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Preparation for the SAT and Life November 16, 2010

Posted by Jason McDonald in : SAT tips , 2 comments

The way you do anything is the way you do everything. I heard this statement at a lecture on how to build wealth. The speaker’s point was if you slack on something small in your life like changing your car’s oil regularly, you’re bound to approach the more important elements that way too (like saving your way to wealth). We’re creatures of habit. So if you want to change the way you do anything big, start with the smaller items!

Be prepared. Assuming you want to pass, you wouldn’t go into your driver’s test without preparing. You wouldn’t show up to the state finals track meet without being trained. And although you may have landed your first job without much preparation, you shouldn’t go into future job interviews without being prepared. Know the employer. Know your strengths. Know your weaknesses.

The SAT is no different. It is not an aptitude test. It does not test what you’ve learned in school. It tests how well you’ve prepared for the test. Some argue that the test is biased against minorities. Others argue the wealthy have an advantage because they can afford expensive prep. The truth is people that do well on the SAT are those that are prepared for it.

Happiness and the SAT. Let’s make one thing clear. I am not advocating that the SAT is the all-important factor in your success. I’m simply claiming that if you’re not happy with your current score, you can do one of two things: accept it or change it. If you accept it and are happy with your college options, that’s great; stop reading now and go do something fun. If you’d like to change your score, approach it like anything for which you want success; be prepared and use your resources.

Most students take the test for the first time, are disappointed with their scores, take the test again (with no prep) and get the same results. They figure the results are somehow a measure of their intelligence and they accept them. Don’t do this! This is not the way to be successful at anything. So how do you prepare for the test?

Use your resources. Formal review courses and private tutors aren’t the only way. EVERY student who is considering taking the SAT should, at a minimum, do these three things before the test:

  1. Take a practice test online or from “The Official Study Guide.”
  2. Learn if you could have scored higher by developing a pacing plan.
  3. Memorize the directions and formulas.

If you go into the SAT without completing the above, you’ve probably got an excuse or two. Just remember, the way you do anything is the way you do everything. Now would be a great time change that. You can maximize your score. You can prepare yourself for the SAT. You have all the resources you need. No excuses.

The real deal. Of course any student that does the above is going to see positive results and want to do more. Nothing wrong with that! Successful students find that the more they prepare, the more resources they discover and the higher they score!

So if you want to be successful at everything you do, start now. Not once you get into college, not when you declare your major, not when you graduate or even when you get your first job. You’ve worked on homework for thousands of hours at this point in your life. For what? To prepare you for school tests.

You’ve spent TENS of thousands of hours in school classes. For what? That’s debatable, but the most common answer is “to prepare you for the real world.”

Now it’s time to take the SAT.  Use your resources and prepare yourself. It’s that simple. After increasing your SAT score, you’ll be left thinking, “if I did this, what can’t I do?”

SAT math pacing plan examples June 2, 2010

Posted by Jason McDonald in : SAT tips , 7 comments

If you haven’t already taken an SAT practice test, take one before reading this section. Use the score from your practice test or from an official SAT as a baseline. Add 50 points to this score in each section — this is your target score. This target score should be realistic and attainable.

As you may already know (if not, be sure to sign up for my free five-day e-tips), you should not answer all the questions if you want to maximize your math score.  You’ll only have to answer nearly all of the questions if you’re realistically shooting for 750-800.  If that’s the case, you’re pacing is great; go study some time-saving math strategies!

So, how long should you spend on each problem?  Long enough so that you get 75 to 90 percent of the ones you spend time on correct.  At what point should you circle a question in your booklet and move on?  The actual time cap per problem depends on your target score.  Let’s do a couple examples:

Pacing Plan Example 1:

Jimmy Dean took the SAT and scored 410 in math.  His target score for the next practice test should be 460 (410 + 50).  How many questions should Jimmy omit in the 20-question section?  On average, how long should he spend on each problem?  What should his time cap be per problem?

Let’s start with a few relevant rows pulled from the pacing table in Day 1 of the free five-day e-tips:

Target
Score  (800 possible)
Attempt this many
questions (54 possible)
Accuracy on attempted questions Omit this fraction of section
400 17 75 % 2/3
450 28 75 % 3/5
500 29 90 % 1/2

How many questions should Jimmy omit in the 20-question section? From the middle row above, Jimmy should omit 3/5 of problems in each section.  For the 20-question section he should omit 12 questions (3/5 of 20) and focus on 8.  Notice he would NOT omit three questions, do two, omit three, do two, etc.  It would be better for him to omit 12 trickier and time-consuming questions.  In other words, he should pick his eight problems to focus on from the first half or two-thirds of the test.

