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# Algebra And Trigonometry I MA 15300

Purdue

GPA 3.97

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Date Created: 09/19/15

PURDUE UNIVERSITY V STUDY GUIDE FOR COLLEGE ALGEBRA ANDOR TRIGONOMETRY MA 153 or 154 For Students Who Plan To Obtain Credit In MA 153 or 154 By Examination This study guide describes briefly the topics one should master before one attempts to take the examination in Algebra and0r Trigonometry This material can be found in many currently available textbooks many of which are entitled Algebra and Trigonometry or Precalculus Mathematics The outline that follows is based on the text Algebra and Trigonometry with Analytic Geometry Classic 11th edition by Earl W Swokowski and Jeffery A Cole Brooks Cole Publishing Co 2005 IMPORTANT l Study all of the material listed in the outline mAww If you plan to establish credit by examination read this material thoroughly Work many practice problems Whenyou feel you are prepared for it take the sample examination When you believe your preparation to be completed go to your academic advisor obtain a credit exam request form and follow the instructions given therein A scienti c calculator is required when you take the exam singleline display non programmable nongraphing PART I MA 153 FUNDAMENTAL CONCEPTS OF ALGEBRA real numbers coordinate lines in tegral exponents radicals rational exponents polynomials and algebraic expressions factoring fractional expressions EQUATIONS AND INEQUALITIES linear equations quadratic equations miscel laneous equations inequalities applications FUNCTIONS coordinate systems in two dimensions properties of functions graphs linear functions composition of functions inverse functions variation POLYNOMIAL FUNCTIONS operations on polynomials quadratic functions poly nomial functions of degree greater than 2 graphs EXPONENTIAL AND LOGARITHMIC FUNCTIONS exponential functions loga rithmic functions properties of logarithms and exponents exponential and logarithmic equations SYSTEMS OF EQUATIONS AND INEQUALITIES systems of equations systems of linear equations in two variables PAIcrIIr4A154 THE TRIGONOMETRIC FUNCTIONS the trigonometric functions angles in ra dians and degrees trigonometric functions of angles values of the trigonometric func tions graphs of the trigonometric functimis additional graphical techniques applica tions involving right triangles ANALYTIC TRIGONOMETRY the fundamental identities trigonometric identities trigonometric equations the addition formulas multiple angle formulas sum and product formulas the inverse trigonometric functions the law of Sines the law of cosines vectors COMPLEX NUMBERS de nition of compleic numbers operations on complex num bers complex roots of equations trigonometric form for complex numbers ADDITIONAL TOPICS rational functions conic sections5 polar coordinates and parametric equations A table of formulas is included for PART II Some sample questions are attached 0505 g N G0 01 a q C 0 10 11 Simplify Write without negative exponents Simplify by rationalizing the denominator MA 153 PRACTICE QUESTIONS FOR THE FINAL 801 15 1 2 A 23 E 2 C 32 D 8 E None of the above Factor 1612 m 438 A 43 342 y B 41 234 C 42x mm if D 429 32 E None of th above 404118 quotdig Simplify c2 All letters denote positive real numbers I Zagb 1453 c W c I632quot D W None Of the above 33 1 Subtract and sunphfy 3x 1 a w 2 222 1 M332 43 21 39 3x 1x 2 B39 33 1X3 2 0 31 11 2 D39 31 1x 2 E None of the above Ii 2 m2 2 Dlvxde and snuphfy m T W 37 22 33 33 1 1 quot 32m3 31 0 31 3 E None of the above A job takes 4 hours for two people working together If one person works alone he can do the job in 6 