SAT数学：Math IC Algebra Strategies

1、SAT数学：Math IC Algebra Strategies    Math IC Algebra Strategies There are several ways to answer most algebra problems You could try to solve a problem by using standard algebra and setting up and solving an equation Alternatively， you could try to avoid algebra and simply pl

2、ug the answer choices back into the question until one of them works out Or you can pick numbers to substitute into the various expressions given as answer choices None of these methods is necessarily better than the others Remain flexible in your approach to each question and choose the method that

3、 best suits the problem For a problem you know how to solve， using algebra is probably the quickest method In contrast， a tough problem that you are unsure how to solve might become easy if you try to plug in some answers When you study your practice tests and look over the algebra questions you got

4、 wrong， you should think about the method you employed Did you plug in answers when you should have used algebra? Did you use algebra when you should have plugged in answers?Well lay out for you the different problemsolving approaches and tell you all you need to know about them Then you can decide

5、for yourself which method to chooseLets use a sample algebra problem to illustrate these separate approaches： A baseball player travels from his home city， Jasonville， to Giambia City for a baseball game He drives at 50 miles an hour After the game， he travels back home and takes a flight that

6、travels at 500 miles an hour If the distance from Jasonville to Giambia City is 250 miles， and it took him j hours longer to drive than to fly， what is j? （A）1（B）35（C）4（D）45（E）12 Using AlgebraThis question is a simple rate problem that can be solved with a few basic equations Since traveli

7、ng time distance speed， it took him：to drive to Giambia City To find the duration of his flight， we use the same rate formula：It took the player：longer to drive D is the correct answerPlugging In AnswersSometimes you might not be sure how to approach a problem or dont have the time to think out the

8、proper equations In such instances， plugging in might be the best method for you， especially as you come across the more difficult questions at the end of the test All you have to do is substitute the answer choices back into the problem， and see whether the given information holds true The process

9、of plugging in is simple First， you should make full use of the fact that the answer choices on Math IC are always presented in ascending value So start by plugging in answer choice C， since if it doesnt turn out to be the answer， you can usually tell whether to try a smaller or larger answer choice

10、 Now， to solve the question： it takes the baseball player 25050 5 hours to drive to Giambia City So， if it takes him C 4 hours more to drive， than it takes him 5 4 1 hour to fly back to Jasonville But the question tells us that in 1 hour， he could fly 500 miles Therefore， it must take him longer tha

11、n 4 hours more to drive than to fly Next， we try D 45 It takes him 5 45 5 hours to fly， which means that he travels 5005 250 miles on his flight D is the answer Picking NumbersPicking numbers is a variation of plugging in and should only be used when the answer choices contain variables A modified v

12、ersion of our original sample question shows what kind of problems might lend themselves to picking numbers A baseball player travels from his home city， Jasonville， to Giambia City for a baseball game He drives at m miles an hour After the game， he travels back home， and takes a flight instead

13、 at p miles an hour If the distance from Jasonville to Giambia City is v miles， and it took him j longer to drive than to fly， what is j? This question asks you to figure out which set of variables in the answer choices is the right one But thinking in terms of variables can be confusing to som

14、e people Picking numbers allows you to transform variables into concrete numbers To use the picking numbers method， you need to select numbers and plug them into the answer choices Youre essentially testing the relationships between the variables in each given answer and ensuring they remain true It

15、 doesnt matter what specific numbers you plug into a problem The same answer choice will always surface as long as you plug in consistently and follow all guidelines given by the problemFor example， in the baseball player problem， let m 5， v 100， and p 10 Clearly， these numbers arent realistic （who

16、flies at 10 miles an hour?）， but your goal is to pick easytomanipulate numbers Using our numbers， it takes the baseball player 1005 20 hours to drive and 10010 10 hours to fly So， it takes him 20 10 10 hours longer to drive After plugging m， v， and p into all the answer choices， we find that only D

17、produces an answer of 10Very rarely， more than one answer choice will result in the correct answer for the first set of numbers you picked When this occurs， simply plug in a different set of numbers You will almost never have to plug in more than two sets of numbersWhen picking numbers， you must che

18、ck through all the answer solutions with your chosen numbers Obviously， this will slow you down， but thats the price you pay for using this method Picking numbers gives you a mechanical method of solving tricky problems， and it also allows you to check your math for careless calculations， but it is

19、timeconsumingFinally， when you are picking numbers， avoid 0， 1， or any numbers that appear in the answer choices Picking these numbers can overly simplify the expressions you are dealing with and cause you to pick the wrong answerThe Bottom LineAs you can see， there is no “right” method to solving a

20、ll algebra problems Some methods work best some times， and others work best at other times Part of your practice for the Math IC test will be to get comfortable with algebra questions so that you can choose which method you want to use for every question Now， well review the algebra topics covered i

21、n the Math IC Subject TestEquationSolvingThere are a number of algebraic terms you should know in order to be able to talk and think about algebra： Variable An unknown quantity， written as a letter The letters x and y are the most commonly used letters for variables， but a variable can be represente

22、d by any letter in the English alphabet Greek letters are also used quite often Variables will sometimes represent specified quantities， like apples or dollars， for example Other times， a specific meaning wont be attached to them Youll need to manipulate variables just to show that you understand ce

23、rtain algebraic principles Constant A quantity that does not change In other words， a number Term The product of a constant and a variable Another way to define a term is as any quantity that is separated from other quantities by addition or subtraction For example， in the equation below， the left s

24、ide contains four terms x3， 2x2， 7x， 4 and the right side contains two terms x， 1 The constants， 4 and 1， are considered terms because they are considered coefficients of variables raised to the zero power For constant 4， 4 4x0 So every term， including constants， is the product of a constant and a variabl