On average, how long should he spend on each problem? There are 70 minutes to complete 28 problems.  This gives an average of 2.5 minutes per problem (70 ÷ 28).

What should his time cap be per problem? Jimmy doesn’t have to limit himself to the average time on every problem.  Many problems will take less than half the average, so it’s ok if several problems take 1.5 times the average, or about 3.5 minutes in Jimmy’s case.

Pacing Plan Example 2:

Jimmy’s sister Jane took the PSAT and scored 59 in math (projected to 590 for the SAT).  Her target score for the next practice test should be 640 (590 + 50).  How many questions should Jane omit in the 16-question section?  On average, how long should she spend on each problem?  What should her time cap be per problem?

Again, we’ll start with a few relevant rows pulled from the pacing table:

Target
Score (800 possible)
Attempt this many
questions (54 possible)
Accuracy on attempted questions Omit this fraction of section
600 43 90 % 1/5
650 48 92 % 1/10
700 51 95 % 1/20

How many questions should Jane omit in the 16-question section? From the middle row above, Jane should omit 1/10 of problems in each section. For a 16-question section she would omit one or two questions (1/10 of 16 = 1.6). It would be better for her to omit the trickier and time-consuming questions. In other words, she should skip one or two of the questions towards the end of the section.

On average, how long should she spend on each problem? There are 70 minutes to complete 48 problems. This gives an average of 1.5 minutes per problem (70 ÷ 48).

What should her time cap be per problem? Jane doesn’t have to limit herself to the average time on every problem. Many problems will take less than half the average, so it’s ok if several problems take 1.5 times the average, or a little more than 2 minutes (1.5 × 1.5 = 2.25).

Summary

The number of problems you attempt as well as the time you allow for each problem depends on your target score.  From the above examples, Jane needs to omit 1/10 problems while Jimmy needs to omit 6/10!  Jane can’t afford to spend 2.5 minutes on any problem, while Jimmy should spend 2.5 minutes on most problems he attempts or else he’ll bomb them!

Some Common Pacing Questions

So, will I actually have time on the test to do the above calculations?

ABSOLUTELY NOT!  You need to develop your pacing plan now on practice tests so it’s second nature when you take the “real deal.”

While I’m taking my test should I glance at my watch before every problem so I know when it’s been 2 minutes?

For your next practice test, the answer is yes.  But after that, you’ll have a sense of when it’s time to circle a question and move on without looking at your watch for each problem.

Why only add 50 points to my most recent score?  If Jimmy’s last test score was 410, why shouldn’t he shoot for 600?

It’s not realistic for him to score 600 by pacing alone.  This entire pacing topic is based on how to increase your score without even learning any new math concepts or strategies!  Once Jimmy maximizes his score through pacing (the easiest, quickest way to improve his score), then he can review some essential SAT math skills and learn some SAT math strategies to increase his score even further.  It’s possible for Jimmy to improve to 600, but only by learning new strategies, skills and adjusting his pacing as his score improves.

Don’t stop now

Now that you know how to figure out your optimal pacing plan, take a few minutes to answer the following questions for your next math practice SAT exam:

What is YOUR target math score? (add 50 points to your last math score)

How many questions should you omit in the 8-question, 10-question, 16-question, and 20-question sections? Reminder: the 8 and 10-question sections are the multiple-choice and grid-in subsections of the 18-question section. Each has its own order of difficulty even though the numbering doesn’t start over!

On average, how long should you spend on each problem?

What should your time cap be per problem?

If you figure out the answers the above four questions, and more importantly, follow that pacing plan, you’re sure to score higher than your last test.

SAT math strategy prerequisite

Posted by Jason McDonald in : SAT tips , 20 comments

Think with your pencil!

No matter how rusty students’ math skills are, they could benefit first from learning SAT math strategies to increase their score. When I tutor students for the SAT, they often start our tutoring session with “I had NO idea how to do lots of those problems.”  I can often tell which problems they couldn’t get right before they even ask me a question.