hours How long will it take the other person working alone to complete the job A 4 hrs B 6 hrs C 8 hrs D 10 hrs E None of the above 1 III 2 23 C m D 39E l E None of the above 2 AM B 52 my 33 4 39vy 3 2 39 A 32 o2 3 o 2 Let a and y be two consecutive positive integers such that a is less than 3 and the difference of their squares is 145 Find 3 A 73 B 3392 C 12 D 8 E None of the above If A PU rt then t A quot P B A P o i 1 3 E None of the above A truck enters a freeway traveling 40 mph One hour later a car enters the same freeway traveling 55 mph After how many miles will the car overtake the truck A 146 miles E 201 miles 3 120 miles D 106 E None of the above 12 13 14 15 16 17 18 19 20 21 22 23 24 A square of side a is inscribed in a circle Express the area A of the circle as a function of 3 A A 1 35 2 B A 32 C A 2 D A vii32 E None of the above 4 10 1 Solwforpmm m 25 5 C There is no solution D p z 6 A p 3 B p m 3 How many ml of a 50 acid solution should be added to 40 ml of a 20 acid solution to obtain a solution that is 25 acid A 10 ml B 8 ml C 6 m1 D 4 ml E None of the above Solveformx145x Az3xl4 B3 2r 033 2 D4221quot E None of the above E None of the above Find all solutions m4 m2 6 0 A m 2 3 B m z 2 if C m izxg 172139 D m i hx i E None of the above Solve the inequality and express the solution in terms of intervals 31 2 gt 63 1 A 00 1 B 11 C 00 1 D 1oo E None of the above Solve the inequaiity I 6 22 3 3 Aazg 1323 C ggxgg D wgngg E Noneoftheabove Find all values of is so that the solutions of the following equation are real numbers 222 42 k 0 Ak2 B kgt2 C 1922 D 152 E Noneoftheabove The base of a triangle is three inches more than its height If each is increased by 3 inches the area is 14 square inches Find the original base b and original height h in inches A b 4h 1 B b 29 6 C 68 5 D b 72 2 E None ofthe above Solve for 2 222 92 1 my1 A a 23 B 1 0 23 C a 23 D x 032 E None of the above If the point 2 3 is midway between A and B and the point A has coordinates 1 2 nd the coordinates of the point B A 15 B 31 C 3 8 D 32 12 E None of the above Thenlopeo ul aopcpodicuhrtothelinedtmisz 3 E None of these A 13 3 quot13 c 3 D 3 If m varies directly as the product of z and y and inversely as 239 nd the constant of propor tionality k ifm iz 3 when a 4y x 2 and 5 6 A k 16 B k 94 C k 3 D k 14 E None ofthe above 2 25 26 27 28 29 30 31 32 Give the equation of the line in slcpewintercept form which is parallel to the line 22 3y 2 7 and containathepoint41 Aygz 7 nyz z 0y a 3 1 The equation it the circle shown is Y D 3 x 1 E None of the above I Vi As y24 B LEW4140 C y24 Dx2y24y0 Et y 4z4yv 80 Determine g o f x for the following functions fc 1 J5 and gx 193 any B1 1x 014 D LNG E 1H 1 1 A 310 B 3316 O 163 I 103 E None of these The graph below could but he described by which equation 7 I 3 5 WM Ay2 2 B yrs 2272 Cy 2s22 Dy2m22 Ey a 22 The guxe befow most closely resembles the mph of which function 7 Agauz Byzf6 2 Di 12 Ey1 2f Express 33 one mama log y 1ogb yz legs 34 3 2 n a 1030112 B 1 85 y 0 Iowa y 34 D 10gb 314 Which are true of the function x 2 log 2 if a gt 1 I f is an increasing function II f has a as an 3 intercept III I has 1 as a y intercept IV The domain of f is 000 List all correct answers AIIIandIII BIandII CIIandIV DIandIV ElandHI E None of the above 4 2 33 Which of the following is equivalent to log A 109132 mgms 310g 721 B log 432 1 1og095 m it 10g 21 0 log 432 210g 095 310g 721 D log432 m 3 log 095 3105724 E log 432 210g 095 w 3 log 721 34 Solve for x 3 5 m 4 I 4 Ax310g4510g3 Bm510343 C39x3513 5Iog4 Dxw5log4 1333 10g3 35 Solve forx oga f232 A4095 1335113 3x39 DI17 Ear quot3 36 Given I gam 8 legs n and logs 6 Calculate logs A 9 153 g C 22 D 56 E