4a 4ab b (count number of places from first non-zero digit to

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1 . Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate the expession: 4a 4ab b, when a = and b = 4a 4ab b = 4. Fiefightes use the fomula S = 0.P + 6 to compute the hoizontal ange S in feet of wate fom a paticula hose, whee P is the nozzle pessue in pounds. Find the hoizontal ange if pessue is 90 lb. Given P = 90 lb. Hence hoizontal ange S = 0.(90) + 6 = 7 feet.. Simplify: 6 x x x x x 7 x = 8 4x 6. Simplify: 8 u v 8w w 64w 8w u v 4u v u v 0 4 6w u = 4 v 0 7. Expess in scientific notation: = the decimal) (count numbe of places fom fist non-zeo digit to 8. Expand:.0 0 = = Solve: x Multiply both sides of the equation by 8 8 x x x 4 0. Solve: 8(x ) (x + 4) = 0 + x 8x 6 x 0 = 0 + x x 6 = 0 + x x x = x = 6 x = 8 PAGE OF 4

2 . Solve fo m: mv F F mv F m v. A. Solve P: A P Pt A P( t) t P. Solve: 6 4 x x 6x 4x 6x4x0 6x 4x 0 x 0 x 0 4. Solve: x x x o x x o x x o x x 4 x 4. Solve: ( x 4) ( x 4) ( x 4) x4 4x x4 4x 4 ( x 4) x (4 x) 4 x x x 4 x 4 x 8 x 4 Howeve, if x = 4 the denominato becomes zeo in the oiginal equation. ANSWER: No Solution 6. Simplify: x x y 6xy x xy = x x xy 6y x x y x y x y = x y = x y 7. Simplify: = x x x x 4x x x = x x 8. Solve: -(x ) 7 6x 9 7 6x 8 x 9. Solve: x 4 x 4 0 x 4 x 6 x PAGE OF 4

3 0. John aveaged 8 out of 00 on his fist thee tests. What was John s scoe on the fouth test if his aveage afte the fouth test dopped to 79 out of 00? TT TT x Test Aveage = x 6 46 x 70 x. The sales tax ate in Wilson County is 6.7%. Suppose total pice of an item that you bought in Wilson County including taxes is $4.9, what is the pice (ounded to two decimal places) befoe tax? Pice befoe tax + 6.7% sales tax = Total pice x x = x = 4.9 x = $.99. The long tem paking ate at Raleigh-Duham Aipot is $ pe hou (o pat of an hou) with $0 daily maximum (:00 a.m. to :00 a.m.). Suppose you pak you ca on Fiday aftenoon at 8:0 p.m. and pick it up on the following Tuesday at 9:0 a.m., what will be you paking fee? Fiday =. hous $ 8 Paking Fee = = $48 Satuday = 4 hous $0 Sunday = 4 hous $0 Monday = 4 hous $0 Tuesday = 9. hous $0. Solve: x(0x + 8) = -(x+) 0x 6x x x 9 9 x o = x 9x o Solve: x 8 0 x x 4 ( ) 4 4 x 8 0 4x x x x = The pofit, P, ealized by a company vaies diectly as the numbe of poducts s it sells. If a company makes a pofit of $7800 on the sale of poducts, what is the pofit when the company sells 000 poducts? P = k s 7800 = k() 7800 k 4 k P = 4 s = 4(000) = $0,000 PAGE OF 4

4 6. If the voltage, V, in an electic cicuit is held constant, the cuent I, is invesely popotional to the esistance, R. If cuent is 0mA (milliampee) when esistance is ohms, find the cuent when the esistance is ohms. k k I k I R R = 40 ma 7. A 6 foot long tube is cut into two pieces with atio 4:. Find the length of the shote piece. The atio 4: 4x + x = 6 9x = 6 x = 4 Shote piece = 4(4) = 6 feet 8. A lage squae pizza has 49 pieces (squae slices). John, Jack and Jane ate all the pieces in the atio 4:: espectively. How many pieces did Jack eat? The atio 4:: 4x + x + x = 49 7x = 49 x = 7 Jack ate (7) = 4 pieces 9. Solve: x x x x 4 x x x x 4 0. Solve fo V given V h V h h V h V V h. Find the equation of the staight line passing though the points (,-4) and (,0) y mx b slope m 4 y 4x b 0 4() b 4 b y 4x 4. Detemine the x and y intecepts of the gaph of 7x y = 7x 0 7x x x-intecept: let y = 0 y-intecept: let x = 0 y Answe: (, 0) and (0, -7) 7 0 y y 7 PAGE 4 OF 4

