 |
| SAT MATH TRICKS |
INTRODUCTORY ALGEBRA AND SAT MATH TRICKS
ALGEBRA
AND SAT MATH TRICKS
| want to learn SAT MATH TIPS ! So what! Let's Play with numbers. I find that arithmetic can Be as entertaining
as magic. But to understand the MATHS TRICKS magical
secrets of arithmetic.requires algebra, Of course, there are other reasons to
learn algebra (SAT, modeling real-world problems, computer programming, to name
just a few), but what called me first interested in algebra was the desire to
understand some mathematical magic tricks that Now I present to you!
SAT MATH TOPICS
CHAPTER 6
PSYCHIC MATHEMATICS
Tell a volunteer from the audience,
"Think of a number, any number, but to do
It’s easy for you, "I should
say," think of a 1 or 2 digit number. "After
He reminded his volunteer that there is
no way to know his number, ask him to:
1. Double the number.
2. Add 12.
3. Divide the total by 2.
4. Subtract the original number.
Then: "Was the answer you got by
chance number SIX?" Try this
In yourself first and you'll see that
the sequence always produces the number 6 without
It matters what number was originally
selected.
For example, if the original number is
15.
1. 2x15 = 30
2. 30 + 12 = 42
3. 4 2/2 = 21
4. 21-15 = 6
Why this SAT trick works
Let's represent the original number by
the letter y. Here are the functions that
Done in the order in which you made
them:
12 and
2. 2y + 12
3. (2y + 12) / 2 = y + 6
4. y + 6 - y = 6
So don’t worrier what number your a volunteer chooses, the final answer will always be
6. If you repeat this trick, have the
volunteer add a different number in step 2 (say 18).
The final answer will be half that
number (2 x 15 = 30; 30 + 18 = 48; 48 + 2 = 24; 24 - 15= 9). MAGIC 1089!
Have the member of your audience take
out a piece of paper and pencil and:
1. Secretly write a 3-digit number in
which the first digit is larger than the
last digit.
2. Invert that number and subtract it
from the first number. If the result is
Number of 2 digits; tell them to put a 0
in front.
3. Take that answer and add it backward
to itself.
At the end of this sequence, your answer, 1089, will appear magically, it does not matter What number did you originally choose?
For example:
Why this trick works
No matter the 3-digit number that you or
anyone else chooses in this game, the final
The result will always be in 1089. Why? Let
abc denote the unknown 3-digit number.
Algebraically, this equals:
When you invert the number and subtract
it from the original number, you get them
ABC number,
algebraically equal to:
Therefore, after subtracting in step 2,
we must have one of the following multiples of 99: 099, 198, 297, 396, 495,
594, 693, 792 or 891, each of which will produce 1089 after adding it upside
down from itself, as we did in step 3.
LEAPFROG ADDITION
This trick combines a quick mental
calculation with a surprising prediction. Giving the viewer a card with ten
lines, numbered from 1 to 10, make the viewer think of 2 positive numbers
between 1 and 20, and enter them on lines 1 and 2 of the card. Then have the viewer
write the sum of lines 1 and 2 on line 3, then the sum of lines 2 and 3 online
4, and so on, as illustrated below.
WHY
THIS SAT WORKS
To perform the quick calculation, simply
multiply the number on line 7 by 11. Here 61 x 11 = 671. The reason why this
works is illustrated in the following table. If we denote the numbers on lines
1 and 2 with x and y respectively, then the sum of lines 1 up to 10 must be 55x
+ 88y, which is equivalent to 11 times (5x + 8y), that is, eleven times the number on line 7. As for the prediction,
we exploit the fact that for any positive number,
MATHEMATICS AND MATHEMATICS OF SAT.
Mastering math can help
students take the SAT, a required entrance exam many universities Even in its latest version, the mathematical reasoning section of the SAT.
It still requires an
understanding of basic arithmetic but does not ask questions that require Long
tedious calculations. In fact, he is even allowed (and recommended) to use a calculator
during the exam. There is a greater emphasis on mathematical reasoning instead
of laborious computing. The Mathematics user is encouraged to explore
creativity.
Solutions to problems.
Look at your numbers. Are there special characteristics of the problem?
What can you exploit?
As an introduction, can
you see a smart way to add?
Do not let the
parentheses fool you. Since the sum is associative, we can rewrite the Problem
like
Notice how the numbers
will cancel each other out, and all we have left is
Here is one for you to
try. Simplify:
Notice how the 3, 5, 7,
9 and 11 cancel each other, which leaves us with 1/3 Although the SAT also
covers topics such as algebra and geometry, it has a numerical sense is
invaluable. Do your answers seem reasonable? With Mathemagics, I hope we have given you a greater numerical sense.
TAGS-sat math topics, sat
maths pdf, sat math formulas, sat math practice worksheets, sat math tips, khan
academy sat math, new sat math topics
