SAT Math Survival Guide - Amazing GrAdes Tutoring

Transcription

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Copyright © 2014
This book is copyright 2014 with all rights reserved. It is illegal to copy, distribute, or create
derivative works from this book in whole or in part or to contribute to the copying, distribution,
or creating of derivative works of this book.
Certain paid and royalty-free images are used in this book and reproduced with permission when
necessary. In the event that any material is incorrect or has inadvertently been used without
permission please contact me so that the error can be immediately corrected. Email me at
[email protected]
CONNECT WITH DR. STEVE WARNER
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Table of Contents
Introduction
What is an SAT Specific Math Strategy?
Overview of the Math Sections of the SAT
The Correct Way to Prepare for SAT Math
The Math Formulas You Should Memorize for the SAT
The Correct Way to Take the SAT
How Many Questions Should You Be Attempting in Each SAT Math Section?
Should You Go with Your First Instinct to Take Guesses in SAT Math?
Stop Making Careless Errors in SAT Math
Eliminating Test-taking Anxiety on the SAT
Stop Getting Those Last Few Hard SAT Math Questions Wrong
Should You Take a Prep Course for the SAT?
Using Your Time Efficiently to Raise Your SAT Math Score
About the Author
Books by Dr. Steve Warner
Connect with Dr. Steve Warner
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Introduction
Congratulations on taking your first step toward acing the math sections of the SAT. By taking
just a little time to read through this book you will save yourself a tremendous amount of time in
the long run.
The first question you might be asking is why you should trust my advice? Well let me tell you
just a little bit about who I am so you can feel secure that I will be providing you with valuable
information.
My name is Dr. Steve Warner. I am currently a math professor at Hofstra University, but more
importantly for you I have been tutoring test prep (the SAT in particular) for over 15 years. In
2012, I founded Get 800 SAT Math Prep. My goal when setting up this company was, and still
is, to provide inexpensive SAT math preparation to all students who require it.
You can also find me on Facebook, on Twitter, and on Pinterest.
Since 2012 I have written several SAT math prep books, SAT math subject test prep books and
an ACT math prep book. You can see all of my books at my website, or on my Amazon author
page. It is also always a good idea to check the following page for any special promotions I
might be running before making any additional purchases:
http://satprepget800.com/2014/04/14/get-800-promotion/
I do still actively tutor a limited number of students. You can find my current rates for SAT math
prep here: SAT Math Prep with Dr. Steve
My teaching philosophy for the SAT has always been to focus on test specific strategy designed
to save time, avoid carelessness, and exploit the weaknesses of standardized tests, as opposed to
spending valuable time on the conventional teaching of mathematics. Furthermore, I realize that
students at different score levels must be taught differently and this is reflected very strongly in
all of my teaching material.
This book does not have to be read from beginning to end. Each chapter is independent of every
other chapter, so if you have a specific concern you need to address right away, feel free to jump
right to that section in this book.
So without further delay, let’s get to the important stuff…
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What is an SAT Specific Math Strategy?
Whenever I give SAT math prep advice, the first thing that I always tell my students is to learn
as many SAT specific math strategies as possible. So naturally, some of my students will ask me
exactly what an SAT specific math strategy is.
These strategies are methods to getting the answers to SAT math problems in ways that are
different from the way you were taught in school. Some of these strategies will save time, some
will save you from making careless errors, and some will get you the correct answer even when
you do not understand the question.
Many of these strategies are not even mathematically correct, but as long as they work there is no
reason not to take advantage of them. I know that I may raise a few eyebrows with this
statement, but on the SAT you only lose credit if you get the answer wrong – it does not matter if
your work is correct.
Here I will give you two sample strategies – one basic and one advanced.
Let us begin with a basic strategy.
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Start with choice (C)
In many problems you can get the answer simply by trying each of the answer choices until you
find the one that works. Unless you have a specific reason not to, you should always start with
choice (C) as your first guess.
The reason for this is simple. Answers are generally given in increasing or decreasing order. So
very often if choice (C) fails you can eliminate two of the other choices as well.
As a simple example, consider the following problem:
Three consecutive integers are listed in increasing order. If their sum is 531, what is the second
integer in the list?
(A) 176
(B) 177
(C) 178
(D) 179
(E) 180
Begin by looking at choice (C). If the second integer is 178, then the first integer is 177 and the
third integer is 179. Therefore we get a sum of 177 + 178 + 179 = 534. This is a little too big. So
we can eliminate choices (C), (D) and (E).
We next try choice (B). If the second integer is 177, then the first integer is 176 and the third
integer is 178. So the sum is 176 + 177 + 178 = 531. Thus, the answer is choice (B).
And now a more advanced strategy.
Differences of Large Sums
The College Board likes to put seemingly tedious problems on the SAT where it may appear that
you have to do a large amount of addition followed by a subtraction.
Most students that attempt to solve this kind of problem directly waste a lot of time and wind up
getting the problem wrong anyway.
I am going to illustrate the best way to do this type of problem with an example.
If x denotes the sum of the integers from 1 to 50 inclusive, and y denotes the sum of the integers
from 51 to 100 inclusive, what is the value of y – x?
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We write out each sum formally and line them up with y above x.
51 + 52 + 53 + … + 100
1 + 2 + 3 + … + 50
Now subtract term by term.
51 + 52 + 53 + … + 100
1 + 2 + 3 + … + 50
50 + 50 + 50 + … + 50
Now notice that we are adding 50 to itself 50 times. This is the same as multiplying 50 by 50. So
we get (50)(50) = 2500.
With a bit of practice this type of problem can become as simple as multiplying 50 times 50 in
your calculator. How is that for solving a Level 5 problem in about 5 seconds?
In summary, if you really want to do well in SAT math it is absolutely critical that you learn as
many SAT math strategies as possible. I teach my more advanced students 34 key strategies that
I feel are particularly important.
The more of these techniques you have at your disposal the less likely you are to waste time,
make careless errors, and get tricked during the test, and the more time you will have to check
your answers. Each new strategy you learn will take you one step closer to a perfect 800 in SAT
math.
You can find all of the strategies that you need to know in the “Get 800”collection of SAT math
prep
books.
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Overview of the Math Sections on the SAT
The SAT consists of ten parts. There are three math sections, three critical reading sections, two
writing sections, one essay, and an experimental section which may be math or verbal.
Each math section begins with some directions along with a small list of basic formulas. These
include some area and volume formulas, the Pythagorean Theorem, and two special triangles.
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Each of the three math sections has a different number of questions.
(A) A 20 question multiple choice section – you have 25 minutes to complete this part.
(B) A 16 question multiple choice section – you have 20 minutes to complete this part.
(C) An 18 question section with 8 multiple choice questions followed by 10 “grid-in” questions
– you have 25 minutes to complete this part.
These sections can appear in any order on the SAT.
Multiple choice questions:
Each multiple choice question comes with five choices. You get one point added to your raw
score for each of these questions you get right, and unfortunately, you lose a quarter of a point
for each one you get wrong. The quarter point penalty is to ensure that random guessing will not
help your score.
