SAT Math Articles - WyzAnt Tutor Blogshttps://www.wyzant.com/resources/blogs/sat_mathThis is an aggregate of all of the SAT Math articles in WyzAnt.com's Tutors' Blogs. WyzAnt.com is your source for tutors and students.Sat, 13 Feb 2016 15:51:16 -0600https://www.wyzant.com/images/wyzant-logo-type-white.pngSAT Math Articles - WyzAnt Tutor Blogshttps://www.wyzant.com/resources/blogs/sat_mathhttps://www.wyzant.com/resources/blogs/sat_math411907https://www.wyzant.com/resources/blogs/411907/learn_from_math_mistakesCharles C.https://www.wyzant.com/resources/users/view/85718758Learn from Math Mistakes<p>Okay, we have all made a math mistake, but for one reason or another we never took advantage of that opportunity to commit the correct step to memory. I have news for you. You can still remedy the situation. Here is how you achieve it. 1. For every time that you’ve made a wrong step in solving a problem, repeat the correct step three times. 2. If it is a multi-step problem, WRITE all the steps in the correct order at least three times. 3. READ out all the correct steps to yourself at least three times so that you HEAR the correct steps. Here is the rationale for this strategy. We have multiple ways of learning for a reason and we need to make use of multiple intelligences in order to maximize our ability to understand and memorize the correct steps. Once we commit the correct procedure into long-term memory, we are essentially freeing our short-term memory to work on other tasks. This way we won't get stumped months later when we come across the problem. So this strategy is a win!</p>Wed, 09 Dec 2015 23:36:10 -06002015-12-09T23:36:10-06:00372892https://www.wyzant.com/resources/blogs/372892/the_new_sat_march_2016Daniel C.https://www.wyzant.com/resources/users/view/85887244The New SAT (March 2016)<div>Over the last few years, the SAT has lost a tremendous amount of market share to the ACT.<br /><br />Over 1.84 million high school graduates sat for the ACT in 2014, while only 1.67 million took the SAT.<br /><br />The College Board changed the SAT to look more like its competitor.<br /><br />Both exams now feature:<br />*An optional essay<br /><br />*Longer sections – The old SAT had 10 sections. Each was around 20 minutes in length. Both the new SAT and the ACT have four sections (the exact number depends on how you count), which average around 45 minutes.<br /><br />*More science related content. The ACT has a Science section. The new SAT will not, but includes these concepts in the Reading and Math sections).<br /><br />*No penalty for guessing.<br /><br />*No esoteric vocabulary. Gone are the days when people described five dollar words as SAT words!</div>Thu, 20 Aug 2015 23:10:48 -05002015-08-20T23:10:48-05:00366726https://www.wyzant.com/resources/blogs/366726/summer_vacationMichael M.https://www.wyzant.com/resources/users/view/83411340Summer Vacation<div>summer vacation is the perfect time for starting to study for the fall college admissions tests. It's also a great time to keep those math skills up so that you don't lose any of the skills that you learned last year. So many students lose so much of the skills that they have gained in the past year, and math is just like anything else, don't practice and you'll lose all that you learned.</div>Mon, 13 Jul 2015 07:19:22 -05002015-07-13T07:19:22-05:00363185https://www.wyzant.com/resources/blogs/363185/preparing_for_the_act_or_satJosh W.https://www.wyzant.com/resources/users/view/85679504Preparing for the ACT or SAT<div>Almost every college or university requires students to submit an ACT or SAT score. This score affects not only your admission application but also scholarship opportunities and which classes you will be able to enroll in. The vast majority of students do little to no preparation work before taking these exams. They may feel that all their hard work in high school should have prepared them already. Although this is partially true, it is actually quite easy to raise your score a significant amount by just putting in a little bit more work. Students can see composite ACT scores raise 5 or more points and SAT scores raise 300 or more points. Why is this?</div>
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<div>1) Both the ACT and SAT test many of the same concepts repeatedly and by learning these core concepts, you will easily get a higher score. </div>
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<div>2) You will get more familiar with the format of the test and start to see patterns in how they ask questions. Once you identify these patterns, finding the answers becomes much easier. It's like learning to ride a bike. At first, your brain is using most of its energy and concentration trying to stay balanced. But you quickly stop thinking about that and your brain is free to focus on something else. Once you learn the test format, your brain is free to stop thinking about the test and start thinking about the actual questions and answers. </div>
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<div>3) ACT and SAT are not knowledge tests. The test makers freely admit that these tests are designed not to see how much you know, but to see how skilled you are at learning and processing information. When you learn how the test makers set up the exam and practice answering their questions, you will learn how to think like they expect you to think and will raise your score. </div>
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<div>Spending some time and effort preparing for the ACT or SAT will absolutely be worth it. You are about to spend years of your life and tens of thousands of dollars in higher education. By spending a few weeks preparing, you will ensure that your ACT or SAT score will get you into the college you want to go as well as getting you the scholarships and class placement that you deserve. </div>Sat, 27 Jun 2015 14:27:14 -05002015-06-27T14:27:14-05:00362356https://www.wyzant.com/resources/blogs/362356/mathematical_journeys_solve_only_for_what_you_needEllen S.https://www.wyzant.com/resources/users/view/75479140Mathematical Journeys: Solve Only for What You Need<div>Standardized test math doesn't behave like normal math. On a normal math test, your knowledge of the concepts and material is being tested, using (hopefully) fair test questions. On a standardized test, though, they're looking for you to think outside the box, to apply math concepts and algorithms to unusual situations, and to really understand what they're looking for and find the quickest way to go about it. Let's take a question from a recent GRE student's lesson:<br /><br />If 4x – 5y = 10 and 6y – 3x = 22, then what is x + y?