Saturday, December 23, 2006
The Good, The Bad & The Ugly
Triggers & Clues
Sentence completions are not really that hard. They are poorly written, poorly worded, ambiguous, tricky, and full of traps. Usually you can put in more than one answer choice. But the key is "the best choice." That is, what ETS says is the best choice. So you've got to practice these and learn to think like a test writer. There are certain standard formats that are used. If you can recognize the format, you will have an easier time with these lovely wastes of time that you are paying money to torture yourself with.
STEP #1 – Choose your own word
Put your hand or answer form over the choices as you read the question. Try to think of a word that fits. WRITE that word down and then take a look at the answer choices. Find the one closest to your choice and MOVE ON!
STEP #2 – Find the “Clue” word or phrase
If a word does not jump out at you as an answer or you are having difficulty choosing your own answer, relax. ETS is generous; they usually give you one right in the question. Read the question carefully and look for, "the clue." Often the clue can be used as the answer, so find an answer choice that matches the clue.
STEP #3 – Find the “Trigger” word or phrase
Many of the sentence completions are long, often joining two phrases with a “trigger” word that is very helpful. These are words that trigger the flow of the sentence helping to determine the answer choice and the clue. They can be negative or positive; such as: “and;” "although";"while"; "but"; "therefore"; "however"
STEP #4 – The Good & the Bad
If you still cannot find a choice that fits, determine whether the word is a good word or a bad word. No not a four letter "bad" word, I mean happy or sad; positive or negative; agrees with or disagrees with - you get the idea. You can mark a (+) for good & a (-) for bad, up or down arrows or use smiley faces. Whatever works, as long as you practice your style and can use it on test day is all that matters.
STEP #5 – Two Blanks: Find one at a time
When you get to questions that ask for two words there is usually a clue and a trigger to whether the answer choices are both good, both bad or one of each. In the answer choices for two-blankers there WILL BE two answer choices where one of the words works, but they other one will be wrong. Do not get suckered into picking just one that works and move on. You must eliminate the obviously wrong choices and then work on the three remaining.
STEP #6 – The Ugly
Remember that sentence completions, like the math questions are written in "order of difficulty." The first third are supposed to be written so that the average high school student can answer them. (BTW - since the average vocabulary has dropped the words are actually easier. Blame the video generation or whatever, but at least that is good news for us).
For easy questions pick easy answers, ones that are not too ugly.
For the last three questions do not pick words that the average person will know – cross them out immediately because the CANNOT be the answer. On my last SAT, I picked the right answer on 5 or 6 really hard sentence completions, but eliminating the obviously wrong easy answers and then picking the ugliest word that I had no clue what it meant.
STEP #7 – Building Vocabulary
There is no better way to increase your vocabulary than to read and USE a dictionary to look up meanings of words that you do not understand. For hard words, the SAT favors classic works of literature from the 19th and early 20th centuries. Poe, Austen, & Shelly are full of great big words. Ayn Rand would be a perfect vocabulary builder. Here philosophical treatise "The Fountainhead" is considered to be a must read by any intellectual - so of course all of the ETS test writers consider themselves to be intellectual and will use words from someone like Rand.
No Shakespeare; Elizabethan is out but Victorian and early 19th century is very much in; Jane Austen, Poe, Hawthorn, etc.
Sunday, November 19, 2006
Tuesday, November 07, 2006
ax2 + bx + c = 0
If b = 0; then the parabola is centered exactly on the y axis
But if b > 0 (positive), the parabola shifts to the left.
Obviously if b < 0 (negative), the parabola shifts to the right
Looking at this normally, it just looks backwards - but it is true.
So remember, b is backwards.
Wednesday, October 25, 2006
I'd also like to thank the teens who showed and participated, I had a lot of fun and they were highly interactive.
As I was describing how to use literary references on the SAT essay, I asked each student to select a book that they had studied in English class and liked. Ben said, "To Kill a Mockingbird," by Nelle Harper Lee, published in 1960 during the civil rights movement in America.
It is the PERFECT literary reference for ANY SAT essay. No kidding - and you do not even have to read the book. Read Sparknotes.com commentary on the moral character of Atticus Finch and his regard for the deep seated good of mankind. The 1962 movie adaptation starting Gregory Peck is awesome & will give you all that you need to know to use this classic as a reference to the humanistic essay that you will be forced to write for the SAT (& it is available for free in the library).
- Read all 8 essay statements and questions in the BBP.
- Outline responses that will match all of them.
- Prepare polished sentences with literary references ahead of time, to be memorized and included in your essay.
Quoting a noble statement from Atticus Finch or simply describing his character as one of your key supporting points is brilliant; thanks Ben, generations of SAT students will be grateful for your insight.
