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# PRECALCULUS MATH 120

UW

GPA 3.76

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This 7 page Study Guide was uploaded by Addison Beer on Wednesday September 9, 2015. The Study Guide belongs to MATH 120 at University of Washington taught by Matthew Conroy in Fall. Since its upload, it has received 31 views. For similar materials see /class/192068/math-120-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15

Final Review Math 120 0 Chapter 1 2 3 4 The Coordinate Plane Lines and Circles You should understand the idea of imposing a coordinate system and the use of the distance formula You should understand the various forms of the equations of a line and be able to determine a line given either two points on the line or the slope and a point on a line You should understand the equation of a circle and be able to find the intersections of lines with lines and lines with circles You should be able to do this in the context of a model You should be able to create a linear model for the relationship between two quantities eg population varying with time If you have two such models you should be able to answer various questions about the two quantities modeled eg when are they equal when is one twice as large as the other Especially good problems include 213 214 34 37 48 412 414 415 0 Chapters 5 6 Functions and Graphs You should know a function is You should know what the domain range and graph of a function are and if asked be able to find the domain and range of a particular function You should know what the vertical line test is all about You should be able to graph linear functions and multipart functions whose parts are linear You should understand what a multipart function is You should be able to describe rela tionships between two quantities with a multipart function ie you should be able to model with them Especially good problems include 55 510 63 64 0 Chapter 7 Quadratic Functions You should know that quadratic functions are those of the form fx a12 121 c and that these can always be put into vertex form fx az 7 h2 k You should be able to find the vertex of a quadratic function You should be able to create quadratic models given three generic points or the vertex and one other point You should be able to find the maximum or minimum value of a quantity determined by a quadratic function by considering the vertex I like problems 79713 a lot 0 Chapter 8 Composition You should know what it means to compose two functions You should understand what is meant by You should know that fgz and gf are generally different func tions You should be able to write simplified rules for compositions fg and gfz given rules for fx and I particularly like problems 83 84 and 85 0 Chapter 9 Three Construction Tools You should understand horizontal and vertical shifting and horizontal and vertical scaling aka dilating You should understand how to derive the graph of 91 afbx c d from the graph of fx see eg problem 92 I especially like problem 92 93 and 97 0 Chapter 10 Arithmetic This is a very short chapter An important topic in this chapter is step functions which are a nice example of multipart functions You should understand how to graph functions built up from the unit step function see problem 108 You should be able to combine multipart functions and come up with the rule for the new function lreally like problems 104 105 and 108 0 Chapter 11 Inverse Functions Another very short chapter You should understand what an inverse function is what conditions a function must satisfy in order to have an inverse do all functions have inverses can you tell if a function has an inverse by looking at its graph and how to find the inverse of a given function You should understand what a onetoone function is and what is special about the graph of a onetoone function I like problems 117 and 118 0 Chapter 12 Rational Functions A very important chapter We spent two days in lecture on this instead of the usual one You should be able to find the asymptotes horizontal and vertical of a rational function and be able to sketch the graph of a rational function like those in problem 121 You should be able to model with lineartolinear rational functions This comes down to finding a rational function of the form ax 12 me 7 I C whose graph 1 passes through three given points or N has a given asymptote and passes through two given points or 3 has two given asymptotes and passes throuh one given point You will need to translate the language of the modeling problem Pay particularly close attention to the words lineartolinear Note that a lineartolinear function is not a linear function lespecially like problems 121127128 1291211 and 1212 0 Chapter 13 Measuring an Angle You should understand how to convert between degrees and radians You should understand and be able to use the relationships between radii angle arc length and area llike problems 138 and 139 0 Chapter 14 Measuring Circular Motion You should understand the various measures of angular speed aka angular velocity like rpm radians per second or degrees per hour You should understand the relationship between radius angular speed and linear speed You should know how solve a beltandpulley problem eg the bicycle example from lec ture example 1441 problems 143 149 and 1411 llike problems 145 and 147 0 Chapter 15 The Circular Functions This chapter introduces the trigonometric functions You should be able to solve problems using the idea of trigonometric functions as ratios of sides of right triangles eg problems 154 157 158 and some algebra You should understand the definitions of sin I and cos I using the unit circle you should be able to determine certain simple properties of the functions sin I and cos I from this definition eg the range the domain the graph the values at certain value of I like I 57r 2 You should be able to determine the location of an object moving circularly given information about its speed and starting location eg problems 152 155 159 1514 0 Chapter 16 Trigonometric Functions This is a short chapter which adds some final touches to our knowledge of the functions sin I and cos I and related functions llike problems 163 and 164 0 Chapters 17 18 Sinusoidal Functions You should understand