<br /><br />Now, this is a set of two equations with two variables each, so it looks to me like a perfect candidate for solving as a system. If I were solving this one on a regular math test, I'd start off trying the substitution method, since I'm more comfortable with that one. So let's explore that one first:<br /><br />I'll start by solving the first equation for y:<br /><br />4x – 5y = 10<br />- 5y = 10 – 4x<br />y = (-10/5) – (4/-5)x<br />y = -2 + (4/5)x<br /><br />Then I'll plug that in for y in the second equation:<br /><br />6(-2 + [4/5]x) – 3x = 22<br />-12 + (24/5)x – 3x = 22 Now we have to convert the 3x into a fraction<br />-12 + (24/5)x – (15/5)x = 22<br />-12 + (9/5)x = 22<br />(9/5)x = 34<br />x = 34 (5/9)<br />x = 170/9<br /><br />Then plug that back in for x in the first equation:<br /><br />y = -2 + (4/5)(170/9)<br />y = 136/9<br /><br />And, FINALLY, find the quantity asked for in the problem by adding x and y together:<br /><br />x + y = (170/9) + (136/9)<br />x + y = 306/9<br />x + y = 34<br /><br />Well, that's one way to find the answer, but that took a long time, with lots of large numbers, and lots of potential for mistakes. This is a standardized test, remember, so time is a factor here. Take a look at the question again. It's asking for x + y. Why wouldn't it be asking simply for x, or y, or even x and y, for that matter? Is it because x + y is a much cleaner number? Is it to be ornery? To make you waste time?<br /><br />Well, to be honest, the answer to that last question is yes, but not in the way you might think. In our math classes, we're hardwired to try to solve for x – we want to end up with a nice clean number to equal one of our variables. It's the way most math classes work; manipulate the equation until it tells you the missing piece of information. The test builders know that, and they know that everyone's first instinct in a math problem is to try to solve for x. But in this case, they're not asking for the value of x; they're asking for the value of an expression containing x. And they're doing that very deliberately – <em>because finding x + y is much easier than finding x.</em><br /><br />Take a look at our system again – this time I'll re-arrange it slightly in preparation for using the addition method to solve it:<br /><br /> 4x – 5y = 10<br /> – 3x + 6y = 22<br /><br />See it yet? Use the addition method – don't even modify anything – and add straight down the columns:<br /><br /> 4x – 5y = 10<br /> <span style="text-decoration: underline;">– 3x + 6y = 22</span><br /> x + y = 32<br /><br />Well, would you look at that? That's the answer they're looking for – and you'll notice it's not the same answer as our previous attempt. Not only would you have wasted a bunch of time going through all those hoops to solve with substitution, but you would have gotten the question wrong to boot! <br /><br />It's an odd way of looking at a math problem, but one of the biggest strategies I tell my students is to not think about the test as a math test. It's a logic test that happens to involve numbers. Here, the test is remembering to only solve for what you need. Don't bother getting all the way down to x if x won't help you in the end. Sometimes they're asking for a quantity because going any further past that quantity will only cause you grief. Solve for the quantity they ask for, and no more.</div>Mon, 22 Jun 2015 12:46:28 -05002015-06-22T12:46:28-05:00361344https://www.wyzant.com/resources/blogs/361344/need_math_helpREBECCA K.https://www.wyzant.com/resources/users/view/85810429Need math help? <div>Need help in middle school, high school, or college math? Don't hesitate to reach out to me! I'm an easy-going and reliable tutor who loves working with all ages! </div>Tue, 16 Jun 2015 12:18:19 -05002015-06-16T12:18:19-05:00361220https://www.wyzant.com/resources/blogs/361220/spacing_out_your_student_s_sat_and_act_testsElisabeth W.https://www.wyzant.com/resources/users/view/85332275Spacing Out Your Student's SAT and ACT Tests<div>Quickly after beginning work as a tutor, I came to realize that parents are the black belts of scheduling. They not only have to keep up with a number of annoying adult responsibilities, but they also have to keep up with their children's calendars. Parents' organizational skills (and possibly their sanity) are put to a very difficult test daily. So, to all my expertly organized parents out there, in this post I hope to let you in on a scheduling detail that often slips through the cracks but can make a big difference in a student's SAT or ACT scores.</div>
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<div>One of the biggest obstacles I face when preparing a student for the SAT or ACT is the student's test schedule. Far too often, my student is signed up for two tests that are only a month apart. For example, a couple of my past students have been signed up for an SAT in May and then another in June. This short turnaround gives me very little time to receive the student's scores and prep the student in the areas he or she needs to improve.</div>
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<div>You might be thinking, "A month is a pretty good amount of time to study between tests." However, my dilemma is with when I receive my students' scores. After a student takes the SAT, it usually takes two weeks to receive the student's basic score. Then, it takes another 1-2 weeks to see the specific kinds of questions the student missed in each multiple choice section and to receive the essay that the student wrote. In the best case scenario, this gives tutors a week to know which specific areas their student needs help with. </div>
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<div>Scores on the SAT and ACT are not games of chance. Good scores take a lot of hard work and practice. The writing and math section involve memorizing and applying many grammatical rules and equations. Improving a student's understanding of the essay and reading section takes practice. All of this takes more than one week to accomplish. Depending on the frequency of lessons and the amount the student would like to improve, I like to have a month or two <em>after </em>my student has received their scores to prep in between tests.</div>
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<div>Do you have any additional thoughts or comments? Please feel free to add them in the comment box below. You can also see my ideal prep and test schedule at the end of <a href="https://www.wyzant.com/resources/blogs/357536/the_best_time_to_study_for_the_sat_and_act">this article</a>. Check back in August for a new posting in which I will discuss college application essays!<a href="https://www.wyzant.com/resources/blogs/357536/the_best_time_to_study_for_the_sat_and_act"><br /></a></div>Mon, 15 Jun 2015 20:01:10 -05002015-06-15T20:01:10-05:00357536https://www.wyzant.com/resources/blogs/357536/the_best_time_to_study_for_the_sat_and_actElisabeth W.https://www.wyzant.com/resources/users/view/85332275The Best Time to Study for the SAT and ACT<div>During the school year, my students balance classes, sports, social lives, and sleep. Their schedules are hectic. During tutoring lessons, students often only have time to focus on the immediate assignments at hand in their classes. We usually have little time for test prep unless the student and parent has specifically requested that we focus solely on the SAT or ACT. So, when is the best time to study for the SAT or ACT? You guessed it. Summer vacation. </div>
