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# College Algebra MATH 1065

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This 24 page Class Notes was uploaded by Dr. Tyrell McKenzie on Sunday October 11, 2015. The Class Notes belongs to MATH 1065 at East Carolina University taught by Staff in Fall. Since its upload, it has received 66 views. For similar materials see /class/221299/math-1065-east-carolina-university in Mathematics (M) at East Carolina University.

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Date Created: 10/11/15

R5 Factoring Polynomials 0 Factor out Greatest Common FactorGCF or Common Monomial Factoring 1 x3 3x2 2 xx2 6 5x2 6 0 Factor by Grouping Step 1 Group the terms in pairs Step 2 Factor the GCF greatest common factor out of each pair Step 3 Check that the parentheses are equal Step 4 Factor out the parentheses the new GCF 3 6x2 2x9x 3 4 2x2 6xw xy 3wy 0 Factor Trinomials with a Leading Coef cient Equal to One x2 BxC xaxb Where aampbare integersa b C and a b B 5 x28x15 6 x2 2x 24 7 x2 12x32 8 xZ Zx 6 0 Factor Trinomials with a Leading Coef cient Not Equal to One sz BxCWherea i Oorai 1 Step 1 Multiply A C Step 2 Find integers aand b Where ACabandabB Step 3 Rewrite the middle term as two terms using the values ofa and 19 found in step 2 Step 4 Factor by grouping 9 6x2 29x 35 10 4x2 17x 15 1112x2 25x 12 0 Special Formulas a Difference of two squares a2 b2 aba b b SumDifference of two cubes a3 b3 a ba2 ab 192 a3 b3 a ba2 ab 192 12 22 4 13 3632 1 14 Z4 16 16 833 125 171 27x3 0 Perfect Square Trinomials a2 2abb2 ab2 a2 2abb2 a b2 18 4x2 12xy 932 Use any formula to factor 19 2x3 5x2 12x 20 5x4 45x2 21 28z3x 27y 8233 27x MATH 1065 PreFinal Exam Name Class time Please bubble in the correct answer for each question on your bubble sheet 2x z39fxlt 2 Given fx 4 ifx 2 find f 2 f 5 f 1 3x2 5 z39fxgt 2 A a22 b12 q 6 d4 e16 2 Find the equation of the line with an xintercept of 4 and a yintercept of 2 a x2y2 b xy 2 C x 2y 4 d x 2y 2 e x2y4 3 For the given functions fand 9 find g of fx2x2 gx4x21 a4 b6 q 8 d37 e65 4 Find the domain of the function fx 2 3x2x 1 a x 0 b xqr l C xvi l d x2l e xZ l 2 2 2 2 5 Solve 2quot151 2 a x1n5 1n2 b x1n2 1n5 C x1 2xln51 111221n5 21n5 ln2 1112 ln5 2xInS ln2 ln5ln2 d x e x 1n221115 ln221n5 xy1 6 Solve the followmg system The value ofXIs 2x3y 7 ae b8 Q10 ms e7 7 A chef needs to mix a 45 fat content cheese with a 20 fat content cheese to obtain 30 grams of a cheese mixture that is 30 fat How many grams of the 45 fat content are needed a 18g b 15g c 14g d 12g e 17g 8 Given the following graph find f7 the range and the intervals decreasing 74 lJ 1 RD 9 Find an equation of the line that is perpendicularto the line 4x3y 2 and containing the point 13 Express your answer in general form a 3x2y3 b 5x3y6 c 3x 2y12 d 2x 3y 6 e None ofthese 10 For the graph of y e which of the following is TRUE a The xintercept is 10 b The range is all real numbers c The domain is x gt1 d The graph is always increasing e The vertical asymptote is y 0 11 Determine if the graph of the following equation is symmetrical with the xaxis yaxis origin or has no symmetry and also find all intercepts if there are any 4x y x216 a xaxis 00 b yaxis no intercepts c origin no intercepts d no symmetry 00 e origin 00 12 Solve the equation 3x2 6x2 0 61 3i3J b lid 345 1 c T d 7 2 e None ofthese 13 Identify the equation of a circle with center 42 and radius 4 a x 42y224 b x 42y222 c x 42y2216 d