Thursday, November 22, 2012

Venn Diagram

SAT Venn Diagram, systems of equations Problem: In a survey of 200 pet owners, each person has a dog or a cat or both. If there are 180 dog owners and 160 cat owners. How many of the cat owners have no dogs?

Tuesday, October 30, 2012

Cead Mile Failte Romhat~ well half

Between this blog and my YouTube Channel, I have had more than 50,000 page views. I want to thank you with "One Hundred Thousand Welcomes to You" - Cead Mile Failte Romhat

In the internet world, that is a drop in the bucket. In Phil's world, that is huge!

I have embarked on a journey to write and tutor full-time, publishing lessons and practice with interactive video solutions. Enjoy the ride, I am!

Wednesday, October 24, 2012

Isosceles Triangle Perimeter #1 Solution


An isosceles triangle has a perimeter of 50. Two sides of the triangle measure 20 and n in length. If n is an integer, what is the difference between the maximum and minimum values of n? 


Phil McCaffrey
brought to you by Livescribe

click a few ads and help me make some pennies!

Tuesday, October 23, 2012

Triangle Perimeter, Relationship of sides soluiton

The sides of a triangle are all integers. If one side measures 5 in length, what is the least possible value for the perimeter?

Phil McCaffrey
brought to you by Livescribe

Monday, October 22, 2012

Median Problem solution

Median Problem:

The sum of the set of five consecutive odd integers is 195. What is the median value of the set?

Phil McCaffrey
brought to you by Livescribe

Sunday, October 21, 2012

Isosceles Triangle Perimeter #1

An isosceles triangle has a perimeter of 50. Two sides of the triangle measure 20 and n in length. If n is an integer, what is the difference between the maximum and minimum values of n? 

Triangle Perimeter, relationship of the sides

The sides of a triangle are all integers. If one side measures 5 in length, what is the least possible value for the perimeter?

Saturday, October 20, 2012

Median problem

The sum of the set of five consecutive odd integers is 195, what is the median value of the set?

Thursday, October 18, 2012

Vocab Sample

Question #1: Paucity

Question #2: verbose

Wednesday, October 17, 2012

Isosceles Triangle Angle Measurement #1

#1. An Isosceles triangle has angles of 70 and x degrees. What is the least possible value of x?

#2. An Isosceles triangle has angles of 82 and x degrees. What is the greatest possible value of x?

Phil McCaffrey
brought to you by Livescribe

Tuesday, September 25, 2012

The Daughter Clause

On the SAT [and ACT] gender matters. Answers are often biased in favor of female authors and characters. Like every rule, this one can be bent a little.

The passage goes like this.

This passage is about an Asian-American author. She feels conflicted between pursuing her passion for the arts and her family's expectations of academic success.

1] Everyone knows that I am Asian and they simply expect me to get an A in Calculus then get into an Ivy League school. My mother is no exception. She is from a small village in China and has spent her life raising my sisters and I to be academic successes in America.

6]My older sisters have accepted this as their fate. They rejoice in their lives as a doctor and lawyer. My younger sister will probably be an engineer. Goodness, a doctor, a lawyer and an engine chief!  

10] Mother feigns interest in artistic pursuits. I guess she would approve if I had won a contest or had been accepted to Harvard for writing. But I can feel her disappointment... 

The author author uses the term "feigns" to express her mother's attitude of:
A) Displeasure
B) Sarcasm
C) Irony
D) Pretense
E) Pride

Using the "Gender Bias" rule blindly the answer would be E. It is the only positive answer regarding a question about an ethnic woman. But the "Daughter Clause" trumps the Gender Bias. Here the mother is negative towards the daughter.

Mothers of ethnic and female characters can be critical. Especially in the best interest of the child or involving a new situation like coming to America.

Daughters and ethnic sons can be critical of their mothers. Then they come to understand them.

I like the daughter clause, it works well. And it was taught to me by my daughter, Ali.

Tuesday, September 18, 2012

Gender issues: women rule

When answering questions in the SAT Critical Reading sections take note of gender bias. I tell my students to view every answer concerning women was written about Hillary Clinton. Look for adjectives that are strong and powerful.

A female is NEVER weak. Nor is she frightened. She may not yet understand what is happening as a girl, but she will reflect on the whole later in life.

Non-caucasian women are particularly strong. Asian and Latino women and girls have made a regular appearance on recent tests. If you are studying for the SAT, get together with some high school friends and see if they have their old SAT booklets. Search for the critical reading passages that concern ethnic females and then look at the right and wrong answers.