Grid-in questions:
The “grid-in” questions require a free response. Make sure you learn how to enter your answers
correctly. Many students get some of these questions wrong simply because they did not take a
few extra minutes to learn the rules for gridding in answers properly.
On your answer sheet there are four columns.
In each column there is space on top to write your answers and there are bubbles below. The
computer only grades what you have marked in the bubbles.
The space above the bubbles is just for your convenience, and to help you do your bubbling
correctly.
Never mark more than one circle in a column or the problem will automatically be marked
wrong.
You do not need to use all four columns. If you do not use a column just leave it blank.
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The symbols that you can grid in are the digits 0 through 9, a decimal point, and a division
symbol for fractions.
Note that there is no negative symbol. So answers to grid-ins cannot be negative.
There are only four slots, so you cannot get an answer such as 52,326.
Sometimes there is more than one correct answer to a grid-in question. Simply choose one of
them to grid-in. Never try to fit more than one answer into the grid.
If your answer is a whole number such as 2451 or a decimal that only requires four or less slots
such as 2.36, then simply enter the number starting at any column. The two examples just written
must be started in the first column, but the number 16 can be entered starting in column 1, 2 or 3.
There is no zero in column 1, so if your answer is 0 it must be gridded into column 2, 3 or 4.
Fractions can be gridded in any form as long as there are enough slots. The fraction 2/100 must
be reduced to 1/50 simply because the first representation will not fit in the grid.
Fractions can be converted to decimals before being gridded in.
If a decimal cannot fit in the grid, then you can simply truncate it to fit. To truncate is to simply
remove any numbers after the four slots have been filled. But you must use every slot in this
case. For example, the decimal .167777777… can be gridded as .167, but .16 or .17 would both
be marked wrong.
Instead of truncating decimals you can also round them. For example, the decimal .167777777…
can be gridded as .168.
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I like truncating better than rounding because there is no thinking involved and you are less
likely to make a careless error.
Here are three ways to grid in the number 8/9:
Never grid-in mixed numerals. If your answer is 2 ¼, and you grid in the mixed numeral 2 ¼,
then this will be read as 21/4 and will be marked wrong. You must either grid in the decimal 2.25
or the improper fraction 9/4.
Here are two ways to grid in the mixed numeral 1 ½ correctly:
There is no guessing penalty for grid-ins, so you should not ever leave these blank.
Math topics covered:
There are four main math problem types on the SAT:
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Number Theory
Algebra and Functions
Geometry
Probability, Statistics and Data Analysis
Not everything tested on the SAT falls into one of these categories exactly, but this is close
enough for our purposes. For example, counting problems appear on the test – I always group
these with Probability, Statistics and Data Analysis.
As I always say, you most likely have all the mathematical knowledge you need already. So
there is no need to relearn any mathematical theory. Reviewing these topics will happen
naturally as you practice SAT math problems. This does not mean that you do not need to study.
Many SAT questions are intentionally designed to trick you. Therefore you will still need to
prepare. But your emphasis should be on learning SAT specific strategies, and practicing SAT
math problems.
Difficulty level:
Math questions on the SAT come in 5 levels of difficulty. Level 1 questions are very
straightforward, and Level 5 questions are usually quite tricky and may involve two or more
steps to get to a solution. Each math section roughly progresses in difficulty from Level 1 to
Level 5.
I like to think of each math section as being split into three parts – the first third being easy, the
middle third medium, and the last third hard. The 18 question section would then actually have
six parts – three for the multiple choice questions and three for the grid-ins. In other words, the
eight multiple choice questions go from easy to hard, and then number nine is an easy grid-in
question. The grid-ins then get progressively harder up to number 18.
Calculator use:
You can use a calculator on the SAT. I recommend using a TI-84 or
something comparable.
Make sure you consistently practice with the calculator you plan to use. This
way you will be comfortable with it on test day.
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SAT Score
You get one point added to your raw score for each question you get right. You lose a quarter of
a point for each multiple choice question you get wrong. You are not penalized for getting a gridin question wrong. You can get your raw score by typing the following into your calculator: c –
w/4 where c is the number of questions you got right and w is the number of multiple choice
questions you got wrong. You should then round this number to the nearest whole number to get
your raw score. From there, each SAT has its own conversion chart that turns your raw score into
your scaled math score. This is a number between 200 and 800.
To get an 800 in math you usually have to get every question correct. Once in a while there is an
SAT where you can miss one question and still get a perfect score.
If you want to prepare in an efficient manner that will get you an 800 in SAT math in as short a
time as possible, you should check out the “Get 800” collection of SAT math prep books.
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The Correct Way to Prepare for SAT Math
There are three key components to improving your score in SAT math:
(1) Learning test taking strategies that are specific to the SAT.
(2) Practicing SAT math problems ten to twenty minutes per day for approximately three to four
months.
(3) Taking at least four practice tests before test day, approximately one per month.
Let us discuss each of these three components in detail:
Strategy: If you have at least three months to prepare, you should learn between one and three
SAT specific math strategies per week. Whenever you come across a problem where a specific
strategy can be used, you should always attempt the problem using that strategy. In fact, I
recommend trying to solve every practice problem in up to four ways:
(1) Using an SAT specific strategy
(2) The quickest way you can think of
(3) The way you would do it in school
(4) The easiest way for you
In many problems, some of these methods might be the same, and each of these methods might
not be relevant to every problem. Nonetheless, this is the general guideline you should follow.
Keep in mind that the actual answer to a given SAT problem is not important. You will never see
that specific problem on the SAT. But it is important to learn as many techniques as possible.
The more strategies, techniques, and methods you learn, the greater the increase you will see in
both your current SAT score, and your level of mathematical maturity. To see a list of the 32
most important strategies I teach my students check out this infographic on my pinterest page:
http://www.pinterest.com/pin/561542647261116885/
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Practice: If your SAT is less than four months away, set aside a block of time right now that you
will dedicate to SAT math practice every single day! You should begin each study session by
learning one new SAT specific strategy or quickly reviewing a strategy you already know. Recall
that you are only learning between one and three new strategies each week, so on many days you
will simply be quickly glancing over a strategy you already know. Keep this strategy in mind as
you practice, and use it whenever possible.
Next you should choose one of the four topics: Number Theory, Algebra and Functions,
Geometry, or Probability and Statistics. You should cycle through these topics, so that each day
you are working on a different topic, and you are hitting each topic once or twice per week.
You should spend the first half of your study session reattempting problems from this topic that
you have previously gotten wrong. If you get a problem right this time you can discard it and
never look at it again. If you still get it wrong, keep it marked off, and reattempt it again in
another week or so. It is important that you wait at least a few days before reattempting a
problem you got wrong – you want to give yourself a chance to forget the nature of that specific
problem. This will ensure that you are actually solving the problem, and not just “recalling the
solution.”
Redoing problems you get wrong is extremely important – more important than attempting new
problems. This is what separates students that show dramatic improvement from students that
show only average improvement. Remember, you learn from your mistakes, not your successes!
