Organization: Not a Nightmare

It’s your = junior year, college is suddenly looming on the horizon= . Welcome to your first taste of col= lege level classes. Yes, that is w= hy precalculus can seem like a tough course. You are using a college level text= and are on the last lap of preparation for an Advanced Placement course. To get ready for AP Calculus (or AP= Econ, Statistics or Physics), we will try to get you to shift more toward indepen= dent problem solving and analysis of mathematical situations, rather than follow= ing explicit procedures. Our goal= is to get you accustomed to use mathematics to breakdown a complex problem into smaller pieces, analyze each piece, and put the pieces back together to construct a solution. You wil= l also be expected to learn to communicate what you did and be able to justify your approach.

You will find th= at this course is not bad if you change your study habits just a bit. If you follow the advice given her= e, you will become an active, rather than passive learner. You will develop college level stu= dy skills, which will help you in the future.=

Organization: Not= a Nightmare

Since many of you are starting your 5^th year at Harvard-Westlake, you = have heard the word organization many times before. You may have pr= eviously had teachers evaluate your ability to organize by checking your homework or= your notebook setup. They were try= ing to get you to develop some good habits early to allow you to concentrate your = time and energy on learning the mate= rial rather than searching for the m= aterial in your book or notebook. The= older you are, the less likely it becomes that you will have teachers or professo= rs make demands on exactly how they would like you to set up your notebook or study area. On the other hand, at the 11^t=
h grade level, it becomes crucial for you to establish a system of order that encourages and compliments your success.&n= bsp; Here are a few suggestions:

In class, be pre= pared with essential materials specific to your tasks.

Being prepared for class means that you have a pencil, calculator and notebook to take notes in every day. Your teacher may also ask you to b= ring your book to class every day.

&= nbsp;

You will need a pencil with an eraser in class to take quizzes and tests. Your teacher may ask you to exclus= ively use a pencil so that your work will be neater and you can erase steps when you = make mistakes. Everyone occasional= ly makes mistakes the first time they try a problem. A pencil facilitates the process of attempting and revising your steps toward solving a problem. It also gives you a way to make yo= ur work presentable. =

You will need your calculator in class each day for many reasons. On regular class days, your teache= r may use her calculator on the overhead and you will want to understand and practice the steps she uses on= a calculator problem. You can certainly follow along even without a calculator but you’re more like= ly to remember how to reproduce the problem on your own if you try it yourself= in class.

You must bring your notebook to class each day to take notes. If you have trouble with your handwriting/neatness (you know who you are!) choose a notebook with small l= ines or graph paper which will force you to write your work clearly following the lines. Graph paper can be hel= pful for all students as math notes often contain written equations and diagrams or graphs of functions. =

If you bring a book to class, you’ll be able to more easily recall what = the homework problems were and how they were phrased. If you don’t have the book, you’ll be looking at your written homework and admiring how beautiful= it is but your solutions are not meaningful without a question. While explaining the next lesson, = the teacher may refer to an example in the text and if you have the book with y= ou, you can look up this example and follow along with your book and your teach= er simultaneously. Also, your te= acher may give you some free time to start your homework so you may want to have a book available for that.

An organized not= ebook is easy to navigate and will save you time!

Deciding to have an organized notebook is a choice and a commitment rather than a ta= lent or an innate ability. Many st= udents have not kept organized notebooks for a variety of reasons. Perhaps, they were not required to= and could get A’s without organizing! Perhaps they were too lazy, or they were never shown how to organize= . In any case, it will greatly help = your ability to access the information that you need.

A medium-sized three ring binder is the best place to keep your math homework, notes, handouts and quizzes/tests. This type of binder allows you to access materials from any of the aforementioned categories easily. It would be helpful if your binder had front and back pockets also.<= span style=3D'mso-spacerun:yes'> Keep some paper clips in these poc= kets and make a habit of leaving a paperclip on your current notes page and on y= our current homework assignment. = Many students get into the habit of leaving their latest homework assignment in = the inside pocket of their notebook for easy access.

Using sturdy pages with tabs, label the following categories: General, Notes, Homework, Handouts, Quizzes/Tests, Blank Paper.

The “General” tab will be where you store any handouts from your teacher that are not specific to any one chapter in the book. These could be a course syllabus, assignment sheets, or any helpful diagrams or handouts that you will refer = to throughout the year. If the assignment sheets that your teacher hands out do not have due dates on them= , you may want to write these dates in yourself.= Other students find it helpful to make a check mark beside the assignments that they have completed. This will minimize the chance of doing the wrong night’s assignment. You may also want= to keep a phone list of your classmates or a grade sheet in the “General” tab.

You should keep a few sheets of blank lined or graph paper in your “Notes” tab. This= is the section where you will take class notes every day. Make sure you label your notes wit= h a date and preferably a section (ex: 9.3a).&= nbsp;

For the “Homework” tab, buy a slim, three hole<= /span> punched, graph paper notebook that will fit into the three hole punched binder. Refer to the “Homework” chapter in this book for more specifics about homewo= rk assignments.

The “Handouts” tab should contain all of the worksheets and diagrams your teacher gives you for your current chapter. When you receive these, examine them and determine how their information is helpful or fits your topic. Then you can store it = in this section. If some of these handouts are solutions to problems, make sure that you still write out the steps to problems.

The “Quizzes/Tests” tab should contain your returned quizzes and te= sts and should also contain any revisions you have made on your own to problems= you missed the first time around. Your teacher will mostly likely not grade these corrections but they allow for personal reflection and growth. Doing personal quiz corrections will hopefully mean you will avoid t= he same traps on the chapter test!

The “Blank Paper” tab is for your graph and lined paper reserves. Keep only enough note paper here to finish your current chapter. =

At the end of each unit, your teacher will collect your notebook and look thro= ugh all of its contents. Please d= ouble check that your notebook is not cluttered with materials from other courses, material from previous chapters, or inappropriate notes or doodles. (Hey, we all doodle sometimes, but please remember that your teacher will see everything you write/draw in your notes.) After the unit is fin= ished and your notebook has been graded, remove all of your class notes, homework, handouts, quizzes and test from that unit.= Invest in some document clips from an office supply store and clip a= ll of that unit’s materials together and store it in a safe place (a des= k at home or under your bed?). Thi= s way, these materials will not clutter up your notebook all year but you will sti= ll have them handy to study for exams.

Set up a neat, q= uiet workspace to maximize your homework efficiency.

