Parabola Blog

Another Parabola

Here is another parabola problem that has a square labeled PQRS with an area of 64. The top corners intersect a parabola that sits on the bottom side.

The function of the parabola is y=ax^2

The key to solving this problelm is remember that parabolas are symmetrical. Since the square root of 64 = 8, then all sides have a length of 8. QR = 8, and so the point R is (4,8)

Substitute these two points into the equation and solve

8 = a*(4)^2

8 = a* 16

8/16 = a * 16/16 a = 1/2

Fun with Parabolas

To get a good handle on SAT parabolas - download my cheat sheet. It covers the basics and has questions from the BBP listed on the bottom.


Fun with Parabolas

Email me any question

Hi - thanks for reading SAT - Tutor

If you can think of the problem, email it to me.

If you can sketch it & scan it all the better

My email address is phil@mccaffreytutoring.com

I'd love to hear from you

Symmetrical Parabola's: opposit "a"

Thanks for the feedback, come back and tell your friends. Sat-tutor is about to have a whole lot more, including practice problems and video explainations.

When two parabolas are defined by quadratic equations that have "opposite" coeffecients, the SAT is giving you a REALLY BIG clue. Looking something like:

f(x) = x^2

f(x) = -x^2 + k (where ^ is the symbol for exponent & k is a constant)

The SAT will give you points where these two intersect. Notice that they are both symmetrical about the Y-axis, making the two points of intersect equal distance from the Y-axis (where x = 0). Let's call those two points: P & Q

They give some clue about these two points, something like: the distance of line segment PQ is 6. What is the value of k?

First step:

The distance between PQ is important. Since the parabola's intersent at a point x, -x, the total distance between them, 2x is equal to 6. 2x = 6. x = 3, -x = -3

Second step:

Substitute x = 3, into the first equation. 3^2 = 9. The points of intersection P & Q are (3, 9) & (-3, 9)

Third step:

Substitute P or Q into the second equation: f(x) = -x^2 + k

9 = -(3)^2 + k

9 = -9 + k

18 = k

The one thing that I highly recommend SAT prep students is to buy "The Official Study Guide" published by The College Board. It has 8 practice tests from REAL SAT's. It is the only one that has REAL practice problems - so it is the best piece of intelligence.

I have my students go through and do every parabola problem in The Guide.

Check back in a few days and I will post all of the parabola problems in The Guide, with notation for "Symmetrical Parabola" problems.

Excuse the really crude drawing but it is now 3:30 in the morning. I had crashed in a chair after coming home from my night school class & was on my way to bed when I saw you had posted, so I cranked out this thought before I forgot it.

Now that I know how easy it is to make a drawing and post it - watch out!

Symmetrical Parabola's

The SAT loves to give a trick question: finding something out about a parabola by solving another puzzle first. More on this later - I just wanted to write down the idea so that I can come back and do it justice

SAT Dates

Here is the schedule for the SAT:




SAT Test Date Registration Late Registration
Nov 3 2007 Oct 2 2007 Oct 11 2007
Dec 1 2007 Oct 30 2007 Nov 8 2007
Jan 26 2008 Dec 26 2007 Jan 4 2008
Mar 1 2008 Jan 29 2008 Feb 7 2008
May 3 2008 Apr 1 2008 Apr 10 2008
Jun 7 2008 May 6 2008 May 15 2008

Root Words

Here is a list of the some of the most common root words from Latin & Greek. Some will say to not try to learn root words themselves. But to use them as tools in building a better vocabulary.

I do not completely agree. Building a better vocabulary is one of the most important things to which an educated person strives . But I have found root words useful in making very good guesses on the SAT. On October 2006's exam, I did not miss a single sentence completion [19 total], though I did not know all of the words.

I remember well taking the SAT in 1980 after two years of excellent Latin instruction [thank you Sister Celestine]. I know that I did better on the then "Verbal" portion because I knew some Latin. The only preparation I did for the SAT was to review a long list of root words and modern words formed from them.