For the second half of your study session you should attempt problems from this topic that you
haven’t tried before. Make sure you are working on problems of the appropriate level. For
example, if you are struggling with Level 3 Geometry problems, then do not attempt Level 4
Geometry problems. You can work on those in a few weeks after you become more proficient in
Level 3 Geometry.
Make sure you clearly mark off any questions you get wrong. It does not matter why you got it
wrong – if you got it wrong, mark it off. I can’t emphasize this enough. Many students think that
making a “careless error” is an excuse to never look at a specific problem again. But doing well
on the SAT is all about eliminating careless errors! You will reattempt these “marked off”
problems next time you come back to this topic. Remember to try to solve each problem in more
than one way (see above).
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Tests: You want to take about four practice tests before test day to make sure that you are
implementing strategies correctly and using your time wisely under pressure. For this task you
should use the second edition of the “College Board’s Official SAT Study Guide.”
Take one test every few weeks to make sure that you are implementing
all the strategies you have learned correctly under timed conditions.
Note that only the second edition has three actual SATs.
I recommend that you take your practice SATs on a Saturday or Sunday
morning and make sure you time yourself correctly. Also mark off the
questions you get wrong and throw them into the group of questions you
will be reattempting at your short study sessions. This will make your
time spent much more effective. Also, make sure you score these
practice tests, and keep track of your scores to make sure you are
showing improvement.
At first you can just do the three math sections, but for at least your last two practice tests you
should do the whole SAT in one sitting. I even like to add in an extra math section to simulate
the experimental section of the SAT. This will ensure that you are practicing taking the test for
the full length of the actual SAT.
How to learn strategies and find good practice problems: So I have already told you where to
find a large supply of practice tests, but where can you learn SAT specific math strategies and
find daily practice problems? You can actually find both of these in one place – the “Get
800” collection of SAT math prep books.
To see how these books should be used in conjunction with each other, take a look at this nice
infographic on my pinterest page: http://www.pinterest.com/pin/561542647261239705/
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The Math Formulas You Should Memorize for the SAT
I frequently get asked about the key math formulas that students really need to know for the
SAT. After 12 years of tutoring SAT math, I have created a small list of the most important
formulas that students should memorize. Everything you need to know on this subject is below.
(1) Let’s begin with the formulas that are given to you in the beginning of each SAT math
section. Memorize these. Here they are.
(2) The following simple formula will make it very easy for you to solve problems involving
Percent Change.
Note that this formula works both for problems involving percent increase and
problems involving percent decrease.
Let’s look at a simple example:
Suppose that x increases from 8 to 9. By what percent does x increase?
Well, the Original value is 8, and the Change is 9 – 8 = 1. Therefore we have
Percent Change = 1/8 × 100 = 12.5.
So x increases by 12.5%.
(3) To change an average to a sum, use the following formula.
Sum = Average · Number
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This formula can often be used to save a lot of time on statistics questions of all difficulty levels.
Let’s look at a simple example.
The average (arithmetic mean) of five numbers is 20. When a sixth number is added, the average
of the six numbers is 30. What is the sixth number?
Well, the sum of the five numbers is 20 · 5 = 100.
The sum of the six numbers is 30 · 6 = 180.
The sixth number is 180 – 100 = 80.
(4) You should know the following formula to compute the slope of a line on SAT math day.
Here, (x1,y1) and (x2,y2) are any two points on the line, and m stands for slope. Note that the ycoordinates are subtracted first in the numerator. A common error is to subtract the xcoordinates first.
Here is an example.
What is the slope of the line that passes through the two points (-1,3) and (2,5)?
Algebraic solution: We have
y2 - y1 = 5 – 3 = 2, and x2 - x1 = 2 – (-1) = 2 + 1 = 3.
So m = 2/3.
Geometric solution: To get from (-1, 3) to (2,5) we move up 2, and right 3. So rise = 2, and run
= 3.
Therefore, m = 2/3.
Remark: To get a better understanding of the geometric solution it may be helpful to plot
the two points, and visually observe how you would move up, then right to get from the first
point to the second point.
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(5) In addition to the slope formula, you should know the slope-intercept form of an equation of
a line.
y = mx + b
Here, as usual, m is the slope of the line, and b is the y-coordinate of the y-intercept of the line.
In other words, the point (0,b) is on the line. b is where the line hits the y-axis.
As an example, let’s write an equation of the line that has a slope of 3 and passes through
the point (0,-5).
We are given that m = 3, and b = -5. Thus, the equation of the line in slope-intercept form is
y = 3x – 5.
As a special case of the equation y = mx + b, note that a horizontal line has an equation of the
form
y=b
This is because the slope of a horizontal line is 0.
For example, the horizontal line passing through the point (5, 3) has equation y = 3.
You should also know that a vertical line has an equation of the form
x=a
Note that a vertical line has no slope, and therefore cannot be written in slope-intercept form.
For example, the vertical line passing through the point (5, 3) has equation x= 5.
You should also know the following two facts:
Parallel lines have the same slope.
Perpendicular lines have slopes that are negative reciprocals of each other.
(6) The triangle rule states that
the third side of a triangle is between the difference and sum of the other two sides.
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This is a very simple rule which is often not taught in the classroom. Triangle rule problems tend
to be Level 4 or 5 even though they are usually quite easy. I attribute this to the fact that many
students simply have never learned this rule. Here is a simple example.
If x is an integer, how many different triangles are there with sides of length 2, 6 and x?
6 – 2 = 4, and 6 + 2 = 8. By the triangle rule, 4 < x < 8. Since x must be an integer, x can be 5, 6,
or 7. So the answer is Three.
(7) This next formula sometimes comes in handy when dealing with sets. If you have a set
with X objects and another set with Y objects, then the total number of objects is
Total = X + Y – Both + Neither
Let’s look at a simple example.
There are 30 students in a music class. Of these students, 10 play the piano, 15 play the guitar,
and 3 play both the piano and the guitar. How many students in the class do not play either of
these two instruments?
Substituting these numbers into the formula, we have
30 = 10 + 15 – 3 + N.
So, N = 30 – 22 = 8.
(8) Many students get confused when counting the number of consecutive integers in a list.
The number of integers from a to b, inclusive is b – a + 1.
Remark: The word “inclusive” means that we are including the endpoints a and b.
For example, the number of integers from 2 to 7 is 7 – 2 + 1 = 6.
This can be easily verified with the list 2, 3, 4, 5, 6, 7.
Here is an example that would be harder to verify.
The number of integers from 62 to 512 is 512 – 62 + 1 = 451 .
(9) One last formula that every student should know.
distance = rate · time
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As a simple example, if you drive your car at a speed of 30 miles per hour for 5 hours, then you
will travel (30)(5) = 150 miles.
For many students, that should be sufficient. In fact, if you are currently scoring below a 500 in
SAT math, then please stop here. There is no need to bog yourself down with these last few
formulas.
For those of you that really want to score an 800, let us look at a few more.
