2-3r)(2 + 3r) d) (p + q)(p - q) e) (y5-8)(y5 + 8) f) (0 + 9)2 g) (6 - y)2 h) (42 + 5y) 2 For the given functions f and g, find (f g)(). 2) a) f() = 8-5, g() = 9 + 7 f() = + 0, g() = 2 + 7 f() = 53 -, g() = 42 + Find the requested value for the given functions. 3) f() = + 9, g() = 2-4 - 3 a) Find f(5) and g(5) a) Find (f g)() Find (f g)(5). Divide and simplify. 4) a) 5r 6-25r3 5r -24 6 + 24-202 -44-4 6y6-283y5 + 22y4 72y4 Divide using long division. 5) a) 4m 2 + 22m - 42 m + 7 p 2 + 3p - p + 6 5 3 + 2 + 3-3 5-3 d) 8t 4 + 2t3-2t2 + 5t - 9 2t2 + 2t - 3 Find f g (). 6) a) f() = 2 + 5 + 47; g() = + 8 f() = 363-9; g() = 6 - Factor out the greatest common factor. Be sure that the coefficient of the term of highest degree is positive. 7) a) 8-9 323-8 365y + 20y6 d) -22-0 + 6 e) 249y9-846y5-723y3 8) a) 6(y + 4) - (y + 4) 9a(a - + (a - ( + )(4-5) + ( + )(9 + 3) Factor the polynomial completely. If the polynomial cannot be factored, say it is prime. 9) a) 2 + 4-2 2 + 65 + 66 a2 + 3ab + 36b2 d) 4y3-4y2-48y e) -w2 + 2w - 27 f) 72 + 32-5 g) 52 + 29 + 2 h) 02-23 + 2 i) 92-6 - 8 j) 4w2 + 63w - 35 k) 52 + 9 + 2 l) 243-342 - 0 20) a) 2-8y + 8y2 642-80 + 25 002-20 + d) 322 + 44 + 62 2) a) 2-00 492-9 (7 + 3)(7-3) d) 22-50 e) 4-8 f) 3y2-47 g) 254-9y6 h) 25y3 + 26 i) 3433 - j) 23-768 k) 252 + 4y2 Factor the polynomial function. 22) a) f() = 2 + 0-24 P() = 22 + - 5 G() = -32 + 75 d) S(y) = 5y3-0y2-40y Solve the equation. 23) 3(8-5) = 0 24) (2-9)( + ) = 0
Review for Test 3 Page 3 25) m2 + 2m - 24 = 0 26) 2 - = 42 27) 202 + 23 + 6 = 0 Determine the domain of the rational function. 7-7 37) a) f() = h() = + 8 22 + 7-9 g() = 9-6 2-49 - 8 d) p() = 3-42 - 5 28) 2-27 7 = 7 29) q(5q + 3) = 6 Simplify the rational epression. 2 + 2 38) a) 02 + 6 + 6 8-6 53-52 a 2 + 5a + 6 a + 2 d) 2 + 5 + 6 2 + 6 + 9 30) (2 + 6)( - ) = 0 3) 3 = 9 Find the values of such that the given function has the stated value. 32) f() = 2 + 2; f() = 35 33) g() = 42-5; g() = 9 Solve. 34) If the cost, C(), for manufacturing units of a certain product is given by C() = 2-0 + 9000, find the number of units manufactured at a cost of $3,200. 35) The width of a rectangle is 6 meters less than twice its length. If its area is 08 square meters, find the dimensions of the rectangle. 36) An object is thrown upward from the top of a 60-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 = -6t2 + 48t + 60. a) After how many seconds will the height of the object be 96 feet? How long will it take for the object to hit the ground? Multiply the rational epression. Epress the product as a rational epression in lowest terms. 96 8-24 39) a) 2-9 22 z 2 + 6z + 64 z2-9 z 2 + 3z z + 8 2-3 + 30 2-3 + 42 2-7 + 66 2-5 + 50 d) y 2-25 y2-9 y 2 + 9y + 8 y2-8y + 5 e) 4m 2 + 8mn + 4n2 m2 - n2 f) n - m 5m + 5n z3-25 z2-8z + 5 2z2 + 5z - 33 9z2 + 45z + 225 Find R() = f() g() and state its domain. 40) f() = 2 + 5-6, g() = - 7 2-4 - 2 22 + - 6 Divide the rational epression. Epress the quotient as a rational epression in lowest terms. 5a2 2-9 b3 3y 4) a) 4a 3b2 (y - 0)2 7 7y - 70 49 d) 3-5y y2 + 5y - 6 y2 + 9y + 8 y2 - y2 + 7y + 2