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<div>Many of my students have a summer schedule that gives their school year calendar a run for it's money. However, their busy summers do not contain nearly as many academic activities as their school year schedules. Most have summer sports, camp, or jobs. This is the perfect time to balance those physical and social activities with test prep. In addition, students can learn the ropes of the SAT or ACT better when they are not juggling other classes and tests. Every kind of standardized test is unique and it takes time and practice to master each one. </div>
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<div>Another great reason for your student to prep for the SAT or ACT over the summer is that he or she will be more likely to retain skills learned during the school year. Students generally lose some academic skills over the summer if they are not engaged academically. Studying for the SAT and ACT hones students' reading, writing, and mathematical skills and prepping over the summer keeps students engaged and ready for school in the fall. </div>
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<div>So, what does an ideal prep and test schedule look like in my eyes? Well, first let's discuss what is not ideal. Most students take their SAT or ACT their junior year. The majority of my students wait to take these tests until the spring of junior year, when many are also taking numerous AP tests and finals. Juniors' course loads are generally the most laden with APs, so you can imagine the stress that mounts when they have to worry about the SAT or ACT and AP tests. </div>
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<div>I recommend that students begin test prep as soon as summer begins after their sophomore year. Students can then take their SAT at the beginning of junior year with less stress than those who wait until spring. For juniors who'd like to improve their scores, I recommend studying for the SAT in the fall and taking it again in the winter, preferably a month or two after midterms. Most students take the SAT three times, and I would recommend studying over the summer after junior year and taking the test in the fall of their senior year. </div>
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<div>Are there other factors you take into account when scheduling your student's SAT or ACT? Please leave comments in the box below!</div>
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<div>In addition, please look forward to a blog post in a few weeks about spacing out SAT and ACT tests and giving your tutor enough time to prep your student for the test.</div>
<div> </div>Mon, 01 Jun 2015 11:41:22 -05002015-06-01T11:41:22-05:00347776https://www.wyzant.com/resources/blogs/347776/psat_sat_act_math_summer_workshopPaul J.https://www.wyzant.com/resources/users/view/85606071PSAT, SAT, & ACT Math Summer Workshop<div>Greetings!</div>
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<div>Are you preparing for the PSAT, SAT, & ACT quantitative exams?</div>
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<div>So are we!</div>
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<div>My name is Paul J. and currently I have 3 students in Vero Beach, Florida who are preparing for these exams this summer. We are looking for motivated students to join us for private lessons. A limit of 5 students has been placed, so there are only 2 positions available. </div>
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<div>Lessons will cost $30 an hour, and we plan to do 2 one hour lessons a week for 5 weeks starting in early.</div>
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<div>Our goal is to score well enough to compete for scholarships such as Bright Futures and the National Merit Scholarship.</div>
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<div>If you are interested, please message me on my WyzAnt Profile.</div>
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<div>Best regards!</div>Fri, 24 Apr 2015 20:39:21 -05002015-04-24T20:39:21-05:00315045https://www.wyzant.com/resources/blogs/315045/technique_for_sat_math_tutoring_outside_the_boxMonica B.https://www.wyzant.com/resources/users/view/79733410Technique for SAT Math Tutoring - Outside the Box<div>My top tips for 'outside the box' -</div>
<div>1. If possible 'interview' the student by phone before the first lesson to establish a bit of a rapport, and to show that you are there as the student's tutor, not the parents' ally.</div>
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<div>2. Bring chocolate if you are having a long session, once you have asked if your student likes chocolate. I believe in rewards for hard work, and a 90 minute plus session is hard work!</div>
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<div>3. I give students some tools for instant relaxation, which they all enjoy learning.</div>
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<div>4. Often, especially with anxious students, I help them with visualization of a successful test report coming in the mail!</div>
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<div>5. I make sure that the last 2-3 minutes are used to record the homework, and to note what pages we left off, if we were in the middle of a review section.</div>
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<div>Re how I tutor for math: </div>
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<div> My approach is to individualize the lessons - first do a diagnostic assessment of what areas will need the most work (e.g., geometry, ballparking, word problems, advanced algebra, etc.). Then we focus our lessons on reviewing some 'rules', and practicing problems, paying the most attention to problems that need correcting. I find it useful to at least briefly cover each math topic that can appear on the test. For students that typically have trouble with the last 4 or 5 problems, I suggest that they practice just those problems for a few sections, and to repeatedly analyze the corrections to their errors. I have found some less popular books that divide the math topics and then offer multiple problems for a narrower area.</div>
<div><br />Please let me know if you have any other tips for great math tutoring!</div>
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<div>Best, Monica</div>Mon, 19 Jan 2015 17:45:05 -06002015-01-19T17:45:05-06:00311834https://www.wyzant.com/resources/blogs/311834/sat_preparation_tipsAthar R.https://www.wyzant.com/resources/users/view/85445878SAT Preparation Tips<div>Some basic tips for students preparing for the SAT exams. </div>
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<div>If your goal is to score high on the exams (and who doesn't want to score high) then you must start preparing early and spend the time. The preparation must be organized into a daily study schedule with a detailed list of tasks. A high score on the SAT translates directly into money in your financial aid package in college.</div>
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<div>How to organize the preparation:</div>
<div>1. Study time should be scheduled for the time when you are most alert. For most people, this is the morning hours and it is entirely possible to study an hour before the start of the school day - if you go to sleep early.</div>
<div>2. Cut back or eliminate other social activities to properly prepare for the SAT</div>
<div>3. Purchase a preparatory book (used from Amazon is ideal) and use that book to organize a daily schedule for studying</div>