the notion of a sinusoidal function as a shifteddilated version of the function sin I You should understand the effect of the four parameters 147B7 C and D on the graph of 27f Asm 7 Cgt Di You should be able to model with sinusoidal functions In particular you should be able to determine the parameters A7 B7 C7 and D from a verbal description of a quantity that varies sinusoidally with time see problems 172 173 174176 You should be able to solve equations of the form fr k where f is a sinusoidal function if there are any solutions there are infinitely many and you should be able to find them You should be able to do this in the context of a modeling problem eg problems 182 184 186 181018111812 0 Chapters 19 20 21 Exponential functions modeling and logartithms You should be able to recognize functions of the form fr A0127 or equivalently fr Age You should be able to put exponential functions into these forms You should be able to create exponential models of quantities that change over time Given two values of the quantity at two data points in time you should be able to come up with an exponential model that fits the data Given a single data point and information about the quantity s rate of growth eg percentage annual increase or doubling time you should be able to come up with an exponential model that fits You should be able to solve equations involving exponential functions using the natural log arithm Relevant problems include 201202 2192111 2112 2115 and 2116 0 Chapters 22 23 Parametric Equations and Uniform Linear Motion You should understand what it means to describe motion using a pair of parametric equa tions 1 ft7 y gt You should know that uniform linear motion ie constant speed motion along a line can be described parametrically with two linear functions zt a bt yt c dt You should be able to model uniform linear motion using linear parametric equations given a variety of forms of description of the motion For instance knowing the moving object s starting point direction of motion and speed Or knowing the object s location at two differ ent points in time See eg problems 231 232 233 and 2310 Summary for Midterm Two Math 120 Here are some thoughts I was having while considering what to put on the second midterm The core of your studying should be the assigned homework problems make sure you really understand those well before moving on to other things like the old midterms on the test archive 0 Chapter 10 Arithmetic This is a very short chapter An important topic in this chapter is step functions which are a nice example of multipart functions You should understand how to graph functions built up from the unit step function see problem 108 You should be able to combine multipart functions and come up with the rule for the new function lreally like problems 104 105 and 108 0 Chapter 11 Inverse Functions Another very short chapter You should understand what an inverse function is what conditions a function must satisfy in order to have an inverse do all functions have inverses can you tell if a function has an inverse by looking at its graph and how to find the inverse of a given function You should understand what a onetoone function is and what is special about the graph of a one to one function 0 Chapter 12 Rational Functions An important chapter it introduced a new class of functions for modeling You should be able to find the asymptotes horizontal and vertical of a linearto linear rational function and be able to sketch the graph of a rational function like those in problem 121a or b You should be able to model with lineartolinear rational functions This comes down to finding a rational function of the form iazb i zc f 96 whose graph 1 passes through three given points or 2 has a given asymptote and passes through two given points or 3 has two given asymptotes and passes throuh one given point You will need to translate the language of the modeling problem Take a look at old midterm 2 exams from the archive for examples to work on Pay particularly close attention to the words linear to linear Note that a linear to linear function is not a linear function I especially like problems 126 127 128 1210 and 1211 0 Chapter 13 Measuring an Angle You should understand how to convert between degrees and radians You should understand and be able to use the relationships between radii angle arc length and area I like problems 138 and 139 0 Chapter 14 Measuring Circular Motion You should understand the various measures of angular speed aka angular veloc ity like rpm radians per second or degrees per hour You should understand the relationship between radius angular speed and linear speed You should know how to solve a belt and pulley problem eg the bicycle example from lecture example 1441 problems 143 149 and 1411 I like problems 145 and 147 0 Chapter 15 The Circular Functions This chapter introduces the trigonometric functions You should be able to solve problems using the idea of trigonometric functions as ratios of sides of right triangles e g problems 154 157 158 and some algebra You should understand the definitions of sin z and cos x using the unit circle you should be able to determine certain simple properties of the functions sin z and cos x from this definition eg the range the domain the graph the values at certain value of z like z 57r2 You should be able to determine the location of an object moving circularly given in formation about its speed and starting location e g problems 152 155 159 1515 and the three non textbook Chapter 15 problems 0 Chapter 16 Trigonometric Functions This is a short chapter which adds some final touches to our knowledge of the func tions sin z and cos x and related functions I like problems 163 and 164 0 Chapters 17 Sinusoidal Functions You should understand the notion of a sinusoidal function as a shifted stretch squished version of the function sin z You should understand the effect of the four parameters A7 B7 0 and D on the graph of f Asin 7 0 D You should be able to model with sinusoidal functions In particular you should be able to determine the parameters A7 B7 C7 and D from a verbal description of a quantity that Varies sinusoidally with time see problems 172 173 174176

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