Our good friends over at another company have put this list together:
Cap/Cip/Ceipt/Cept/Ceiv/Ceit [take]

Gen [birth, race or kind]

Dic/Dict/Dit [tell, say or word]

Spec/Spic/Spit [look, see]

Super/Sur/Sum[above]

Tent/Tens/Tend/Tenu [stretch, thin]

Trans [across]

Doc/Duc/Dac [teach, lead]

Co/Con/Com [with, together]

Vers/Vert [turn]

Loc/Log/Loqu [word, speech]

Sen [feel, sense]

De [away, down, off]

Nom/Noun/Nown/Nam/Nym [name, order or rule]

Cla/Clo/Clu [shut,close]

Vo/Vox/Vok/Vow [call]

Mal [bad]

Fra/Frac/Frag [break]

Gress/Grad [step]

Sec/Sequ [follow]

Que/Quis [ask, seek]

Sacr/Sanct/Secr [sacred]

Scrib/Scrip [write]

Pathy/Pas/Pat [feeling]

Dis/Dif [not]

Circu [around]



Prefixes & Suffices, a taste of what's to come

Pro [much, for or a lot]

Sub [under]

Ab [away, from]

Ob [against]

The absolute BEST SAT Site Online!

Of course I believe that SAT preparation is an absolute must for any serious student. Here's why (at the end of my rant is the link to the great site)

I remember well walking out of the room in my high school where I took the SAT in 1980 - the sickening feeling still haunts me. What made me so mad was that I had not prepared and could have scored much higher than I did.

We were misled. We were told that it was a true "aptitude" test [of course ETS has stricken any meaning from SAT - it is no longer an acronym, the only letter that is still true is "T" for Test]. We were told it has its roots in IQ testing - rubbish, lies, filth.

It tests nothing but how well you do on it! No other math has the poor wording of this confusing and purposefully tricky examination. No one edits by multiple choice!

I was mad also that the math content was so easy. Yet, in the midst of a hectic junior year studying Trig, AP Chem, AP Bio, AP English, etc., I was stumped by middle school level problems! That is true, the concepts tested on the exam are ones that most students have not seen in years.

So to prepare, READ the content of preparation material and familiarize yourself with the key concepts that you probably once knew well but now will take some time to pull from your long term memory. That way you will not sit on exam day looking like a fool from "Are you smarter than a 5th grader?"

Go to www.proprofs.com/sat/

It is simply fantastic & it is FREE!

I can tell you by experience of taking the exam and reading every practice test out there that the key concepts are covered! Read them - practice the problems and get your mind ready for the sum of a three consecutive odd prime integers greater than 9 is twice the difference of your birthday minus the absolute value of pi during a leap year. In terms of x what is the time that you go insane solving problems that have no basis in real academic instruction.

I'll plan on editing the postings from this blog and heading on over to join ProProfs. I'll see you there

Back Again, are my roots showing?

After a long hiatus of working with students, boy do I have a lot to post.

Here is a nice find, Latin & Greek roots, prefixes & suffixes. Can't help a po' boy with the vocab!
This will shortly be available at www.mccaffreytutoring.com as a pdf [I only have about a hundred pdf's to post!]

Greek and Latin Root Words*

Root	Meaning	English Words
arch	ancient	archetype
aster/astra	star	astronomy
audi	hear	audible
bene	good/well	benefit
bio	life	biology
brev	short	abbreviation
chloro	green	chlorophyll
chrono	time	chronology
derm	skin	dermatologist
dic/dict	speak	dictionary
fer	carry	transfer
fix	fasten	affix
gen	birth	generate
geo	earth	geography
graph	write	graphic
hemo	blood	hemoglobin
herb	plants	herbaceous
hydro	water	hydrate
jur/just	law	jury
log/logue	word/thought	dialogue
luc	light	lucid
manu	hand	manual
meter/metr	measure	thermometer
neg	no	negate
ocu	eye	ocular
olig	few	oligarchy
op/oper	work	operation
osteo	bone	osteoporosis
path	feeling	sympathy
ped	child	pediatrics
phil	love	philosophy
phys	body/nature	physical
pod	foot	podiatrist
proto	first	prototype
pseudo	false	pseudonym
scrib/script	write	scribble
sect	cut	dissect
sol	alone	solitary
struct	build	construct
tact	touch	contact
tele	far off	telephone
ter/terr	earth	territory
vac	empty	vacant
ver	truth	verify
verb	word	verbal
vid/vis	see	video