x42y 224 e x42y2216 14 One factor of 64 x3 is a 8 x b x 8 c x 4 d x28x64 e x24x16 15 The volume Vof a given mass of gas varies directly as the temperature Tand inversely as the pressure P A measuring device is calibrated to give V 66 in3 when T 120 and P 201bz n2 What is the volume on this device when the temperature is 380 and the pressure is 251bz n2 a 16721713 b 1521713 C 18721713 d 14721713 e 1972 in3 7 x 16 Solve the inequality and express the solution in interval notation 3 Z 21 a 15 b oo1U5oo c 15 d OO1U500 e 5 1 7 2 7 77 smowymo ExpressEm y 09 a i b w c 1 d 2 E l W X7 x yz y 18 1 w y x 7 s 71 um H Re ectabuutthe faXS 77 SM mom 2 mm a y x23 o pal 72 o yX23 o y x23 o Hone omoso 19 5 6cumpuundedquarteryhuwmuchmus LHEnvestrDVW Pn1i a 11138 E7 b 23132 83 E 13323 BU d M 137UB E 4344 U7 2n fx24xi2 aHo m H 7H H o H oo o H a 721 up up E 712 dEIW o 7 4 duvvn up 2 Wurkmg mo yuur musm yuu can spht a turd uffreWEud W 5 huurs WorkHg aune yuur musn can BumpEta theDb W 7 huurs Huvv 7ng womo Make yuu tn sphtthe frevvuud WUrkng a7oHo7 a 17 hrs o 16 hrs o 8 hrs o 72 hrs o 10 hrs 22 Fwd the arger of the somuons omo oooauon pkg71 3 a 7735 o 7 o 7 o 75 o 735 23 In simplified form the period of vibration Pfor a pendulum varies directly as the square root of its length L If P is 1 sec when L is 16 in what is the period when the length is 4 in a 1 sec b 05 sec c 16 sec d 8 sec e 025 sec 24 Change the logarithmic 39 to an I 39 39 39 involving an exponent 10gr 37 x a 37 I b x 37 c 7r d 7 37 e none of these 25 Given A65 and B28 find the midpoint of segment AB and the length of segment AB respectively a M 4 15 d b M215 d 5 c M 2 65 d J d M4 65 d25 e M 265 d5 26 Solve i1256 25 5 11 5 7 7 a g b E c E d E e g 27 The solution set of x5x 2 S 0 is a 52 b oo 5U2oo c oo2 d 25 e Q 28 Given fxx22x6find fx3 a x28x15 b x28x18 c x22x9 d x28x21 e x28x6 29 An object is propelled vertically upward with an initial velocity of 20 meters per second The distance 5 in meters of the object from the ground after tseconds is s 5t2 20t What is the maximum height of the object a 21 m b 20m c 19m d 18m e 17m 30 Which of the following functions is odd a gx3x274 b hx3x472x2 c Fx 3x1 73 d maxi e hxx 7x271 72 31 Solve the inequality express the solution in interval notation 3 2 x 7 5x 6x 2 0 a foo2 U300 b 710 U600 0 760 U 00 d 0 2 U 3 00 e 700 0 U 2 3 32 Determine the domain and range of the function y x2 74 WWW algzhvamlv mm a Domain 20 2 Range 4 0 b Domain 2 2 Range 7400 c Domain 2 2 Range 7400 d Domain 70090 Range 70074 e Domain 70000 Range 7400 33 Solve log7x2 x 710gng 7x 71 a x3 b x 71 c x d no real solutions e x701 34 Find the center of the circle 2x2 2y2 7 4x 4y 0 a 22 b 111 0 00 d 111 35 Express the Equatmn as a sum andDr Mame uf uga thms lug a31ugxlngx121mgxi2 b 310g Iagw1rzluggrm c i d i 2 315g lngg lng1 r zlugxrlagz SB Fwd the mverse functer fur x P Ease mute x 5 unerturune 2 a mquot 2 rec 1 jquot 37 curmnuuusm a a 7 years b 3 2 years c 1 year a 5 1 years a a a years 38 Furvxmat va ues uf X 5 x gt m a 04 b 04 5 740 a 740 5 am 39 Su vefurrmthefurmu a S 1 1 61 d r a E e r4S 4o Solve for R iii R R1 R2 Rle R1R2 a R b R QR R2 R1R2 Rle R1 1 e RR1R2R1R2 d R R1R2 Review for Summer 2010 Final 1 Find the distance between the points 4 7 and 6 1 a 32 b 3245 c 4 d 2J5 e 4J5 2 The profit that the vendor makes per day by selling x pretzels is given by the function Px 4x2 2400x 100 Find the number of pretzels that must be sold to maximize profit a 44 b 100 c 