25 Math Concepts you MUST know for the ACT!

Phil McCaffrey

ACT Math – Top 25 ACT Math Concepts.

I read, analyze, and teach ACT Math problems 4 to 6 hours per day, 5 days per week, sometimes more. Doesn’t sound like fun to anyone but a real geek like me. But I love it, and I love helping the teenagers who come to 3RPrep for help.  When the SAT was changing a few years ago, I convinced David to be my partner (because he is way better at grammar than I am), and we painstakingly counted every “type” (or concept) of question on the ACT.  I just looked at the list of math question types and tried to identify the ones that are on almost EVERY test.

Stay tuned. I am going to make a very short lesson with an example problem or two from every concept.

1.     Word Problems – 99% of the ACT math is word problems.  More, less, fewer, higher, lower, double, half, etc.

2.     Properties of Integers. 90% + of the numbers used by the ACT are integers. Even, odd, positive, negative, consecutive, prime, factor, multiple, square, etc.

3.     Fractions. 1/a + 1/b = (a + b)/ab. 1/2 + 1/3 = (2+3)/(2*3)

4.     Sequences. Arithmetic = add/subtract. Geometric = multiply/divide.

5.     Ratio.  Part+Part=Whole.

6.     Rates & Proportions.

7.     Percent. Increase, decrease, percent of a percent, interest.

8.     Algebraic Operations & solving equations. Combine like terms – watch out for negative signs. Easy – don’t miss these.

9.     Algebraic Inequalities – graph them quickly.

10. Absolute Value.

11. Exponents, roots, logarithms.

12. Linear Functions. ax+by=c & y=mx+b

13. Coordinate Geometry in the xy-plane.

14. Systems of Equations

15. Functions. Evaluate f(x).

16. Quadratics, parabolas, factor and FOIL.

17. Lines & Angles. l is parallel to m, l||m

18. Triangles, right, isosceles, 3-4-5

19. Quadrilaterals, squares, rectangles, trapezoids.

20. Circles & sectors. They love the angle of a piece of a pie chart.

21. Multiple Geometry Figures. Big Area – Small Area is usually the answer.

22. Trigonometry. Two SOHCAHTOA questions, usually straightforward.

23. Average, Mean, Median, rarely mode.

24. Probability.

25. Counting, Factorials, Permutations, & Combinations.

A new post almost 3 years later. So much has happened. I wonder if anyone will read this .

Tutoring is going well at 3RPrep (www.3rprep.com). We offer classes at schools and in our office, one on one tutoring in person and online. 

Cheers

Phil

3RPrep.com is my new Site.

www.3RPrep.com is my new website.  The old site is www.mccaffreytutoring.com. It will stay up for as long as I am tutoring and we will share blog posts from all over.

I've formed a LLC with David Cerniglia. So it will be Phil McCaffrey as Head Math Tutor and David as Head English Tutor.

Areas that we serve for SAT Test Prep or ACT Test Prep:
Pittsburgh
Western Pennsylvania
Sewickley
North Hills
South Hills
West Hills
Beaver County. (I think we are the only full time test prep tutors in the county).

Why back at this blog after two years away?  Search optimization of course. Trying to get our name out to as many possible websites.

High Cost of Test Optional... show me the money?

So all the hubbub about so-called "Test Optional" colleges and universities has me thinking. How do they determine financial aid and academic scholarships?

Is it possible that "Test Optional" is a just a marketing gimmick?  I've looked at the list and suspect two things:

1) Most test optional schools charge over $50,000/year in tuition. They get their name on the list so more and more students look at them. They are small, fairly rich liberal arts schools that want students to pay a high tuition for the privilege of NOT taking the SAT.

2) The schools that are not expensive are NOT name brand big schools with great programs. So I conclude they have the same motives as the group in #1.

Just thinking... I could be wrong.

Top 10+1 Educational Summer Activities

Parliament Tutors has a great list of educational summer activities:

TOP 10 Educational Summer Activities

Though, I think they are missing #1: Get a job!

