Review Sheet for Midterm Exam 2 - Precalculus | MATH 120, Study notes of Pre-Calculus

Download Review Sheet for Midterm Exam 2 - Precalculus | MATH 120 and more Study notes Pre-Calculus in PDF only on Docsity! 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). • 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 10.8) – You should be able to combine multipart functions and come up with the rule for the new function. – I really like problems 10.4, 10.5 and 10.8. • 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 one-to-one function is, and what is special about the graph of a one-to-one function • 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 linear-to- linear rational function, and be able to sketch the graph of a rational function like those in problem 12.1(a) or (b). – You should be able to model with linear-to-linear rational functions. This comes down to finding a rational function of the form f(x) = ax + b x + c 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 12.6, 12.7, 12.8, 12.10, and 12.11. • 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 13.8 and 13.9. • 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 (e.g., the bicycle example from lecture, example 14.4.1, problems 14.3, 14.9 and 14.11) – I like problems 14.5 and 14.7. • 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 15.4, 15.7, 15.8) and some algebra – You should understand the definitions of sin x and cos x using the unit circle; you should be able to determine certain simple properties of the functions sin x and cos x from this definition (e.g., the range, the domain, the graph, the values at certain value of x, like x = 5π/2) – 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 15.2, 15.5, 15.9, 15.15, and the three non-textbook Chapter 15 problems) • Chapter 16 - Trigonometric Functions