Greek and Latin Prefixes-/-Suffixes*

Prefix/Suffix	Meaning	English Words
ad-	to	addict
-al	relating to	maternal
ambi-	both	ambidextrous
ante-	before	antecedent
anti-	against	antifreeze
-arium	place of	aquarium
auto-	self	autobiography
centi-	hundred	centimeter
circum-	around	circumvent
con-	with	concert
de-	from/down	depart
deci-	ten	decimeter
di-	two	diameter
dis-	opposite	disable
-dom	quality/state	freedom
ex-	out	exit
hetero-	different	heterogeneous
hypo-	too little	hypoactive
-ic	relating to	poetic
-ile	quality/state	juvenile
in-	not	invalid
inter-	between	interstate
intra-	within	intramurals
-ism	quality/state	catholicism
-ist	one who practices	biologist
macro-	large	macrobiologist
micro-	small	microbiologist
milli-	thousand	millipede
mis-	bad	miscarriage
mono-	single	monotheism
nano-	billion	nanosecond
neo-	new	neonatology
-ology	study of	biology
omni-	all	omniscient
-ous	quality/state	nebulous
pan-	all	pantheon
per-	throughout	pervade
peri-	all around	periscope
poly-	many	polygon
post-	after	postpone
pre-	before	precede
pro-	forward	progress
re-	again	reappear
retro-	back	retrogress
sub-	under	submarine
super-	more than	supermarket
sym-	together	symbol
-tion	quality/state	preservation
-ular	relating to	cellular
un-	not	unwilling

---

Another great question of the day

In partnership with Kaplan, the New York Times has a test prep question of the day online:

New York Times Question of the Day

It looks pretty good. There is also a word of the day that archives the Kaplan test prep question, be careful to only do archives after the test changed in 2006 -- don't waste your time on analogies.

Sentence Completion

Sentence Completion
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.

Just forFun: Me & Mr. T

Great Algebra Problems

www.edhelper.com is a pretty cool site; though it is subscription based, it has a large number of free problems here is their Algebra Page

There problems are remarkably similar to the SAT

Canadian Math Problems

This is really good, the SAT problems have the same concepts as these problems:

Canadian Math Problems

ABP - Always Be Practing!

b is backwards: Parabola - bx

Tutoring this weekend, I reviewed the standard equation of a parabola:

ax² + bx + c = 0

If you read my last posting on parabolas the constant "b" which is multiplied by x controls the movement of the parabola left and right in relation to the y axis.

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.

Atticus Finch & the Essay

Last night I gave my first "Tricks & Traps of the SAT" Seminars at the Sewickley Public library. Special thanks to Meghann the librarian for help & support. We were both so pleased to see our community library being used by folks from the surrounding community and not from our immediate school district.

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).

ESSAY Advice:

• 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."

The Bad; an example

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.

Seven Days & Counting

It is almost here, I look forward to the cram-jam tomorrow!

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:

Frankenstein

Dr Jekyll & Mr Hyde

The Tales of Edgar Allen Poe (my favorite for long ago, I've got to get this one!)

Answer the right question

I'm a certified, registered, card-carrying math geek. So am comfortable that I am not bragging when I say I have been helping students since I was in the 3rd grade (at school, at home with my older sisters, even longer - they hated that pesky little brother yelling out their math answers, so OK maybe that wasn't helping them). For many years the teachers did not know what to do with me because the system required that all students learn at the same pace.

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.