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.