Tag Archives: math

Guide to the PSAT/NMSQT


PSAT/NMSQT stands for “Preliminary Scholastic Assessment Test/National Merit Scholarship Qualifying Test. It is the precursor to the SAT and, most importantly, it’s used to qualify for those coveted National Merit Scholarships you hear so much about.

Colleges pay attention to National Merit Scholars; that means they will come looking for you, instead of you having to try to get admitted! Even better; they will often actually pay for you to go to their school! As a National Merit Scholar you may be awarded additional scholarships to cover tuition, room and board, and even extra pocket money so you don’t have to work at all during college. In short, landing that National Merit Scholarship can make you tens of thousands of dollars AND make you look really good!

What is it? Continue reading Guide to the PSAT/NMSQT

Get a Head Start On Problem-Solving Courses This Semester


Taking chemistry, biochem, physics, calculus, or their ilk? These courses are light on information to be memorized and heavy on problems to be solved and concepts to be grasped.

That takes time, effort, and repetition, just like learning to play the violin or to draw realistically. Here are some steps to make these sorts of courses much more manageable.

  1. Don’t wait to get started. You can’t cram for these courses, so start studying on day one of the class.
  2. Study regularly with frequent breaks. Your brain needs time between each study session to process new concepts, so study a little in the morning, a little in the afternoon, and do it each day. Research shows that marathon study sessions tend to be less effective.
  3. Don’t substitute learning-about for learning. It’s very tempting to just read through your class notes or the textbook repeatedly. You feel like you are studying, but you really won’t get any better at solving the problems. To get better at the violin, you play the violin; you don’t read about playing the violin. Do practice problems, starting with easier ones and working to harder ones. Of course, your initial introduction to the concepts will usually come from a teacher and/or a text
  4. Get help. When you get stuck, go get help! Possible sources include; friends, teaching assistants, professors, the text book (useful now to help you get over a hurdle), other texts, the internet, and professional tutors.
  5. Don’t wait around to get help either, since the concepts often build on one another. You can’t just skip a difficult concept and hope it doesn’t matter. Before you know it, you’ll have missed three more concepts because they depend on your grasping that first concept.
  6. Set study goals for every class, rather than for every test. Again, since mastery is cumulative, you must learn each concept as it is presented. After each class your goal is to completely master the new concepts before your next class NOT before your next test. The good news is that, if you just keep up, you will have little to do before the tests. Artists don’t need to go back and practice stick figures after they’ve mastered life drawing. You won’t need to go back and practice the basics you learned at the beginning of the semester.
© Cody Blair, All Rights Reserved.

Flash Cards


Flash cards are a powerful tool to help you memorize things such as vocabulary, mathematical formulas, history facts, and spelling. Here are some strategies to help you get the most from your flash cards.

Use flashcards in several different colors. Use each color as a cue to help recall something about the fact on that flash card. For example, if you are using the flash cards to memorize vocabulary words, use a different color for words that have different connotations. Positive words–such as benign, sagacious, and staunch–could go on green or blue 3×5 cards. Negative words–such as mendacious ,stultify, and malevolent–might go on red or yellow 3×5 cards. Neutral words–like rebuttal, soporific, and nominal–could go on white or tan cards. The particular colors you use don’t really matter as long as you are consistent.

Illustrate and embellish the cards. Use different color markers. Draw pictures on the card or even cut them out of a magazine and paste them on the card. The more you work at making the card distinctive, the easier it will be to recall.

Carry the cards around with you and review them whenever you have a chance; at the stoplight, before class, in the line at the grocery store or the bank, on long trips, or walking across campus. Make reviewing the cards a daily habit just like brushing your teeth or taking a shower.

Don’t put too much on any one card. The biggest mistake people make is putting too much information on a single flash card. One card equals one fact.

Put the word to be learned on one side of the card and a short two or three word definition on the other side. On a history fact card, for example, you might have “George Washington” on the first side of the card and “first U.S. president” on the other side. You should NOT have “George Washington,” on one side of the card and “first U.S. president, from Virginia, general in revolutionary war,” on the second side of the card.

Change the order of the cards frequently. If the cards always come in the same order, you will start to memorize the order of the answers. It will be much more difficult later to try and recall the facts in a different order.

Flip the cards over from time to time. If you always review the flash card by seeing “Austin” on one side and recalling “Capitol of Texas,” on the other side, then that’s how you will recall it.  When asked, “What’s the capitol of Texas?” you won’t be able to recall it as well, because that isn’t how you studied it.