5 . The linea elationship between the Fahenheit scale and Centigade scale fo tempeatues is given 9 by F C. Which of the following statements, if any, ae TRUE? 9 9 A. If C = 0 o, then F C TRUE 9 9 B. If C = 40 o, then F C FALSE ANSWER: Only A 4. John (J) is yeas olde than his siste May (M) who is yeas younge than he bothe Paul (P). If J, M and P denote thei ages, which one of the following epesents the given infomation? John is yeas olde than May J = M + May is yeas younge than Paul M = P - x y 4. Solve the system: x y 4 y y 8 4y 8 y. The fist equation becomes Answe: (, ) Subtacting second equation fom fist gives y y x 4 x 0 4 x 6 x The sum of two numbes is. Twice the smalle numbe is moe than the lage numbe. The positive diffeence between the numbes is Let x be the lage numbe and y the smalle. The sum of two numbes is. x + y = y = - x Twice the smalle numbe is moe than the lage numbe. y = x + ( x) = x+ 6 x = x + 6 = x + x = x 7 = x x + y = 7 + y = y = 7 y = 4 The positive diffeence between the numbe is x y = 7 4 = 7. Find the coodinates of a point A whose distance fom the oigin (0, 0) is units. Distance of a point A (x, y) fom the oigin (0, 0) = 0 0 Distance of A (, ) fom the oigin = 8 Distance of A (-, ) fom the oigin = Distance of A (4, - ) fom the oigin = 4 x y x y PAGE OF 4

6 8. Conside the cicle given by the equation (x ) + (y + ) =. Find the cente and adius. x h y k The equation of a cicle with cente (h, k) and adius is (x ) + (y + ) = (x ) + (y (-)) = ( ) Cente is (, -) and adius is 9. The inequality 8x 8is equivalent to By definition of absolute value 8x 8-8 < 8 x < 8 Subtact 8 fom the thee sides -8 8 < 8 - x 8 < < -x < 0 Divide thee sides by - and this will evese the inequalities 6 > x > 0 Rewiting with zeo on the left 0 < x < The inequality x 4 is equivalent to By definition of absolute value x 4 x 4 o x 4 x 4 o x 4 x o x x 4. The inteval solution to the inequality 0 is x Numeato x Denominato x x Quotient x x Hence 0 x when x is to the left of - o ight of Answe:,, 4. Let f ( x) x. Find f( a ) f( a ) = a a = a PAGE 6 OF 4

7 4. Let f x x and g x x BARTON COLLEGE. Which of the following, if any, is false? a) f g(0) f 0 g Let f x x and g x x. Hence it is false.. Which of the following, if any, is tue? f g 0 f g 0 f 0 f g f 0 g f 0 g 0 g TRUE a) b) c) f f ( x) f f x f x x 4 x x 4 4x x g g ( x) g g x g x x 4x 4x 4x 4 4 d) 4. Let f x f x h f x x. Find the diffeence quotient h f x h f x ( x h) x x h x h h h h h 46. Conside the quadatic function f x x 4x. Find the vetex of the gaph of f x. b b Given a quadatic function f x ax bx c the coodinates of the vetex ae, f a a b 4 b Hee a =, b = -4 and c =. Hence and f f() 4 a a Answe: The vetex of the gaph is at (, -) 47. The tempeatue, in degees Fahenheit, ove a twelve hou peiod is given by the function T(t) = -0.t + 6t + 0, whee t = 0 denotes 6:00 a.m. When is the moning tempeatue 47. o F? Solve: 47. = -0.t + 6t t + 6t = 0-0.t + 6t 7. = 0 Divide thoughout by -0. t t + = 0 (t )(t 7) = 0 t = o 7 a.m. o p.m. Answe: a.m. 48. Simplify and expess in the fom a + bi: (- + i)( + i) = -6 4i + i + i = -6 i + (-) = -8 i PAGE 7 OF 4

8 49. Simplify and expess in the fom a + bi: 4ii 4i 4i 4i 4i 4( ) 4 4i i i i i i i ( ) i x 0. Find the domain of the function f( x) x. Since the denominato x 0fo any eal x, the domain is all eal numbes. x. Find the equation of hoizontal asymptote of the function f( x) x Since the denominato has a highe degee than numeato, the hoizontal asymptote is the x-axis. y = 0 x. Find the invese function fo f(x) =. x y To find the invese eplace (x, y) by (y, x) and solve fo y. Hence y becomes x Multiplying both sides by x y 6 x6 y f - (x) = x + 6. Which of the following pais of exponential and logaithmic foms is false? (/) - = 4; log 4 (/) = - is false since / 4 log 4 / 4. Wite in tems of log(x), log(y), log(z): y z 0. log log y z log x log y log z x log x = log(y) + 0. log(z) log(x). Find the hydonium-ion concentation, H +, of a solution given ph = 7. ph = -log(h + ) 7. = -log(h + ) 7. log0 H 7. log0 H H + = moles pe lite H Solve: x e x loge x = ln() + ln x PAGE 8 OF 4