Efficient students tend to set up a systematic daily routine for doing homework. When you are working under “ideal” conditions, you will be able to get as much of your work finished at a reasonable rate. Since each student’s “ideal” workspace varies greatly, let̵= 7;s talk about some general guidelines for where to do homework.

Many students complete their homework in the evening at home. Do your homework in a quiet room a= lone to avoid disturbances. It is = best to sit upright at in a comfortable desk chair when working rather than somewhere too comfortable where= you might fall asleep or veer off task. Resist the urge to turn on the television or radio. If you have a tendency to surf the internet or email, you may want to turn off your computer to concentrate on difficult assignments. It wou= ld be best if you have all of your materials gathered in one place before you beg= in doing problems or studying. You should have your notebook with graph paper, book, pencil, calculator, eraser, and a geometer before you being work. If you stand up and walk around, i= t is easy to become distracted and let your mind become involved with another ta= sk. Refer to the “Homework” chapter to find more suggestions.

Depending on your schedule and your activities, you may do homework during school hou= rs or on campus after-school before an athletics practice or club meeting. The best places to study and do ma= th homework on campus are the desks in the math department office, the library= , or an open classroom. The math department office is a good choice because there are always teachers around= to give you some direction if you need clarification. Any available teacher can help you= on a problem even if you classroom teacher is busy. The library is also a good choice because it is quiet and offers areas for silent study as well as places to = work with a study group (see the Study group section of the “A little help here…” chapter). Another more option is to do homework in an open classroom. You will need to ask a teacherR= 17;s permission to use a free classroom as sometimes they are locked. A classroom is a great place to me= et with your study group as you can move the desks together and you can make u= se of the dry erase boards to draw large diagrams and experiment with problems (Again, see the Study group section of the “A little help here…” chapter). = There are few distractions if you chose to work in a classroom and you and your s= tudy group are more likely to keep focused.&nbs= p;

Probably the worst place to do homework on campus is outside on the Chalmers patio.<= span style=3D'mso-spacerun:yes'> When you work outside while friend= s eat and converse, your concentration is fragmented and it is easy to lose sight= of the steps you are writing down. The reason for doing homework is to learn, implement, and practice new skills as well as make connections. You= often need to remember these skills for weeks at a time and apply them to later a= nd more sophisticated problems. = It is difficult to dedicate yourself to this process while you are: eating, tryin= g to help a friend decide how to ask out their crush, or avoiding getting hit wi= th an airborne Frisbee.

To summarize: Stick with traditional study areas for studying and play areas f= or playing.

Maximizing Class = Time Efficiency

Making the most of what you learn in class is crucial to understanding precalculus. Paying close attention in class and participating often insures that= you will later approach your homework assignments and studying with full confidence. There are a varie= ty of ways in which students behave during class time but there are many similari= ties in the manner successful students use their time. You will need to take detailed and navigable class notes, contribute aloud using mathematically mature communi= cation, and work as a leader (and sometimes follower) in small groups of students.<= span style=3D'mso-spacerun:yes'> This chapter will remind you of the habits that you should adopt to make the most of your 3 hours of class time= per week.

Take notes in cl= ass like a pro!

Learning to take organized class notes is a skill that will not only be necessary th= is year but in the college years that lay ahead. In one 45 minute class, you should= , on average, be taking two pages of notes, depending on your handwriting size.<= span style=3D'mso-spacerun:yes'>

When class begins, your teacher will go over a few of the previous night’s homework problems. LABEL your= note page with “Homework Review” and then indicate what section (9.4= b, for example). Copy the steps = you see on the board. This board work may be provided by your teacher or another student. Even if you did the problem correctly and had the same final answer, your teacher or classmate = may have done the problem differently or you may have skipped over a crucial st= ep and still managed to find the correct answer. It is always better to take down n= otes on the previous night’s homework and then compare your work to the approach noted in class later.

It is also crucial to take thorough notes on the new section presented in class. Your success on homewo= rk is directly related to what you can recall from class, interpret from your not= es, and read from the book. One p= roblem many students face is whether to focus on listening and mentally following a teacher’s lecture or taking notes.&n= bsp; If you find class is moving too fast for you, do not sacrifice taking notes! Stop your teacher by a= sking a clarifying question. This w= ill not only pause the flow of the lecture but allow= you to practice communicating AND hopefully better understand the concept being discussed. If you get lost in= the middle of a multi-step problem’s explanation, keep taking notes and m= ake a star in the margin next to your notes.&n= bsp; Your teacher will either ask for questions when she is finished with= the problem or you can reach her after class to ask more questions. Occasionally your teacher may cover example problems from your text book in class. You should still take notes on the= se examples! Add the page and ex= ample number from the text book into your notes to cross reference the steps.

The biggest pitfall of students when it comes to note taking: laziness. Class time is an excellent time to= practice new skills and follow the models of work demonstrated by your teacher. You are doing yourself a disservic= e if you leave out steps or omit diagrams and pictures to compliment your work.<= span style=3D'mso-spacerun:yes'> Class time allows you to take risk= s, ask “why” questions, and hone new skills. It is up to you to use this time w= isely by taking detailed class notes each day.

Top students dev= elop confidence by asking and answering questions.

Do you remember doing two-column proofs in Geometry? I bet you do (but maybe you are attempting to repress that memory). In a two column proof, you are required to proved statements AND rea= sons for each statement. In Precalculus we do not utilize the two-column proof explicitly, but you should still find its structure helpful in every problem you write. When your teacher = or fellow student presents a problem on the board, you should follow (and writ= e) down each step they write but in your head, you shoul= d be filling in the “Reason” column of the proof. After each algebraic line of a pro= blem, you should make sure you can confidently answer “why” that step= is necessary and “why” you are allowed to make that step. Students become confused when they= are unclear about the “why” of a step in a problem. When this happens, it is your turn= to speak up! Make sure before you speak up that you can pinpoint where it was in the problem that you became lost. The more detailed your language is, the better equipped your teacher will be to set you on the rig= ht track again. “I donR= 17;t get this example” or “This problem is hard” do not leave = your teacher or fellow students a means to effectively help you. Saying, “I am confused on why you could follow from the thi= rd line to the fourth line because I didn’t think the graphs would intersect” is detailed and identi= fies not only the “why” step that confuses you and the reason (by sa= ying “because”) you are having trouble. Be detailed in your communication.= Do your best to use correct mathem= atical terms to explain your point. =

Answering questions is a great way to practice communication also. A good teacher will ask her studen= ts to fill in the “why” blanks as she teaches. When you answer a question in clas= s, do your best to use correct mathematical language and to give a detailed response. Answering questions= in class is a risk-free way to allow yourself to be evaluated without being explicitly graded.= The more practice you have responding to in class questions, the bet= ter prepared you will be responding to similar questions on quizzes. Take advantage of this dress rehearsal! It is better to le= arn from a mistake in class when answering a question than to make mistakes on quizzes and tests.

