Wednesday, August 30, 2006

Great Question

Which of the following CANNOT be the lengths of the sides of a triangle?

  1. click to choose answer number 1 1, 1, 1

  2. click to choose answer number 2 1, 2, 4

  3. click to choose answer number 3 1, 75, 75

  4. click to choose answer number 4 2, 3, 4

  5. click to choose answer number 5 5, 6, 8

Tuesday, August 29, 2006

Do you know the BIG SIX Triangles

note: Blogger no longer considers me a spammer, yeah.

The SAT uses 6 triangles over and over again, over 90% of the triangles you will see on the SAT are one of the big six.

Name them (answer in the comment to follow):

Wednesday, August 23, 2006

Amazon just sent me the lastest SAT math only books from Princeton Review, Barrons & Kaplan; I'll be giving a review of each one shortly. If you want extra work in SAT math & a little more detail of what is on the test, any of these three will do.

  • 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.
I also went to each company's website, they all have free stuff. Free is good remember. and each have a free practice test. But is much better, because it has a free question bank.

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

Sightseeing - Estimating - Guessing - Eliminating

The ability to guess the right answer on a multiple choice test cannot be overstated. The answers are right in front of you.

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.

ABC; 123; Easy, Medium, Hard & no Spam

Hey, I'm not a spammer. I'm a SAT Tutor who is looking to make an honest living.

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).


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

Yo! Check it out: Flocabulary

Vobab Prep has come a long way, I have already listed a number of vocabulary resources, but this one commands a posting of its own.

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

Another free online practice exam

Here is another online free SAT practice exam from Peterson's.

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

Review: Spark Notes

One thing that I will attempt is to review as much of the available resources on SAT Test Prep as I can find.

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 Quick Reviews

Here are the four books that I highly recommend (linked to Amazon); each of them cover the topic in an easy to read "no-bull" manner. Since most of what is on the SAT is just a refresher for the average student, these books are the perfect refresher. Brand new they sell for about $10 each. But you can find them at used books stores, like my favorite: Half Priced Books or online, links below.

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; 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

Great Math Site

A wonderful math teacher named, Elizabeth Stapel, has created a very useful math site called, "Purplemath."

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

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

Time =

Work Done









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

The Mixture Problem



“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

Weight X

Per/Weight Unit =




Total Mixture

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

Weight X

Per/Weight Unit =






Total Mixture



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

Weight X

Per/Weight Unit =






20 - Wr


Total Mixture



Now figure the cost by multiplying across the box (and this forms the system of equations).

Things to be mixed

Weight X

Per/Weight Unit =







20 - Wr



Total Mixture




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:

Word of the Day Part II

looks pretty good; practice makes perfect sense for improving scores (no one is perfect, except the Lord)

Distance Table

Rate X

Time =


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

Names of Numbers used by the SAT: #1 INTEGER

The SAT Math problems are all word problems; it is imperitive that you understand the meaning of the words being used.

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

Word of the Day

WordSmart has a nice email vocabulary word of the day. Though not all of the words are challenging, it is still excellent practice.

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

Rough Rules for Math

Eight years ago, I wrote this to a student. I've changed my mind on a few things, like when to bubble, but otherwise this advice holds true

Phil’s SAT Math Reminders:

  1. SLOW DOWN – you have plenty of time to score well. Remember that getting a 70% gets a 600! 
  2. SLOW DOWN - Breath deeply during the exam. Take breaks to take deep breaths, your brain NEEDS the oxygen & it helps to control your nerves.
  3. SLOW DOWN - I have tutored hundreds of students and overwhelmingly mistakes are made in haste.
  4. WRITE DOWN YOUR WORK - do not do every math problem in your head. Get your hands involved.
  5. 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.
  6. 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. 
  7. 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.
  8. 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.
  9. 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.
  10. Average – Arithmetic mean [Mean, Median, Mode]
  11. Probability – simply have to practice these.
  12. Permutations - how many ways can seven runners finish a race: 7! = 7*6*5*4*3*2*1
  13. 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
  14. Plug In! – If there are variables in the question & variables in the answer, put in your own numbers and see which one works.
  15. 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]
  16. 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.
  17. 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. 
  18. 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?
  19. Three Dimensional (3-D) problems usually have a two dimensional answer. There is usually a quick trick with 3-D.
  20. 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.
  21. Sum of the interior angles of a polygon, 180(n-2), where n=number of sides.
  22. Rules of Divisibility, 2, 3, 4, 5, 6, 9 are the most common.
  23. 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.
  24. SLOPE INTERCEPT FORM  y = mx + b; solve for slope (m); parallel slopes, perpendicular slopes, lines in a coordinate plane, midpoints, rise/run.
  25. Make a ruler out of your answer sheet and measure the figures, most are drawn to scale.
  26. Algebraic factoring; usually not that hard so don’t over think it.
  27. 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! 
  28. Circles, circumference, diameter, radius, tangent, area, arc’s. Practice, practice, practice. These are all easy, so they have to word the problems with tricks.
  29. Quadratic & Parabolas.
  30. Exponents. Rules of adding, multiplying and raising to a another power. Squares & cubes.
  31. INTEGER – get to know & love this word, it WILL BE on the SAT that you take.
  32. Consecutive, even, odd, prime integers on the number line.
  33. Digits; Distinct numbers; real numbers; rational numbers; factor; multiple; remainder; prime – know them.
  34. Arithmetic rules for evens/odds e+ e = e; o + o = e; o x o = o, etc
  35. Read the question thoroughly, take your time and aim to get the first 2/3 of each section correct – that’s a 600!
  36. Order of Operations – PEMDAS
  37. 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.
  38. 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.
  39. Distributive law
  40. Adding/subtracting/multiplying/dividing fractions. The answer choices are in fractions, so a calculator may not be an advantage.

Tuesday, August 01, 2006

SAT Vocabulary Book List

Here are some excellent vocabulary building resources. The new thing in learning words for the SAT is READING. Now who would have thunk it?

Of course there are plenty of people willing to capitalize on this "new" sensation, so they have written books around the SAT Vocabulary list. Here are the ones that I have run across so far (plus a few more)

  1. The Marino Mission, Karen Chapman
  2. The Mayan Mission, Karen Chapman
  3. The Tales of Edgar Allen Poe
  4. Frankenstein: A Kaplan SAT Score-Raising Classic (Kaplan Score Raising Classics) (Mass Market Paperback), Mary Shelly=
  5. Dr. Jekyll and Mr. Hyde: A Kaplan SAT Score-Raising Classic (Kaplan Score Raising Classics) (Mass Market Paperback), Robert Lewis Stevenson
  6. Spark Notes SAT Novels: Busted (SparkNotes SAT Vocabulary Novels) (Paperback)
  7. Tooth and Nail: A Novel Approach to the New SAT (Paperback), Charles Elster
  8. Test of Time: A Novel Approach to the SAT and ACT (Harvest Original) (Paperback), Charles Elster
  9. Simon's Saga for the SAT I Verbal (Paperback), Philip Geer
  10. Wizard of Oz Vocabulary Builder, Mark Phillips
  11. The Pinocchio Intermediate Vocabulary Builder, Mark Phillips
  12. Picture These SAT Words in a Flash (Cards), Philip Geer
  13. The Ring of McAllister: A Score-Raising Mystery Featuring 1,046 Must-Know SAT Vocabulary Words (Paperback), Robert Marantz
  14. The Dropanchor Chronicle: A SAT Vocabulary Novel (Paperback), Stephen D. Ring
  15. SAT Vocabulary Building Novel: From the Other Side (Paperback),Raymond Karelitz
  16. Vocab Rock! Musical Preparation for the Sat And Act (Paperback), Keith London
  17. Rock the SAT, Michael Moshan
  18. Vocabulary Cartoons: Building an Educated Vocabulary With Visual Mnemonics (Paperback), Sam Burchers et al
  19. Vocabulary Cartoons II: Building an Educated Vocabulary With Sight and Sound Memory AIDS (Paperback), Sam Burchers
  20. Vocabulary Cartoon of the Day: 180 Reproducible Cartoons That Help Kids Build a Robust and Prodigious Vocabulary, Marc Tyler Nobleman
  21. Illustrated Word Smart: A Visual Vocabulary Builder, Tom Meltzer
  22. More Illustrated Word Smart (Smart Guides), Morgan Chase
  23. 500 Key Words for the SAT, and How to Remember Them Forever!, Charles Gulotta
  24. Fiske WordPower, Edward Fiske