300 d 600 e 1200 1661251 4a4b 039 3 Simplify as much as possible 32 2 4b3 8 a5 b1 i c e a ab a 4 Compared to the graph of fx J gx M Z has which of the following transformations a left 2 down 3 b right 3 up 2 c right 2 up 3 d right 3 down 2 e left 3 down 2 7 x21 5 Solve the inequality and express the solution in interval notation 3 2 a 15 b oo1u5oo C 15 d oo1u5oo e 5 1 6 Solve for w w2 5w3 0 are hie are we 2 2 7 Find an equation of the line that contains 6 O and 9 2 Write your answer in general form a 2x3y 12 b 6x11y 76 C 2x3y 12 d 6x 11y 76 e None of these 8 Solve 10g6x2 x1 a 23 b 23 C 16 d 32 e 32 9Solve 210g3x4 10g392 a x 46JE b x 5 3 c x 135 d x 3 e x5 10 BodyMass Index or BMI varies directly with one s weight in pounds and inversely with the square of one s height A person who weighs 136 pounds and is 60 inches in height has a BMI of 266 What is the BMI to the nearest tenth for a person who weighs 190 pounds and is 74 inches in height a 253 b 244 c 228 d 239 e 251 11 The amount of paint needed to cover the walls of a room varies jointly with the perimeter of the room and the height of the wall If a room with a perimeter of 60 feet and 10foot walls requires 6 quarts of paint find the amount of paint needed to cover the walls of a room with a perimeter of 80 feet and 8foot walls a 64 b 10 c 12 d 64 e 640 2x z39fxlt 2 12Given fx 4 ifx 2 find f 2 f 5 f 1 3x2 5 z39fxgt 2 a 22 b 12 C 6 d 4 e 16 13 Find the vertex of the parabola fx x2 6x2 a 3 25 b 3 25 c 3 7 d 311 e None of these 14 Find the equation of the line that is perpendicular to the line 2x3y 6 and contains the point 14 a 3x2y11 b 2x 3y 14 c 2x3y10 d 3x 2y 11 e 2x 3y 10 15 Write the slopeintercept form of the equation ofthe line passing through the point 12 and parallel to the line 2xy 6 a y 2x 5 b y2x4 c y 2x 4 d y 2x 5 e None ofthese 16 Solve the inequality express the solution in interval notation x3 5x2 6x Z 0 a 00 2 U3oo b 10 U6oo c 60U1oo d 02 U3oo e oo 0 U2 3 17 Solve the inequality Express the solution in interval notation 2x1x 42x 5 gt 0 a 434 b aw c 003 d mum e wbuem 18 A college student earned 6300 during summer vacation working as a waiter in a popular restaurant The student invested part of the money at 9 and the rest at 8 If the student received a total of 543 in interest at the end of the year how much was invested at 9 a 3900 b 3150 c 787 d 2400 e 1650 19 Solve 8x 5 4 C 12 d 12 e No solution 5 5 8 8 5 2 1 20 Solve the system x y The xvalue is x4y35 34 a 2 b 9 c F d 8 e 3 21 Find the domain of the function fx 2 3xJ2x 1 a x 0 b w1 c mat l d x2l e 962 1 2 2 2 2 22 Change the exponential equation a5 12 into the equivalent logarithmic form a 10g12a5 b 10g5a12 C 10g512a Cl loga125 E loga512 23 Change the logarithmic expression to an equivalent expression involving an exponent 10gr 37 x a 37 b x 37 c n cl x37 e none ofthese 24 The equation y2 x1 has symmetry with respect to z39 xaxis z39z39 yaxis in origin a i only b ii only c z39z39z39 only cl 139 ii and iii e None of these 25 Determine if the graph of the following equation is symmetrical with the xaxis yaxis origin or has no symmetry and also find all intercepts if there are any 4x y x216 a xaxis 00 b yaxis no intercepts c origin no intercepts cl no symmetry 00 e origin 00 26 Solve 2 15H a x1n5 1n2 b x1n2 1n5 C x1 2x1n51 111221n5 21n5 1n2 1n2 1n5 2xInS lr12 ln5an cl x e x 1n221n5 111221n5 27 For the given functionsf and 9 find gof fx2x2 gx4x21 a 4 b 6 c 8 cl 37 e 65 28 Given the following