Practice written= communication by contributing on the board.

Another great way to demonstrate your understanding is to contribute homework solut= ions on the board. There will be a= mple opportunity to display your work in class every day after homework is assig= ned. When you see a homework problem th= at you are willing to write on the board, make sure you organize your steps, compliment your work with a diagram, and leave your answer as a complete sentence. By writing legibly = and giving your best work, you are again allowing yourself to be evaluated risk-free by your peers and more importantly, your teacher. Make mistakes, ask questions about= your own work, and ask questions about the work others display. This is your time to improve and learn.

During the “Homework Review” portion of class, students use their time= in a variety of ways. Consider t= he following three suggestions as a glimpse of what your teacher sees as an effective use of your time during homework review. Students who choose ACTIVE PARTICI= PATION during “Homework Review” tend to improve their understanding at= a faster rate than those who choose to let others contribute on the board and communicate problems.

First, after choosing a problem to present on the board, copy the original problem statement, followed by each of your steps, a complete diagram, and your fin= al answer. Just as with a two-co= lumn proof in geometry, be prepared to support each of the steps you have made w= ith a reason. This means, be prepared to answer “why” any step or conclusion you provide can be assumed.

Secondly, if you are not at the board doing a problem, you can still actively participate. At your desk, wo= rk with a partner to communicate problems.&nb= sp; Select a problem from the board (that another student is in the proc= ess of writing) and take turns explaining the steps to your partner. This will help you rehearse your homework problems and develop confidence in oral communication.

Finally, another way to participate actively is to approach the board and work WITH a student who is writing a problem. Choose a problem that you understand well, and then help the writer justify each of her steps. Ch= ose a problem that confuses you, and then challenge the writer to support the ste= ps that are unclear to you.

PASSIVE PARTICIPATION means that you are keeping to yourself and quietly taking not= es on the problems that others are presenting. You may also just be looking at ot= hers work to try to understand where you made a mistake without even taking notes! Passive participation = is only marginally helpful and does not reinforce the concepts you must learn = from class. Passive participation = does not boost your confidence like active participation does.

To summarize: Take advantage of opportunities to communicate with your teacher and other students whether t= his be at the board or during class discussion. Taking risks and allowing yourself= to make mistakes takes bravery but will help you learn and eventually help you build confidence in your abilities. Make the most out of your time in class through active participation= !

Homework as daily practice

What does “doing homework” really mean?

Just about any student could define home= work as “the exercises and problems assigned for completion by a teacher”. However, this= definition is overly simple and does not explain why or how to do your homework. This section will hopefully help c= larify those two questions and offer some exercises to try.

Homework is assigned every night in order to continuously refresh concepts from class and to allow you to practice employing these concepts on your own to build confidence. You should plan on spending approximately 45 minutes a night on your homework every night. Wh= en you let assignments accumulate and try to catch up just before a quiz or test, = your brain misses out on the daily build up of knowledge that homework is intend= ed to provide. Cramming like thi= s does not allow you time to review past concepts as you are too busy trying to learn new ones. <= /span>

When you sit down in a quiet study space (see the first Chapter) to do your homework, make sure that you have all necessary materials available (book, notebook, pencil, graph paper, calculator, and possibly a computer). Write your name, the section number (8.7a, for example), and the date on the upper right corner of your homework paper. List all of the proble= ms assigned at the top of the page. In addition, you may want to go through your book and circle all of the assign= ed problems. This tip will help = you avoid doing the incorrect problems especially if the assignment calls for “every other odd” or another pattern. The best paper to use on precalculus homework is graph paper because it provid= es great structure for drawing graphs (which you will do a lot of) and diagrams (which are required on some “exercises” and all “problems”).

Before you start writing, there are two very important things that you should do.<= span style=3D'mso-spacerun:yes'> First, review your notes. Open your notebook to the notes that you wro= te in class for the homework section you are about to attempt. Your thorough notes will include important definitions, theorems, diagrams to support these theorems, and finally, various example problems. Reading your notes will take no more than a couple minutes and will = help you understand the goals of the homework assignment you will be completing. Secondly, open your book to its examples. Your book will offer some different examples (and maybe some similar to those from class) and it would be in yo= ur best interest to review all of the book’s examples. On most homework assignments, abou= t 80 to 90% of all assigned problems can be directly or indirectly compared to t= he examples from the text. One suggestion to try would be the following:&= nbsp; Go through each homework problem (either before you do the work or as you are completing the work) and locate the example in the text that appears most alike to the homework problem. Again, since most of your homework will be at least indirectly comparable to the book examples you will probably want to incorporate ideas from these examples into your own work.&nb= sp;

How= to Approach Each Individual Exercise/Problem<= /p>
With each homework assignment you do, you will want to classify each problem as = an “exercise” or a “problem”. Most of your homework will consist= of “exercises”. An “exercise” is a task where you will implement concepts directly that you’ve learned in class to find your solution. “Exercises= 221; will help you practice using the theorems you’ve learned and will encourage you to organize your steps similarly to how you’ve seen your book and your teacher do so. “Exercises” may seem formulaic but remember that it is y= our responsibility not to just memorize the necessary steps to a solution but to analyze and understand your process. “Exercises” almost always require an accurate diagram and multiple steps to reach a conclusion.

A “problem” is a challenging question that will ask you to synthe= size the concepts you’ve learned from class and perhaps material from earl= ier in the year or a previous course. “Problems” do not immediately offer you an explicit meth= od to solving. Remember that in = grade school and middle school you learned many approaches to “Problem Solving” including: “Guess and Check”, “Find a Pattern”, “Work Backwards”, “Draw a Picture”, etc. Begin a problem by emplo= ying at least one of these techniques. Slowly read the problem one clause at a time and pause to write down= all pertinent information (numbers, units, equations, diagrams). Next, write down exactly what the problem is asking you to find and this will be your “goal”. Finally, re-read the problem for a= ny last bits of information. Loo= k for patterns in data, look for intermediary steps you can take towards the goal, and look for ways to simplify by organizing or grouping information. When “problems” are as= signed for homework, remember that some aspect of the daily lesson will be a clue = to the problem’s solution. Maybe there is a creative way to apply a new definition or theorem?