In the new post-industrial, post-information age economy a person's education is just one of many steps in a long road of work. Rarely will your education be your end career.

If you don't have a trust fund and/or large assets to pull from, at some point in the future you are probably going to have to buy food and pay rent. Get started in the right direction now by working.

Work is not always enjoyable, it is often hard and requires discipline. My one friend often quotes his dad, "It is spelled J-O-B not F-U-N." One thing that I have found is that if you are passionate about your work, it is extremely enjoyable and often fun.

I love my job tutoring teenagers. Though the mostly hate the SAT, I love reading about ways to help them reach their goals. I love talking with other tutors, teachers, and counselors. David Greenberg from Parliament Tutors asked if we could socially network and share each other's posts. Many, many times I find myself working until I am too tired to keep going and that is a very enjoyable experience.

Go ask for your dream job. You won't get it if you don't ask.

Phil's take on Critical Reading

Here's my take on SAT Critical Reading, Part I

SAT Critical Reading by the numbers:

3 Sections that count toward your score

19 Sentence Completion Questions, at least 30% with two word answers.

2 Sections with Short Passages, (8 questions) one with passage - 2 questions - passage - 2 questions, the other with Passage 1 - Passage 2 - 4 questions.

5 Long Passages, 3 passages with questions, 1 Passage 1 - Passage 2 then questions.

Long passage can fit generally into four categories:

1. Fiction.  Given away by the word novel  in the italicized introduction. Great place to insert some gender/ethnic issues.

2. Factual Non-fiction. Usually a science like physics or sociology. Facts, facts, facts, questions almost always have line references.

3. Editorial/Opinion. This author might just be pissed off about something and wants to break it down why the IDEAS of other people are wrong. Great place to put Passage 1, Passage 2 related passage format.

4. Journal/Personal Experience. Here the author relates something very intimate and personal without being biographical. A most excellent place for an ethnic or arts passage.

Issues:
1. Gender. Being the politically-correct edu-weinies that they are, the College Board makes life so easy to be a tutor. In edu-weinie-world, women are ALWAYS positive and the are most certainly better than men. If the sentence contains a woman the answer is going to be positive 99% guaranteed*. Come on, I have to leave myself some room in case they lose their minds and actually write something that is not, "It takes a Village/Earth in the Balance/The Audacity of Hope"-esque. (aka The Audacity of the Village in the Balance. - AVB)

Gender shows up often in the fiction passage. It might be a story about a Victorian woman establishing herself against society norms and the men who suppress her. Or it may be a first generation Asian or Latino woman trying to adjust to her parents living in one culture while holding on to the beauty of the culture they left.

*The only time I have seen an answer about a woman being negative is when an ethnic daughter has a bitch for a mom.  The daughter has to come to terms with her mom's bitchiness. And in the questions there is one time a negative answer is appropriate - when an non-native mother is a bitch to her daughter.  My own daughter pointed it out to me and we named it the "Daughter Clause."

2. Ethnic/Racial. Non-white people are great in every way. They are strong and passionate and truthful and hopeful and every other politically correct adjective you can find. If the passage is about an African, Asian, Latino, Native America (and the occasional east European immigrant), the answers are positive. Martin Luther King Jr. is NEVER EVER negative. Love the MLK passages.

3. White men suck. Or are neutral at best (can you tell that I'm a white man). Thomas Jefferson sucks and so does Mark Twain. Ghandi and Martin Luther King Jr. do not suck, they are "complex" and their mature beliefs are not fully appreciated.  White men can be the things that a woman or ethnic/racial person can never be: greedy, mean, and just downright evil. If it is an Journal/Personal Experience just about men it will be about a drive across the country or a fishing/hiking/canoeing trip to somewhere beautiful that is about to be ruined by other white men that suck.

4. Academics and Artists are Great! Colleges are the real customer of the College Board. Though you are paying to take the test, college admissions is the actual consumer of the product. The SAT never makes fun of academics and artists. They might go down a wrong path, but that is the way they find their way out to the truth, through courage and perseverance.