graph determine whether the function is even odd neither all intercepts and the domain a Odd Intercepts i40amp00 D 4 4 b Neither Intercepts 00 D 44 c Even Intercepts i40 D 2 2 d Odd Intercepts 00 D 2 2 e Even Intercepts i40amp00 D 44 29 Find the center hie and radius r of the circle whose equation is x2y2 4x 2y 60 a hk21rJ b hk 2 1 r11 c hk12rJE cl hk 1 2r e hk26r3 30 Solve 9 275 3 7 5 7 15 a x g b x E C x Cl xg e 95 31 Which of the following are factors of x4 10x2 9 I x29 II x21 III x3 V x l a I and II b III only c III and IV cl IV only e None of the above 32 One factor of 64 x3 is a 8 x b x 8 C x 4 cl x28x64 e x24x16 33 Consider the function fxi If fx6what is x x 5 1 52 52 2 b cl a 52 C 2 5 e 5 x3 x2139 34 fx Evaluate f 1 a 3 b 2 c 1 cl 6 e None ofthese 35 Write the expression as a single logarithm 21nx 1nx2 1 1ny xZQE xy x2 chZ 1 a 1nm b 1n x21 C In T xx2l ZxW Cl 11 7 l 1 l y l e MIL u 36 Solve for R iii R R1 R2 R1R2 R1R2 R b R R a R1R2 Rle c 11212 039 R 1 e RRRRR RR 37 A chef needs to mix a 45 fat content cheese with a 20 fat content cheese to obtain 30 grams of a cheese mixture that is 30 fat How many grams of the 45 fat content are needed a 18g b 15g c 14g d 12g e 17g 38 Consider the function gx e Which of the following is true regarding the graph of this function a The graph is decreasing on the interval oooo b The vertical asymptote is x 0 c The domain is oooo d The range is oooo e The xintercept is 10 39 Use the compound interest formula AP1 quot to find the amount that results from investing 450 at 7 compounded daily after a period of 4 years Round your answer to the nearest cent a 193050 b 54011 c 62173 d 45026 e 59539 40 The function fx 2 is onetoone Find its inverse x 1 2 1 3 2 1 2 3 a f x x b f x x c f x x x x d f IOC 3x2 e None ofthese x 41 A population of doves obeys the law of uninhibited growth Nt N0ek If there are 1000 doves initially and there are 2000 after 1 day what is the size of the colony after 3 days a 3000 b 6000 c 8000 d 16000 e None of these 42 Solve the equation x2 2x 4 4 a 24 b 4 2 2 C 4 2 d 20 2 4 e 024 43 Find the smaller solution of the equation 6x2 7x 20 a b g c 2 d g e 2 44 Iffis a real function then the graph of gx fx 5 7 is the graph offthat is a shifted 5 units right and 7 units up b shifted 5 units right and 7 units down c shifted 5 units left and 7 units up d shifted 7 units left and 5 units down e shifted 7 units left and 5 units up 45 Solve the equation logs 36 5x3 8 0 b i c d 1 e 5 46 You invest 20000 in two accounts paying 7 and 9 annual interest respectively If the total interest earned for the year is 1550 how much was invested at 7 a 12500 b 8500 c 11500 d 8000 e 9275 47 Find the center of the circle 2x2 2y2 4x4y 0 a 22 b 11 c 00 d 11 e 22 48 Determine the domain and range of the function yx2 74 WWW algzhvahzip mm a Domain 202 Range 40 b Domain 12 Range 4500 c Domain 2239 Range 7400 d Domain 70000 Range 70074 e Domain 70000 Range 7400 49 Find the vertex and axis of symmetry of the parabola defined by 72x2 74x 5 a 17 1 b 17 v c 17 x 1 d 17 x 1 e 17 x 1 50 The number of trees that can be planted per acre is inversely proportional to the square of the distance between each pair of trees If 150 trees can be planted per acre with a distance of 6 ft between each pair of trees what is the necessary approximately distance between trees in order to plant 200 per acre a 52 ft b 33 ft c 23 ft d 41 ft e 47 ft

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