Most importantly, the best way to improve your performance on exercises and prob= lems is practice. While “exercises” tend to be more approachable thanks to their simplicity, “problems” can be daunting because they are sophisticated and contain so many unknowns. You will find that the more practi= ce you have with problem solving, the more confidence you will gain. So approach problem solving with intellectual maturity: willingness to take risks and creativity.=

Hom= ework Resources

A variety of internet resources are available to precalc= ulus students at Harvard-Westlake. Since the internet is a dynamic structure, these resource locations are constantly changing. Talk to your teache= r and peers and keep adjusting your searches to keep abreast of all resources available to you. =

Hotmath.com

Hotmath is a homework help site which gives solut= ion steps to selected homework problems from our book. Your teacher will provide you with= a Hotmath password at the beginning of school. Record this password in your noteb= ook and then save it on your computer at home.= Hotmath is great to use when you are abl= e to begin a problem but stumped on one particular step in the process. Hotmath will not only provide that next step for you but will justify the reasoning used= to make that new step. Make a no= te (using an asterisk) on all the problems you’ve used Hotmath to help you with and this will remind you that you need more practice with = that type of problem. Also, consid= er alternatives to the steps you see provided on Hotmath<= /span>. There is not always only one way to solve a problem so be creative when you can.

Precalculus: Larson and Hos= tetler On-line Resources

Our book is a new edition this year and offers on-line materials to help you wi= th studying and homework. These = pages are passworded and you will receive the correct log-in name and password after you register with the information card that = came wit your textbook. You will be able to view example problems with solutions and homework problems. There will also be additional problems, not found in the text, which you can test yourself with while on the computer. This s= ite is a great place to go not only when you are doing homework but also when you = are studying and feel as if you have exhausted all of the book’s problems= .

Other Internet Resources=

There are many other “Math Help” or “Homework Help” web-sites. Some sites offer e= xtra problems to try. Choose problems from = these sites carefully as their goals may not match the direction of your course.<= span style=3D'mso-spacerun:yes'> On the other hand, different ̶= 0;Math Help” sites may be helpful if they allow you to compare problem solvi= ng methods or encourage alternative solutions. Before you adopt a new technique different from one demonstrated in class, ask your teacher if your new meth= od allows you to give a complete solution and therefore permissible in class.<= span style=3D'mso-spacerun:yes'>

Other sites offer direct homework assistance.&nb= sp; Often you are asked to email a problem into an on-line “Dr. Math” and you will receive a response in 24 hours. Using a “Dr. Math” may= seem like a simple solution, but it keeps you from grappling with a challenging problem and working with your peers or teacher to find your own solution. Difficult concepts in precalculus are much more likely to stick when you st= ruggle to find your own answer rather than try to follow someone else’s hard work.

Reviewing your Homework and Notes=

In addition to your daily precalculus assignment, = you should save five to ten minutes each day to review your previous assignments from the chapter. Since quizz= es are scheduled at least once a week, reviewing your assignments continuously will keep concepts fresh in your mind and will eliminate the need to cram on the night before a quiz or test. = First, find the previous night’s assignment (the one that you went over in c= lass most recently) and take out a highlighter or colored pen. Review your work on the exercises = you felt confident completing. Do= es this work still make sense to you? Highlight any problems that you question. Follow your steps on the more diff= icult exercises and try to objectively evaluate your work and any diagrams you’ve drawn. Would you= do any of this work differently knowing what you know now? Feel free to write in any changes you’d like to make on your original work. Review the assignment’s most challenging problems. Some of= these problems were probably reviewed in class.&= nbsp; Take the time to read through the steps and any adjustments you made while correcting your work in class. Is this problem’s logic clear? Finally, circle the problems that = you feel best summarize the concepts you’ve learned and the goals your teacher has identified in the lesson. When you begin studying for a quiz or test, these problems will be y= our best “go to” study problems.&n= bsp; You can re-read them at that point and you should look for other rev= iew problems (maybe at the end of the chapter or on your book’s computer resources) similar to these homework problems.

To summarize, “doing homework” does not simply mean, completing the problems assigned. Daily work= in precalculus should be looked at as a three step proce= ss:

1= .     Review the day&#= 8217;s notes: concepts and example problems.

2= .     Complete your assignment (using your book and notes as a guide).

3= .     Review and criti= que the previous day’s homework assignment.

Fearless Quiz and Test Taking=

Studying for Quizzes and Tests

By learning how to effectively prepare for quizzes and tests, you will be able= to save time by studying smartly and approach tests with efficiency and confidence.

QU= IZZES

Although your teacher may assign quizzes on a weekly or even daily basis, successful students continuously review their homework assignments every night to study for their next quizzes. (See = the “Reviewing Your Homework and Notes” section of the “Homework” chapter.) By reviewing your homework each night, you will be able to select appropriate example problems directly from your homework and look for similar review problems at the end of the section or in your book’s CD-Rom materials. =

On the day before your quiz, identify definitions and theorems that you will be asked to recall or apply. Gre= at problems to re-analyze would be example problems from the text, examples yo= ur teacher did in class, or challenging homework problems you’ve gone through in class. Keep in min= d that depending on the length of the quiz, you will probably not be asked to work= out the most difficult problems you’ve seen in the section. Teachers tend to save a challenging or sophisticated problem for a t= est situation rather than a quiz so they can allocate more time to it.

If you have questions about the content of a quiz, be sure to ask your teacher= at least a day before the quiz. = Although a teacher can sometimes give you encouragement and direction, do not expect them to tell you exactly what types of exercises to study or what will be on the quiz. Use pat experience = to determine which exercises encapsulate the concepts and goals of the lessons= on the quiz. With practice and preparation, your ability to predict the content of quizzes will improve!

Another exercise in studying for quizzes is quiz creation. If your study group meets before a= class quiz, create a ten minute quiz for your study partner and have them create = one for you. Making a quiz for so= meone else will encourage you to choose problems that identify important concepts. Taking a student-ma= de quiz will give you a risk-free trial run while you also get to see what pro= blems your partner identifies as important to study.

TE= STS

Studying for tests is a big job and successful students break the work into multiple study sessions rather than one late night study binge. Assuming that you have completed a= ll of the homework assignments in the chapter, reviewed your homework on a daily basi= s, and dutifully studied for quizzes, studying for a test should not be a daun= ting task.