I simply look at their test booklet and over 80% of the time, if a problem has no writing near it, they didn’t get it.  I don’t ask them which of the six essential strategies they tried because I know they didn’t.  Why didn’t they?  They were like a deer in headlights.

Whether you know the essential six math strategies or not, you need to know where to begin when you’re stuck. The saying in whitewater kayaking is, “When in doubt, move your paddle.” This helps someone struck with fear and not sure which way to go.

Heading in any direction is better than not moving at all, even if it’s the wrong direction! Simply recognizing you’re moving in the wrong direction is enough to tell you to change course! Physical movement keeps the brain involved and doesn’t allow you to “freeze up.”

The SAT question writers have an amazing ability to write questions that lead you to think, “I have no idea what to do here.” The saying that applies to the SAT is, “When in doubt, move your pencil.” If you’re stumped on a geometry problem with a diagram, create a crude protractor or ruler and start measuring! Sketch your own diagram if it doesn’t have one! If a problem is “wordy” or confusing, display the information differently. Make a table or a chart. Draw a tree diagram or a simple picture.

If you’re stuck on a problem with variables, make up numbers or plug in answer choices; and more importantly – write them down and work them through (think with your pencil)! Do anything that gets your pencil moving! If your pencil is moving, your brain is engaged. If your brain is engaged, you are one step closer to a solution; even if that solution is, “I’ll come back to this problem later if I have time.”

The most important fact you need to experiment with is it takes little to no more time to write stuff down than it does to do it in your head. The points you gain by avoiding errors and sparking ideas when stumped, by far, outweigh the time it takes to move your pencil. If you review your practice test and find yourself saying, “I should have got that right,” or “that was a stupid mistake,” you need to write more stuff down and let your pencil do the thinking.

Don’t let the limited blank space intimidate you – use scratch paper.  Ask for it before the test begins.

Guessing on the SAT May 31, 2010

Posted by Jason McDonald in : SAT tips , 7 comments

Not everyone should guess on the SAT. In fact, most people shouldn’t.  Decide for yourself before test day if you should guess or not.

The majority of test takers have heard there’s a “guessing penalty” on the SAT. This is a partial truth. While the computer grading system has no way of knowing which answers were guesses, it does subtract a fraction of a point for wrong answers.

Many major test prep companies encourage guessing on SAT questions if one or more answers can be ruled out. See table below for a sample of this oversimplified logic. Their logic states that statistically, in the long run, scores will increase with “educated guessing” because the points received for correct guesses are greater than the fractions lost for those missed. This logic is flawed for most guessers for three reasons:

  1. It assumes the ruled out answers are, in fact, incorrect. If test takers fall for one of the many SAT traps to determine an answer looks wrong, they’re out of luck no matter how much guessing karma they have!  Read myth #3 to see an example of how uninformed test takers can rule out the correct answer.
  2. If the guesser correctly rules out one or more answers, (s)he is likely to choose the final answer based on what looks right (This is not random guessing!) That’s right, the test writers have laid traps with answers that look right and they’ve included questions with correct answers that look wrong.
  3. Even if the guesser correctly rules out one or more answers, and randomly chooses one of the remaining answers, (s)he is not likely to do this enough on a single test for the statistics to reliably play out (ever heard of too small a sample size?). Everyone knows that landing heads on a fair toss has a probability of 50%. Does that mean it will definitely land heads 2 out of 4 times? 5 out of 10? No way! It’s not unusual to land heads (or tails) more than 7 out of 10 times. This same principle applies to your guessing on a handful of questions.  You may not have only wasted valuable time coming up with those guesses, but you may very well have lost points on the five or ten questions in which you guessed.
Potential benefit for SAT guessing on 100 questions
Rule out before guessing Likely correct answer points Likely incorrect answer points Likely net increase
0/5 20 ¼ of 80 = -20 0
1/5 25 ¼ of 75 = -18.75 6.25
2/5 33 ¼ of 66 = -16.5 16.5
3/5 50 ¼ of 50 = -12.5 37.5

NOTE — for the above table to have any significance, the following three conditions must be met:

1. Correct answer is never ruled out
2. Guessing is truly random
3. Guesses are made for a significant number of questions (the above table was based on 100 guesses! There are only 54 in the entire math section!)