Review for Test 3 Page 4 Find R() = f() and state its domain. h() 42) f() = 2-5 + 4, h() = + 3-52 + 3-6 Perform the indicated operation and simplify the result. 5 43) a) 4 + 9-2 4 + 9 8-5 + 3 5-2 - 8-37 - 8-2 - 3-3 8 - Add or subtract, as indicated, and simplify the result. 7 44) 27 + 2 32 45) y - 4 y + 3 - y - 4 y + 46) 47) (- 4)( - ) - 3 (- )( - 2) 2-6 - 4 2 + 5 + 4 Perform the indicated operations and simplify the result. 5 48) + + 6 - - 0 2 - Simplify the comple rational epression. 49) a) 2 a + 2 2 a - 2 Solve the equation. 6 50) p - 8 = 4 p + 8-5 - 25 36t2-49s2 st 6 s - 7 t 53) 5 + 2-8 - 2 = 0 2-4 54) - 5 = 24 + 5 55) b + b - 4 = b - 3 b - 4 Solve the problem. 56) a) For the function f() = 2 + 4, solve f() = 9. For the function f() = + 3, solve f() = 2. - Solve the formula for the indicated variable. A 57) P = for t + rt 58) P = Fd t for t 59) a + b = c for b 60) p + q = f for f Solve the work problem. 6) 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 them to complete the job if they were working together? (Round your answer to the nearest tenth, if necessary.) 62) One pump can drain a pool in hours. When a second pump is also used, the pool only takes 5 hours to drain. How long would it take the second pump to drain the pool if it were the only pump in use? (Round your answer to the nearest tenth, if necessary.) 5) m - 6 m = 5 52) + y = 30 y2
Review for Test 3 Page 5 Solve the motion problem. 63) A plane flies 600 miles west into the wind and makes the return trip (against the wind) following the same flight path. The effect of the jet stream on the plane is 5 miles per hour. The round trip takes 9 hours. What is the speed of the plane in still air? 64) A boat moves 7 kilometers upstream in the same amount of time it moves 20 kilometers downstream. If the rate of the current is 5 kilometers per hour, find the rate of the boat in still water. (Round your answer to the nearest tenth, if necessary.) Solve the problem. 65) When Milo got promoted at work, he received a 20% pay raise. He now earns $45,600 per year. What was his annual salary before his raise? 66) After a 9% price reduction, a boat sold for $ 28,20. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.) 67) A certain aircraft can fly 52 miles with the wind in 4 hours and travel the same distance against the wind in 8 hours. a) What is the airspeed of the plane? What is the speed of the wind?