First, collect all of your materials from the chapter: your book, notebook, homewo= rk assignments, and quizzes. You will have al= ready selected great example problems in the book and in your homework. Keep looking for similar examples = at the end of the chapter or on your book’s CD-Rom. Again, when studying, you should concentrate on quality of response rather than quantity of problems. Make sure that you are practicing = a good variety of problems but more importantly, evaluate the depth and completene= ss of your solution. =

While re-reading your book and notes is always a good idea and re-working problem= s is helpful, active studying will give you an edge on tests. Work with a partner and assign each other a (different) problem to solve. (It’s best to choose a problem where you already have access t= o a complete and correct solution. Borrow your teacher’s solution guide if necessary.) Give yourselves about 3 to 5 minut= es (depending on difficulty, this is the amount of time you will realistically have to design a solution on a test) to create and polish a complete solution. When you are finish= ed, trade problems back and grade your partner’s work on a scale of one to ten. Does their diagram match= their steps? Have they jumped to conclusions or skipped steps? Even if you find it difficult to give them a specific grade, point out strengths= and weaknesses in their organization and presentation. This takes your focus off grading “correct vs. incorrect” and “detailed, clear, and logical work vs. unorganized and careless work”. This is a great exercise to try wh= en you feel confident about the material but want to polish your test solution presentation.

Another idea you should consider when studying for tests is reviewing the format of your old tests. Look at the n= umber of questions your teacher typically asks.&= nbsp; Are there patterns in the way he/she writes problems? Are the graphs near the beginning?= Are the harder problems at the end= ? Will you need a calculator on this= test and for what kinds of problems? It is always best to feel confident knowing what the test will look like before you’ve got it sitting in front of you. Old tests can give you clues so sk= im through them for ideas. =

Taking Quizzes and Tests

Taking quizzes and tests causes anxiety in some students and the best cure for the= se insecurities is preparation. = Always remember that if you have an extenuating circumstance (for example: sicknes= s, family emergency, etc.) contact your teacher as soon as possible to establi= sh an alternative schedule. Your teacher will want to make sure you to have a fair test that evaluates your knowledge of precalculus material and that you = take the test as soon as possible.

The day before t= he test:

·         Study independently or with a partner/study group. Assuming that this is not your first study session, reviewing for= 30 to 45 minute (maximum) should be more than enough time.

·         Prepare your notebook to be handed in to your teacher. Follow all organizational guidelin= es your teacher has established. See the “Notebook Organization” section in the first chapter for so= me specifics.

·         Follow your normal schedule, including bedtime.&n= bsp; You should plan to get 7 to 8 hours of sleep on the night before the test.

The day of the t= est:

Eat breakfast. Feeling hungr= y or thirsty during a test can be distracting to your focus.

Bring penci= ls, erasers, your calculator, and your notebook to class.

Get to clas= s as soon as you can, ideally a few minutes before the test begins. Pass in your notebook and tak= e out all the materials you will need for the test.

Once you finally have the test in your hands, flip through and skim the problems. Make sure that all = of your pages are legible and you have all parts to the test. Maybe you’ve already decided= to do the graphing problems first or the word problem at the end. Maybe you always work in order. It is up to you which problems you= work on first. <= /p>

On some tests, the numbers of points assigned to each problem are listed near = the number. It would be smart to = check this out before you spend 15 minutes stuck on a problem that is worth only 8 out of 100 points, for example. Budget your time accordingly. In addition, noting that a problem= is worth 12 points on a 60 point test, for example, means that your teacher wi= ll assign points that add up to 12 to different steps, equations, or diagrams = in the problem. A two line answe= r will probably not contain all of the details that your teacher will be evaluating.

If you are stumped by a problem, go through the statement of the problem one clause at a time. Hopefully you’ve been practi= cing this. (See the “How to = Approach Each Individual Exercise/Problem” section in the “Homework̶= 1; chapter.) Write down all of t= he given information and list any equations that may be helpful in solving the problem. Finally, write down = the goal and any units that may be necessary in the problem or in the solution. Do your best to beg= in the problem. If you are stuck in = the middle of the problem, take a break and work on another problem before you = try to move on from your first effort or look for an error in your work. By outlining a problem, listing gi= vens, writing necessary equations, units, and goal of the problem you will undoubtedly receive some points. Instead of stressing for 10 more minutes for the last 4 or 5 points, move on to a fresh problem and come back when the rest of the test is compl= ete.

When you are finished with your test, take= the time remaining to review and evaluate your work. Are there places where you could c= larify your steps? Is your writing o= rganized and legible? Did you remember= to write units on word problems? Are your answers to word problems believable?&= nbsp; Does your train leaving Penn Station due west travel 893,103.1 miles= per hour? I hope not. Double check any calculator answer= s you found. Your test is a present= ation of your best work in a pressure situation.= Make sure it is as detailed, complete, and professional looking as possible. Good luck!

A Little Help Here…

One goal that you should have as a precalculus stud= ent is to become confident with challenges and comfortable working independently.<= span style=3D'mso-spacerun:yes'> On the other hand, it is also cruc= ial that you know where help is available, how to ask for help, and how to work efficiently with others. No o= ne masters precalculus without a little assistance occasionally (or often…) and it is natural to feel nervous or vulnera= ble when you are unable to accomplish a goal independently. Luckily, there are many resources available to you as a Harvard-Westlake student which I will outline below.<= span style=3D'mso-spacerun:yes'>

Wor= king with your classroom teacher

Your teacher will be your primary resource when you need help. Your teacher selects homework prob= lems and, more importantly, quiz and test problems. You will want to listen carefully = to the suggestions they make to help you focus your studying. Teachers are can be available befo= re and after school, during free periods, and during your class’s X-period b= ut in order to guarantee that your teacher will be prepared to meet make an appointment with them ahe= ad of time. Your teacher’s fr= ee time is limited, as is yours, and they will be better prepared to effective= ly answer your questions when they have a scheduled meeting time with you. Below are some DO’s and DONT’= s for working with your teacher.

DO…

Bring all o= f your course materials to the appointment including your notes, homework, bo= ok, calculator, and pencil. A highlighter might also be helpful to outline topics in your notes or problems that you discuss with your teacher.

Ask your te= acher to help you analyze and evaluate problems that you have already put ef= fort into. This will give you= the opportunity to preview how your teacher will evaluate your work on a q= uiz or test problems.

