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.Sun, 22 Oct 2017 15:27:38 -0500https://www.wyzant.com/images/logos/wyzant-logo.pngSAT Math Articles - Wyzant Tutor Blogshttps://www.wyzant.com/resources/blogs/sat_mathhttps://www.wyzant.com/resources/blogs/sat_math539644https://www.wyzant.com/resources/blogs/539644/what_it_was_like_to_take_the_satJoey L.https://www.wyzant.com/resources/users/view/86703409What it was like to take the SAT<div><strong>Getting Started</strong></div>
<div><br />I took the exam at Irvine Valley College.<br />Unlike most schools, whose administrators post classroom assignments on a billboard, IVC showed up around 8:15, had students stand in the quad, and verbally had students split into separate groups like cattle. Then students ended up having to walk down a confusing pathway to a classroom, where we had to have our IDs checked one-by-one. You can tell which schools have the check-in process down, and which schools need to work on it. IVC is definitely a school that can stand to be more efficient.</div>
<div><br />Once in the room, the proctor had difficulty with the test set-up process. She was unaware of the fact that there were now three components that come with the exam. It used to be that there was just a test booklet and an answer sheet. Now, with the revised exam, there is an essay booklet as well. I don’t think that she was supposed to hand out the essay booklet at the beginning of the administration, especially because it wasn’t sealed.</div>
<div><br />All-in-all, the exam didn’t start until about 9:00am, almost an hour after most administrations start.<br />For students who value efficiency and timeliness, I would recommend that you stay away from Irvine Valley College (as well as UCI) when taking the SAT.</div>
<div><br /><strong>Reading Comprehension:</strong><br />I was intrigued to see that there was a variety of reading passages. Similar to the old exam, there was still prose fiction as well as a persuasive essay, but I also read a coupe essays about topics that were much more contemporary and relevant to today’s students.</div>
<div><br />In addition, some of the contemporary passages required a new level of data analysis. As College Board promised, there were questions that asked students to analyze graphs (akin to ACT science). Interestingly enough, though, these data was paired with passages that were more argumentative in nature. Furthermore, the evidence used within these passages was more quantitative in nature. I wish I would be more specific, but I do not want to incur the wrath of College Board for sharing classified test questions. I can say this though. It used to be that the passages used rhetoric strategies to try to convince the reader of a certain argument. Now, it seems some of the passages will build their arguments using data, research, and analysis of that research.</div>
<div><br />From the perspective of a teacher, I view this as promising as most students will be required to utilize this skill at some point in college. Most majors require some type of statistical analysis as well ability to dissect a modern-day argument. The range of reading material is more varied and, in my opinion, less esoteric in nature.</div>
<div><br />There was still a level of trickiness to the new exam. There is a new question type: the evidence-based question (i.e., “Which line best supports the answer to the previous question”). This type of question requires students to not only answer a question but also select a line reference as justification for choosing the previous answer.</div>
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<div>For example.<br />1. What does the passage suggested about the authors feelings about candy:<br />A. He hates it<br />B. He likes it<br />C. Candy punched him in the face<br />D. He has a deathly fear of candy</div>
<div><br />2. Which choice provides the best evidence for the answer to the previous question?</div>
<div><br />A. Lines 1-2<br />B. Lines 3-10<br />C. Lines 11-12<br />D. Lines 39-60</div>
<div><br />At times, I looked for a certain answer but couldn’t find it. After reading the line references, I realized that the idea that I was searching for wasn’t even included among the answer choices. Eventually, I reached a certain rhythm answers these questions. However, after going back to check my answers, I realized that although there were about 5 or 6 questions that were started with the phrase “Which choice provides the best evidence…” not all of them referenced the previous question. I had seen line references in the answer choices and assumed that they referenced the previous question.</div>
<div><br /><strong>Grammar</strong><br />It has always been my firm belief that the SAT grammar is just the sibling to the ACT English section. After taking the test, my conviction has not wavered. Except for a couple small nuances, the fundamental components of both tests were quite similar – I saw many of the same question types, and the structure of the tests were quite similar.<br />However, one of the major distinguishing components that still distinguishes the SAT from its counterpart is the wording. The majority of the grammar portion I found quite simple. However, a couple questions I did find a bit weird due to strange word choice/diction.</div>
<div><br /><strong>Non-Calculator Math</strong><br />I have always found calculators a crutch to most students, so I am happy with the addition of the SAT Math without calculator. Strangely enough, even though the practice tests have indicated that they have ventured into more advanced topics, there wasn’t anything particularly advanced that caught my attention. I don’t remember having to deal with any trigonometry questions and I don’t necessarily remember having to answer questions that involved advanced pre-calculus topics.<br />The one thing I did not about this section was that having the ability to graph equations to solve visually was something that helped me check my work.</div>
<div><br /><strong>Calculator Math</strong><br />Here, I found myself having to solve problems that I would in real life. Just in general, I would say that the questions have veered toward multi-step, intricate algebra problems. For a couple of the problems, I found myself having to do five or six different steps to arrive at the answer.</div>