Answer Key Testname: IAREVIEW3F ) a) 343 6-256 d) 64 e) f) - g) 2 i) 4 h) 6 j) 625 k) 9 l) 27 2) a) 53 4-54p2 d) c4 e) f) -7 g) 4 h) 2 3) a) 2 y5 8z2 25y8 4 7 0 d) y6z2 4) a) -37-3 -4h2-9h + 9h 5) a) 32 + + 2-8 6) 38 ft 7) $82,000 8) a) P() = -0.063 +.82 + 244-800 $3062.50 9) a) 6 8 4 d) -2 0) a) -82y3 32y3-56y2 45a22 + 55a9 + 50a26 d) 42 + 36-88 e) -52-3 + 2 f) 02 + 6y + 72y2 g) 33 + 92 + 36 + 32 h) 3 + 27 ) a) 2-36 4p2-4 - 69r2 d) p2-2q2 e) y0-64 f) 002 + 80 + 8 g) 362-2y + y2 h) 64 + 402y + 25y2 2) a) 722 + - 35 3 + 02 + 7 + 70 205 + 53-42 - 3) a) f(5) = 4, g() = 2 (f g)() = 3 + 52-39 - 27 (f g)(5) = 28 4) a) 3r5-5r2 62-3 + 5 2-24y2-4y + 3 5) a) 4m - 6 7 p - 3 + p + 6 32 + 4 + 5 + d) 4t2-3t + 3 9 6) a) + 7 - + 8 62 + - 3-2 5-3 3 6-7) a) 9(2 - ) 8(42 - ) 4y(94 + 5y5) d) -2(2 + 5-3) e) 23y3(26y6-73y2-6) 8) a) (y + 4)(6 - ) (a - (9a + ) ( + )(3 + 8) 9) a) ( + 6)( - 2) Prime (a + 9(a + 4 d) 4y(y + 3)(y - 4) e) -(w - 9)(w - 3) f) (7-3)( + 5) g) (3 + 4)(5 + 3) h) (2-3)(5-4) i) (3 + 2)(3-4) j) 7(2w - )(w + 5) k) Prime l) 2(3-5)(4 + ) 20) a) (- 9y)2 (8-5)2 (0 - )2 d) 2(4 + 9)2 2) a) ( + 0)( - 0) (7 + 3)(7-3) (5 + 9)(5-9) d) 2( + 5)( - 5) e) (2 + 9)( + 3)( - 3) f) 3(y + 7)(y - 7) g) (52 + 3y3)(52-3y3) h) (5y + 6)(25y2-30y + 36) i) (7- )(492 + 7 + ) j) 2( + 8)( - 8) k) prime 22) a) f() = ( + 2)( - 2) P() = (2-5)( + 3) G() = -3( + 5)( - 5) d) S(y) = 5y(y + 2)(y - 4) 5 23) 8, 0 24) -, 9 2
Answer Key Testname: IAREVIEW3F 25) {-6, 4} 26) {-6, 7} 27) - 2 5, - 3 4 28) {0, 4} 29) -3, 2 5 30) - 3, 0, 3) {-3, 0, 3} 32) {-7, 5} 9 33) 4,- 34) 70 units 35) length = 9 m, width = 2 m 36) a) hint: -6t2 + 48t + 60 = 96 ; ans: t = 4 sec hint: -6t2 + 48t + 60 = 0; ans: t = 5 sec 37) a) { -8} { - 9 2, } { 7, -7} d) { 5, -, 0} 38) a) a + 3 5 + 3 39) a) 40) 6 52 64 ( + 3) ( - 3)( - ) ( - 7)( - 5) e) - 4 5 d) + 2 + 3 d) f) z(z + 8) z - 3 (y + 5)(y + 6) (y - 3)2 2z + 9 (- )( + 3) ;{ 7, -6, 2-2 } 4) a) 5a 4b -5( + 3) y - 0 d) y + 4 y + 42) ( - 4)(5-2); {, -3, 2 5 } 43) a) 5-2 4 + 9 8-3 - 5 2 + 5 7 + 8 44) 272 45) 46) 47) -2(y - 4) (y + 3)(y + ) -2( - 5) ( - 4)( - )( - 2) 2-3 + 6 ( - 4)( + 4)( + ) 48) 5-4 - 49) a) + a - a + 5 7s + 6t 50) - 40 5) {-, 6} 52) {-6, 5} 53) {-2} 54) {25, -} 55) {} 56) a) = or = 4, = 5 2 57) t = A - P Pr 58) t = Fd P 59) b = 60) f = a ac - pq p + q 6) 3.9 hours 62) 9.2 hours 63) 35 miles per hour 64) 0.4 kilometers per hour 65) $38,000 66) $3,000 67) a) 26 mph 72 mph