9 x x 7. Solve the equation: log ( x) log ( x) log x x x 4x x 4x 4 4 4x x x x. t 8. Suppose the population of a town is given by the model Pt 70 numbe yeas since 000. Which of the following statements is tue? /0, whee t denotes the a) The population in 000 was 86. False since when t = 0, P(0) = 70. b) The population doubles evey 0 yeas. False since when t = 0, P(0) = 86. c) The population is halved evey ten yeas. TRUE since when t = 0, P(0) = 86 = ½(70). d) The population is gowing by 0% evey ten yeas. FALSE since population is deceasing If the angle adians, then since π = 80 o, 08 Answe: o 60. If the light beam makes one complete evolution evey 0 seconds, how long will it take to sweep and angle of 0 o? evolution = 60 o in second the light beam sweeps 60 o 8 to sweep 0 0 = 0 = 8. sec 0 8 Answe: between 7 and 0 seconds 6. Given an isosceles tiangle with base length cm and altitude cm, find the length of the conguent sides. X X 6 6 X = 6 + = 400 X = 0 cm 6. If tan and sin 0, then cos equals Y θ Since tan > 0 and sin 0, the angle is in the Quadant I tan opp hyp 0 cos = adj adj hyp = 0 PAGE 9 OF 4

10 6. If csc and cos 0, then cot equals Since csc 0 > 0 and cos 0, the angle is in the Quadant II cot 0 csc hyp opp adj 44 cot = adj opp = 64. Find the exact value of csc o is in Quadant III csc( o ) < 0 The efeence angle is 4 o. csc( o ) = -csc(4 o ) = o 6. Find the exact value of cot 40. Since 40 o = 60 o + 60 o Cot(40 o ) = cot(60 o ) = tan 60 o = 66. If the angle in standad position meets the unit cicle at sin and cos. Since the point is in Quadant IV, x cos with. Hence sin and cos 6,, find the value of the functions 6 6 sin 0 and cos 0. Futhe on the unit ciclesin 6 y and 67. Find the expession that is equal to sin sin sin sin = csc sin sin csc sin sin 68. Find the expession that is equal to tan cot tan tan cot cot tan cot tan cot = sec csc PAGE 0 OF 4

11 69. The minute hand of a clock is 6cm long. How fa does the tip of the minute hand tavel in minutes? θ adian θ h = 60 minutes = 60 o = π adian minutes = 90 o = π/ adian Distance tavelled by tip of minute hand = 6(π/) = π cm 70. Find the aea of a secto of a cicle with cental angle = adians, if the adius of the cicle is 6 in. θ adian Aea = Aea = 6 = 4 in. 7. The aea of the secto of a cicle with cental angle of θ = adians is 6m. Find the adius of the cicle. Aea = m 4cos 6 cos, Solve 4cos 6 cos 4cos 6 cos cos 0 o sin cos 0, 0 7. Solve sin cos 0 sin 0 o cos 0 sin o cos f sin and f cos is [ -, ] this equation cannot be solved. Since the ange of both functions Answe: No solution. 74. Solve sin sin, sin sin, 6 sin sin 0 sin sin 0 sin o sin PAGE OF 4

12 7. In a ight tiangle ABC with m C 90 A x x, if AC = andsin AC x sin B AB x B, find AB. If AC = x = x = 4 AB = x = 0 C B 76. In tiangle ABC with m A 0, m B 4 and BC =, find AC. A 0 4 B C AC BC Using the Sine Fomula sin B sin A AC AC sin 4 sin 0 / / AC AC 77. In tiangle ABC with m A 0, m B 60 and AB =, find BC. A=0 C=90 B=60 ma 0, m B 60 mc o BC AB cos 60 = 6 In ight tiangle ABC, cos B cos 60 BC BC 78. Eliminate the paamete t in the given paametic equation x cos t x cos t y sin t y sin t y x y cos t sin t x PAGE OF 4

13 79. Eliminate the paamete t in the given paametic equation x sin t cos t x sin t cos t y sin t y sin t cos t y = x 80. Given vectos u 4, and v,, which if the following statements, if any, is false. u 4 TRUE a) b) u v c) v u 4,, 4 (), 0, 0 False, 4, 4, 6,4 TRUE PAGE OF 4

14 ANSWER KEY. c. b 4. c 6. c. b. c 4. c 6. c. b. c 4. a 6. b 4. d 4. a 44. b 64. a. d. a 4. d 6. b 6. c 6. a 46. c 66. b 7. a 7. b 47. b 67. b 8. c 8. c 48. c 68. d 9. a 9. b 49. b 69. d 0. b 0. c 0. a 70. a. d. a. d 7. c. c. a. d 7. a. c. a. b 7. a 4. b 4. d 4. b 74. a. d. b. a 7. a 6. d 6. b 6. a 76. b 7. d 7. c 7. c 77. b 8. c 8. c 8. c 78. d 9. c 9. d 9. b 79. b 0. d 40. b 60. d 80. b. PAGE 4 OF 4