Make the flash cards as you learn.  Carry around a stack of blank 3×5 cards. As you come across a piece of information you want to memorize, make a flash card and add it to your daily stack. Caution: don’t try and take notes from a class lecture on flash cards, since the connections between ideas are often just as important as any one fact. Take notes and then–immediately after class–decide what key facts should be committed to memory. Put each of those facts on a flash card.

Don’t mix your subjects, since you tend to recall things in context. If you mix up your math flash cards with your history flash cards, it will be much more difficult to recall the history by itself (on a history test, for example), because you learned the two subjects together.

Flash Card Stacks

Separate your cards into stacks that get reviewed at different intervals. You should have an initial stack that gets your attention several times a day. Each time you instantly and correctly recall a card, make a small check mark on it. When the card has two check marks, move it to the next stack.

The next stack is only reviewed every three days; Wednesdays and Saturdays, for example. When cards in that stack can be perfectly recalled, move them to a stack you only review once per week, say every Sunday.

After that, move cards to a once-every-three-weeks stack, which you will probably need to schedule on your calendar. You can then add a nine-week stack, a six-month stack, a one-year stack, etc.

Everyone’s brain is different, so you’ll have to find the intervals that work best for you. Your goal is to review each card as little as possible while still getting excellent recall.

Let’s say you are looking over that once-a-week stack on Sunday and there are two cards that you’ve spent five minutes on, trying to remember them, but it just isn’t coming to you. Move those two cards back to the stack you carry around with you, and send it through the system again. Don’t move a card to the next stack until your recall is instantaneous and perfect; for example, you see the Spanish word, la vaca on one side, and you immediately think cow.

Hint: If you can’t immediately recall the word, don’t cheat and look at the other side!  Struggle with it and rack your brain to recall it, even if it takes four or five minutes.  When you finally do recall it, the memory will be much stronger!


© Cody Blair, All Rights Reserved.

How to Become a Math Expert


You aren’t going to like the answer, I’m afraid. They way to become an expert is to really work at it. I’m not being glib. Malcolm Gladwell explains (brilliantly, as usual) in his new book, Outliers, which I highly recommend.

Gladwell builds a very convincing argument that math skill is much more closely related to persistence and hard work than any innate ability. Bottomline: The more you do math, the better you get at math.

Most convincing study: Every four years, elementary and junior high students around the world take the TIMSS test of math and science. The test begins with a long, boring series of 120 questions designed to get the students’ background–parents level of education, home life, views on science, etc.

Continue reading How to Become a Math Expert

© Cody Blair, All Rights Reserved.

The SAT: An Overview


The SAT Reasoning Test (note: NOT the subject specific SAT tests) is used widely by colleges and universities as one of their admissions criteria.  It is also often used as a criterion in awarding scholarships. It is claimed to test students’ abilities in subjects such as reading, writing, and mathematics; subjects that are supposed to predict those students’ college success. It does not, however, do a very good job at this task, even by the admission of the College Board, the company that makes the SAT.

Normally taken by high school juniors and seniors, it’s become a dreaded rite of passage for many high school students around the world.  Let’s take a look at the basic layout of the test.

Given seven times a year in the U.S., and six times a year overseas. the SAT tests three different areas; reading, writing, and math.  Each of these are scored on a 200 to 800 point scale, and people usually talk about a combined score, adding the scores from each section together.  A mid-level score might be 1500, while a perfect score would be 2400.

SAT Sections

The SAT has several different question types including a short essay, five-choice multiple-choice questions, and grid-ins, where the student enters their answer on a number grid.

The Writing Section

The SAT Writing section takes a total of sixty minutes; thirty-five minutes test grammar and word usage in the form of multiple-choice questions.  Students will also be asked to spend twenty-five minutes writing an essay.

More details about this section, including exact question types and examples can be found here.  The writing section is relatively new and many colleges and universities do not even consider it in their admissions.  To find out how your schools of choice handle it, you will have to ask their admission’s counselors directly.

The Reading Section

The critical reading sections of the SAT include two twenty-five minute sections and one twenty minute section.  Question types include sentences with a blank or two blanks in which you must pick the best word or words to go in the blanks.  This mainly tests vocabulary.  There are also short reading passages over which students must answer a series of questions about passage details, structure, main idea, author’s intentions, etc.  These questions mainly test reading comprehension and are the single, hardest section in which to increase your score, mainly because reading comprehension takes months or years to improve significantly.

See more details and examples of these question types here.