Stop whining about students and smartphones

I read many blogs, articles, and tweets about student learning. A constant stream of boring crap that I am reading is about how today's generation of students is becoming more dependent on technology.

Let's me examine a few bull-crappy ideas that I have read later, with more to come. I will call the Luddite version "In My Day"

In My Day:
Students text each other after class. They fail to make plans beforehand. This hurts the students by not getting them to schedule, they are too whimsical, too capricious, too dependent on tech for instant gratification.

Reality:
Get over it. Weren"t you ever late? Didn't you ever change plans? Didn't you want to know where your friends were?  The ability to find your friends in a crowd is sweet. You don't have to stand under the Department Store Clock on 5th Ave waiting for 45 minutes when your friend can text you that he will be late.

In My Day:
Students did not multitask. You did homework in a quiet room without distractions.

Reality:
Crap and double crap. Teens hate homework and almost need distractions as a treat to the torture of studying, in my case, English Literature.  I would put on Styx, Kansas, and The Eagles while I read and wrote my papers on stupid 17th Century English poetry. I still hate it and would not read it if I had to!

In My Day:
Students did not rely on the internet to google topics. They, blah, blah, blah...

Reality:
Wikipedia & Dictionary.com rock!  I google search so many things every day I can't count. My students carry the complete knowledge of the world in their pockets and are adept at using it. I would put them up against the best students of 20 years ago and they would win just using their phones.

Why is this last point so important? Students may not be memorizing as much, but they are accessing way more. And let's face it, when will anyone be without their phones and the internet? Not often enough to worry. Though please do not be stupid enough to think that a smartphone will help get you to the top of a mountain in Alaska (I love that episode on Alaska State Troopers).

Essay historical topics

Christian's Essay Topics are awesome:

Top Essay Topics

http://www.esatpreptips.com/historical-examples-for-sat-essay/

Dictionary.com on iPhone is one sweet tool

Check out my latest tool for SAT Vocab. When a student misses a word, she immediately looks it up on the dictionary.com app. Then she marks it as a favorite. Within minutes she has permanent iPhone flashcards for her specific weaknesses. Once she knows them, she can unfavorite. 

What is the advantage? When will she be without her phone? Not often.

I make my students show me their phones at the beginning of tutoring and quiz them on the list. Words should be coming on and off every week. Another great advantage is the pronunciation tool. Being able to say a word correctly is imperative because when you read you say the word in your head.

Get the app and get to work.

If 1/t is an integer...

Remainder Problems

18.08 Graph of a Quadratic Function

A+B>C Sum of the sides of a triangle

Greatest Possible Area of a Triangle

Eliminate the SAT?

I am always reading articles on why to eliminate the SAT. Here's another:

Five Reasons to Eliminate the SAT.

Allow me to address one issue, "rich" students can afford to pay for tutoring and increase their scores.

All six of you who read this post already know that I am a professional SAT Tutor. My clients are economically successful. Mainly because they have great educations and unbelievably hard work ethics. And they instill the same in their children.  Excuse me, but isn't this one of the primary reasons we want people to go to college - economic opportunity [not to mention having an educated population is simply better than an world full of ignorance].

Yes, practicing math increases scores. Duh. Going to the gym and lifting weights increases strength. Running increase speed and decreases body fat. A fat rich kid cannot pay a personal trainer to lose weight for him or make him stronger. The kid has to do the reps and pound the pavement.

Scores go up when students work. My "rich" parents know this because they work. My "rich" students are the hardest working group of people I have ever met. They are genuinely nice teenagers who strive for excellence. They do a ton of homework, they play sports, they are in activities, and they spend many additional hours preparing for college admissions.

Some may argue that my college prep students do not have a free and fulfilling childhood because they do not get to play as many video games. Yet, later in life when they are enjoying the rewards of their work in an expensive vacation home and traveling the world will it sill be argued that their life is unfulfilled?

So here is the bottom line, I KNOW for a fact that high SAT scores directly correlates to a student's ability to work hard. Work that many other students are unwilling to undertake like practicing prime numbers, factors, functions, geometry, and reading vocabulary words.