W4 37 Th graph of y 2 2 3me the y axis at A 331 02 D3 1334 3 mammmmmmmxyu xmmniz 233y8 3z4y5 2134334 x 6 E 3x 2y4 393raw2y4 39638y18 39426y3 2xw4ym6 39634 m8 40 Determine where the two lines m4y 3 and 2x 63 8 intersect Ax51 2 Bx y Cxy Dx ym ENoneoftheabove 41 The value cf a rare book is increasing linearly It was worth 51 in 1981 and 62 in 1983 What is the formula fer he value v of the book at years after 1980 A vw5o4t 8 934843 C v503t D vm514t E None ofthe above 42 Iffmx2 2x4thenWm A2mh3 Bt2h2 Cx212 D2xh2 E2 h2 43 An aquarium in the shape of a rectangular box is to have a height 0f 15 feet and a volume of 6 cubic feet Let a enote the length of the base and y the width of the base Express 3 as a function of 3 Ay152 B y 0322 DyEy9zc 4 44 If log 2 5 solve for 3 Give you answer correct to four decimal places Hint Change to exyonential notation A 22361 B 14142 C 06990 D 11487 E 03010 SOLUTION 1 D 2 C 3 A 4 C 5 B 6 E 12 1151 A 8 C 9 B 10 E A PPr 11 A 12 A 13 I 14 B 15 E a 7 16 D 17 A 18 C19 D 20 A 21 B 22 C 23 D 24 B 25 C 26 B 27 D 28 D 29 B 30 A 31 B 32 D 33 B 34 C 35 C 36 A 37 D 38 A 39 C 40 Ex 23 a 271 41 A 42 A 43 B 44 D MA 154 PRACTICE QUESTIONS FOR THE FINAL 804 1 m is in the second quadrant and sine 06 nd c030 075 02 08 08 None of the above manna 2 The angles with measures listed are all coterminal except gt Lula 57239 300 420 60 wan w 3 The radian measure ofan angle of 1350 is A 4 33 2 3111 4 23 8 E None of the above 4 Use a calculator to nd the sec 126 correct to 4 decimal places 12361 05878 17013 12361 None of the above w moo MA 154 PRACTICE QUESTIONS FOR THE FINAL 804 5 The point 12 16 is on the terminal side of the angle 8 Find tanB i 3 fl 5 E None of the above 6 If the diameter of a circle is 6 cm find the length of the are that subtends a central angie of 30 1571 cm 2356 cm 3142 cm 9425 cm None of the above 1335003 7 Find the area of a sector determined by 6 in problem 6 1571 cm2 2356 cm2 3142 cm2 9425 cm2 None of the above meowgt 8 Sketched below is a portion of the graph of which trigonometric function 1 A y eos ixJ B y 40082x I C y eos x 1 D 4005 x y b Ala ml E y 2 icost MA 154 9 The graph ofy 3 sin x 10 12 PRACTICE QUESTIONS FOR THE FINAL 8f04 Choose all the correct answers I crosses the y axis at 3 II crosses the x axis at multiples of at III is always above the xaxis IV has period 21 meanest Give the domain D and the range R of fx cos x monwgt I II I III IV I II V II IV None of the above D I set of all real numbers R l I D 0 00 R set of all real numbers De 0 21 R l D set of all real numbers R 0 2n None of the above 1 From a point P on level ground the angle of elevation of the top of the tower is 26 50 From a point 250 meters closer to the tower and on the same line with P and the base of the tower the angle of elevation of the top of the tower is 43 3039 Find the height ofthe tower eorrect to one decimal place tan x The expressxon I secx 2 is equal to mUOmgt mvowe 393 meters 126 meters 271 meters 237 meters None of the above I seox l tanxsinx 2 tan xsmxtanx escxsinx 8304 2 2 tan xcos x l esczx 0 tan2 x sin 21 B sin 2A B cos 2A B cos 24 B r None of the above 0 27 None of the above MA 154 PRACTICE QUESTIONS FOR THE FINAL l3 Simplify W cotx secxsmx A B C D E 14 Reduce to a single term cos2A cos B sin 2 sin B A B C D E l Find all the solutions of 3cos2 x 23in x 2 0 in the interval A B C E 16 How many solutions of the equation sin26 c056 lie in the interval 0 21 A B C D E ZWJBWN one of the above MA 154 PRACTICE QUESTIONS F OR THE FINAL 8194 17 Find e030 in the given triangle E None of the above 18 Given cost 23 and 270 lt 6 lt 360 nd sinZ A 143 8 3 i7quot 4 c l 8 D 22 8 E None of the above 19 Which equation best describes the