Ask your te= acher direct and specific questions about challenging problems rather than indirect and vague ones. Detailed questions have detailed answers and are efficient to answer.

Be prepared= to support and defend your work with your teacher. You may want to try the follo= wing exercise: Choose an exam= ple from the text or a homework problem that you have completed. Follow each step and explain = to your teacher why each step follows naturally in the problem and why ea= ch step is justified. This = should help you practice the natural organization and flow of a problem.

DON’T…

Don’t= throw a pity party for yourself or ask vague questions. When you come to an appointme= nt and only offer, “I don’t get it. This work is too hard!”, it only communicates negativity. First, it shows that you have= not prepared for your appointment by taking the time to establish specific questions. This lack of = organization will waste your and your teacher’s time. Also, complaining shows a lac= k of confidence and an unwillingness to accept challenges.

Don’t expect your teacher to solve example problems by themselves while you = look on passively. Your teach= er is not the person who needs to practice and learn. Watching a teacher do problem= s will not bring you any closer to solving them yourself.= However,
Don’t= waste your or your teacher’s time by expecting them to watch you do homework problems. You s= hould complete your homework independently or with your study group and then meet with your teacher. = Use your appointment time wisely by communicating with your teacher, asking and answering questions, and analyzing problems.

=

= Forming a study group

Forming a study group with 2 or 3 other classmates is a worthy endeavor for two reasons. First, you will form= a mature and academic relationship with your peers who will encourage your learning and booster your confidence in precalculus. Also, you will be able to take you= r new collaborative skills with you to college, where often study groups are often the primary means of survival in difficult courses. By learning to communicate with yo= ur peers, you will speak and write in a detailed and effective manner. You will listen closely and deeply analyze material that your peers convey.&n= bsp; The skills that you develop by working closely with your peers will = be assets that you bring to college, your first jobs, and your personal relationships throughout your life.

At the beginning of the year, try to identify a few other students that you mi= ght work well with. The best study group partners might not necessarily be your best friends socially, but rat= her friendly students who seem to take their responsibilities seriously and are= willing to communicate (or at least work on their communication skills). It might be best to look for partn= ers who have different strengths than you.&nbs= p; Maybe find one student who you feel comfortable explaining work to a= nd another who often is able to help you out when you have questions. Keep in mind that a group full of “aggressive leaders” or a group full of “introverted followers” might not be the best combination so look for a variety of personalities. Remember that = within your study group, you will take turns leading and following your partners.<= span style=3D'mso-spacerun:yes'> Exchange email addresses, phone nu= mbers, and/or AIM screen names with potential study group partners.

To form your group and start meeting, you must identify a time and a place convenient for all members. L= ook for common free periods but also consider before or after school. As far as where to meet, ask your teacher if there is an open classroom during your groups meeting time. Working in a classroom is ideal as= it provides a quiet study environment without distractions but also gives you space to work at desks or use the board to write work large enough for all = to read. When your study group m= eets in a math classroom, you are close to books in the math department, teacher= s to ask questions of when you are really stuck, and the Chalmers computer labs,= how convenient! A study area in t= he library would also be a good option for your meeting place. Remember that using school space t= o meet with a study guide is a responsibility and not a right. Keep your study area clean and res= pect others who are working nearby when you are on campus.

When working with a study group, your main task will be to explain problems to o= ne another and to discuss and analyze concepts from class. You’ll want to have your not= es, homework, textbook, and plenty of blank paper available. When you work with other students,= it is easy to become lazy and not use detail in your language. Make sure that you do your best to clearly articulate your meaning when speaking. Hold others to high standards and = look for alternative explanations to how problems can be solved.

For examples of exercises to use when meeting with your study group, read the “Organization” chapter on asking and answering questions in cla= ss and written communication on the board.&nb= sp; When you practice holding yourself to high standards and producing detailed and accurate work among your peers, your presentation on quizzes a= nd tests will be more complete and thorough.&= nbsp; Honor quality of response rather than quantity of problems showing little or no work. With pract= ice, quality of work and efficiency = will follow.

Peer Tutoring

Harvard-Westlake offers an excellent peer tutoring program that you may want to take advanta= ge of. Peer tutors are selected = not only based on their success in precalculus but = also their confidence, strength in communication, and willingness to work with others. A peer tutor can give= you insight as to what you should focus on in order to improve your quiz and te= st performances and raise your confidence.&nb= sp; Ask your teacher or Ms. Bek (who runs th= e peer tutoring program) to find out more information about getting a peer tutor.<= span style=3D'mso-spacerun:yes'>

Watch your peer tutor (or any tutor for that matter) closely and try to identify = the questions that go through their mind as they prepare to solve a problem. Ask your tutor to verbalize what g= oes through their mind and the logic that leads them to begin a problem. A good peer tutor will be able to = model problem solving for you but your tutor session should not solely consist of= your tutor doing problems for you. Make sure that you are encouraged to actively participate and communicate.

When you go over a problem or an example from the text with your peer tutor, ask them to hold you accountable for explaining each and every step. The steps that you gloss over when= you practice will be the steps you become confused with on the next quiz!

Value any advice on “approach” that your peer tutor can offer you. Obviously, your peer tutor has lea= rned study methods and experienced success in precalculus. Ask them to objectively assess your strengths and weaknesses in precaluclus. This is a personal task but also an extremely difficult exercise to do by yourself! There is no need to compare yourse= lf to other students, but rather you should look for ways to enhance your perform= ance based on maximizing your personality and academic strengths. Find out what skills you need to w= ork on and then set goals for yourself to improve your weaknesses.

Using “outside of school” tutors=

Some students and families choose the option of working with a professional tutor outside of school. If you dec= ide to seek a tutor outside of school you should look for a person who challenges = you, encourages you to communicate often, and holds your work to a high standard. A good tutor will m= odel excellent communication and organization in their problem solving. Always remember that the following exercises outlined are also good tips for when you work with your teacher! =

Because your meeting time with your tutor is always limited, make sure that you are prepared to work efficiently with them.&nb= sp; This means that before your tutor arrives, you should set up your st= udy area complete with book(s), notebook, pencils, calculator, geometer, and yo= ur most recent homework assignments. You should have your most recent homework assignment (or at least mo= st of it) completed with difficult problems that you’ve attempted circled. As you do your homew= ork, write out questions that you’d like to ask your teacher or tutor in t= he margins so you won’t forget them when the time comes. Look through the last few sections= of your book and locate challenging examples that you’d like to try to explain for your tutor. Even = if you’re not quite sure how to complete the entire problem your tutor c= an help you when you are stuck and then assess your understanding of the conce= pts involved. Take risks when wor= king with a tutor.