<div>4. Read printed material that you DON'T like - especially newspapers like the New York Times, Washington Post, etc.</div>Tue, 06 Jan 2015 11:41:10 -06002015-01-06T11:41:10-06:00290010https://www.wyzant.com/resources/blogs/290010/khanacademy_cryptography_discussionElias H.https://www.wyzant.com/resources/users/view/79074590KHANACADEMY Cryptography Discussion<div>The answer is “Yes” you can learn Cryptography from these videos, but honestly you are going to need a real degree to do the real stuff. You can find out that number theory and probability theory are used.<br /><br />Their video says, “a lock is only as strong as its weakest point” and suggests that conceptually codes may be reduced to fingerprints. I learned its called Frequency Analysis when you count repetitions, presumably with the purpose of breaking a code. It helps if you have some practice. I have some through my classes and standardized tests.<br /><br />There is believe it or not some code braking on tests like The SAT and the SHSAT. On The SAT it was an advanced problem.<br /><br />I used the following technique to solve the SAT problem: serially shift and algebraically move, decode from a latin alphabet to a numerical one. This is problem 16 page 418 from ISBN-13: 978-0-87447-852-5, The College Board’s The Official SAT Study Guide:<br /><br />A four-digit integer, WXYZ, in which W,X,Y and Z each represent a different digit, is formed according to the following rules.<br /><br />X = W + Y + Z<br />W = Y + 1<br />Z = W - 5<br /><br />What is the four-digit integer?<br /><br />Casually I noticed that there is a lot going on here. Whereas often The SAT presents three linear equations with three unknowns, like three numbers, x,y,z outputting, here we have four unknowns. I pre-select the line “each represent a different digit” as best I can. From experience, I know that W = Y + 1 and Z = W - 5 pop into X = W + Y + Z. I get, with brushes and scratchings on the paper:<br /><br />X = 3 W-6, Y = W-1, Z = W-5<br /><br />So for whatever reasons I simply have never furnished the concept, but I take my chances and realize that this is a problem of extra-freedom. <br /><br />In continuation, I create the beginnings of a table in my imagination. The variable W is used as an index to the table. I tell ahead of time that certain values of W either create duplicates in the collection of the four digits or over-sizings in the digits. <br /><br />I find out the problem is with the over-sizings. The variable is W is at least 5. When the variable is above 5 though, say 6, X = 12. That is a violation. I conclude that W = 5, with a spread of<br /><br />W = 5, X = 9, Y = 4, Z = 0 . I conclude that the four-digit integer is 5940. This is correct.<br /><br />In conclusion, the Khan Academy did give me nomenclature for frequency analysis, and I sort of used that to prep for The SAT. My frequency analysis held all frequencies at 1. After going through the videos I stumbled upon the Caesar Cipher Exploration, but not without the strange feeling that I was intruding upon something. I encoded “eat my shorts” to “wsl eq kzgjlk”. That feeling then desisted after as much time as…it took me to write this post. Go figure. Go Math!</div>Wed, 17 Sep 2014 22:24:05 -05002014-09-17T22:24:05-05:00287074https://www.wyzant.com/resources/blogs/287074/ellen_s_choice_are_you_taking_the_sat_this_yearEllen S.https://www.wyzant.com/resources/users/view/75479140Ellen's Choice: Are you Taking the SAT this Year?<div>Well, the new school year has started, and that means SAT test dates are fast approaching. In fact, the first one is this coming weekend. To anyone taking the SAT on Saturday, good luck! Remember to get a good night's sleep on Friday! <br /><br />If you are thinking about applying to college in the next few years, it might be time to schedule an SAT date! Remember, you can retake the test as many times as you need to, so don't be afraid to schedule an early date.<br /><br />Also, remember that the big SAT Redesign will be kicking into effect in the Spring of 2016, so if you are in the class of 2016 you may want to start your testing early, to make sure you have time to retake the current style of test and not have to relearn everything for a completely new test the following year.<br /><br />This semester's SAT test dates and registration deadlines are as follows:<br /><br />October 11th – Registration ends September 12th<br />November 8th – Registration ends October 9th <br />December 6th – Registration ends November 6th<br /><br />I still have tutoring openings available this season. The SAT is not a test of the material; it's a test of how well you take the SAT, so I highly recommend that everyone get at least a few private sessions in to discuss strategies and develop an individual game plan. Feel free to contact me if you're in need of some help this semester!</div>Tue, 09 Sep 2014 07:41:16 -05002014-09-09T07:41:16-05:00282182https://www.wyzant.com/resources/blogs/282182/first_week_back_to_schoolStephanie A.https://www.wyzant.com/resources/users/view/77480730First Week Back to School<div>For many students in the surrounding Richmond, Columbia and Burke counties welcome back to the classrooms! if you have any difficulties in class, do not hesitate to let your teachers or your parents know so that they can find you the most appropriate level of help before it is later in the school year and you end up being in failure of being promoted! I can't wait to see how I am able to help this school year!</div>Sun, 10 Aug 2014 17:32:57 -05002014-08-10T17:32:57-05:00278141https://www.wyzant.com/resources/blogs/278141/are_your_standardized_test_scores_lower_than_you_expectedJacqueline E.https://www.wyzant.com/resources/users/view/82230490Are your standardized test scores lower than you expected?<div>Test anxiety can impact everyone. However, with a few strategies, you can overcome these anxieties and excel on your next standardized assessment.</div>
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<div><strong>Should you guess?</strong></div>
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<li>This is a choice you will need to make based on the assessment you are taking. For certain tests, such as the Praxis, you are scored based only on your correct answers. However, keep the guessing to a minimum. On the SAT, you lose 1/4 of a point for an incorrect answer, but if you leave it blank, you lose 1 point. So guessing should be used as a last resort. Obviously, you should not guess on too many questions. Which leads me to...</li>
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<div><strong>Should you omit questions?</strong></div>
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<li>Only skip questions you find <span style="text-decoration: underline;">extremely</span> difficult. Use other strategies to help you determine if you can, in fact, answer these questions before omitting them. However, do not spend too much time using these strategies, as time is limited.</li>
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<div><strong>Should you answer questions in order?</strong></div>