I have learned that the best thing about being a teacher is learning from my students; "When you teach, you learn twice."
Thursday, October 12, 2006
Here is today's Question of the day from Collegeboard.com:
The dramatist was -------over his lack of funds and his inability to sell any of his plays, and his letters to his wife reflected his unhappiness.
a. despondent b. supercililous c. prudent d. encouraged e. fortified
If you put your hand over the blank and read the sentence a natural response might be "depressed" or "bummed out." Lets look for clues - inability, unhappiness are connected by the trigger AND - so they are in agreement. The blank must be bad. c, d, & e are eliminated right away. If you do not know despondent from supercilious - which one sounds worse? Despondent - which is the best choice, for it describes that dramatists emotional state.
Saturday, October 07, 2006
If you are going to take the test again (or for the first time) and want to raise your Vocab scores here are few classics that Kaplan has made into SAT Vocab Study Aids:
Dr Jekyll & Mr Hyde
The Tales of Edgar Allen Poe (my favorite for long ago, I've got to get this one!)
Monday, October 02, 2006
I am so pleased with our public school that now recognizes those kids and accelerates them in all subjects. Truly it is a sin to bore a child with something that they already know.
Well, it's been 34 years of watching people do problems and I can state emphatically that the #1 mistake in doing word problems is NOT answering the right question. I do it myself, I am just as guilty.
This mistake stems from reading the problem too quickly and beginning to answer the question even before you have read all the way through. I just did it yesterday. I read a question, thought I knew the answer, which of course was one of the answer choices. When I took the time to read it slowly, I found that it was actually asking something other than what I had answered.
Yesterday I watched four students in a row read word problems and saw this mistake again.
Please be conscience of this tendency and slow down, read the WHOLE question. Ask yourself, "What is the question asking for?"
Then unlike the sentence completion where you do not want to look at the answer choices, in math you absolutely want to look at the answer choices so you can get an idea of the format or style of the answer.
When I miss a problem (& I do miss them); it is usually because I have not read it completely.
On Oct 14th; we all have to slow down and answer the right question.
Sunday, October 01, 2006
PRP – Percent, Ratio, & Proportion (& maybe fractions)
The SAT used to be full of PRP problems, but in studying all eight sample tests in the BBP (last night watching
I am not absolutely sure that all future SAT’s will have the same proportion of problems as the BBP, but it is a pretty good guess. I’ll know more in the future as I keep taking the tests that allow me to buy the actual test booklet, but that will be of little help on Oct. 14th.
These problems are very easy & a great place to score. They are almost all in the medium section, the one section that we are all targeting to get 100%. They can be “tricksie,” so it will pay dividends to look over the following examples and know how to do them cold & quickly – but don’t rush. There are most certainly traps in the answer choices – they will put in the most common arithmetic mistakes as answer choices.
PRP ?’s from the BBP:
Wednesday, September 27, 2006
With most of you I have gone over content, we need to keep that up. But in addition we need to talk about the style of the problems and some techniques that will help you solve them.
Among the techniques are:
1. Estimating -- this works especially well when there is a geometric figure drawn to scale -- MEASURE; use your answer sheet as a ruler and estimate the answer.
2. Eliminating wrong answer choices - so at least you can have a better guess. I can't use any names here for privacy, but there is one young lady who is an eliminating machine. Use your noggin and if you can't solve it immediately think of what the answer can NOT be and cross it off. Guess on every problem, no matter what you read, fill in every circle.
3. Backsolving - putting the answer choices into the question and see which one fits; this is particularly strong with algebra equations that have number answer choices.
4. V2V go to 7/11; or Plugging in your own numbers. If there are Variables in the problem and Variables in the answer choices. Pick numbers of your own and put them into the equation; then plug them into the answer choices and find the match. "7/11" means to pick convienent #'s; it also means try a different set, like 7 & 11, since both are prime and easy to handle they usually work.
I'll try to pick out a few problems from the BBP that is a good example for each type.
I have given a few lessons on the essay - pick a few good pieces of literature that you have read; Melville, Poe, Jane Austin, Steinbeck, Hemmingway. If you have not read ANYTHING it is a little too late, but not too late to learn about a work and use it in your essay.
The essay is EXTREMELY generic. It has to be 1.4 million people take the SAT. Read all 8 essay topics in the BBP, I did that with a student last week and we laughed because our generic outline could be molded to each one.
Make a brief outline of the major ideas that you can use; plan ahead with phrases that you will write in your answer book to pull from as the body of your essay.
Do not be religious or political
Use real examples - but be short and to the point. Always write about how education is the solution to every problem (remember that English teachers are reading this) & that education comes in many forms.