Train your eye to pick up on the bias written into the test.

Up next: The daughter clause.

Monday, September 10, 2012

SAT Critical Reading Bias, use it to score.

SAT Critical Reading is biased in many ways. Learn how and use the test's biases against it for an improved score. In this new series of blogs, I will show the most blatant bias, how the writers of college entrance exams have a tendency to be politically correct. Though this is not always true, it is mostly true and therefore a technique to know and follow.

They lean toward positive comments regarding females, as well as ethnic and racial minorities. Why? I don't really know, though I could speculate. But I don't really care. All I care about is that my students have an increased score. I do know this much, it does exist, it is recognizable, and mastering the technique of using the bias creates a higher score.

Today's's question of the day is such a classic example that it was the catalyst to write about their leanings. The sentence completion question was about Shakespeare heroines. The answer choices were:

A). imperious
B). suffering
C). excitable
D). resourceful
E). precocious

The obvious answer is D, simply because it is the only 100% positive, pro-female, politically correct response. The first clue from the sentence that the answer MUST be positive is the use of "heroine" to identify the characteristic of the women. The second clue is that the answer is a modifier of a female.

Answer choices A, B, and C are not 100% positive and pro-female. E is not necessarily negative, but precocious means premature development and is used to modify a child. The term "women" in the sentence refers to mature females and not children.

Look for the positive responses in regard to SAT Critical Reading sentences and passages that deal with women and ethnic or racial minorities.

Friday, September 07, 2012

Twice as many is half as less

Sometimes two times as many is half as less.A problem that is a problem over and over goes something like this:

The track team has twice as many members as the cycling team. The cycling team has three times as many people as the water polo team. If a student can only be on one team and there are 100 students on all three teams, how many run track?

Twice as many and three times as many both mean multiplication. But students often reserve the order. Let’s take a look at the wrong answer and then a way to remember how to do it correctly.

First let’s set some variables.  Notice that the teams or clubs almost always start with a different letter. I like to use that letter as my variable. Some students work better with always using x & y. That’s fine, just keep them straight.

T = number of students who run track. It is the answer to the question.
C = number of students on the cycling team.
W =  number of students on the water polo team.

Here is the mistake “twice as many on the track team as cycling.” Students often multiply twice the track team.

2T = C

Wrong. I see this algebraic equation written time and again.

Here is a simple memory trick that I teach my students, ask yourself which team has MORE people. 
If there are twice as many on the track team, doesn’t that mean that the track team has MORE people than the cycling team?  If the equation 2T = C is correct then put 10 people on the track team, substituting 10 in the place of the variable T. 

2(10) = C
20 = C, [T]10 is less than [C]20 meaning that the track has LESS people.

Twice as many on track means that there is 2C for every one T.

T= 2C; Track (T) Has (=) Twice (times 2) Cycling (C) .

The way to keep your translations straight is to do as I did above and put in a basic number like 10 and see which one has more, the one with twice is always more. 12 often works since it is the first number that has more than four factors, hence the reason that a dozen is still a highly popular base unit in baking and in inches.

If track has twice as many than cycling, than cycling has HALF as many as track.

T = 2C or T/2 = C

Cycling has three times as many as water polo. Cycling has MORE people.

C = 3W

Put 12 people on the cycling (three times as many, use a multiple of three).

12 = 3W
4 = W, we’re ok because 4 is LESS than 12. 12 is three times as many as 4.

If cycling has three times as many as water polo then water polo has one-third as many as cycling

C = 3W and C/3 = W

The total number of students is 100.

T + C + W = 100.

If we want to know how many run track, then we have to put the other variables “in terms of”  T.

C = T/2, one done.

W = C/3 W is in terms of C now substitute C in terms of T.

W = [T/2]/3


W = T/6

Substitute for C and W

T + T/2 + T/6 = 100.

Find the common denominator, which is 6.

6T/6 + 3T/6 + 1/6 = 100

Add up the fractions:

10T/6 = 100

Multiply both sides by 6/10 to find the value of one T
(6/10)(10T/6) = (100)(6/10)

T = 60

Let’s check our work

If twice as many people run track than cycle, then there are 30 cyclers. If there are three times as many cyclers as water polo players then there are 10 polo players. Added up 60 + 30 + 10 = 100 total. Check.