(10) In addition to the simple formula distance = rate · time, the more advanced student
might want to memorize the Harmonic Mean Formula.
This formula can be used to find the average speed when 2 individual speeds for the
same distance are known. Here is an example.
Dr. Steve drove to work at an average speed of 40 miles per hour, and home from work at
an average speed of 60 miles per hour. What was his average speed for the entire round trip,
in miles per hour?
We simply plug in the given numbers into the Harmonic Mean Formula.
Important note: Your intuition might tell you that the answer to this question should be
50 miles per hour. In this case, however, we need to compute the Harmonic Mean,
and not the Arithmetic Mean.
(11) The advanced student may also want to know the Generalized Pythagorean Theorem.
d2 = a2 + b2 + c2
This simple formula is used to find the length of the long diagonal of a rectangular solid. Here
is a straightforward example.
If a box has a length of 3 feet, a width of 4 feet, and height of 12 feet, what is the
longest distance from one corner of the box to another corner of the box?
The question is asking for the length of the long diagonal of the box. We just plug the numbers
into the formula for the Generalized Pythagorean Theorem.
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d2 = 32 + 42 + 122 = 169. So d = 13.
(12) The general form for a quadratic function is
y = ax2 + bx + c.
The graph of this function is a parabola whose vertex has x-coordinate
The parabola opens upwards if a > 0 and downwards if a < 0.
Here is an example.
Let the function f be defined by f(x) = -2x2 - 3x + 2. For what value of x will the
function f have its maximum value?
The graph of this function is a downward facing parabola, and we see that a = -2, and b = -3. So
the x-coordinate of the vertex is x = 3/(-4) = -3/4.
(13) The standard form for a quadratic function is
y – k = a(x – h)2
The graph is a parabola with vertex at (h,k). Again, the parabola opens upwards if a > 0 and
downwards if a < 0.
Here is an example.
Let the function f be defined by f(x) = 3(x – 1)2 + 2. For what value of x will the
function f have its minimum value?
The graph of this function is an upward facing parabola with vertex (1,2). Therefore, the
answer is 1.
Remark: Note that in this example k = 2, and it is on the right hand side of the equation
instead of on the left.
(14) The total number of degrees in the interior of an n-sided polygon is
(n – 2) · 180
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For example, an eight-sided polygon (or octagon) has
(8 – 2) · 180 = 6 · 180 = 1080 degrees
in its interior. Therefore each angle of a regular octagon has
1080/8 = 135 degrees.
Remark: A regular polygon is a polygon with all sides equal in length, and all angles equal in
measure.
There are not that many formulas to memorize for the SAT, and many of them you probably
already know. So make it a point to commit the rest of these formulas, tested on the math
sections of the SAT, to memory over the next few days. Then you can focus on practicing SAT
math problems.
Practicing math problems: So now that you know all the math formulas you need for the SAT.
It is time to start practicing using them on a wide range of SAT math problems. You can find a
huge selection of practice problems in the “Get 800” collection of SAT math prep books.
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The Correct Way to Take the SAT
The system I will be giving is simple, but nonetheless you will need to apply it a few times to
become comfortable with it before test day. Remember that you should take at least four practice
SATs before taking your actual SAT, approximately one practice test per month. Follow the
advice given in this chapter every time you take a practice test as well as on test day.
For students currently scoring at least 600 in SAT math
Pacing: On average, you have about one minute and fifteen seconds per question. If you have
been preparing properly, then this is more than enough time. You should not need more than 30
seconds per question on average for the easy SAT math questions, 60 seconds for the medium
SAT math questions, and 75 seconds for the hard SAT math questions.
Let’s look at the 20 question multiple choice section in detail. In this case, roughly speaking we
have that numbers 1 through 7 are easy, 8 through 14 are medium, and 15 through 20 are hard.
So in this section you might need 3 and a half minutes for the easy questions, 7 minutes for the
medium questions, and 7 and a half minutes for the hard questions. This will leave you about 7
minutes to check over your answers, and spend more time on that one question that is giving you
a bit of trouble.
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Let me just mention that I am actually being very generous here. I can finish any 20 question
section in about 8 minutes WITHOUT rushing. This leaves me 17 minutes to spare to go back
and catch any careless errors. There is nothing special about me that allows me to do this. When
I take the test I simply apply the same strategies that I teach to every one of my students. If you
know these strategies, you will find that on many of the hard questions you may actually need
less time than you need on some of the easy questions.
Now, how should you pace yourself properly so that you do not run out of time prematurely?
Well after spending about 30 seconds on ANY question, you should decide if you understand the
question enough to finish it fairly quickly. If not, then mark it off and move on. Do not worry – it
is not forgotten – you will come back to it later. The worst thing that you can do is to get hung up
on one question.
If you have eliminated at least one answer choice, or it is a grid in question, feel free to take a
guess. But you should still mark it off and come back to it later.
Make sure that you are using your calculator when appropriate. But be aware that your calculator
can slow you down if it is overused.
One note about the 18 question section – this section has 8 multiple choice questions followed by
10 grid-ins. Keep in mind that numbers 7 and 8 are hard, whereas number 9 is easy. So you may
want to temporarily jump from number 6 to number 9, and go back to numbers 7 and 8 a bit
later.
Now, after going through the test once, you can then go through each of the questions you have
marked off and solve as many of them as you can. You should be able to spend 5 to 7 minutes on
this, and still have 7 minutes left to check your answers. If there are one or two problems that
you just cannot seem to get, let them go for a while. You can come back to them intermittently as
you are checking over other answers.
For students currently scoring below 600 in SAT math
Pacing: Do not waste your time on a question that is too hard for you or that will take too long.
After spending about 1 minute on ANY question, you should decide if you understand the
question enough to finish it fairly quickly. If not, then mark it off and move on. Do not worry – it
is not forgotten - you can still come back to it later, time permitted. The worst thing that you can
do is to get hung up on one question.
If you have eliminated at least one answer choice, or it is a grid-in question, feel free to take a
guess. But you should still mark it off and possibly come back to it later.
Make sure that you are using your calculator when appropriate. But be aware that your calculator
can slow you down if it is overused.
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One note about the 18 question section – this section has 8 multiple choice questions followed by
10 grid-ins. Keep in mind that numbers 6, 7 and 8 are pretty difficult, whereas number 9 is
easy. So you should jump from number 5 to number 9.
Attempt the right number of questions: You should not be attempting to solve every single
question. This may actually lower your score. See the chapter titled How Many Questions Should
You Be Attempting in Each SAT Math Section? for details.
By pacing yourself to answer less questions you will no longer feel rushed, you will have more
time to “check over” your answers properly, and you will not be wasting time on questions that
you are very likely to get wrong anyway.
The rest of the information here is for all students
The correct way to check over your answers: So you have answered all the questions specified
above, and you have about seven minutes left. What is the best way to check your answers?
DO NOT simply look over your work. Start the test over and redo each question from the
beginning without looking at your prior work. Ideally you should try to use a different method
than you used the first time.