Tie your example into a character from literature.
Keep your hard work up & get plenty of rest, eat right and exercise!
Tuesday, September 19, 2006
Do not let these burden you with any stress, they are not difficult. But the answers have traps - every possible arithematic mistake you could possibly make is one of the answer choices.
So choose wisely.
Always ask yourself, "What is the question asking?"
These are rarely if ever in the first third of questions in a section (aka: easy); they are mostly in the medium level.
Friday night I plan on going through the BBP & pulling out all the PRP and make a list for practice.
Then the following week, system of equations and word problems that use system of equations.
Lastly sequences and word problems involving the use of our wonder-word INTEGER
Friday, September 08, 2006
SLOPE INTERCEPT FORM
OK, everyone has worked with the graph of a line in the XY Plain; where y is the vertical axis & x is the horizontal axis.
The standard form of a line is written y = mx + b. There will probably be only one or two problems on your SAT that requires using this wonderful knowledge from several years ago. But it is not rocket science & if you spend a few minutes working on it, most of the rust will be removed and you will get these questions.
Warning: The questions can be tricky, so practice reading the wording and then try to ask yourself all of the different ways that a slope question can be asked. They can be easy medium or hard. Do not over-think the easy questions, they really are easy. But most of the examples in the BBP have medium and hard problems.
Y & X are coordinate points in the plain. m and b are constants, where m is the slope and b is the y intercept.
m - “SLOPE = RISE/RUN.” Slope is the ratio of the change in y to the change in x.
The numeric value of m is determined by how many units of y increase for every increase in units of x.
GIVEN TWO POINTS: x1,y1 & x2, y2 are points on the line. Calculate slope, m using the formula: (y2-y1)/(x2-x1)
b – “Y Intercept”
The value of b is the value of y when x=0. If the line passes through the origin (0,0), then b = 0. This can be a trick in a slope question.
Parallel & Perpendicular.
Parallel lines have the same slope with a different y intercept. (If they had the same intercept, they are NOT parallel, they are the SAME).
Perpendicular lines have a slope that is “the opposite inverse.” -1/m
Reflection is another issue that I will cover later.
Here are the problems in the BBP regarding slope intercept form.
Know what a line looks line when m = + or - & b = + or –
Thursday, September 07, 2006
Fun with parabolas!
A parabola is the bowl shaped graph of the simple equation f(x) = x2
Most SAT students do not remember how to graph a parabola, so it is considered a hard question. But in reality parabola questions are often very easy and almost always, usually, most of the time involve simple questions about the constants a, b, c from the classic equation:
ax2 + bx + c = 0
In total, there are only six things to know about a, b, c. If you can learn the “Parabola Six” you can answer most, many and hopefully all parabola questions on your SAT.
The Parabola Six:
- a is negative - parabola points down
- a is positive - parabola points up
- b is negative - parabola moves to the right
- b is positive - parabola moves to the left
- c is negative - parabola moves down (y intercept <>
- c is positive - parabola moves up (y intercept > 0)
I’ll list all the parabola problems shortly from the BBP; they are worth doing because any parabola is a hard to medium and is an easy scoring opportunity.
Wednesday, September 06, 2006
Tuesday, September 05, 2006
The truth is that the SAT contains easy math and tricky problems. But I did buy my first TI this summer for a class and am amazed at with its capabilities.
So in my never-ending quest to help my students beat the test, I went a searching and found this:
downloadable programs that solve SAT problems & Vocabulary words programmed into it, pretty sweet.
Our economy is one of skilled labor and knowledge workers; a college degree is a job's entry ticket. (Along with employment comes money, with which you can buy food and shelter - you do want to live in doors and eat, don't you?)
Acceptence into almost every college and university in the U.S. requires that you take the SAT. It is the one thing that admissions officers can hold as a standard among the many diverse students begging to walk their hallways and fork over money.
So follow my logic in asking for just a little sacrifice over a short period of time that will have a lifelong impact. Take a look how you spend your time, activities, work, sports and studying. If you can devote a scheduled amount of time to preparing for the SAT, your score will improve.
In talking with a new student today, I asked, "What do you do on Sunday afternoon?" "Videogames," was the answer(I am sure with his AP classes there is some homework in there). I pointed out that if he simply took that same time over the next four weeks and did one SAT practice exam every week, his score would rise dramatically.
So I am challenging him:
Four weeks of hardcore study, that will result in four years at his chosen school with a result that will last forever.
To raise your score, the best thing to do is to write a schedule of work that requires sacrifice and committment. Having re-entered the SAT world, I think that the best program for success is for a junior to begin prep work in late July, early August before their junior year and then plan to take the test three times (it is offered six times), with Oct & Jan as must dates. These have the QAS program, which allows you to purchase your test booklet and actual answer responses for $15. If you do not get the score you are aiming for after these first two attempts, you have data on where to improve and can attack the next round of exams.