Working with a tutor should not seem like a “one-sided” conversation. Here are some bad habits that tuto= rs and “tutees” occasionally engage in:

Don’t= plan to simply do your homework while your tutor watches. This is not a good use of tim= e and you will learn less from the time you spend with your tutor. More efficient would be to co= mplete as many problems on the assignment as possible and use your tutor to critique your presentation. Then save the most challenging problems only to do with your tutor.

When doing example problems, choose problems that you’ve already attempted = to solve or work out rather than brand new problems. Again, you need to prepare be= fore you meet with your tutor in order to do this! When you focus on fewer probl= ems but delve deeper into their structure and design, you will have a bett= er idea of how to give a meaningful and complete answer to a problem.

Do not let = your tutor do problems in front of you while you watch. This would be considered pass= ive participation on your part and your tutor is not the one who needs practice with the material. Do not fall into the pattern of “tutor does a problem, student does= an identical problem”. This involves little thought or creativity. Make sure that you are always working together with your tutor.

Vary the ty= pes of problems that you analyze with your tutor. If you keep repeating the same types of examples, you will miss out on other types of problems leaving your understanding lopsided. The time to practice and re-practice these concepts is after you meet with your tutor. Us= e your time together effectively.

Internet resources

Don’t forget sites such as Hotmath.com and our books computer resources when you = need help. Use these sites on a da= y to day basis when you are troubled with occasional homework problems or you’re studying and in search of some additional example problems. For more suggestions about how the internet can provide assistance in precalculus,= see the section on “Resources” in the “Homework” chapte= r.

Grades

Grades are the quantitative evaluation of your performance and progress in class.<= span style=3D'mso-spacerun:yes'> Although your teacher will keep tr= ack of all of your homework, quiz, test, and exam grades, it is your responsibilit= y to record your grades, to analyze them for trends, and to adjust your study ha= bits according to these trends.

Record all of your grades (homework portfolio, quiz, test) in the general section of your notebook. You will want to describe which sections the evaluation covered, the date of the evaluation, and your number grade. At the top of this page, note what percentage weight is given to homework, quizzes, tests, and exams. This way, you will be able to calc= ulate your overall average at any time.

Keep watch over your grades and notice your strengths and weaknesses. Maybe you have perfect homework sc= ores, strong quizzes, and weaker test grades.&nb= sp; This means you must focus your energies into consolidating entire chapters of material and pulling together concepts for the test. Maybe your test and quiz averages = are strong but your homework portfolio average is low and bringing your grade down. You will need to take s= teps to organize your daily work and make homework and notes a priority. By recording your grades and knowi= ng yourself as a student, you will be able to pronounce your strengths and foc= us on improving your weaknesses.

Another strong recommendation would be to go so far as to keep a log of all of your class evaluations. This means rather than just recording your number grade, write down how much you studi= ed, where you studied, which problems you stumbled on (and why you think you stumbled on them), and any other specific notes about the test/quiz. Record how you were feeling as you= took the test: relaxed, prepared, confident, sleepy, stressed, sick, or anxious. Think of this as a q= uiz and test “diary” of sorts.&nbs= p; After analyzing the trends in your “test diary” you will= be able to see what kinds of study efforts, preparation, and moods lead you to produce your best work. You w= ill also see patterns in the types of errors you are making. By facing these trends and adjusti= ng your work habits, you will be better equipped to create ideal studying and = test taking environments for yourself.

Oops!....<= /span> Minimizing Negat= ive Effects of Errors

Everyone is bound to make mistakes once in a while but top students know how to mini= mize their losses in the aftermath of their errors. It is M\most important that you kn= ow how to catch up with the rest of the class after falling behind and you learn to move forward and not dwell on mistakes made. Every blunder is a potential for g= rowth and progress. The following e= rrors are those which even the best students make and grow from.

I was late to class!

When you are late to class, quietly enter the room and take your seat. Open your notebook and text book as quickly as possible and resume work with the rest of your classmates. No matter how hard you try, being = late is a disturbance to those around you so please minimize this disturbance. It is absolutely inappropriate to = enter the room talking or to interrupt the teacher or another student with an explanation of why you are late. This creates an even larger disturbance. Speak to your teacher only after c= lass is over to explain your tardiness.

If you have missed significant homework review or note-taking, wait until the = end of class, then ask to borrow a classmates notes to copy during a free period. When you miss any par= t of class, no matter how small, you are responsible for material covered in class. Speak to another stude= nt to make sure that you did not miss important announcements (quizzes!) or homework problems a teacher emphasized. It would be a mistake to assume your teacher is responsible to go over homework problem explanations that you missed as a result of being late to class. Pay careful attention to this unit= when you are studying for quizzes or a test, since you missed the presentation in class.

When you are late to class on a regular basis, this shows you teacher and fellow students that you do not value your class time and that you do not mind disturbing their teaching and learning.&nb= sp; This is a negative message to send!= If you think that a teacher has been regularly letting your class out late, you= must work with all of the adults involved and find a way that you can arriv= e at your class on time. When a te= acher consistently lets you out late, speak to them, speak to your dean, and spea= k to the teacher whose class meets next. It is your responsibility to help create a solution.

I forgot to bring my _______ to class!

When you are consistently unprepared for class, it sends a message that you are = not responsible. If you do not ha= ve an appropriate writing utensil (pencils only for quizzes and tests), quickly borrow one from another student. If you forgot your book or a calculator, ask to share with another student for= the day. It is always best to hav= e your own materials, especially a calculator to follow along with. Pushing the keystrokes yourself, r= ather than looking on with someone, is the best way to learn and remember calcula= tor functions. If you do not have= your calculator, look on with another student but write down all of the keystrok= es so you can practice at home. =

If you do not have your notebook, use a blank piece of notebook paper to take notes on. Do not keep this sh= eet in a different notebook because you will most likely forget where you took the notes that day. Carefully not= e the date and section number at the top of the page and put the stray sheet in y= our precalculus notebook on the first chance you have. In general, if you do not have appropriate materials for class, do not draw attention to yourself, rather remedy the situation as quickly as you can. Make a habit of being prepared for= class every day!

I forgot/didn’t do my homework!=

If you do not have your homework when your teacher checks assignments, let him know that you don’t have it. There is no need to give an excuse for why the assignment was not completed or explanation of where you misplaced the assignment. Instead, focus on how to remedy the situation and make the best of your error.

