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# PRECALCULUS MATH 120

UW

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This 4 page Class Notes was uploaded by Addison Beer on Wednesday September 9, 2015. The Class Notes belongs to MATH 120 at University of Washington taught by Alexandra Nichifor in Fall. Since its upload, it has received 50 views. For similar materials see /class/192057/math-120-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15

Math 120 Final Exam Review Ch18 MAIN TOPICS not in order 1 LINES 2 Modeling SlopeIntercept amp Two Point Eqs Special lines horizontal and vertical Parallel lines Perpendicular lines HwkExam Pbls Closest Distance 414 Tangent lines 412 etc Any qty changing at a constant rate is linear with the rateslope CIRCLES x xcenter2 y ycenter2 R2 TopBottom y ycenter i xR2 x xcenter2 3 QUADRATICS y 2 am2 bx c Solve y0 nd the roots aka zeroes aka xintercepts via Quadratic Formula Find xcoordinate of minmax via Vertex Formula 0 Applications max pro tareaproduction 79713 Graph concave upconcave down 4 INTERSECTING CURVES yfx with ygx two lines a line and a quadratic 0 set fxgx and solve for x 0 Typical ex Missile and roof midterm Balloon and slope 75 line yfx with a circle 0 replace y in the circle eq with fx from line then solve for x 0 Typical ex 37 c 48 ball and green many previous exams 5 FUNCTIONS amp GRAPHS Domain Range MinMax etc 6 MULTIPART FCTS O O O O 0 Given graph nd multipart Win 03 2b Given multipart fct draw graph Given multipart fct solve equation later chapters compose or do arithmetic with multiparts Hwk pbls pizza cutting baseball diamond crosssection of ditch 7 COMPOSITION OF FCTS 0 Be able to compose two functions pbls 8288 0 Determine the domainrange of the composition 811 8 DISTANCE FORMULA d x2 x22 3 2 3 02 0 EX hwk Pbls in Ch 2 bungee cord peoplecars walking away etc 9 MODELING given some data points nd functions to t the data which are 0 Linear pbl 46 or Quadratic or o LineartoLinear from Midterm 2 o Sinusoidal Exponential from postMidterm 2 Math 120 Final Exam Review The nal exam is cumulative it covers Chapters 1 23 That is it could include AN YTHING from this quarter To answer the exam questions you will need to apply material from lecture the text andor the homework I recommend that you first review those topics and homeworkexam problems which you struggled with this quarter Afterwards you can practice for the test by attempting old exams from the Exam Archive link on website It is best to practice in examlike conditions limited time quiet place no peeking at the answers using only your calculator and sheet of notes The following review list mentions some of the key points from Chapters 1723 postmidterm 2 only In addition you should also look over the earlier review files which highlight some of the key points of the material covered by the midterms available on our website The three major topics we covered since our second midterm are 1 N Sinusoidal Modeling and Inverse Trig Functions Ch 17 and 18 There are three main skills to answering questions in these sections I III Constructing and sketching the model The general sinusoidal model is y A sin 2 t C D where MAX Y VALUE 7 MIN Y VALUE 0 A amphtude MAX Y VALUE Mmi Y VALUE 0 D mean o B period how long it takes the wave to repeat distance from peak to peak or any two identically placed points on the graph 0 C phase shift x coordinate of a peak xcoord ofa point where the graph crosses the mean line going up Review how to draw a sinusoidal graph when knowing these values Applying inverse trig functions to solve equations which involve trigonometric functions Interpreting your solutions ie finding other solutions Recall that when you use sin 1 I or cos 1 I to solve a trig equation you generally need to have your calculator in RADIAN mode and you only get the principal solution PS so you need to also nd the symmetric solution SS either algebraically see Table for Inverse Trig Functions or by drawing a graph and using the symmetry of your PS and SS with respect to a peak or valley don t forget that adding any integer multiple of the period results in infinitely many additional solutions When using tan 1 l steps a and b still apply but there is no symmetry solution and the period of tanx is n not 2n rad 53 C Exponential Modeling and Logarithms Ch 19 20 and 21 a The general exponential model is of the form y A0 bx which can also be written in the form y A0 e1X use a lnb b Understand the relationship between exponential and logarithmic functions logbx is the inverse of bx and in particular In x is the inverse of ex V G V Modeling understand how to nd the general exponential model when you are given two pieces of information data points Be able to use the logarithm rules to solve equations with variables in the exponent such as the equations you get in a word problem involving exponential modeling The main rules written for the natural log are 0 lnab lna lnb ln ab lna lnb lnbX Xlnb lne 1 11110 O O o e1quotzz lnezz 3 Parametric Equations and Linear Motion Ch 22 and 23 a Understand the basic idea behind parametric equations what are they why are they useful how do you sketch 6 O V a graph in an xycoordinates system when g1ven parametric equations Be able to recognize and come up with parametric equations for circular motion Xt Rcos60 mt Xcenter Y RSin60 mt YCenter Review what each part in these formulas means and how you can compute them in a problem Understand how to come up with parametric equations for linear motion at a constant speed Xt X0 vX t W y0 vy t where o X0 y0 are the coordinates of the point corresponding to t0 Ax x 7x o vx end Wm WWW is the horizontal velocity At time elapsed A y 7y o v y w is the vertical velocity y At time elapsed Usually in linear motion problems like in all modeling problems you are given only a couple of pieces of information and you have solve for the other parts

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