<div><br />In general, I was really pushed to work on problem solving and really understanding what an equation means. My firm belief is that most math students survive high school math by memorizing formulas one after the other. The SAT question combats that by asking questions that push students to understand what a graph, table, or equation really represents. Very few questions were as straightforward as they are on the ACT. The content matter is relatively straightforward; the applications, though, are quiet challenging.</div>
<div><br />The other part that I found a bit unnerving was the rounding of decimals. Some of the questions ended up not being as “clean” as some math problems are. I ended up with weird decimals and then had to round to the nearest whole number. While I’ve had to do that in the past, something about this format bothered me.</div>
<div><br /><strong>The Essay</strong><br />This new essay was quite fun to write about. I think that I had such a difficult time with AP English Language as a Junior, that I am so much happier writing this essay as an adult. I loved being able to analyze his technique in writing and I am curious to see how my essay turns out.</div>
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<div>Oh. I got a 1600.</div>Sun, 16 Apr 2017 15:01:59 -05002017-04-16T15:01:59-05:00488939https://www.wyzant.com/resources/blogs/488939/ellen_s_choice_applying_my_rules_for_effective_time_management_to_the_sat_part_2_break_timeEllen S.https://www.wyzant.com/resources/users/view/75479140Ellen's Choice: Applying my Rules for Effective Time Management to the SAT, part 2: Break Time!<div><span class="citation">Ellen's Rules for Effective Time Management, Part 2</span><br /><br /><span class="citation">3. Know when it’s time to take breaks.</span><br /><span class="citation">Spending a good chunk of time on one subject is good; it helps you settle into a rhythm and lets your brain get into the correct frame of reference for the subject. But there exists a horizon beyond which no progress can or will be made. It’s the point at which your brain has become over-saturated with the current material, and if you continue on you’ll just end up working yourself into circles of frustration. In paper writing, it’s the point at which anything you wrote would make sense to you regardless because you’ve been reading the same few paragraphs to yourself for hours. In math, it’s the point at which you will just end up confusing yourself more and more as you try desperately to work it out. When that moment arrives, you know it’s time to take your break.</span><br /><br /><span class="citation">4. TAKE BREAKS.</span><br /><span class="citation">I don’t care how much work you have, there’s always enough time for a fifteen-minute break. The trick is making sure that that fifteen minutes doesn’t turn into two hours. Stick to your schedule, take your breaks when you need them (and take one every couple of hours even if you don’t think you need one), and you’ll stay refreshed and energized much longer.</span><br /><span class="citation">And on those days when you’re fortunate enough to have plenty of time to finish something, take advantage of the time to take more breaks. Feeling confused about that one paragraph in your paper you can’t seem to get right? Stop writing and go take a walk. Let your mind forget completely about your paper for an hour or so. Then come back and you’ll have a much better idea of how to progress. Sometimes, especially with paper-writing, you just have to give it time to process.</span><br /><br />Once again, these rules apply to studying for standardized tests just as much as any other subject, but with a slight twist. My rule of thumb for studying for a standardized test is to simulate test conditions as much as possible as often as possible during the studying process. For a standardized test, this often means timed drills. Before the big SAT redesign of this past year, the SAT was comprised of nine sections averaging 30 minutes each, which meant practicing staying focused for 30 minutes and then quickly switching subjects. After the redesign, though, it works much more like the ACT, with fewer sections that are much longer, keeping each subject confined to one section. Now, the strategy is to practice maintaining concentration for an hour at a time. Take the first of the two points above. That horizon beyond which no progress can be made? We want to train that horizon to happen after the section is over, not in the middle of it. So practicing with a timer, noticing when your personal point of no return is, and adding just a few problems each successive time can help to extend your concentration past the end of the section, when it's okay to stop thinking about it.<br /><br />The second of those two points is important as well, though once again, on test day you don't get to choose when you take breaks. You'll be given a short break, possibly two, between sections at a predetermined time in the test. Training yourself to shrug off the previous section and start the new one with fresh eyes is important, because strictly speaking you'd want to take more breaks than the test allows you. Learn to give yourself a tiny break, even if it's just five seconds with your eyes closed, to help re-center in between sections on the test. Even within a given section – if you're one of the lucky ones who doesn't struggle with finishing in time, that gives you more time to take mini-breaks. Take a moment between passes through the section or after a particularly daunting problem to shake it from your mind. No use dwelling on question 13 when there's 45 more of them and you won't get any new information from mulling it over and over.<br /><br />Stay tuned for part 3: Mix and Match!</div>Mon, 03 Oct 2016 09:38:28 -05002016-10-03T09:38:28-05:00474237https://www.wyzant.com/resources/blogs/474237/mathematical_journeys_occam_s_razor_and_sat_mathEllen S.https://www.wyzant.com/resources/users/view/75479140Mathematical Journeys: Occam's Razor and SAT Math<div>I mentioned this problem from one of my earliest blog posts with one of my students last week, so I thought I'd bring it back as this week's Math Journey. Enjoy!</div>