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<li>This really depends on the type of test you are taking and how you take tests. You can answer questions in order. You can also answer based on how much knowledge you have about a topic. The strategy you choose depends on you determining what strategy works best.</li>
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<div>If you familiarize yourself with the standardized test you will be taking, you can determine which strategies to use when. Research the test. Being prepared will help keep you focused.</div>
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<div>That's all for this post. More strategies to come in the future!</div>
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</div>Fri, 18 Jul 2014 23:04:41 -05002014-07-18T23:04:41-05:00275961https://www.wyzant.com/resources/blogs/275961/how_to_solve_simultaneous_equationsMartin S.https://www.wyzant.com/resources/users/view/85112346How to solve simultaneous equations.<div>Normally, an equation has a single solution when it contains only one undefined variable. For example, take the equation 3x + 7 = 19.</div>
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<div>3x + 7 = 19 [original equation]</div>
<div>3x = 12 [subtracted 7 from both sides]</div>
<div>x = 4 [divided both sides by 3]</div>
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<div>This is one case of a larger trend in algebra. As I've already said, you can solve an equation for one answer when it contains a single variable. However, this is derived from the larger rule that you can solve a set of equations where there are as many distinct equations as there are variables. These are called simultaneous equations, and occur any time that two equations are both true over a certain domain. In the more practical sense, this is what you should do if an exam asks you to solve for a value and gives you two different equations to use.</div>
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<div>To solve simultaneous equations, we can use three strategies.</div>
<div><ol>
<li>Addition</li>
<li>Subtraction</li>
<li>Substitution</li>
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<div>The first two strategies are easier, faster, and cleaner to use. Unfortunately, they don't always work. By contrast, using substitution is a more time consuming method and won't always be as clean-looking, but will <em>always</em> work.</div>
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<div>Addition and subtraction work when you compare the two equations and see the same value appear in both. Let's look at an example.</div>
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<div>4x+3y=23</div>
<div>7x-3y=-1</div>
<div> </div>
<div>In these, we see that the value 3y appears in both equations. In this case, it's positive in one equation and negative in the other. When we see one positive and one negative value, we use Strategy 1: Addition. To do this, we add the left sides of both equations, add the right side of the two equations, and set the two sums equal to each other. Let's take a look:</div>
<div> </div>
<div>Left sides</div>
<div>4x+3y+(7x-3y)</div>
<div>4x+3y+7x-3y [distributed across the quantity (7x-3y)]</div>
<div>11x+3y-3y [algebraic combination of 4x+7x]</div>
<div>11x [algebraic combination of 3y-3y]</div>
<div> </div>
<div>Right sides</div>
<div>23+(-1)</div>
<div>23-1</div>
<div>22</div>
<div> </div>
<div>And now we set the two values equal and solve for the remaining variable:</div>
<div> </div>
<div>11x = 22</div>
<div>x = 2</div>
<div> </div>
<div>But we're not done yet! We've solved for x, and now we can use that to solve for y. What we do here is take one of the two original equations and plug in the value x=2 to solve for y. It doesn't matter which equation we use, so I'll use the first simply because it looks easier to work with.</div>
<div> </div>
<div>4x+3y=23 [original equation]</div>
<div>4(2)+3y=23 [plugged in the value x=2]</div>
<div>8+3y=23 [multiplied 4×2]</div>
<div>3y=15 [subtracted 8 from both sides</div>
<div>y=5 [divided both sides by 3]</div>
<div> </div>
<div>That gives us our final answer: the ordered pair (2,3). If you were to plot the two equations on the same graph, you would find that the point (2,3) is where the two lines overlap.</div>
<div> </div>
<div>So that's one strategy. What about the others? We'll look at subtraction next. This strategy works almost the same way, with one exception. It's used when the identical term in both equations is either positive in both equations or negative in both equations. Take this pair of equations:</div>
<div> </div>
<div>2x-4y=6</div>
<div>7x-4y=31</div>
<div> </div>
<div>We see 4y in both equations, and both times the value is negative. This tells us to use subtraction. The process is almost identical to the previously described addition method with the exception that we're subtracting values. It's important to note that we can subtract the first equation from the second or the second equation from the first, so long as we do the same operation to both sides. In this case, I'm going to subtract the first from the second simply because the second equation has larger values.</div>
<div> </div>
<div>Left side</div>
<div>7x-4y-(2x-4y) [equation 2 - equation 1]</div>
<div>7x-4y-2x+4y [distributed over the quantity (2x-4y)]</div>
<div>5x-4y+4y [algebraic combination of 7x-2x]</div>
<div>5x [algebraic combination of -4y+4y]</div>
<div> </div>
<div>Right side</div>
<div>31-6 [equation 2 - equation 1]</div>
<div>25</div>
<div> </div>
<div>Set the two sides equal to each other, and solve for the remaining variable:</div>
<div> </div>
<div>5x = 25</div>
<div>x = 5 [divided both sides by 5]</div>
<div> </div>
<div>Again, we now take the value x=5 and plug it in to one of the original equations. It doesn't matter which equation we use, so I'll arbitrarily choose the first.</div>
<div> </div>
<div>2x-4y=6 [original equation]</div>
<div>2(5)-4y=6 [plugged in the value x=5]</div>
<div>10-4y=6 [multiplied 2×5]</div>
<div>-4y=-4 [subtracted 10 from both sides]</div>
<div>y=1 [divided both sides by -4]</div>
<div> </div>
<div>Again, we have an ordered pair: (5,1). As with the previous problem, if we plotted the two equations on one graph, the point (5,1) would be where they intersect.</div>
<div> </div>
<div>The last method of solving a pair of simultaneous equations is substitution. It would also have worked for either of the first two problems, but we didn't use it simply because the first two methods are easier and faster. Where we need to use substitution is cases that don't have an identical variable in both equations. Let's take this set of equations:</div>
<div> </div>
<div>3x+5y=38</div>
<div>8x-2y=40</div>
<div> </div>
<div>Seeing that we don't have any shared values between the two equations, we need to use substitution. There are a few steps involved here. First, we need to choose either of the equations to start with. I'm going to use the second one for the reason that its numbers are all multiples of 2, which will make it easier to manipulate. Ultimately, I could have used the first equation successfully as well. The second step is to isolate the value x or y. I'm going to isolate y because at first glance, doing so will mean I don't have to deal with fractions, which makes my life easier.</div>