Is it perfect? Of course not! That is ridiculous. It is A measure of work. And a cost effective one at that. In utopian drivel regarding college admissions looking at everything about a student allow me to ask the real question: Who is going to pay for the legions of admissions officers it will take to read mountains of AP's, essays. and unique applications? I know no one really wants to.

So a common test that is a starting process in admissions in not evil. It is just a starting point. And it does measure work ethic. Period. I wish that I had had prep material to practice on in 1981 when I took it. I would have had a higher score and maybe even more scholarship money because I would have worked at it.


By the way, being poor never stopped anyone from becoming stronger through doing pushups. Information on how to increase SAT scores through practice is free and widely available. The library and YouTube are rife with tips and tricks. I have a free YouTube channel on SAT math problems. And I taught at an inner city school full of the poorest people I have ever met. I was paid to come early and stay late to tutor for free. In the years that I attempted to give to the poor what the rich pay for, I could count on one hand the number of students who seriously took advantage of the opportunity.

Just don't do it

There is a SAT Critical Reading strategy that says a test taker does not need to read the passage.

It works. BUT - please read the caveat - however, it takes a lot of training and is not worth it for the average student.

After 20 years (on and off) of test prep, I can answer many of the questions on the critical reading sections of the SAT without ever glancing at the passage. I have not done a thorough statistical analysis of the reading questions. And now that I know Erica Meltzer, I don't have to.

Caveat #2:  If I was actually taking the test, I would go back to the passage and check the answers that I guessed.

Caveat #3: If I was actually taking the test, I would actually read the passage. It is one thing to do it in a coffee shop, it is entirely different to do it on game day.

I just answer the test questions without reading for fun. I guess at the structure of the answer choices and listen for the common SAT style.

For example, on the January QAS, there was a question on the "Ethnic Passage" that had the answer, "compare food with culture."  Loved it - knew it was the answer.  My student said, "I hate you." We both laughed as I went on to get all of the other ethnic questions correct.

What's the lesson? Swiftly read the passage and then re-read based on the answer choices. Lot's more to follow.

Slope #2 Reflection & Absolute Value

Slope Video Parallel & Perpendicular

Venn Diagram Worksheet and Solutions

Venn Diagram Worksheet

Video Soltions:
Problems 1-4: http://youtu.be/QoOGTC--1nk

Problems 5-8: http://youtu.be/tlb4Fy_A3VY

What's the Remainder

Integer Operations, Remainder

1. 2. 3.	Warm-up: What is the remainder when 9 is divided by 6? When the positive integer n is divided by 6 the remainder is 3. What is the lowest possible value of n? The positive number n is a two digit integer greater than 50 but less than 70. When n  is divided by 6 the remainder is 3, what are all the possible values for n?
4.	When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?
5.	When the positive integer h is divided by 8, the remainder is 2. What is the remainder when h + 9 is divided by 8?
6.	When positive integer w is divided by 6, the remainder is 3. When positive integer t is divided by 6, the remainder is also 3. What is the remainder when the product of w and t is divided by 6?
7.	When the positive integer k is divided by 7 the remainder is 4. What is the remainder when k + 4 is divided by 7?
8.	When the positive integer k is divided by 7 the remainder is 4. When the positive integer j is divided by 7 the remainder is 3. What is the remainder when the product of k  and j is divided by 7?
9.	When the positive two-digit integer n is divided by 9 the remainder is 3. When n is divided by 7 the remainder is 5. What is one possible value of n?

"Buy Your Score?" - What a Load of Bunk

A month or so ago, Jennifer Karan, the Executive Director of the SAT Program from the College Board, emailed me regarding an article about the SAT in the Baltimore Sun. As a SAT Tutor, I had to do a double take and see that the the executive in charge was actually reading my blog.  So I read the article she asked me to read. And then I did some research.

I have written and rewritten this article several times trying to not sound too harsh. Finally, here it is...

In a recent letter written to the Baltimore Sun, Carlene Buccino, a Columbia Student, claims that the paying $600 for a college test prep course earned her the decisive edge to gain admissions to the Ivy League.