If you do just an hour or two of intense prep before the school year starts, you can maintain momentum through those hectic first few weeks. Yeah, I know it stinks to have to work on boring academic subjects in the summer, especially math and grammar. But four weeks of sacrifice has a forever impact.
Besides, most of the SAT math is stuff that you studied so long ago that you literally have to relearn somethings like slope intercept form of a line, geometry, parabolas and integers. Not to mention mastering the tricky wording and questions that are truly brain-teasing puzzles.
But if you are reading this now, it is too late for this type of prep. So we have to go to plan B and fit test prep into an already busy schedule.
Let's find some time in your schedule:
- Do you have an iPod/MP3? Get your hands on Flocabulary, Rock the SAT or Vocab Rock and listen to Vocab words when you have some time - even five or ten minutes. The perfect time is your commute to school and back. If you commute for a total of 10 to 15 minutes per day, do you realize that is an hour of studying?
- Record yourself. If you have a cassette recorder or can digitally record yourself - read the vocab list from any of the study guides, especially The Princeton Review. Then play it back during your commute, exercise or downtime. Go for a walk after dinner and get 20 minutes of vocab into your head.
- Flash cards. Get with a friend and do old fashioned flash cards; or (gasp) ask your parents to help you. I've met with tons of parents and am one myself - parents want you to do well and will help with flash cards for a few weeks (heck, they might learn something too).
- The SAT question of the day from the College Board - it is a must.
- The Official Study Guide - "the big blue pillow" (BBP) it is a must, get it, read it, do all the practice tests. All of them.
- Kaplan's kaptest.com has 1000 free questions on line - crunch out 15 to 20 questions a couple of times per week.
- Online, free, full-length, diagnostic SAT exams - there are several. Take them! One each week, if you can. There is nothing like being timed and getting feedback in terms of a score.
- Memorize the six triangles - play with their angles, lengths, areas & perimeters - you WILL be tested on them & it pays to have these cold.
- Memorize the movement of parabolas - these are easy questions that most students get wrong. There are only six possible answers to a parabola question: a (+ or -); b (+ or -) & c (+ or -). I'll write up a study sheet on parabolas.
- Memorize circles - Area, Circ., tangent, degrees, arc -- pull out 10 circle problems from the Big Blue Pillow and work through them with an eye for understanding the limited number of questions that the SAT asks on circles. You will see a circle.
- Memorize the Box Solutions for rate, work, mixture, d=rt, ratio's
- Practice percent of a percent
- Relax and have fun
Sunday, September 03, 2006
All others you can order your responses and whether they were right or wrong, SAS.
This is an absolute must. Mistakes are made, so get what you can and double check ETS.
From their website:
The Student Answer Service (SAS) and The Question-and-Answer Service (QAS) can provide you with excellent feedback on your performance on the test.
QAS and SAS are only available for the SAT Reasoning Test.
The Question-and-Answer Service (QAS): includes your response to each question and the correct answer, information about the type of question and level of difficulty, and scoring guidelines. QAS is available only for the October (Saturday), January (Saturday) and May (Saturday and Sunday) test dates.
The Student Answer Service (SAS): includes your response to each test question, a record of whether you answered each question correctly, incorrectly, or not at all and information about the type of question and level of difficulty. Copies of test questions are not included with SAS. SAS is available for all test dates other than those where QAS is available.
Ordering SAS or QAS After You Register
If you don’t order SAS or QAS when you register, you can still request these services later either online or through the order form you receive with your score report.
I believe it is a very useful study tool since sentence correction on the SAT is primarily concerned with spotting errors.
Bartleby.com (a bookstore named after one of the worst books to be called a "great classic" in the English language) has a free grammar site, from the publishing house, American Heritage. This site is easy to read, relatively short and does the opposite of Professor Brian's in that it tells what TO DO. Hence one site reports mistakes and the other teaches proper usage, covering two bases!
Do not forget to sign up to recieve the daily question from the College Board. The founder of Wal-Mart, Sam Walton, is credited with the maxim, "Small profits, frequently taken," meaning earn just a little bit of money, very often and you will be successful. The same applies to SAT prep, doing just a little bit several times per week creates comfort with SAT questions.
Discussing these questions with a student this week, we agreed that the questions were somewhat easy. But that is just fine. It keeps real questions in front of you and it will not take too much time to read the email and hit an anwer choice. If you hit the incorrect one, the answer is explained. And remember that the easy question count just as much as the hard ones, so we want to get ALL of the easy questions correct, MOST of the medium questions and a FEW of the hard. Answering 2/3 of all the math questions correctly is roughly a 600.