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<div>The SAT messes with your head. Don't feel embarrassed, it messes with everyone's head. It's designed to. The SAT is a test of your critical reasoning skills, meaning it's actually far more about logic and figuring out the correct course of action than it is about actually knowing the material. This is nowhere more evident than on the Math section.<br /><br />The SAT Math trips up so many students because they expect it to behave like a math test. The truth is, the SAT Math is about figuring out how to answer each problem using as little actual math as possible. It's all about working quickly, and the questions are structured such that they conceal the quick logic and context-based route behind the facade of a more complicated math question. They're trying to psych you out; to make you think the problem is harder than it is. In math class you're taught to be thorough, to show your work and not leave out any steps. On the SAT, it's not only possible but downright preferable to solve as many questions as you can without ever picking up your pencil.<br /><br />Let's take an example that caught me on the first go-round.<br /><br /><br />If a + b = 3 and ab = 4, what is (1/a) + (1/b) ?</div>
<div><br /><br />Since you have two equations with two variables, your first instinct might be to treat them as a system of<br />equations. Namely, solve one for a, plug the result in for a in the other one, get it into quadratic form and solve from there, then use the newly-found roots in place of a and b in the final equation. If you take the time to go through the problem this way, you find that your answer is almost one of the options, but the sign is wrong (your answer is negative when the answer choice is positive). This can frustrate you to no end and cause you to waste precious minutes of your testing time checking and rechecking your math. The intended course of action is much simpler.<br /><br />What the SAT wanted you to do with that problem is to just look at the last expression, the one you're trying<br />to find. How would you normally add two fractions with different denominators? You'd find the lowest common denominator and multiply, right? So just treat the variables as you would numbers:<br /><br />(1/a) + (1/b) = (b/ab) + (a/ab) = (a + b)/(ab)<br /><br />By now you should have noticed that both the numerator and denominator of this final expression are<br />identical to the first two equations they gave you. All you have to do is plug them in.<br /><br /><span style="text-decoration: underline;">a + b</span> = <span style="text-decoration: underline;">3</span><br /> ab 4<br /><br />And that's literally it. They knew you'd over-think it if they set it up to look like a system of equations rather than simply an algebraic manipulation where they happened to give you the answers in the problem. They also knew you'd likely taken advanced algebra and trig, and would probably forget that the test doesn't cover those topics. The realization that it looks like a system of equations, and that you know how to solve those, would push you into starting the (somewhat long) procedure and it wouldn't occur to you to find a simpler way. Since their goal is to trip you up, make you waste time, psych you out, and mess with your head, they'll do everything they can to camouflage the quick shortcut behind big scary problems. <br /><br />It's helpful to remember Occam's Razor; the simplest solution to a problem is usually the best one. Always look for the common-sense answer, and remember not to over-think it. This is also why I think it's beneficial for a student to go into the SAT with an attitude of healthy indignation and skepticism; if you're always looking for the traps, you'll be less likely to fall into them. Rather than getting frustrated, if you can see the trick question coming and confront it with a “Seriously?!” you'll be better prepared to deal with it.</div>Tue, 16 Aug 2016 07:10:02 -05002016-08-16T07:10:02-05:00411907https://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/sat_free_practice_testsPaul J.https://www.wyzant.com/resources/users/view/85606071SAT - Free Practice Tests<div>Please find the link below to free practice SAT Tests</div>
<div> </div>
<div>http://prep.ivyglobal.com/sat/practice_tests.asp</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>
<div> </div>
<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>
<div> </div>
<div>3. I give students some tools for instant relaxation, which they all enjoy learning.</div>
<div> </div>
<div>4. Often, especially with anxious students, I help them with visualization of a successful test report coming in the mail!</div>
<div> </div>
<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>
<div> </div>
<div>Re how I tutor for math: </div>
<div> </div>
<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>
<div> </div>
<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>
<div> </div>
<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>
<div> </div>
<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 -06002015-01-06T11:41:10-06:00287074https://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>
<div> </div>
<div><strong>Should you guess?</strong></div>
<div>
<ul>
<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>
</ul>
<div> </div>
<div><strong>Should you omit questions?</strong></div>
<div>
<ul>
<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>
</ul>
<div> </div>
<div><strong>Should you answer questions in order?</strong></div>
<div>
<ul>
<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>
</ul>
<div> </div>
<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>
<div> </div>
<div>That's all for this post. More strategies to come in the future!</div>
</div>
</div>
<div> </div>
</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>
<div> </div>
<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>
<div> </div>
<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>
<div> </div>
<div>To solve simultaneous equations, we can use three strategies.</div>
<div><ol>
<li>Addition</li>
<li>Subtraction</li>
<li>Substitution</li>
</ol>
<div> </div>
<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>
<div> </div>
<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>
<div> </div>
<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>
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<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 -05002014-04-29T02:21:39-05:00