graph given below A y 25in x I x R B y COS C g I D sinquot1 3E 2 2 y 2 y 2cosquot x E None of the above NLA 154 PRACTICE QUESTIONS FOR THE FINAL 20 Find the cos 2 aresin D Do not use a calculator 21 804 None of the above Point A is 20 miles north of B The hearing from A to C is S3 5 W and the hearing from B to C is 386 W Find the distance from A to C correct to one decimal place FUDGE71gt 22 Find the magnitude of the vector 23 mace 23 LIMw n l mpowe If 52 22 and I 23 the sketch below corresponds to 26 miles l6 miles 15 miles 35 miles None of the above 6 J6 13 J13 None of the above None of the above MA 154 PRACTICE QUESTIONS FOR THE FINAL 804 24 If 60 lb 1 10 is the magnitude and direction of one force and 20 lb 240 is the magnitude and direction of a second force calculate the magnitude to one decimal place and the direction to the nearest degree of the resultant 25 Which equation best describes that graph given below 3 A iQ 7X 26 Classify the equations given below 22 y2 2 15 I II x23y24x2y 50 111 x2 4xy 70 I ellipse parabola III hyperbola I hyperbole parabola III ellipse III III hyperbola ellipse parabola parabola ellipse hyperbole mUOWgt 50 lb 128 74113 121 501b 121 74 lb 128 None of the above mltz4gti 2 3 xsf 0401 9 9 wry 2 1 9 39 4 vane 2 4 9 xzr ya 1 9 4 I parabola II hyperbola III ellipse I ellipse II hyperbola III parabola MA 154 2 23 29 8104 PRACTICE QUESTIONS FOR THE FENAL The graph of 912 25y2 n 225 most closely resembles which graph sketched below Find the vertex of the parabola y2 4y 2x 4 0 A 2 8 B 412 C 2 4 D 432 E None cfthe abdvc An arch of a bridge ever a roadway is semi elliptical With major axis horizontal The base cf the arch is 30 feet achSS and highest part of the arch is 10 feet above the hcrizcntal roadway Find the height of the arch 10 feet from the center of the base 94 feet 89 feet 335 feet 100 feet None cfthe above 1115003 MA 154 PRACTICE QUESTIONS FOR THE FINAL x2 30 What are the vertical asymptotes of the graph of x 311905 3 804 9 262 22 2 2 x 32 Find the reference angle for 8 156 mpowgt Find the reference angle for 9 ff 33 3 1370 34 sin 8 415873 Round your answer to two decimais TICme 1 6R 156 893204quot 9R 66 8R 24quot None of the above None of the above Find alt the values of 8 in the interval 0 211 that satis es he equation 063 35quot 663 251 377 566 534 220 None of the above MA 154 PRACTiCE QUESTIONS FOR THE F INAL 04 35 Sketched beiow is a portion of the graph of which trigonometric function i A y 1mg 2 K B ym4sinix 3 C y n sinx Mia mm m 42quot but M 31 M M Niki E W D 43in x y 2 M E y m si x 33 N W 36 Find the unit vector of 5quot 8j A m S i j J J83 B 5 i f J5 x C Li Adi J89 xE D 5 i 8 wj 23 J35 E None of the above 37 Find the vecmr of magnitude 5that is in the oppasite direction 0f 47 A lt 35 39 J35quot 4253 3 313 K lt2 E None of the above MA 154 PRACTICE QUESTIONS FOR THE FINAL 82 04 Answers 1 C 20 B 2 E 21 A 3 C 22 D 4 C 23 D 5 E 43 24 A 6 A 25 C 7 B 26 B 8 C 2 A 9 B 28 B 10 A 29 C H C 30 C 12 B 31 D 13 B 32 D 14 C 33 A 15 scam2 34 C 16 C 35 A 139 D 36 C 18 A 37 A 19 B MA 154 FORMULA SHEET ADDITION AND SUBTRACTION FORMULAS sinu v sin ucosv cosu sinv sinu v sin ucosv cosusin v cosu v cos ucos v sin usinv cosu v cos ucos v sin usin v tanutanv tanu tanv tanuvgt magmva 1 tanutan v 1 tan utan v DOUBLEANGLE FORMULAS sin2u 23in ucos u ycos2u cos2 u sin2 u tan2z 2m 1 tan 1 PYTHAGOREAN IDENTITIES sin28605291 1tan28 selt326 1cot29 205028 C LAW OF SINES LAW OF COSINES b 3 mm m c2 a2 212 2abcosy a b c A c B ANGLE BETWEEN TWO VECTORS Err5 quotall M 0038 STANDARD FORM FOR CONICS L h12 k12 uh k2 xaz ybz 1 x02 ybz 3 k24px h 42 k2 42 422 ngLszL1 Lagl x7i x h24pyk 802

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