<div> </div>
<div>8x-2y=40 [original equation]</div>
<div>-2y=40-8x [subtracted 8x from both sides]</div>
<div>y=-20+4x [divided both sides by -2]</div>
<div>y=4x-20 [rearranged the right side to make it easier to work with]</div>
<div> </div>
<div>Now we'll take this equation, and substitute it into the other equation for y. In this case the other equation means the first. If I solved for x, I would substitute in for x and things still would have worked out fine.</div>
<div> </div>
<div>3x+5y=38 [original equation]</div>
<div>3x+5(4x-20)=38 [substituted the quantity (4x-20) for y]</div>
<div>3x+20x-100=38 [distributed 5 across the quantity (4x-20)]</div>
<div>23x-100=38 [algebraic combination of 3x+20x]</div>
<div>23x=138 [added 100 to both sides]</div>
<div>x=6 [divided both sides by 23]</div>
<div> </div>
<div>Don't forget, we're only halfway done! Now we take the value x=6 and substitute it into one of the original equations to solve for y. As before, it doesn't matter which of the two original equations so I'll arbitrarily choose the first.</div>
<div> </div>
<div>3x+5y=38 [original equation]</div>
<div>3(6)+5y=38 [plugged in the value x=6]</div>
<div>18+5y=38 [multiplied 3×6]</div>
<div>5y=20 [subtracted 18 from both sides]</div>
<div>y=4 [divided both sides by 5]</div>
<div> </div>
<div>And there we are. Our final answer is the point (6,4). Like in the previous examples, this is the point where the two lines intersect if the equations were plotted on a graph.</div>
<div> </div>
<div>There is one exception to the rule about choosing one of the three methods. If you can manipulate or both equation so that they have an identical value, you can use either addition or subtraction instead of substitution. For example, take these simultaneous equations:</div>
<div> </div>
<div>x-5y=40</div>
<div>7x-2y=9</div>
<div> </div>
<div>In this case, substitutions would be the best method, particularly because of how easy it would be to isolate the variable x in the first equation. However, if you wanted, you could also manipulate one or both equations so that they contain an identical variable. Looking at both equations I immediately see that multiplying the first equation by 7 would give us the value 7x in both equations. So let's do that. Remember, you need to multiply both sides of the equation by the same value to preserve its validity.</div>
<div> </div>
<div>7(x-5y)=7(40)</div>
<div>7x-35y=280</div>
<div> </div>
<div>Which now gives us a new pair of "original" equations.</div>
<div> </div>
<div>7x-35y=280</div>
<div>7x-2y=9</div>
<div> </div>
<div>These equations may now be solved using subtraction.</div>
</div>Sun, 22 Jun 2014 11:31:27 -05002014-06-22T11:31:27-05:00271953https://www.wyzant.com/resources/blogs/271953/how_many_practice_sats_should_you_takeHuzefa K.https://www.wyzant.com/resources/users/view/84571890How Many Practice SATs Should You Take?<div>Practice is the key to SAT mastery. No matter what preparatory course you take, what tutor you hire, or what study guides you purchase, all of your resources are for naught if you don’t devote significant time and effort towards practice exams.<br /><br />Knocking out a healthy load of practice tests is particularly important for standardized exams. Why? Because standardization means that the test makers (a.k.a. the College Board) are bound by an obligatory adherence to consistency. As such, from year to year, while the precise questions vary, the core subjects and concepts are constant. Moreover, the style of questions is uniform. Translation: the more questions you see, the fewer curve balls can be hurled your way. With enough practice, you can familiarize yourself with the majority of possible question types, which will (1) improve your test taking abilities and (2) bolster your confidence come test day.<br /><br />Another reason why practice tests are so important is that they are excellent learning tools. It’s one thing to know a concept, but it’s another thing entirely to put that concept into use. The more practice you get, the more comfortable you will be with the material. Additionally, if you are diligent with your post-practice test review of missed questions, you can effectively fill in knowledge gaps in a very targeted and efficient manner.<br /><br />Point made: practice tests are extremely important. But how many should you take? What is the magic number to achieve SAT stardom?<br /><br />Stop. Hold up. Before you read any further, recognize that results can vary wildly depending on education level, familiarity with the tested concepts, and overall test taking abilities. There might be some standardized test wunderkinds who can nail down stellar scores with little to no practice. Alternatively, some students may need to rack up a hefty number of practice tests before their scores begin to climb. So, this is a highly nuanced question. But if I were pressed to give general advice without a proper consultation or additional information, I would err on the side of excess. Basically, I would suggest taking as many as humanly possible.<br /><br />Now, if you insist on pinning me down for a precise number, here it is: 15. That’s right, 15 practices tests is my minimum number. I took 15 practice SATs when I was a high school student, and if you plan right, you can do it too. And I didn’t take 15 tests while watching TV and eating ice cream. Nope. Instead, I replicated exam center conditions each and every time I sat down to take a test. Plus, I graded each one promptly and read through the answer explanations for all of my missed questions.<br /><br />I've read a number of test prep sites that recommend taking four or five practice SATs during the course of preparation. If you are sincerely shooting for excellence, this simply will not do you justice. The reason why 15 is such a powerful and practical number is because it is around this point where you truly hit your stride. I can't precisely explain why, I can only tell you that I've witnessed it over and over again. The tipping point generally occurs for students somewhere around the ninth or tenth test. It is at this mark of progress that students begin to feel at ease with the test format. After this point is reached, the remaining tests firm up any lingering weak spots and forge a stable and confident mindset. It simply works.<br /><br />If you have additional time to prepare for the SAT, I would push for even more practice tests. Say, for example, that you’re studying over the summer. In that case, I recommend squeezing in 25-30 exams. That’s approximately one every three days.<br /><br />If you want to practice like a champion but don’t know where to locate the practice tests, there is an abundance of resources that can provide you with the requisite material. Below are four study guides that contain high quality practice SATs.<br /><br />1. <span style="text-decoration: underline;">The Official SAT Study Guide</span> – this book comes with an overview of each subject along with 10 full-length practice tests. These are the best tests you will find because they are authentic SAT exams.<br /><br />2. <span style="text-decoration: underline;">Gruber’s Complete SAT Guide</span> – this guide has five full-length tests along with strategies and key vocabulary words.