Chp 9 Introduction To The Act Mathematics Test Chapter 9
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Chapter 9<br />Introduction to the ACT Mathematics Test<br />
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The second section of the ACT will always be the Math test<br />This chapter will familiarize you with the structure and strategy of the ACT Math test.<br />
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33 ALGEBRA QUESTIONS<br />There are usually 33 Algebra questions : these include<br />14 pre- Algebra questions based on<br />Integers, prime numbers, rules of zero, order of operations, and multiplication of fractions and decimals<br />10 elementary algebra questions based on<br />Inequalities, linear equations, ratios, percents and averages<br />9 intermediate Algebra questions based on<br />Exponents, roots, simultaneous equations, and quadratic equations<br />
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23 GEOMETRY QUESTIONS<br />There are usually 23 Geometry questions<br />14 plane geometry questions based on<br />Angles, lengths, triangles, quadrilaterals, circles, perimeter, area, and volume<br />9 coordinate geometry questions based on<br />Slope, distance, midpoint, parallel and perpendicular lines, points of intersection and graphing<br />
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4 trigonometry questions<br />4 trigonometry questions based on<br />Sine, cosine and tangent functions, trig identities and graphing<br />
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ACT writers will not supply you with formulas<br />Questions are generally arranged from easy to medium to hard<br />Easy problems have one or two steps, a medium problem has two or three steps, a difficult problem has more than three steps<br />Still do problems you know your sure you can do on the first pass<br />Do problems you think you know how to do on the second pass<br />For seemingly impossible questions pick the letter of the day and move on<br />
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ONE STEP PROBLEM<br />Cynthia, Peter, Nancy and Kevin are all carpenters. Last week each built the following number of chairs. <br /> Cynthia-16 Peter – 45 Nancy – 74 Kevin – 13 <br /> What was the average number of chairs each carpenter built last week?<br />A. 39<br />B. 42<br />C. 55<br />D. 59<br />E. 63<br />
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HERE’S HOW TO CRACK IT<br />To find the average of a group of numbers, add the numbers together and divide by the number of terms.<br />In this case, the thing we don’t know is the average, but we know everything else, so let’s put the numbers into the formula. (Chp. 11 will cover this more fully)<br />The answer to the question is B<br />
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TWO OR THREE STEPS<br />Four carpenters built an average of 42 chairs each last week. If Cynthia built 42 chairs, Nancy built 74 chairs, and Kevin built 13 chairs, how many chairs did Peter build?<br />F. 24<br />G. 37<br />H. 45<br />J. 53<br />K. 67<br />
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HERE’S HOW TO CRACK IT<br />Let’s put the information we have into the same formula we used before.<br />Medium and difficult average problem often give you the number of terms and the average. What they don’t give you is the sum of the numbers to be averaged – a very important point.<br />
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If we multiply both sides by 4, we get the sum of all four numbers. <br />36 + 74 + 13 + Peter = 168<br />To find out Peter’s number of chairs, we just have to add the other numbers and subtract from 168. 168 – 123 = 45<br />The answer is H<br />
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MORE THAN THREE STEPS<br />Four carpenters each built an average of 42 chairs last week. If no chairs were left uncompleted, and if Peter, who built 50 chairs, built the greatest number of chairs, what is the least number of chairs one of the carpenters could have built, if no carpenter built a fractional number of chairs?<br />A. 18<br />B. 19<br />C. 20<br />D. 39.33<br />E. 51<br />
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HERE’S HOW TO CRACK IT<br />Let’s put what we know into the same formula we have used twice already<br />The only individual about whom we know something specific is Peter. We’ve represented the other three carpenters as x, y and z. Because the sum of all four carpenters’ chairs add up to 168, we now have<br />50 + x + y + z = 168<br />By itself an equation with three variables cannot be solved, so unless we can glean a little more information from the problem then we are stuck. It is time to put a circle around the problem and move on.<br />
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2nd PASS<br />Let’s assume we skipped the problem temporarily, and you have now come back to it after completing all the problems you thought were easy.<br />The problem asked for the least number of chairs one carpenter could have built. According to the problem, Peter constructed the most (50). <br />So lets say two of the other carpenters constructed 49 each (the most number of chairs they could have built and still have built less than Peter). By making carpenter z and y construct as many chairs as possible, we can find the minimum number of chairs carpenter z would have to make. <br />Now the problem looks like this:<br />50 + 49 + 49 + z = 168<br />So z = 20. The answer is (C). <br />