If you picked numbers the first time, then at least pick new numbers. If you cannot think of a
different way to solve it, that’s okay. Just do it again. Then compare your two answers. If they
are the same, move on. If not, then take a little time to catch your careless mistake.
Summary:
(1) When taking your SAT make sure you pace yourself properly.
(2) Be aware of how much time you are spending on any problem.
(3) “Check” over your answers the right way.
Use this method on at least four practice tests before you take the real SAT. This way you will be
very comfortable when you take the actual exam. Pacing yourself properly will give you plenty
of time to check your work and ensure that you get a perfect 800 or near perfect score. Now this
system only works if you have been preparing for the test properly. You may want to take a look
at the “Get 800” collection of SAT math prep books for this purpose.
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How Many Questions Should You Be Attempting in Each SAT Math Section?
In this chapter we are going to discuss how to increase your SAT math score by answering
FEWER questions. The information given here is only for students currently scoring below 630
in math on College Board practice SATs.
Many students are under the misconception that they are supposed to get through every question
on every section of the SAT. This is 100% false. If you answer 2/3 of the questions on each math
section of the SAT you can score as high as a 600. Note that a 600 in SAT math is a very good
score.
This may seem strange at first. How can answering only 2/3 of the math questions on the SAT
give you a very good score? If you only answer 2/3 of the questions on a test in school, this
would usually be considered a failing grade.
Remember that the purpose of a standardized test like the SAT is to classify students by their
ability level so that colleges can tell the difference between students coming from different
schools. The purpose is NOT to give you a passing or failing grade.
Now, note that roughly 1/3 of the math questions on the SAT are easy, 1/3 are medium, and 1/3
are hard.
This means that a score of 600 can be attained without answering a single hard question.
So how many questions should you be answering?
Well, there are three math sections on the SAT. They can appear in any order. there is a 20
question multiple-choice section, a 16 question multiple-choice section, and an 18 question
section that has 8 multiple-choice questions and 10 grid-ins.
Let us call these sections A, B, and C, respectively. You should first make sure that you know
what you got on your last SAT practice test, actual SAT, or actual PSAT (whichever you took
last). What follows is a general goal you should go for when taking the exam.
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For example, a student with a current score of 400 should attempt the first 12 questions from
section A, the first 10 questions from section B, the first 4 multiple-choice questions from
section C, and the first 4 grid-ins from section C.
This is just a general guideline. If you are particularly strong in one subject area, you may want
to attempt one or two harder questions in that specific subject.
As your score on practice tests improves you can begin attempting more problems as given by
the chart above.
Try to pace yourself so that you are getting through the appropriate number of questions (as
given by the above chart) with at least 5 minutes left to “check over” your answers. By “check
over” I always mean redoing each question from the beginning, preferably using a different
method than the method that you used the first time around.
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Should You Go with Your First Instinct to Take Guesses in SAT Math?
In this chapter I would like to discuss a piece of test taking advice that is often given in error.
This piece of advice is to “go with your first instinct.” Many people will tell you that after
choosing an answer, you shouldn’t go back and change that answer because your first instinct is
usually correct. When it comes to the SAT we need to scrutinize this advice very carefully.
VERY IMPORTANT NOTE: Do not mistake understanding for instinct. If you actually have
some understanding of the problem, you can use that to help choose your answer. This is very
different from what I am describing here.
Now, going with your first instinct only makes sense for about one third of the SAT math
questions. Roughly speaking, on any math section the first third of the questions is easy, the
second third medium, and the last third hard.
Let’s look at the 20 question multiple choice section in detail. In this case, roughly speaking,
numbers 1 through 7 are easy, numbers 8 through 14 are medium, and numbers 15 through 20
are hard.
Basically you should go with your instinct on questions 1 through 7, but not on the rest of the
questions.
In fact, for those last 6 questions you are better off going AGAINST your instinct. In other
words, if you have no idea how to do number 17, but your instinct is telling you that the answer
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is B, then you should actually eliminate choice B and take a guess from the remaining four
choices. This is one example of using the technique of Quasi-elimination.
Going against your instinct may sound like a crazy strategy, but if you understand how the SAT
is made, it actually makes perfect sense.
Each SAT has an experimental section. This extra section may be math or verbal, and it is not
graded. It is used to determine the difficulty level of each question so that these questions can be
placed properly on a future SAT. If one of these questions is answered correctly by most students
it becomes an easy question and it gets placed in the first third of a math section. If this question
is answered incorrectly by most students, it becomes a hard question and it gets placed in the last
third of a math section.
So a question became number 17 because most students got it wrong on an experimental section.
Many of these students used their instinct to get a wrong answer. They were tricked. This is why
your instinct will fail most of the time on these hard questions. On the medium questions your
instinct will fail some of the time – enough that it shouldn’t be used.
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Stop Making Careless Errors in SAT Math
In this chapter we will go over the steps you should take to put an end to the careless errors you
keep making when attempting SAT math problems.
Before we can put an end to careless errors we need to discuss what a careless error actually is. If
you look up the definition of “careless” you will get something like “not giving enough attention
and thought to what you are doing.” So most people would say that a careless error is one that
could have easily been prevented if only they had paid a bit more attention to what they were
doing. But on the SAT this is only one of the types of errors that students call “careless.”
In fact, it is very common for students to say “my SAT math score would have been × points
higher if only I didn’t make so many careless errors.” How can it be that so many students are
making so many careless errors on the SAT? The answer is that most of the time students are
referring to errors as “careless” even though these errors do not fit the actual definition of the
word “careless.”
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Most “careless” errors are not careless at all. These are usually mistakes that the student made
because he or she was tricked by the question. SAT math questions are intentionally designed to
be tricky. The underlying math, however, is usually so simple that when the student sees the
correct answer he or she immediately understands what was done wrong. The student then
erroneously dismisses the mistake as a “careless error.”
In other words, students very often mistake understanding their error quickly for having made a
careless error. This kind of misinterpretation leads to bad preparation. In a sense the student falls
into the test makers’ trap twice. The first time is when they are tricked into getting the question
wrong. The second time they are tricked into believing that they only got the question wrong
because they weren’t being careful enough.
The first trap is no big deal. It can easily be fixed by redoing that problem periodically until you
can get the answer right on your own. But the second trap is fatal. When you fall into the second
trap you are tricked into never reattempting that problem. Guess what? If a similar type of
problem comes up on the SAT you may very well get tricked again.
So for our purposes there are two kinds of careless errors – errors made due to lack of focus and
attention, and errors made because of being tricked. When reading through the following list,
keep in mind that I am teaching you how to minimize both of these types of “careless errors.”
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(1) Stop rushing: One of the main reasons that students make careless errors on SAT math
problems is that they are so worried about getting to the end of the section that they are not
focusing on the problem in front of them. Do not worry about getting to the end of the section.
Do each problem carefully and even take a few moments to check over your answer before you
move on. You should never answer a question quickly just to get to the next question. Your
speed will increase naturally as you practice and learn SAT specific math strategies.