Monday, September 03, 2012

Mean Cuisine: The Unknown Average Quantity

I have seen this problem so many times that I need to write about it, it is so easy that all of my students should get this one right. You should too.  It goes like this example:

The average (arithmetic mean) age of a certain group of 20 people is 35. If five additional people join the group, the new average (arithmetic mean) is 36. What is the average age of the five new people?


Average = (the sum of the things)/(the number of the things)

What do we know?

Our average is 35;   AVG = 35  [notice that in any word problem the word "is" can be substituted with an equal sign, I always tell my students "IS is EQUAL" "IS" is "="]

Our number of things is 20

What don't we know?
The ages of our group of people. We don't need to know each one, just the sum total of them all.

Let's let S = [sum of the age of the 20 people]

fill in the known information into our equation

35 avg = (S sum of things)/ (20 number of things), solve for S by multiplying both sides by 20

S= 700

Next step the problem changes the average and the number of people. The unknown quantity it the sum of the new people's ages. No sweat, just a little algebra will get us an answer in a hurry. Let's call the new sum the variable N.

New Average = (Old Sum plus New Sum of things)/(Old number of things plus new number of things)

36 = (700 + N)/(20 + 5)

36 = (700 + N)/(25), multiply both sides by 25

36*25 = 700 + N

900 = 700 + N, subtract 700 from both sides

200 = N

To find the average age of the new people, we divide the sum of their ages, N, by their total number, 5.

200/5 = 40

Generically speaking, the question format goes like this:

The average (arithmetic mean) MEASUREMENT of a certain group of a NUMBER of THINGS is the AVERAGE.

IF SO MANY MORE  new THINGS are added to the group, then the NEW AVERAGE of the THINGS  is SECOND AVERAGE.


I think that I shall write a computer program to fill in random measurements, things and numbers for practice.

Sunday, September 02, 2012


An isosceles triangle has angles of 70 and x degrees, what is the least possible value of x?

An isosceles triangle has angles of 82 and z degrees, what is the great possible value of z?

An isosceles triangle has a perimeter of 50. Two sides of the triangle measure 20 and n in length, where n is an integer. What is the difference between the maximum and minimum value of n?

See solutions tomorrow, or answer them today.

Friday, August 31, 2012

The SAT Essay Question Types

I am copying this from, July 2009 posted by ObsessedOne. It is simply the single best resource on the SAT Essay that I have ever seen. Thanks for showing this to me Skanda

I have compiled every SAT essay prompt administered by the College since the essay was introduced in 2005. Because the prompts are so generic, several archetypes seem to have emerged. Could it be possible to write an essay before seeing the prompt?


--Following the Crowd

Do people need to compare themselves with others in order to appreciate what they have?
Are widely held views often wrong, or are such views more likely to be correct?
Is there any value for people to belong only to a group or groups with which they have something in common?
Is it always best to determine one's own views of right and wrong, or can we benefit from following the crowd?
Is it more valuable for people to fit in than to be unique and different?
Are people more likely to be productive and successful when they ignore the opinions of others?

--Following Authority

Should we pay more attention to people who are older and more experienced than we are?
Should society limit people's exposure to some kinds of information or forms of expression?
Can a group of people function effectively without someone being in charge?
Is it important to question the ideas and decisions of people in positions of authority?
Should society limit people's exposure to some kinds of information or forms of expression?
Is education primarily the result of influences other than school?
Should schools help students understand moral choices and social issues?

--Following Creativity

Is it always better to be original than to imitate or use the ideas of others?
Is it better for a society when people act as individuals rather than copying the ideas and opinions of others?
Is creativity needed more than ever in the world today?
Can people ever be truly original?
Do we put too much value on the ideas or actions of individual people?
Does planning interfere with creativity?

Motivation and Success

--Hardship and Success

Do people truly benefit from hardship and misfortune?
Do we really benefit from every event or experience in some way?
Do people place too much emphasis on winning?
Do people learn more from losing than from winning?
Does true learning only occur when we experience difficulties?
Does being ethical make it hard to be successful?
Can knowledge be a burden rather than a benefit?
Is persistence more important than ability in determining a person's success?
Is the effort involved in pursuing any goal valuable, even if the goal is not reached?

--Self-Determination and Success

Is identity something people are born with or given, or is it something people create for themselves?
Is it best for people to accept who they are and what they have, or should people always strive to better themselves?
Do success and happiness depend on the choices people make rather than on factors beyond their control?
Are people more likely to be happy if they focus on goals other than their own happiness?
Is it more important to do work that one finds fulfilling or work that pays well?