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BALLPARK<br />Cross out the crazy answers by using the Process of Elimination<br />What’s the average of 100 and 200<br />A. 500<br />B. 150<br />C. A billion<br />
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AVOID PARTIAL ANSWERS<br />Sometimes students think they have completed a problem before the problem is actually done<br />The test writers at ACT like to include trap questions for these students<br />
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How to Avoid Partial Answers<br />You can prevent yourself from picking partial answers by doing the following 3 things:<br />Slow down. It isn’t going to help do a problem so quickly that you miss important information and get the problem wrong.<br />Once you’ve read the question, underline what it’s really asking. Then go back and do the question piece by piece. If you find your reading the whole question over again STOP! You are not going to solve the problem all at once. Just take it one step at a time<br />When you finish the problem reread what you underlined to make sure you’ve answered the question.<br />
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You can and you should<br />ACT states that none of the test problems require a calculator, but the test writers clearly expect you to have a calculator. <br />Furthermore, there are plenty of questions on the test that will go much more quickly and smoothly if you know how to use your calculator properly.<br />TI-89 and TI-92 are NOT allowed on the ACT<br />For a complete list of acceptable calculators & rules go to http://www.actstudent.org/faq/answers/calculator.html<br />
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IF YOU DON’T HAVE A TI-83<br />Make sure that your calculator is acceptable for use on the test <br />And that it does the following:<br />Handle positive, negative and fractional exponents<br />Uses parenthesis<br />Graph simple functions<br />Convert decimals to fractions and vise versa<br />Change a linear equation into y = mx +b<br />
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RED HERRINGS<br />Of the 60 problems in the math section, several will contain extra information that is not necessary to solve the problem.<br />The test writers want to see if you can distinguish important information from filler<br />Because there are so few of these, it is not necessary to examine each new piece of information to determine if it is “extra”<br />In almost every problem on the ACT you will need all information given to solve it.<br />However, if you find yourself you find yourself starring at a number that doesn’t seem to have anything to do with the question you are doing, it might be a RED HERRING. <br />
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HERE’S AN EXAMPLE<br />Susan’s take-home pay is $300 per week, of which she spends $80 on food and $150 on rent. What fraction of her take-home pay does she spend on food?<br />A. 2/75<br />B. 4/15<br />C. ½<br />D. 23/30<br />E. 29/30<br />
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HERE’S HOW TO CRACK IT<br />The last lines tells you what you need to do. A fraction is a part of a whole and in this case, the whole is $300. <br />WHICH REDUCES TO<br />Where does the $150 fit in? <br />It doesn’t. The writers just threw that in to confuse you.<br />Notice that if you got confused and found the fraction of the take-home salary that was paid in rent, $150/$300, you would have picked (C). The correct answer is (B). <br />
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WHAT’S THE RED HERRING IN THIS SERNARIO?<br />
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USE TRIAGE & ESTABLISH A TWO-PASS SYSTEM<br />On the first pass actively search for questions that only require a few steps and/or deal with topics that you find manageable.<br />Save some multiple-step, unfamiliar, or difficult questions for your second pass. As time runs out, or if a question seems exceedingly difficult, pick a Letter of the Day and invest your time in something more worthwhile.<br />
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USE POE TO ELIMINATE WRONG ANSWERS<br />Incorrect answers are sometimes partial answers – answers you arrive at on the way to the final solution.<br />Frequently you can eliminate answer choices because they are no where near what common sense says the answer would have to be.<br />Incorrect answers are sometimes based on red herrings – pieces of information that are not necessary to solve the problem.<br />
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TAKE BITE-SIZE PIECES<br />Use the space in your test booklet to translate each sentence into its math equivalent.<br />Be sure to label your information to avoid confusion.<br />
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THERE’S NO PENALTY FOR GUESSING<br />Be sure you put an answer down for every question.<br />Even the ones you don’t have time to do.<br />There is no penalty for wrong answers. <br />
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