(2) Do not get hung up on one question: Getting hung up on one SAT math question leads to
rushing which in turn leads to careless errors. The remedy for this is quite simple. Always be
aware of when you have spent about 30 seconds on a question. At that point you should decide if
you can get the answer within the next 45 seconds. If so, then finish the problem. If not, mark it
off and move on. Don’t worry – it’s not forgotten. You will come back to it later. And when you
come back to it you will still remember the work that you have done, so that none of that time
was wasted.
Remark: “30 seconds” is intended for a student that is currently scoring a 650 or higher on
practice tests. If you are scoring between 500 and 650, then you can spend about 45 seconds
before deciding if you should move on to the next question. If you are scoring below a 500, then
you can spend a full minute on each question before deciding if you should move on.
(3) Learn SAT specific math strategies: The more strategies that you know, the less likely you
will be to make careless errors. Using strategies will ensure that you do not get tricked. Practice
using these strategies as often as possible before test day so that you can use them quickly, and
effortlessly when you take your SAT.
(4) Practice solving problems in several different ways: The more ways you can solve a
problem, the easier it will be for you to avoid falling into any traps that have been set for you.
When practicing, I recommend trying to solve every practice problem in up to four ways:
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(1) Using an SAT specific strategy
(2) The quickest way you can think of
(3) The way you would do it in school
(4) The easiest way for you
During the actual exam you should try to solve each SAT math problem using one method, and
then use a second method later on when “checking over” your answer (see (9) below).
(5) Practice 10 to 20 minutes per day: If you are studying effectively, the number of careless
errors you make should continually be decreasing. Make sure that you periodically keep redoing
problems that you get wrong in addition to attempting new problems.
(6) Do not dismiss errors as “careless” when practicing: Anytime you get a problem wrong,
make sure you mark it off, and reattempt it again in another week or so. It does not matter why
you got this problem wrong. A mistake that many students make is to say “it was just a careless
error – it won’t happen again,” and then to never look at that problem again. The reality of the
situation is that you may very well keep making that same “careless” error because you may fall
into the same trap. So do not just assume you will get the problem correct next time you attempt
it. Wait at least a few days, then reattempt the problem again, and you will see firsthand whether
you get it right or wrong. If you still get it wrong attempt it again in another week. Repeat until
you get it right on your own.
It is important that you wait at least a few days before reattempting a problem you got
wrong - you want to give yourself a chance to forget the nature of that specific problem. This
will ensure that you are actually solving the problem, and not just “recalling the solution.”
Redoing problems you get wrong is extremely important – more important than attempting new
problems. This is what separates students that show dramatic improvement from students that
show only average improvement. Remember, you learn from your mistakes, not your
successes!
(7) Make sure you have answered what the question was asking for: After you get your
answer look back at the question and make sure you are answering what they asked for. For
example, are they asking you to solve for x, or for 3x? Are they asking for the quotient, or the
remainder?
(8) Do not go with your instinct on hard questions: The more difficult SAT questions are
specifically designed to trick you. This means that if you go with your first instinct on these
questions, you are probably falling right into the trap that was laid out for you. On high
numbered math questions on the SAT you should actually eliminate a choice if your intuition
leads you to that answer too quickly. If you have a proper justification for why that particular
answer is correct, then of course you can choose that answer. Otherwise however you should
take a guess from the other choices. Also relevant here is the method of Quasi-elimination.
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(9) “Check” your answers the correct way: If you are pacing yourself properly during the
exam, you should wind up with several minutes to check over your answers. So what is the best
way to do this?
DO NOT simply look over your work. Start the test over and redo each question from the
beginning without looking at your prior work. Ideally you should try to use a different method
than you used the first time (See (4) above).
If you picked numbers the first time, then at least pick new numbers. If you cannot think of a
different way to solve it, that is okay. Just do it again. Then compare your two answers. If they
are the same, move on. If not, then take a little time to catch your careless mistake.
(10) Use your TI-84 calculator effectively: Your calculator can be used to save time or to waste
time. Sometimes I see students typing away on their calculators without taking any break. What
they are usually doing here is wasting time. Your calculator is a tool that is there for you to speed
up computations. It is not there to solve the problem for you.
If you are taking the test right, you shouldn’t be using your calculator all that much.
That said, make sure that you do use your calculator for arithmetical computations. This is
usually quicker than doing computations by hand or in your head, and you are less likely to make
a careless error.
Finally, make sure that you know how to input things into your calculator correctly. Many
students mess up their order of operations when using calculators, especially using parentheses
correctly. Remember that, as a general rule numerators, denominators and exponents should all
be in parentheses when using your calculator.
How to prepare in a way that minimizes careless errors: You may want to try preparing for
SAT math with the “Get 800” collection of books. If you do, you will notice that you will begin
making fewer and fewer careless errors as you go through your preparation.
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Eliminating Test-taking Anxiety on the SAT
A little bit of anxiety is actually not a bad thing. That bit of excitement can actually help you
perform better at a task. Most students have some level of test-taking anxiety, but some have
more than others. It’s when the anxiety is so great that it actually begins to hurt your score that
we need to deal with it.
There are some reasons for nervousness that can easily be avoided. For example, when you come
to a problem that is giving you a lot of trouble there is no reason to get all nervous. Simply move
on, and come back to it later if you have time.
Here are some of the best ways that you can keep test-taking anxiety from hurting your score.
(1) Be prepared: Being prepared for the test will go a long way toward reducing your test-taking
anxiety. Start preparing for the SAT about three to four months before taking your exam. Make
sure you learn as many SAT specific math strategies as possible.
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Throughout these three to four months, practice SAT math problems for ten to twenty minutes
every day right up until two days before the test. The day before the test you should take time out
to relax. If you have taken the right amount of time to study, cramming the day before exam day
could hurt your score because you will be increasing your anxiety level. Take off from studying
the day before your SAT. This one extra day of studying will not improve your score.
Make sure you take at least four practice tests before the actual SAT. Use the second edition of
the College Board’s Official SAT Study Guide for this purpose.
(2) Increase confidence: A lack of confidence manifests itself as anxiety. Being prepared will
go a long way to increasing confidence. Your confidence will naturally increase as you get more
and more SAT math questions correct. If you are a nervous test-taker, it is important that you are
getting some questions correct during your short study sessions. I therefore recommend that at
each study session you attempt some problems that are easy for you. For example, if you are
currently struggling with Level 4 number theory SAT math problems, then at your number
theory study sessions do a couple of Level 2 and 3 number theory SAT math problems in
addition to some Level 4 problems.
Remark: Remember that your score only improves by turning failure into success. So it is very
important that you are getting some questions wrong. The particular strategy just mentioned is to
make sure that your score is not lowered by test-taking anxiety.
(3) Know how to take the test correctly: When you walk in to take the SAT on test day make
sure you have a plan for how you will take the test. You should have memorized all the
directions and formulas given on the test. You should know exactly how you will pace yourself
during the test, and how to check over your answers correctly.