Knowing the wording and the style of the math questions cannot be over stated. Kaplan's free question bank at Kaptest.com is another excellent resource. (For the most part, I like their books as well).
Friday, September 01, 2006
Wednesday, August 30, 2006
Tuesday, August 29, 2006
Wednesday, August 23, 2006
- At first glance, Princeton Review is pretty much the same as its big book, just with more practice.
- Barron's has some pretty hard problems that mix it up. I like that because if you can master hard problems in the SAT style, you will be well prepared come test day.
- Kaplan is fairly detailed, they have a very nice list of 100 top math concepts.
This question bank of over 1,050 SAT style questions allows you to customize your own work, in the subject area and in a level of difficulty. I took 12 Hard Math questions on my quiz and sad to say, only got 11.
But it is a must for anyone who wants to have serious practice for the SAT.
Tuesday, August 22, 2006
Geometric Figures are drawn to scale, unless they say "Not drawn to scale." So you can literally measure them with the edge of a piece of paper and your pencil. Try it, you are going to be simply amazed at how many triangle questions you can answer without doing any complicated geometry.
Being able to "see" what the question is asking is so important. So DRAW it out, mark up that test book. Many students cannot write in textbooks in high school and I think this makes them reluctant to writing on the "official" test booklet. Baloney - its your's, you paid for it, mark it up.
Write out the question in other words and try to get an estimate, many answers are an order of magnitude away from the right answer, so you can scratch them off and through elimination find the correct answer choice without doing the complicated math.
The key is to mark the right answer, not do the question in the right way. Scoring is the ONLY thing. So if you have to count on your fingers and write out a problem as if you were in 5th grade, do it and get over a 600! Trust me your friends will never see your test booklet ever again & neither will you.
I hope to compile my own resources and have them available for my students and anyone else who is interested in learning how to beat the SAT. I will not deny that I INTEND to make a profit off of my musings, but it is a long road from intentions to the teller station. Until then, take off the spam verification.
If it was a spam site, why would I type in verification every day? Maybe I just don't know that much about what you are trying to do & yes, I understand that spam sucks.
on to my post . . . (i hope to edit all of that out once ya'll actually check the site like you advertise that you will).
EASY -- MEDIUM -- HARD
Questions on the SAT are for the most part arranged in order of difficulty. That is the easy questions come first & the hard questions are last. This is especially true for the Math section. The truth is that the average student does not even need to attempt many of the difficult questions in order to acheive the target score.
The SAT prep literature is full of recommendations about mastering the basics and earning a 600 by correctly answering the easy & medium questions. Yup that's right if you get about a 70% on the test, you get a 600.
Truth be told, each question is worth the same amount of points -- so take your time and work on the first 2/3 of each math section. Just because the test is timed does not mean that you have to rush to finish each section (unless you want to get into MIT or CMU, then you had better be able to finish each section).
Take your time. Practice taking timed sections. As I have written, there is plenty of available testing resources. Anyone who has improved their score has practiced. You may not need a coach like me, but a coach keeps you on track and keeps you looking at the material.
Complete the entire practice section and only then go to look at the answers.
Medium questions are only slightly tricky, if you are stuck, well move on. You might just get one of the really hard questions right through your practice and preparation, so make sure that you at least look at them - but do NOT give them a huge amount of your time by rushing through the most important part of the examination -- the first 2/3.
Monday, August 21, 2006
Flocabulary sets SAT Vocab to hip-hop & rap songs in a truly artist, poetic, clean and non-threatening way. Hip-hop is a genre whose popularity cannot be denied. Using it as a tool to increase vocuabulary skills is simply brillant.
You can buy the book with CD or download MP3's & the worksheets in .pdf format. Or you can simply list online and follow along with the lyrics, that is one thing that I like best about this site - with internet access their resources are readily available for free.
Bravo Zulu [Navy-speak for: "Good Job"] to creators Adam & Blake.
Friday, August 18, 2006
I am going to try to carve out some time and take it in the next week or so; maybe Labor Day weekend, when all I have scheduled to do is finishing building a fence I started when our two-year old lab, Buddy was a puppy!
Thursday, August 17, 2006
SparkNotes is a relative newcomer to the study industry. Started in 1996 by some Harvard students, it was acquired in 2001 by Barnes & Noble and has great interesting material.
What I particularly like is that there are FREE tests & test questions, along with an analysis. Most high schoolers are all about free, so why not take advantage of this opportunity. There is so many study guides available how do you know what to spend money on? Well, don't spend any if you can help it [so says the capitialist who wishes to turn this site ultimately into a business].