The Math Section

The math section of the SAT is also divided between two twenty-five minute sections and one twenty minute section.  While the majority of the questions are five-choice multiple choice questions, there are also grid-in questions (the College Board calls these “student-produced response” questions), where students must fill in their answers.  The math section tests algebra, geometry, graphing, functions, basic statistics, and data-analysis.  American students can expect to have learned everything they might see on the SAT by tenth grade.

Students are allowed to use a calculator, although every question can be answered without one.  To see the specific question types and examples as well as more details on calculator usage look here.

The Unscored Section

Students will also have an additional twenty-five minute section in either critical reading, mathematics, or writing multiple-choice.  This section is used by College Board to try out new questions, and it does not count towards your score.  However, it will not be identified as an experimental section, and you shouldn’t try and guess which section is the unscored section.  Just do your best on all the sections.

College Board claims that this section is used to make sure tests and question types are comparable from test to test and to “insure fairness.”  It also enables them to do some research at your expense.

Test Format

The SAT has a total of 10 sections. The 25-minute essay always comes first, and the final section will always be a 10-minute long, multiple-choice, writing section. Sections two through seven are always 25-minutes each and will alternate between reading, math, and writing in relatively random order. Sections eight and nine are 20-minutes each. In a single SAT administration you and the test-takers next to you may all have different versions of the test with section types (math, reading, writing) in different orders.  There are also two, ten-minute breaks; one after the third test section, and one following the sixth section.


It is very important to prepare for the SAT, not only to make it easier for you to get into the college of your choice, but also to put yourself in the best position to get scholarships and fellowships.  Plan on taking it two or even three times.  You can take a free SAT test here.  I’ve also written about my preferred test prep books here, and I’ve written about the advisability of taking a prep course here (although the article is specifically about the GRE test–similar to the SAT but used for graduate school admissions–the principles are much the same.  I’ve also written on the best schedule to prepare for a test such as this (again, it’s written specifically for the GRE, but the principles are identical.)

The GRE; An Overview

The GRE, officially known as The Graduate Record Examination General Test, is supposed to test verbal, mathematical and writing skills learned by students during college. Most graduate programs require GRE scores to consider students for admission.

Key Facts:
  • In the US, the GRE is given as a Computer Adaptive Test, or CAT. In other countries, the GRE may be paper-based.
  • You’ll take the test on a computer at special testing centers located throughout the U.S. and around the world.
  • The computer-based GRE entails about 2 hours of multiple-choice testing combined with 75 minutes of essay writing.
  • You can’t go back to previous questions. Once you give an answer and confirm it the question is GONE. You will never see it again.
  • On the quantitative section, you cannot use a calculator. So dust of the old times tables. You’ll need them.


The GRE is scored on a scale of 200-800 for the verbal and quantitative sections. The writing section is scored on a 0 to 6 point scale in half-point increments.  You will also be given a percentile ranking for your score.  If you scored in the 50th percentile, it would mean that half the test takers did better than you in that section, and half did worse.

GRE Structure:

  • Verbal Section: 30 questions/30 minutes
    • Antonym Questions
    • Analogy Questions
    • Sentence Completion Questions
    • Reading Comprehension Questions
    • 470 is an approximate 50th percentile score
  • Quantitative (Math) Section: 28 questions/45 minutes
    • Quantitative Comparison Questions
    • Problem Solving Questions
    • 610 is an approximate 50th percentile score
    • No calculators
  • Writing Assessments: 2 essays in 75 minutes
    • Analysis of an Argument (30 minutes)
    • Analysis of an Issue (45 minutes)
    • 4.5 is an approximate 50th percentile score
  • General Structure
    • Essays always come first, followed by a ten-minute break
    • Verbal and Quantitative come in random order, with a one-minute break between sections
    • You will have either two verbal or two quantitative sections, because one of those will be an experimental section used to test out new questions.  You will not know which section is experimental (don’t waste time trying to identify it), and it won’t count towards your score.
  • Key Contacts
    • For the latest information and news and to sign up for the actual GRE test go to gre.org.
    • To sign up for a weekend GRE prep class at Texas A&M University in College Station OR to sign up for a live class, taught online anywhere in the world, go here.

Re-reading Your Notes Wastes Time!


Did you know that reading over your notes repeatedly is one of the LEAST effective ways to study?  Psychology research has demonstrated repeatedly that you remember much more effectively when you work with information rather than just reviewing information.

Solution: Teach your study materials to a partner.  Look briefly at a main heading in the notes, then try to teach the rest of that section (from memory) to your friend.  Go slowly.  Explain carefully.  Devise illustrations and examples to help make your point.  This method is much more effective than just rereading your notes!