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(4) Take extra full length practice tests: A little extra practice may be what you need to gain
more confidence and reduce anxiety. Do a few extra full length practice tests. Remember to add
in an extra section to simulate the experimental section.
(5) Learn how to get yourself into test-taking “state”: Think of something that you know you
are good at. Maybe it’s a sport, or playing a certain instrument. Think about how you feel when
performing this activity. You probably have complete confidence in what you are doing, and
performing this activity comes so naturally that you do not even need to think about it. When you
are confident in your ability to perform a certain activity, you can enter the “state” necessary for
performing that activity very quickly. If you are not confident in your ability, you may need to
“warm-up” a bit before getting into state. Once you are in the appropriate state, anxiety no longer
becomes an issue – at this point your performance is determined by your ability alone. “Warmup” can be accomplished by beginning to physically perform the desired activity. But it can also
be done just by thinking about performing the activity. You can use successful past experiences
with the activity as reference points for your “warm-up.”
(6) Getting out of your head: Negative thoughts cause anxiety. Your thoughts have power over
you. You can take back this power through some simple mental techniques. If you are
experiencing high levels of anxiety, try one of the following:
Focus on your breathing, and only on your breathing. Take deep breaths, and let those breaths be
all that exist for you.
Focus on a simple task. Put all of your mind and energy into that mundane activity – make it all
that exists.
Listen carefully to the sounds around you. Try to isolate each sound
and listen to them individually. Then try to find the silence from
where all of these sounds are emanating. Focus on that silence (note
that it does not need to be silent for you to find this silence).
When negative thoughts try to attack you just listen to them. Do not
try to respond to them, do not judge them, just listen, and they will
eventually pass through you.
If you feel that anxiety will affect your SAT score, then I
recommend trying one of these techniques for at least a few minutes
each day. Also try one of these meditations right before taking
practice tests, and especially the morning of your SAT. Note that
these meditative techniques take practice. They will become more
effective the more you use them. To learn more about these types of
meditation techniques you may want to take a look at a book
called Full Catastrophe Living.
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(7) Quick warm-up the morning of the test: Do a few math problems the morning of your
SAT before taking the test. Make sure that these problems are not difficult for you. The purpose
of this is not to practice; it is to get your mind into the correct state (see (5) above).
(8) Release some tension on the way to the test: In the car on the way to the exam let out a nice
big scream. Get rid of all of that pent up anxiety. You may want to warn anyone else in the car
before you do this. Tell them that Dr. Steve said that it’s okay.
That should be enough information to help manage your test-taking anxiety in the future.
Remember that if you are anxious over the SAT, this means that you care about your
performance on the test. The best way to get over this anxiety is with good preparation.
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Stop Getting Those Last Few Hard SAT Math Questions Wrong
Today we are going to discuss how to stop getting those last few hard questions wrong. If you
are a student currently scoring between a 650 and a 750 in SAT math and you want to get the
best possible score, then this is probably one of your main concerns.
I first want to point out that the College Board determines the difficulty level of each SAT
question by how many students got that question wrong on an experimental section from a
previous SAT. So the reason that a question is appearing at the end of a math section may not
have to do with the actual difficulty level of the question. All we know for certain is that one
large group of students got this question incorrect. There are several possible reasons that so
many students got this question wrong.
These include:
(1) The question actually was very difficult
(2) The question was hard to understand
(3) The question was tricky
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Simply practicing Level 4 and 5 problems will go a long way to handling the first and second
point. Just do a few of these hard problems a day making sure that you reattempt the questions
you get wrong every few days until you can get these questions right on your own. You may
want to review the following chapter on proper preparation: The Correct Way To Prepare For
SAT Math
Now let’s focus on the third point. One way to avoid being tricked is to always remember not to
go with your first instinct on these hard problems. Review the following chapter for more
information on this: Should You Go With Your First Instinct In SAT Math?
Let’s discuss another way to avoid be tricked. Strong math students tend to fall into the trap of
doing the last few math questions the same way that they would do them in school. If you are
solving a more difficult SAT problem this way, very often you will fall into the test makers’ trap.
Then, when you look over your answer, the mistake seems “obvious” and you just assume that it
is a “careless error” (read the following chapter to learn how to eliminate careless errors: Stop
Making Careless Errors In SAT Math).
Therefore you do not think about how the problem could have been done differently.
Unfortunately, this will keep happening over and over because those last few problems in the
section are unique, and you will never see that particular problem again on an SAT. This is why
it is very important to begin to practice solving these problems using SAT specific math
strategies .
I want to emphasize that it is not enough to simply know these strategies. You must practice
implementing them at the right times. As a very simple example, if question number 20 has
variables in the answer choices, DO NOT try to solve this problem using algebra. Use the
strategy of picking numbers instead. This particular strategy is very basic and involves
substituting in specific numbers for the variables before solving the problem.
As an example, let’s look at the following problem.
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There are b bricks that need to be stacked. After k of them have been stacked, then in terms
of b and k, what percent of the bricks have not yet been stacked?
Since this is a percent problem we choose 100 for the total number of bricks. So b = 100.
For k, let’s choose 25, so 25 bricks have been stacked, and 100 – 25 = 75 have not been stacked.
Since we started with 100 as our total, 75% of the bricks have not been stacked. Remember
to put a big, dark circle around75%. We make the substitutions b = 100 and k = 25 into
each answer choice.
(A) 100/7500 ~ 0.0133% (~ means “is approximately”)
(B) 7500/100 = 75%
(C) 10,000/25 = 400%
(D) 2500/100 = 25%
(E) 25/10,000 = 0.0025%
We now compare each of these percents to the percent that we put a nice big, dark circle around.
Since (A), (C), (D) and (E) are incorrect we can eliminate them. Therefore the answer is (B).
Important note: (B) is not the correct answer simply because it is equal to 75%. It is
correct because all 4 of the other choices are not 75%. You absolutely must check all five
choices!
As you can see, even basic strategies like picking numbers, taking guesses, plugging in answer
choices, and drawing pictures can be extremely effective in hard problems.
If you want to learn all of the strategies necessary to keep you from getting these last few
difficult problems wrong, then check out the “Get 800” collection of SAT math prep books.
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Should You Take a Prep Course for the SAT?
In this chapter I am going to help you decide if you should sign up for an SAT math prep course,
or if you should continue preparing on your own. Taking a course can be quite costly, so it is
best to be as informed as possible before making a decision.
The main reason to sign up for a course is for motivation. A prep course can keep you focused
and on the correct path. If you are a student that can motivate yourself successfully, then there is
no need to take an expensive course.
Now I don’t want to give the impression that I am against SAT prep courses. I think that they can
be great. In fact, I have been running them for over twelve years.
If you do decide to take a course, here are some things that you should find out about the person
or company that you will be dealing with.
Their results: what is the average score increase that students get from their PSAT to their SAT
after taking this course? Would you really want to pay for a service that does not produce
results?
Group size: I always prefer groups of about 3 to 5 students. This is small enough to give
individualized attention, and large enough to have a nice group dynamic.