The #1 factor of SAT improvement is practice and here is free practice and feedback - get on it!
Wednesday, August 16, 2006
Cliffs QuickReview Math Word Problem
Cliffs QuickReview Basic Math and Pre-Algebra
Cliffs QuickReview Algebra I
Cliffs QuickReview Geometry
Some of my students cannot find these locally, I saw Basic Math & Algebra in Staples this morning for $9.99 each and will hit Barnes & Noble & half-price tonight to see if I can find it.
You may also want to try www.abebooks.com; I highly recommend it to my students.
Here is a link to Cliffs Word Problems , where it is selling for $1 -- yup that is ONE DOLLAR, good site for anyone to know about. (I just purchased the textbook for my next college course for my teaching certificate. The bookstore wanted $107, I bought it brand new online for $54 - you do the math).
Sunday, August 13, 2006
Here links and lessons are fantastic, especially the "solving word problems" section of her Practical Algebra Lessons page.
The main purpose of this blog is to help anyone who wants to learn more about improving their score on the SAT, finding great sites like Elizabeth's is invaluable for those who wish to improve and NOT spend a ton of money on prep books and materials.
One of her links is Kathryn Shulte's Free Math Worksheets. These are excellent!
Of course, my secondary purpose is to create enough content for my own SAT prep course, materials and internet site! I love doing this and hope to make it a full time occupation in a short period of time. Stay tuned!
Friday, August 11, 2006
The Work Problem
Using the WORK BOX
The “Work Problem” usually sounds like this:
Socrates can paint a room in 2 hours, Aristotle can paint the same room in 90 minutes. How long will it take them to paint the room if they work together?
Just like the “DIRTY” [D=R*T] & the “MIXED NUTS” [Wt * $ = Cost] we can use a box to lay out this unique system of equations.
Work Rate X
You must be able to convert the work rate from the problem into the answer’s expressed units. In this case, how many hours will it take them together.
Socrates paints at 2 hrs for the whole job, so he is 1/2 of the job per hour.
Aristotle paints at 11/2 hrs for the whole job, so he is 2/3 of the job per hour. [This takes some practice ~ but is not as ugly as it looks on first glance].
Since they are working together to complete the whole job, the problem can be expressed as:
x/2 + 2x/3 = 1; combine like terms
3x/6 + 4x/6 = 1
7x/6 = 1hr.
x = 6/7 hrs.
Check your work
6/7*1/2 + 6/7*2/3 = 3/7 + 4/7 = 1
Let’s do a few more:
Thursday, August 10, 2006
“Mixed Nuts” using the “MIX BOX”
There is a problem called the, “Mixture Problem.” It is an algebraic system of equations with two interrelating quantities and prices. It goes something like this:
Guido’s Health Store sells a mixture of raisins and nuts. Guido buys the raisins for $2.50/lb and the nuts for $3.50/lb. How many pounds of each should be mixed to make 20 lbs of this snack worth $3.00/lb?
I like to call this one “Mixed Nuts” because no matter what the SAT is mixing, it is just like the nuts problems & so since I teach problem solving techniques using goofy names (so that you will remember), go with me on this one.
The solution is easy-peasy-lemony-squeezy; all you have to do is use the MIX BOX & the answer falls out every time.
Here is the mix box:
Things to be mixed
Per/Weight Unit =
So what goes in the box? It is a system of equations & the box simply organizes the information. The algebra solution looks like this:
[Weight of nuts x Price of raisins] + [Weight of nuts x Price of nuts] = Total Cost
What do we know, the cost of raisins per pound and the cost of nuts per pound and the total weight and cost for which we are aiming. Lets fill all that in on the chart.
Things to be mixed
Per/Weight Unit =
The total weight is 20, so the weight of raisins plus the weight of nuts equals 20.
Wr + Wn = 20; solving for Wn:
Wn = 20 – Wr; lets put that in the box
Things to be mixed
Per/Weight Unit =
20 - Wr
Now figure the cost by multiplying across the box (and this forms the system of equations).
Things to be mixed
Per/Weight Unit =
20 - Wr
Add ‘em up:
Raisins & Nuts = Total Mixture
2.5Wr + 3.5(20-Wr) = 60; simplify
2.5Wr + 70 – 3.5Wr = 60; combine like terms
-Wr = - 10
Wr = 10; and since Wn = 20 – Wr, Wn = 10
Variations on the mixture problem.
There are only a limited number of options on the mixture problem, you can be asked to calculate the weight or the cost of either of the two components or the total; basically giving us about six variations on this problem. Master the variations and the possible wording on this puzzle and you will have increase your confidence and ultimately your score.