--Self-Expectation and Success

Do highly accomplished people achieve more than others mainly because they expect more of themselves?
Can people achieve success only if they aim to be perfect?
Is it best to have low expectations and to set goals we are sure of achieving?

--Collaboration and Success

Is it necessary for people to combine their efforts with those of others in order to be most effective?
Are organizations or groups most successful when their members pursue individual wishes and goals?
Do people achieve more success by cooperation than by competition?

--Ethics and Success

Does fame bring happiness, or are people who are not famous more likely to be happy?
Are people's actions motivated primarily by a desire for power over others?

--Quality or Quantity and Success

Do people achieve greatness only by finding out what they are especially good at and developing that attribute above all else?
Are all important discoveries the result of focusing on one subject?

Technological “Progress”

Does a strong commitment to technological progress cause a society to neglect other values, such as education and the protection of the environment?
Are there benefits to be gained from avoiding the use of modern technology, even when using it would make life easier?
Has today's abundance of information only made it more difficult for us to understand the world around us?
Is the most important purpose of technology today different from what it was in the past?
Have modern advancements truly improved the quality of people's lives?
Do newspapers, magazines, television, radio, movies, the Internet, and other media determine what is important to most people?
Should modern society be criticized for being materialistic?


Do we benefit from learning about the flaws of people we admire and respect?
Should we limit our use of the term "courage" to acts in which people risk their own well-being for the sake of others or to uphold a value?
Should we admire heroes but not celebrities?
Is there a value in celebrating certain individuals as heroes?


Do all established traditions deserve to remain in existence?
Do people need to "unlearn," or reject, many of their assumptions and ideas?
Should people always prefer new things, ideas, or values to those of the past?
Do incidents from the past continue to influence the present?
Do memories hinder or help people in their effort to learn from the past and succeed in the present?
Is it always necessary to find new solutions to problems?


Should people always be loyal?
Do circumstances determine whether or not we should tell the truth?
Can deception—pretending that something is true when it is not—sometimes have good results?
Is it sometimes necessary to be impolite?
Is acting an essential part of everyday life?

Others (less clearly defined; separated by spaces)

Is compromise always the best way to resolve a conflict?
Should people choose one of two opposing sides of an issue, or is the truth usually found "in the middle"?

Is the main value of the arts to teach us about the world around us?
Can books and stories about characters and events that are not real teach us anything useful?

Can common sense be trusted and accepted, or should it be questioned?
Do people put too much emphasis on learning practical skills?
Should people take more responsibility for solving problems that affect their communities or the nation in general?

Should people let their feelings guide them when they make important decisions?
Can people have too much enthusiasm?
Do images and impressions have too much of an effect on people?

Are decisions made quickly just as good as decisions made slowly and carefully?
Should people change their decisions when circumstances change, or is it best for them to stick with their original decisions?
Is it better to change one's attitude than to change one's circumstances?

Is criticism—judging or finding fault with the ideas and actions of others—essential for personal well-being and social progress?

Does having a large number of options to choose from make people happy?

Thursday, August 30, 2012

The Asian Honor Code

I've tutored literally hundreds of people for 40 years.  No bull, my first tutoring gig was in the 3rd grade when the teacher was so frustrated that I won every multiplication competition that she stopped allowing me to compete and instead helped others. And then there is my sister who I simply loved to help. She was a year older and I desperately wanted to read her materials to see what was next!

In the course of that time it has been my pleasure to be employed by dozens of Asian families. So the question is, "Are Asian kids smarter because of biology or because they work hard?" The answer is BOTH!

Biology is a key factor, but not genetics. There is a difference. Biology is true because a person who actively uses their cognitive powers through studying actually increases the neuron connectors in the brain, INCREASING cognitive capabilities. Like a muscle that is exercised and becomes stronger and leaner, the brain that is engaged in learning and studying gains mental "strength."

But hard work is obviously the main factor. And don't give me the typical American crap that Asian kids who are tortured by their tiger moms lack creativity, spontaneity, and blah, blah, blah. My kids joyfully work and enjoy the rewards of getting high marks. They are proud and last week when I questioned a top student on why he was going so far, he responded, "I want to do my best, it is the Asian Honor Code."

Meaning the students themselves take great pride in their own personal, individual, creative processes.

The overwhelming majority of great athletes and great musicians gain their status not because they were born that way, but because they practiced hard and often with DESIRE.

And Honor.