<br /><br />3. <span style="text-decoration: underline;">11 Practice Tests For The SAT</span> – this book has a lot of practice problems that are really good representations of what you will find on the real test. It actually only contains 10 SATs (as one of the 11 practice tests is a PSAT).<br /><br />4. <span style="text-decoration: underline;">Barron’s SAT</span> – this book comes packed with a high quality diagnostic plus five full-length SATs.</div>Thu, 08 May 2014 12:57:55 -05002014-05-08T12:57:55-05:00270808https://www.wyzant.com/resources/blogs/270808/sat_prep_tackling_tough_math_questionsHuzefa K.https://www.wyzant.com/resources/users/view/84571890SAT Prep - Tackling Tough Math Questions<div>Nailing an 800 on the math portion of the SAT can be a tricky feat, even if you are steadfastly familiar with all of the requisite formulas and rules. A difficult problem can overwhelm even the most prepared individual come test day. Time constraints, test surroundings, and the overall weight of the exam can unnerve the most grounded students.<br /><br />So what do you do when panic strikes and your mind draws a blank? How do you re-center yourself and charge forward with ferocity and confidence? What you do is this: write everything down from the problem. This is the most important part of the problem solving process. As you peruse the question, write down the pertinent data and establish relationships by setting up equations. This exercise will help you see solutions that were previously difficult to decipher.<br /><br />As you work on practice tests and sample problems, you must work diligently to form a solid habit of writing down important bits of information as you plow through the SAT math section. To give you an example of what it means to “write everything down from the problem,” I will explore the following three math questions in great detail. These in-depth explanations will give you an idea of what should be going through your brain every time you see a math problem. With practice, these thoughts and processes will manifest faster and faster until solving problems in this fashion becomes a reflexive response.<br /><br /> <span class="greenText">1. The average of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?</span><br /><br /><span class="greenText">a. 1</span><br /><span class="greenText">b. 19</span><br /><span class="greenText">c. 29</span><br /><span class="greenText">d. 30</span><br /><span class="greenText">e. 33</span></div>
<div> </div>
<div>Right off the bat, the problem states that we have four different integers. We can begin the problem by creating variables to represent the four integers:</div>
<div><br />W X Y Z<br /><br />We also know that the average of the integers is 75. This means that we can set up another equation based on this relationship:<br /><br />(W + X + Y + Z)/4 = 75<br /><br />Isolating the variables, we get:<br /><br />W + X + Y + Z = 300<br /><br />We also know that the largest integer is 90. So:<br /><br />W + X + Y + 90 = 300<br /><br />The question then asks “what is the least possible value of the smallest integer?” This detail is a bit tricky to interpret, but we can reason this out fairly quickly. To get the smallest possible number, what needs to be true about the other two integers? They need to be as large as possible. Since 90 is the highest value for the integers, it makes sense to assign the other two variables to 90, right?<br /><br />Not so fast. If we read the question carefully, it says that there are “four different integers.” This restricts us from using 90 for the other two values. Instead, we must use 89 and 88. We now have an equation to represent the four integers (where W = the smallest integer):<br /><br />W + 88 + 89 + 90 = 300<br /><br />Solving algebraically, we get:<br /><br />W + 267 = 300<br /><br />W = 33<br /><br />Therefore, the final answer is <strong>e</strong>.<br /><br /><span class="greenText">2. Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume? </span><br /><br /><span class="greenText">a. 250/3</span><br /><span class="greenText">b. 500/3</span><br /><span class="greenText">c. 400</span><br /><span class="greenText">d. 480</span><br /><span class="greenText">e. 600</span></div>
<div> </div>
<div>Let’s start writing down the relevant information:<br /><br />.1X = AX<br /><br />.3Y = AY<br /><br />The above equations denote the amount of alcohol given a certain number of milliliters of solution (where AX = alcohol for X, AY = alcohol for Y, X = milliliters of solution X, and Y = milliliters of solution Y). The next part of the question asks how many milliliters of Y must be added to 200 milliliters of X to create a solution that is 25% alcohol? To answer this, we can represent the facts as an equation:<br /><br />.3Y + .1X = .25(X + Y)<br /><br />Once again, we have a two variable equation. Translation: we cannot solve it. But, we have a value for X: 200. So, plugging in 200 for X, we get the equation down to one variable:<br /><br />.3(Y) + .1(200) = .25(Y + 200)<br /><br />Perfect. Solving for Y algebraically, we get:<br /><br />.3Y + 20 = .25Y + 50<br /><br />.3Y - .25Y = 50 – 20<br /><br />.05Y = 30<br /><br />Y = 600<br /><br />Therefore, the answer is <strong>e</strong>.<br /><br /><span class="greenText">3. On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test? </span><br /><br /><span class="greenText">a. Cannot be determined</span><br /><span class="greenText">b. 16</span><br /><span class="greenText">c. 19</span><br /><span class="greenText">d. 21</span><br /><span class="greenText">e. 24</span></div>
<div><br />The first step is to write down what we know and assign variables:<br /><br />+9 points = correct (X)<br /><br />-7 points = incorrect (Y)<br /><br />Sally scored a total of 0 points<br /><br />We can set up an equation with this information:<br /><br />9X – 7Y = 0<br /><br />Since we have two variables, this is not a solvable problem. Unfortunately, we do not have another relationship that we can reference to simplify this further. What can we do in this situation? When all else fails, try to isolate the variables:<br /><br />9X = 7Y<br /><br />X/Y = 7/9<br /><br />What this tells you is that the ratio of questions answered correctly and incorrectly must be 7 correct (X) to 9 incorrect (Y). This is very useful information. According to this ratio, the number of questions on the test must be some multiple of 16 (so that the 7 to 9 ratio can be preserved). For example, 7 right and 9 wrong would work, as would 14 right and 18 wrong.<br /><br />Now comes the critical piece of information: the total number of questions must be less than 30. With this helpful tidbit, the only possibly choice is 16 questions.<br /><br />Therefore, the answer is <strong>b</strong>.</div>Tue, 29 Apr 2014 02:21:39 -05002014-04-29T02:21:39-05:00269243https://www.wyzant.com/resources/blogs/269243/preventing_silly_mistakes_on_the_sat_and_actHuzefa K.https://www.wyzant.com/resources/users/view/84571890Preventing Silly Mistakes On The SAT And ACT<div>The “silly mistake” is quite possibly the most mischievous and irksome of the math demons. It is a sly beast that lurks in the deepest recesses of your mind, emerging only periodically to sully your scores in a most disturbing way. Because of its crafty nature, it is able to lull you into the false belief that your thorough understanding of mathematic concepts will keep you safe from its clutches. But, as I’m sure you know, “silly mistakes” afflict even the most soundly prepared students.