MORAL OF THE STORY

If you think you can increase your SAT score through guessing, do yourself a favor. Learn how to recognize SAT traps and where they frequently occur, as well as common mistakes made in ruling out answers. Then guess randomly from the remaining choices. I suggest choosing the same letter all the time, such as (A) or if that was ruled out, then (B) or if that was ruled out, then (C), etc.

Some people benefit from guessing in the verbal section but not the math, while others gain points from guessing in the easy portion but not the medium or difficult ones. Most test takers consistently lower their score altogether from guessing!

Don’t believe the major test prep companies, your guidance counselor or even your math teacher when it comes to guessing on the SAT.  Heck, don’t even believe me and my ten years of SAT tutoring experience!  Next time you take a practice test, put a mark by questions where you guessed. Score your test with and without those guesses and you tell me, should you guess on SAT math questions?  I bet not.

#1 SAT math strategy May 31, 2008

Posted by Jason McDonald in : SAT tips , 3 comments

MAKE A VISUAL

SAT problems rarely provide information or ask questions in a straightforward fashion. One of the most useful ways to cut through the confusion the test writers provide is to display the information your own way. Forming this habit serves three purposes:

     1. It wakes you up from the SAT trance that zaps your time.
     2. It often displays the key relationship to solve the problem.
     3. It helps you avoid or even catch mistakes that are most common when doing work in your head.

This can be done through a table, ratio box, average pie, rate pie, Venn diagram, tree diagram, list of numbers, graph, or a sketch.  It doesn’t have to be pretty, just do it fast.

Here are a couple video mini lessons you should view as you probably haven’t seen them in school (They’re just a couple minutes each).

     Average pie video lesson.
     Rate pie video lesson.

Example 1 (easy):

If the average (arithmetic mean) of the below six numbers is 2x, what is the value of x?
5, x, x, 20, 35 and 40

After trying the problem on your own (hint: make an average pie), watch the video solution on how to get the right answer in 30 seconds.

Example 2 (medium difficulty): 

Machine A makes 1500 newspapers per hour and works for 6 hours.  If Machine B makes 1000 newspapers per hour, how many hours would it take Machine B to make the same amount of newspapers Machine A made in 6 hours?

(A)  1.5
(B)  5
(C)  6.7
(D)  7.5
(E)  9

After trying the problem (hint: make a rate pie), watch the video solution on how to get the right answer in 30 seconds.

Example 3 (medium difficulty):

A stock rose 60 points in a year.  It gained one-third of those points in the first quarter, one-fifth in the second quarter, one-fourth in the third quarter and the rest in the fourth quarter.  How many points were gained in the second half of the year?

(A)  12
(B)  13
(C)  15
(D)  20
(E)  28

After trying the problem (hint: make a table), watch the video solution on how to get the right answer in about 30 seconds.

Could you have done the above problem without a table? 

Of course you could.  Most people would do this problem without a table.  In fact, many people would try to do this problem without even writing anything down.  Keep in mind though most people score around average on the SAT.  You don’t want to be “most people.” 

Contrary to popular belief, making a table actually saves time.  You won’t spend a second thinking about what to do.  You’ll just do it.  As you can see in the video solution, it only takes 30 seconds to get the answer!

Using a table also keeps you from doing unnecessary math like adding the fractions in this case.

Example 4 (more difficult): 

The least integer in a set of consecutive even integers is
-100.  What is the greatest integer in this set if the sum of these integers is 206?

(A)  52
(B)  54
(C)  104
(D)  106
(E)  108

After trying the problem, watch the video solution on how to get the right answer in less than 30 seconds.

REAL SAT PROBLEMS – MAKE A VISUAL

As you can see, making a visual doesn’t take long.  It leads you to the right answer in less than 30 seconds even on “difficult” problems.  Now it’s your turn.  Prove to yourself this strategy works on real SAT problems from The Official SAT Study Guide

Video solutions to all of the below problems are posted in the members forum.

Easy
pg. 670, #6 (average pie)
pg. 716, #2 (sketch)

Medium
pg. 842, #11 (rate pie)
pg. 793, #7 (average pie)
pg. 671, #8 (table)
pg. 489, #10 (sketch)
pg. 735, #7 (Venn diagram)

More difficult
pg. 843, #16 (ratio box)
pg. 807, #14 (sketch)
pg. 412, #18 (rate pie)