Try these ones on for size:
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Under construction, sorry for the delay on the distance table. I have re-written my study guide on this one after reading several good math word problem books. Oh yeah, I read books on how to solve math problems, tis true, I'm a geek - that's why parents pay me their hard earned money to teach their kids ;~)
Saturday, August 05, 2006
Here is a beginning to the list of Math Vocubulary that you MUST be able to understand:
Integer; Rational Number; Factor; Multiple; Product; Sum - not to mention all of the many Geometry terms used. This gives me a great idea for a Sat Math Vocab list.
Lets start with the #1 math word on the SAT: INTEGER
Integer: 1 : any of the natural numbers, the negatives of these numbers, or zero
since natural number is used in the definition, what does it mean:
Natural Number: the number 1 or any number (as 3, 12, 432) obtained by adding 1 to it one or more times : a positive integer
Examples of integers are: -567,-27, -12, -4, -3,-2,-1, 0, 1, 2, 3, 34, 567, etc.
Another way to look at it is that integers are points on a number line. They are NOT fractions, or decimals.
So the SAT uses the word integer in many ways. But one of the most common SAT math questions is what I call the "Consecutive Integer"
Here is an example:
The sum of two consecutive integers is 11, what is the value of the least?
There are only two numbers that solve this problem, 5 & 6; 5 + 6 = 11. 5 is the correct answer choice (6 will be one of the choices as well, just in case you did not read the entire question).
To solve any of these with algebra, you make one integer n. The "consecutive" means the next number, so the next number is n+1. Your equation is then:
n + (n+1) = 11; solve for n.
2n + 1 = 11
2n = 10
n = 5
That would be an easy problem (the math is broken into easy, medium & hard); a medium problem throws some twists into the verbage.
The sum of two consecutive odd integers is 47 less than their product. What is the value of the smallest integer
The key here is that "odd" requires you to add 2 to n, instead of just one. They are consecutive & odd, like 3 & 5.
Here is the set up:
n + (n+2) = n*(n+2) - 47
2n + 2 = n^2 + 2n - 47
n^2 - 49 = 0
(n-7)(n+7) = 0; n is either 7 or - 7
lets check our work
7+9 = 7*9 - 47
16 = 63 - 47
16 = 16 check
(note: -7 does not work here, because -16 does not equal positve 16; but don't worry our friends at the College Board will have - 16 as an answer choice).
This also would make a great "grid-in" or officially the "student response" where you have no multiple choice answers and have to come up with the answer on your own. There are 10 of these on the SAT.
Friday, August 04, 2006
Vocubulary on the SAT is test IN CONTEXT. So try to study in context by using the word in a unique sentence; created by you. If it is silly and funny, you will remember it.
Flash cards work! Use colored flash cards and write in different colors. Use a sharpie or thick marker so that you can read it easily. Since nouns, verb, adjectives and adverbs are all tested, put them in piles and then try to create outrageous sentences using just SAT Vocab words.
The Princeton Review list of words is priceless. It can be found in their prep book as well as in WordSmart (not affliated with the website above). Princeton Review works very hard to know what words are most likely to be on the exam. Years ago, when I was being trained by them, some of the instructors actually took the exams in order to memorize the words. I don't know if that is the case now, but it was a great idea then and it leads me to trust the list now.
Others like Kaplan will say that there is no way to know exactly what words are on the test & this is true as well. All that Princeton says is that they keep a close eye on words that appear over and over and therefore are more likely to appear again.
There is only one way to gaining a better vocabulary: READING!
From the list of words that I have looked over and the reading that is available, I would spend some time in the classics with the blue Webster's collegiate dictionary and a highlighter. Jane Austen, Edgar Allen Poe and any other "classic" 19th century author.
If you do not have your own dictionary, shame on you. Go to a used book store (I love Half-priced books) or buy one from Abe Books. Write in it, highlight it, mark it up and tear it up - get going on the most valuable resource for vocabulary that there is on the planet. Make up a game with a friend of throwing words at each other and having to give the definition and use it in context.
Vocab builiding is a lot of hard work & there is no short cut. But a sound use of the english language is most definitely something that every college desires of its graduates.
So get to work!
Thursday, August 03, 2006
- SLOW DOWN – you have plenty of time to score well. Remember that getting a 70% gets a 600!
- SLOW DOWN - Breath deeply during the exam. Take breaks to take deep breaths, your brain NEEDS the oxygen & it helps to control your nerves.
- SLOW DOWN - I have tutored hundreds of students and overwhelmingly mistakes are made in haste.
- WRITE DOWN YOUR WORK - do not do every math problem in your head. Get your hands involved.
- Time yourself as practice. Practice doing math problems for 15, 20 and 25 minutes. Set a timer so that you can get a feel for the length of the sections.