What a load of nonsense.

I have read Ms. Buccino's letter and am both amazed and horrified that such a well-educated young lady could even begin to think this way. I suggest she compare the history of higher education in America to her own proposal.

Let's take a look at the facts:
1. SAT Scores are not the sole factor in gaining admissions into ANY college, let alone Columbia, ranked among the best in the world [#11 in WORLD rankings of 2012, US News]. Standardized admissions tests are only a part of the process. Nothing in this world is perfect, but standardized college admissions testing is about as fair as a system can be designed. Millions of students can be compared on at least something that is the same. And that in an amazingly short period of time at exceptionally low costs.

2. Standardized tests may get your foot in the door, but that is as far as it can get you. Schools also consider many other factors: your academic resume, your transcript, your high school's reputation, your extra's, your parents' influence - yes, I said it, your parents' influence. Are you a wealthy legacy with the engineering building named after your grandfather? Carlene did NOT get into Columbia solely on her SAT. She probably is from a very wealthy neighborhood and her admission to the Baltimore School for the Arts (BSA, class of 2012) was by audition. Carlene - did your parents pay for lessons and did you put in years of practice to master your skill that allowed you into the one of the best public schools in one of worst school districts in America?

3. $600 in test prep cannot buy enough "tricks" to earn Ivy League level scores. I have been tutoring test prep for 20 years. I have seen many great scores. They come from great students, who worked hard in school and have solid fundament academic skills. Some benefit from learning logical reasoning skills and thinking of new ways to tackle unfamiliar questions. Call them "tricks" if you will, but it is still learning - i.e. proof that the student is capable of something new.

I repeat, Carlene you practiced your arts skills, your academic skills and you are by no means a normal American student. You are to be congratulated for achieving success in both the arts and academics and you should be thankful for your family's support.

4. I have never seen an average student apply "tricks" and gain an Ivy League score with an average GPA. Repeat, NEVER. I have seen an average student's scores go up by LEARNING. Oh my, the SAT tests learning and the desire of a student to improve in reasoning skills? Say it isn't so, Toto!

So, Miss Buccino is missing a few key components. One, she is a woman, whose name ends in a vowel (much like my Italian mother's maiden name). 30 years ago women did not go to Columbia - yes, THIRTY.  Columbia went coed AFTER Westpoint.  How long ago was it that Italian women did not go to high school?

About 100 hundred years ago, Admissions at Columbia were handled the way she proposes. The college talked to the high school and only the elite were allowed in. PERIOD. You were out Carlene. How did someone like you or me get the chance?

But that all changed and one radical group, The College Board, helped introduce social equality in higher education.  And they changed everything. They proposed that admissions to Columbia (yes it all started at Columbia, Carlene) were neglecting the many qualified students in such crass places as Pittsburgh (me) and Baltimore (Carlene). [May I be so bold as to remind the reader that Pittsburgh and Baltimore were populated with many under-educated ethnic minorities, mostly Catholic, working as unskilled labor with no access to a prestigious college education. Public education denied our parents their civil liberties and religious freedom. Roman Catholics were FORCED to practice Protestantism in public school, but we ended that. We paid our public taxes and paid for our own schools for freedom of religion. We learned the system and along the way we are no longer minorities and religion is not forced in schools].

And we had ONE level playing field in all of higher education. A simple reasoning test that compared our abilities with those of the rich, blue-blooded, elites who were snapping up all the seats at Columbia. We were able to be tested against them through the College Board.

The SAT is the beauty of American meritocracy. Your immigrant family is now at the apex of higher education in the world. I knew my immigrant grandparents and great-grandparents. They were European peasants. I suspect your ancestors were too. Now you are in a situation where you can help change the world. Your parents worked hard to earn their level of social economic standing, most likely through rigorous academics and hard work in their careers. They have invested in your education in the classroom and outside of it. You go to one of the most prestigious schools in the world and the one organization that was most influential in getting you there is the one you disparage. Shame on you. Learn the real history of standardized college testing.