Record all = of the notes and homework review from the assignment you missed. Even though you have not done= the work (or don’t have it with you), you will want to have notes to= reference once you do complete the assignment.&= nbsp; There is no reason to keep the solutions that your teacher goes over a secret from yourself!

Catch up on= the assignment as soon as you can. Students who are always a day behind on homework assignments tend to have lower quiz grades. Success in precalculus relies on solid daily preparation, not just hours of studying for test= s on the weekend. When you do= the missed assignment, you may want to try some extra problems, such as the example problems in the text or other exercise problems closely relate= d to the ones on the original assignment.&= nbsp; Even if you feel as if you understand the assignment that you missed, make sure you do a thorough job writing your steps and showing= all appropriate diagrams. It= may be tempting to be lazy but you will be extra vulnerable on material th= at you are too lazy to study carefully.&= nbsp;

The day aft= er you miss an assignment, first show your teacher the latest assignment he is checking, followed by the assignment you missed. You will probably not receive= daily credit when you catch up on an assignment but your teacher may want to note that you are caught up.

I missed a day of school…

Although it is common to miss a day or two= of school every year, the best students know how to take responsibility for the material they miss when they are out of class. Here is what you can do to keep up= with your class (or even ahead!) when you are sick or chose to miss school for a personal reason.

It is your responsibility to email (or call) your teacher when you know you will = be missing school. If you a= re out of school on that day, try to write to your teacher during school hours. They will hopeful= ly have time to respond to you quickly and remind you what material you a= re missing. Your teacher is= the most reliable source you have for instructions and information about class. If you are missin= g a quiz or test, let them know when you would be free to make it up. Emailing or calling from home= is much easier than trying to track down a teacher once you are back in school. When you keep yo= ur teacher informed about your whereabouts, they will be better prepared = to assist you as you catch up on work when you return to school. Teachers also see your emaili= ng as a sign of preparedness and maturity.&= nbsp; It shows your teacher that you care enough to take responsibili= ty for your assignments and that you value the course.

Collect the= phone numbers, email addresses, and screen names of 3 or more students in yo= ur class on the first day of school.&nbs= p; If you know you will be missing school (or missed school that d= ay) get in touch with a peer to verify the assignment and class announcements. Ask a fri= end in advance if you can borrow their notes once you see them back at school. (Maybe a close friend could even fax you the notes if you needed them = over a long weekend, for example.) Also ask your peers what seemed to be the most challenging part= s of the new lesson. What key concepts should you look out for as you study and try the homework? Use your peers to stay inform= ed.

Do your bes= t to keep up to date with assignments even if you are out of class. Keep your book and notebook a= t home if you are going to be out of school.= The chapter will run more smoothly if you keep up with assignme= nts rather than skip a section and try to come back to it a week later. Do not put off assignments th= at you miss when you are out of school. This bad habit will exacerbate any weaknesses you have with that section on upcoming quizzes or tests.= Understandably, there are times when you are far to sick to wor= k at home. When this happens,= rest as much as you can, have a parent email your dean or teachers, and wor= k on your assignments as soon as you are able.

Make an appointment with your teacher. Even if you feel comfortable with all the material that you mis= sed, meet with your teacher for half of a period. Show them some of your work a= nd allow them to assess your understanding of the unit you missed.

I will be missing more than a day of school…

On occasion, students choose to miss two or more days of school because of sports team trips, youth conventions, or unavoidable personal reasons. When you are out of class for two or more days, catching up with the class becom= es very tricky and it is easy to fall behind or become frustrated and overwhelmed. For this reason,= it is best to avoid these types of absences as much as possible. When you do miss two or more class= es, it is essential that you work closely with your teacher before and after (and occasionally during, through email).

Have your upcoming absence registered with administration by obtaining a green f= orm from your dean. Your tea= chers will have to sign this form and remind you what material and assignmen= ts you will be missing while you are gone. This is a great first opportu= nity to communicate with your teacher your plans on keeping up with your wo= rk and making up quizzes or a test. Take advantage of this short meeting with your teacher by organizing and writing down due dates for each assignment you will mis= s. Remember to return your green form to your dean far enough in advance before your absence. (If you are sick, the green t= rip forms do not apply. When= you are sick for two or more days, ask your parents to have a short conversation with the attendance clerk and your dean.)

Do not hesi= tate to email or call your teacher when you are away if you are working on = an assignment and need assistance. During the week is the best time to get a quick response as some teachers do not check phone or email messages over the weekend.

Make an appointment with your teacher when you return to campus. You will want to schedule qui= zzes and tests immediately upon your return. Your teacher will allow you a reasonable and fair amount of time to make up assessments, especially = if your absence was more than two days or unexpected. Please remember that it is yo= ur responsibility, and also an advantage to you, to complete all of your assignments and quizzes in a timely manner.

I gave a poor performance on a quiz/test…

Absolutely everyone has an occasional test or quiz that they would classify as a poor performance. Although it̵= 7;s never possible to go back in time, “erase”, and “replay” a bad test, here are some steps you can take to learn = from your mistakes and perform more soundly on the next test.<= /p>

Carefully a= nalyze each problem on the test where you stumbled. This means find the section (= or sections) it comes from, find homework problems that are similar to it, and redo the problem on a separate sheet of paper. Look for similar book example= s or examples in your notes in order to write a complete solution to the problem you got wrong. S= taple or clip all extra notes and redo problems to your original test.<= /o:p>

Meet with y= our teacher once you have completely analyzed your test. Ask your teacher any question= s you have when comparing your work on test problems to a complete solution. Work with your teacher to analyze the types of errors you made.

Keep track = of your strengths and weaknesses on test problems to better prepare for y= our next test. You will want= to keep a log of your findings to look for patterns. Do you make a lot of arithmet= ic mistakes? Do you jump to conclusions without reading carefully? Do you forget to include work= steps to support your answer? = If you have trouble being objective with your own work, find a partner, trade tests, and analyze each other’s errors.

Practice, practice, practice! Lear= n from your mistakes by focusing on problems that you find challenging.

Remember to= store all of your old quizzes and tests in a safe spot. You will use them to study for midterms and finals but you might also want to look them over at other times. Evaluate the aver= age length of tests, looking at the number of, difficulty of, and placemen= t of questions. Do you notice patterns? This exercise = will help you know what to expect from tests and feel more comfortable with= the organization of tests in the future.&= nbsp;