- Mark your answers in your test booklet and then transcribe them onto the bubble sheet as you are about to turn the page to the next set. This "batch processing" is the most efficient.
- RTFQ – Read The Flippin Question; before each question, take a deep breath and then read the entire question. Too many mistakes are made when students start attempting an answer BEFORE they even read the entire question. Too many mistakes are made by reading into the question. Get your hands on as many SAT practice tests as you can; form a study group with friends and each buy one of the big books with only practice tests - Barrons, Kaplan, Princeton Review. Read the question style.
- W? – WHAT is the question asking? Make sure that you know what you are solving for. If it is past half way, there is probably two steps and you have to solve for one thing and then use that answer to solve for real answer. You can bet that 9 times out of 10, the first answer and all permutations of it are in the answer choices.
- Know the RATIO BOX or RATIO GRID; you can solve the four hardest word problems on the SAT: 1. Ratio’s; 2. Work; 3. Solutions (as in Acid solution); 4. Time-Speed-Distance. Princeton Review has a great Ratio box; my more thorough box will be posted shortly.
- Average – Arithmetic mean [Mean, Median, Mode]
- Probability – simply have to practice these.
- Permutations - how many ways can seven runners finish a race: 7! = 7*6*5*4*3*2*1
- Time = Speed x Distance these can be very tricky; I will be posting about 50 of these so that you can get plenty of practice
- Plug In! – If there are variables in the question & variables in the answer, put in your own numbers and see which one works.
- Backsolve – for multiple choice questions the answers are right in front of you, set up your equation & put the answer choices into the equation. It is best to start with choice C and then move up or down. [answers are in ascending or descending order]
- Eliminate wrong answers through: Process of elimination. Eliminate wrong answers. Get rid of a few choices that are obviously wrong. You may get to the right answer without even having to do the problem. If you are stuck, pick one of the remaining and move on.
- GUESS!!!!! --- If you can estimate or eliminate possible wrong answers, guess! For Grid-ins, there is very little chance of simply guessing the answer but it doesn't count against you so mark something down.
- Spend time wisely – do your best on the hard problems, but remember answering an easy or medium problem correctly is worth the same amount as the hardest problem. Did I say slow down and breath deeply yet?
- Three Dimensional (3-D) problems usually have a two dimensional answer. There is usually a quick trick with 3-D.
- Special triangles. Know them, cold. They WILL BE on the test. 3-4-5; 5-12-13; equilateral; isosceles;30-60-90; 45-45-90.
- Sum of the interior angles of a polygon, 180(n-2), where n=number of sides.
- Rules of Divisibility, 2, 3, 4, 5, 6, 9 are the most common.
- REMAINDER – look up the remainder problem and practice it. You have probably not done a remainder problem for several years. NOTE: a calculator will not help you on a remainder problem as much as knowing how to solve it.
- SLOPE INTERCEPT FORM y = mx + b; solve for slope (m); parallel slopes, perpendicular slopes, lines in a coordinate plane, midpoints, rise/run.
- Make a ruler out of your answer sheet and measure the figures, most are drawn to scale.
- Algebraic factoring; usually not that hard so don’t over think it.
- 180 degrees on a line; 360 degrees about a point - This question is on every test. Funky multi-step intersecting lines and triangles; find the 180’s!
- Circles, circumference, diameter, radius, tangent, area, arc’s. Practice, practice, practice. These are all easy, so they have to word the problems with tricks.
- Quadratic & Parabolas.
- Exponents. Rules of adding, multiplying and raising to a another power. Squares & cubes.
- INTEGER – get to know & love this word, it WILL BE on the SAT that you take.
- Consecutive, even, odd, prime integers on the number line.
- Digits; Distinct numbers; real numbers; rational numbers; factor; multiple; remainder; prime – know them.
- Arithmetic rules for evens/odds e+ e = e; o + o = e; o x o = o, etc
- Read the question thoroughly, take your time and aim to get the first 2/3 of each section correct – that’s a 600!
- Order of Operations – PEMDAS
- Memorize the instructions and the given formulas. Please at least read them over. They are given for a reason, they WILL BE used. So get used to them and make note of your practice problems that use the given formulas. Using your time wisely means being able to see when this formulas will be used and NOT having to turn back the page to search for them.
- Write down each step as if this was middle school and you were getting graded on your work. Joe Cool does math in his head and skips steps. Write down every miserable step to avoid simple math mistakes. You have the time to get a 600! So use the time and get the easy and medium difficulty questions.
- Distributive law
- Adding/subtracting/multiplying/dividing fractions. The answer choices are in fractions, so a calculator may not be an advantage.