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Grouping method: Do they group students by their PSAT scores? If you scored a 650 in math
on your PSAT, you do not want to be in the same group as someone who scored a 400. You will
most likely be wasting time practicing problems that you do not need help with, and the 400
student will be struggling with problems that he or she will not even get up to on the actual
exam.
Hiring practices: Does the company or person you may deal with hire people just based upon
their SAT scores, or do they make sure that they have exceptional teachers? Do they have
separate instructors for Verbal and Math? What are the credentials of these instructors?
Instructor salaries: In general, you get what you pay for, and in the case of a prep course, you
get what the company is paying for. Make sure that their tutors are paid well.
Feedback: What are other people saying about them? Remember, the best recommendation is
from friends who have already used them and have gotten an exceptional result. If you cannot
get this kind of recommendation, it is EVEN MORE important that you check credentials using
the other suggestions mentioned in this list.
Keep in mind that there are often local tutors that do a much better job than some of the big name
companies, and are less expensive. Local companies and tutors do not generally have many
expenses, so they can pass these savings on to you. And there are many exceptional ones out
there. Ask students that you know who have already taken the SAT where they went for
preparation. Find out their results and if they were happy with the course.
To summarize, first you should decide if you have the motivation to prepare for the SAT on your
own. If so, make sure you stick to a study plan using the suggestions in this chapter. If you
decide you would like to sign up for a course, make sure you get the appropriate information
before deciding whom to use.
How to prepare if you decide to study on your own: If you do decide to study on your own, I
suggest you take a look at the “Get 800” collection of SAT math prep books.
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Using Your Time Efficiently to Raise Your SAT Math Score
In this chapter I would like to emphasize the best ways to use your time as efficiently as possible
on the math sections of the SAT.
(1) Make sure you are familiar with the test: Learn all of the directions long before taking the
test, and make sure that you are familiar with the layout of the test. In particular, there are three
math sections (as you know), each a different length, and there are two different types of
questions – multiple choice and grid-ins. SAT math tests four major subject areas – number
theory, algebra and functions, geometry, and probability and statistics. The questions roughly
increase in difficulty level throughout each section, and each question is worth the same amount
of credit. There is a guessing penalty for getting a multiple choice question wrong so it is best to
guess on these questions only if you can eliminate at least one answer choice. You can use a
calculator on the SAT – I always recommend using a TI-84, or a graphing calculator that is
comparable to this one.
(2) Memorize all relevant math formulas: There is a short list of formulas that you should
commit to memory as soon as you begin your SAT math preparation. For starters, memorize the
formulas that are given to you on the SAT – no need to waste time looking these up when you
can just commit them to memory in a very short time.
(3) Learn SAT specific strategies: You should be learning two to three strategies each week for
a period of three to four months before taking your SAT.
45
(4) Practice SAT math problems ten to twenty minutes per day: Each day you should learn
one new strategy, or quickly review one that you already know. Then choose one of the four
subject areas to focus on. Spend half your study session trying new SAT math problems, and the
second half redoing problems you have previously gotten wrong. It is very important that you are
focusing on questions that are at and slightly above your current ability level.
For (3) and (4) you may want to use the “28 SAT Math Lessons” series. Each book in this series
is targeted for students in a specific score range. Get the book for your score range and you will
get enough practice problems to get to the next score level. In addition you will be learning the
most important strategies, concepts and formulas all targeted specifically for you.
(5) Practice tests should be done in moderation: Taking practice tests is NOT the most
effective way to improve your SAT math score. Some students prepare by doing practice test
after practice test, but their score shows little to no improvement because they are violating the
basic principles established in point (4) above. The purpose of practice tests is to make sure that
you are implementing the strategies you have learned correctly under timed conditions. If you
are going for an 800 or near perfect score, then watch the video below for details on how to take
these practice tests (as well as the actual SAT) the best way. You should take at least four
practice SATs before test day, about one per month. These tests should all be actual SATs or at
least tests created by The College Board. Make sure you time these tests correctly, and score
them yourself using the formula c – w/4, where c is the number of questions you got correct,
and w is the number of multiple choice questions you got wrong.
(6) Break bad patterns: If your score is not improving as you would hope there is usually a
simple explanation. If you find yourself making a lot of “careless errors,” then you need to ask
yourself if you are dismissing these questions too quickly. If you are struggling with the last few
questions at the end of each math section, then review this chapter. Are you redoing questions
that you got wrong? Failing to do so will keep you from showing any major improvement. Make
sure that you keep redoing the problems you get wrong until you can get them right on your
own without messing up at all.
46
Best of luck with your SAT preparation,
Dr. Steve Warner , Get 800
Tel: 718-980-2935
[email protected] |www.SATPrepGet800.com
47
About the Author
Steve Warner, a New York native, earned his Ph.D. at Rutgers University in Pure Mathematics
in May, 2001. While a graduate student, Dr. Warner won the TA Teaching Excellence Award.
After Rutgers, Dr. Warner joined the Penn State Mathematics Department as an Assistant
Professor. In September, 2002, Dr. Warner returned to New York to accept an Assistant
Professor position at Hofstra University. By September 2007, Dr. Warner had received tenure
and was promoted to Associate Professor. He has taught undergraduate and graduate courses in
Precalculus, Calculus, Linear Algebra, Differential Equations, Mathematical Logic, Set Theory
and Abstract Algebra.
Over that time, Dr. Warner participated in a five year NSF grant, “The MSTP Project,” to study
and improve mathematics and science curriculum in poorly performing junior high schools. He
also published several articles in scholarly journals, specifically on Mathematical Logic.
Dr. Warner has over 15 years of experience in general math tutoring and over 10 years of
experience in SAT math tutoring. He has tutored students both individually and in group settings.
In February, 2010 Dr. Warner released his first SAT prep book “The 32 Most Effective SAT
Math Strategies.” The second edition of this book was released in January, 2011. In February,
2012 Dr. Warner released his second SAT prep book “320 SAT Math Problems arranged by
Topic and Difficulty Level.” Between September 2012 and January 2013 Dr. Warner released
his three book series “28 SAT Math Lessons to Improve Your Score in One Month.” In June,
2013 Dr. Warner released the “SAT Prep Official Study Guide Math Companion.” In November,
2013 Dr. Warner released the “ACT Prep Red Book – 320 Math Problems With Solutions,” in
May, 2014 Dr. Warner released “320 SAT Math Problems arranged by Topic and Difficulty
Level” for the Level 2 test, and in July, 2014 Dr. Warner released “320 SAT Math Problems
arranged by Topic and Difficulty Level” for the Level 1 test.
Currently Dr. Warner lives in Manhattan with his two cats, Achilles and Odin. Since the age of
4, Dr. Warner has enjoyed playing the piano—especially compositions of Chopin as well as
writing his own music. He also maintains his physical fitness through weightlifting.
48
Books by Dr. Steve Warner
Connect with Dr. Steve Warner
49

SAT Math Survival Guide - Amazing GrAdes Tutoring

Transcription

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