<br /><br />What exactly constitutes a “silly mistake?” Here are some common examples for standardized tests:<br /><br />Misreading the question (or failing to read the entire instructions)<br />Filling in the wrong bubble on your answer sheet<br />Making a slight arithmetic error<br />Incorrectly copying down the original problem<br />Turning a negative number into a positive number (or vice versa)<br />I don’t care who you are, what your educational background is, or where you go to school… you have been a victim of “silly mistakes” at one time or another. The whole fiasco probably went down like this: you whizzed through an exam with utter confidence, only to receive a shocking and confusing grade. Why? Because you missed several questions that you were sure you had answered correctly. You glossed over some inane details that ended up costing you a slew of points despite your clear understanding of the concepts.<br /><br />When it comes to standardized tests like the ACT and SAT, silly mistakes are just as costly as any deep conceptual misconstruing. Accordingly, it is imperative that you devote substantial resources to ensure that these mistakes are weeded out.<br /><br />At the end of the day, extricating these little demons comes down to a few core principles and strategies. Here are five quick tips on how to tackle these nuisances once and for all.<br /><br />1. <strong>Read Each Question Prompt Carefully</strong> - the most common source of errors is the misreading of test questions. When time constraints are a factor, you will likely be racing the clock, pushing your reading pace to its limits. While speedy reading is important, you must figure out where to draw the line between speed and accuracy. My advice is to read each question prompt slowly and carefully before jumping to the answers. If time warrants, I would take two passes through the prompt. The more certain you are of the actual contents of the question, the far less likely you will be to make a mistake.<br /><br />2. <strong>Write Clearly And Neatly</strong> - As you work through problems on the mathematics section, you will be writing down notes and equations as you make your calculations. If you tend to write in a jumbled fashion, you will be setting yourself up for disaster. You need things to flow clearly and neatly from step to step so that you are able to properly decipher the right answer. A few tips for writing clearly are to (a) always write in straight lines, (b) progress downwards as you move forward with your work, (c) use clear handwriting, and (d) don’t write too small. The most important factor to developing a solid habit of writing clearly and neatly is to practice. As such, make the extra effort to keep your daily homework neat and organized.<br /><br />3. <strong>Master Time Management</strong> – as time begins to run out, you are more likely to make mistakes. Why? Because your speed will increase along with your anxiety, making you much more error prone. To counteract this natural tendency, make sure that your time management skills have been properly honed. The only way to accomplish that is to include many timed practice exams before the actual test. During the timed practice exams, keep an eye on where you are and how much time is left. The SAT math section, for example, has 54 questions that must be completed in 70 minutes. As you are going through the test, you can see how many problems you have finished at the 17.5-minute mark. Then, at the halfway mark, you can check your progress again. Keep in mind that you should ideally be more than halfway through the math section at 35 minutes because the math questions increase in difficulty as you move forward.<br /><br />4. <strong>Verify The Question Number In Your Test Booklet Before Filling In Your Answer Sheet</strong> – there is nothing more frustrating than getting a question wrong because of a misplaced answer. But the solution to this problem is quite simple. All you need to do is get in the habit of verifying the question number each and every time. Most kids get accustomed to deriving and answer and then filling in the next empty row of bubbles on the answer sheet. That method can get you into trouble if you inadvertently skip a question. To be safe, always verify the question number.<br /><br />5. <strong>Practice, Practice, Practice</strong> – the more exams you take, the less likely you will be to misread or miscalculate something. Every error on a practice test is a terrific learning opportunity. Those mistakes will be etched in your brain as constant reminders of what not to do in the future. The more of these practice tests that you rack up, the less likely you are to make mistakes on the real exam. Moreover, getting in substantial practice will calm your nerves come test day. Less anxiety = better overall performance.<br /><br /></div>Mon, 14 Apr 2014 22:32:57 -05002014-04-14T22:32:57-05:00266077https://www.wyzant.com/resources/blogs/266077/what_to_watch_out_for_on_standardized_testsAntonio B.https://www.wyzant.com/resources/users/view/84753940What to Watch out for on Standardized Tests<div>Hey folks, I am sure many of you have plans of going to college or finishing up that last hectic year of school. Well with these endeavors comes not only tests and quizzes created by books and your professors/teachers, but you also have to take nation and statewide test in order to pass and/or qualify for a position in a higher learning institute. Such tests include the SAT, ACT, MCAT, etc. What you want to remember about taking these tests is that these tests are testing you ability to locate small mistakes and easy to miss information. They also want you to understand this material. You have to be prepared for these easy to miss situations. For example, I am sure you all have done a math question, felt like you did it perfectly correct only to find out that you actually got it incorrect. Furthermore, the answer you got appeared as one of the answer choices! Or you were on the right track to answering correctly, but made a simple math error (arithmetic or sign) and got it wrong and the correct answer turned out to be something else. Those type of questions are the ultimate test of understanding and they trick you into thinking you have the right answer when in actuality you don't. They place those wrong answers in as one of the answer choices because they have done the problem and they have found most ways of executing the problem that actually makes sense and stuck those answers in the answer choices, leaving you guessing wildly if you do not understand the problem. So we must be careful what we do, always take your time, and go back and check work and answers if time allows. This is a very important concept to be aware of when taking standardized tests. Remember, one test does not define who you are! Good luck!</div>Fri, 21 Mar 2014 10:23:33 -05002014-03-21T10:23:33-05:00