sat math 1 notes
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8/8/2019 SAT Math 1 Notes
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When Shrugging, Try Plugging
Math 1Plugging in Numbers
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Todays Lesson
Plug in numbers to find a goal number
Plug in answer choices to the question
Obey variable rules provided in the question
Apply Knewtons math philosophy
Today you will learn how to
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x = 3
Divide both sides by 5.5x = 15
5x + 15= 30 Subtract 15 from both sides.
SAT Math
A math teacher wants you to solve equations with algebra.
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2. The way you get to your answer does not have
to be pretty.
3. You have a calculator use it!
4. Never get stuck doing something is better
than doing nothing.
Knewtons SAT Math Rules
When you get stuck, you can almost always
Plug In Numbers (PIN)!
1. SAT Teachers are different from Math Teachers.
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Why Plug in Numbers?
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3(2 + 5) = 3(7) = 21
Why Plug in Numbers?
Matt has 2 CDs, and Elana has 5. If Jeremy has 3 times as many
as both of them combined, how many CDs does he have?
3(2 + 5) = 3(7) = 21
Setting up word problems with arithmetic is natural as well.
You know you can handle arithmetic on the SAT.
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(6 + 4)2? (6 + 4x)2? (6 + 4)2x?
Why Plug in Numbers?
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are x place-settings, how many silver utensils are
there, in terms of x?
Setting up word problems with algebra can be even trickier.
Algebra is often a little trickier than arithmetic.
3(2x + 4) x = 22
(6x + 12) x = 22
5x + 12 = 22
5x = 10
x = 2
But notice what happens when we PIN!
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x + 6(A)
2x + 6(C)
4x + 3(D)
4x + 6(E)
2x + 3(B)
Multiple-Choice
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are x place-settings, how many silver utensils are
there, in terms of x?
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x + 6(A)
2x + 6(C)
4x + 3(D)
4x + 6(E)
2x + 3(B)
Multiple-Choice
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are x place-settings, how many silver utensils are
there, in terms of x?
Pick any number for x...
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x + 6(A)
2x + 6(C)
4x + 3(D)
4x + 6(E)
2x + 3(B)
Multiple-Choice
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are 5 place-settings, how many silver utensils arethere, in terms of5?
Pick any number for x... x= 5
(5 places)
(4 eating utensils) + (6 serving utensils) =20 + 6 = 26
Half of the utensils are silver...
12
(26) = 13 silver utensils
So, when we plug in x = 5, the result is 13.
This result is our Goal Number.
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5 + 6(A)
2(5) + 6(C)
4(5) + 3(D)
4(5) + 6(E)
2(5) + 3(B)
Multiple-Choice
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are 5 place-settings, how many silver utensils arethere, in terms of5?
13 is our Goal Number.
Plug 5 in for xin the answer choicesto see which one yields 13.
ALWAYS
REMEMBER
When Plugging in Numbers to find a Goal Number, you must test all five
answer choices. Its possible more than one will yield the Goal Number.
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Multiple-Choice
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are 5 place-settings, how many silver utensils arethere, in terms of5?
13 is our Goal Number.
x + 6(A)
2x + 6(C)
4x + 3(D)
4x + 6(E)
2x + 3(B)
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The Goal Number
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The Goal Number
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are 3 place-settings, how many silver utensils arethere, in terms of3?
x + 6(A)
2x + 6(C)
4x + 3(D)
4x + 6(E)
2x + 3(B)
What if we had picked a different number?
x = 3
12 + 6 = 18
(3 places) (4 eating utensils) + (6 serving utensils) =
Half of the utensils are silver...
12
(18) = 9 silver utensils
So, when we plug in x = 3, 9 is our Goal Number.
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3 + 6(A)
2(3) + 6(C)
4(3) + 3(D)
4(3) + 6(E)
2(3) + 3(B)
The Goal Number
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are x place-settings, how many silver utensils are
there, in terms ofx?
9 is our Goal Number.
3
3
18
15
12
9
9
ALWAYS
REMEMBERWhen 2 answer choices yield the Goal Number, you need to Re-PIN.
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x + 6(A)
2x + 6(C)
4x + 3(D)
4x + 6(E)
2x + 3(B)
The Goal Number
There are 6 serving utensils in the center of the table, and 4 eating
utensils at each place-setting. If half of the utensils on the table are
silver, and there are x place-settings, how many silver utensils are
there, in terms of x?
13
11
x= 3
x= 5
Goal Number : 9 Goal Number : 13
18
15
12
9
9 Only Re-Pin for answers thatgave you the Goal Number!
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When should you plug in?
The Goal Number
If you see variables in the answer choices.
If you see in terms of in the question.
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When should you plug in?
The Goal Number
If you see variables in the answer choices.
If you see in terms of in the question.
Avoid choosing 0 and 1. They act differently than most other numbers.
x + 6(A)
2x + 6(C)
4x + 3(D)
4x + 6(E)
2x + 3(B)
There are 6 serving utensils in the center of the table, and 4 eating utensils at each place-
setting. If half of the utensils on the table are silver, and there are x place-settings, how many
silver utensils are there, in terms of x?
Variables in the answer choices
In terms of in the question
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2a(A)
8a(B)
If 2b = a, what does (b/4) equal in terms ofa?
(C)8a
(D)a
8
(E)a
4
Multiple-Choice
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2a(A)
8a(B)
If 2b = a, what does (b/4) equal in terms ofa?
(C)8a
(D)a
8
(E)a
4
ALWAYS
REMEMBER
When you see the phrase in terms of you can always
plug in for that variable.
Multiple-Choice
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PIN for the variable after the words in terms of.2a(A)
8a(B)
If 2b = a, what does (b/4) equal in terms ofa?
(C)8a
(D)a
8
(E)a
4
a = 8
2b = 8
b = 4(b/4) = 1
1 is our Goal Number.
Multiple-Choice
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a
4
2a(A)
8a(B)
If 2b = a, what does (b/4) equal in terms ofa?
(C)8a
(D)8
(E)
a
When more than one answer choice gives you the Goal Number, Re-PIN.
When you Re-PIN, you only need to check the remaining answer choices.
Multiple-Choice
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2a(A)
8a(B)
If 2b = a, what does (b/4) equal in terms ofa?
(C)8a
(D)a
8
(E)a
4
a = 6
2b = 6
b = 3(b/4) = 0.75
0.75 is our Goal Number.(E)
a
4
a = 6
Multiple-Choice
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a
4
2a(A)
8a(B)
If 2b = a, what does (b/4) equal in terms ofa?
(C)8a
(D)8
(E)
0.75 is our Goal Number.
a = 6
a
Multiple-Choice
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If 12 percent ofkequals 30 percent ofj, which of the following expresses
jin terms ofk?
Multiple-Choice
3.6% ofk(A)
18% ofk(B)
40% ofk(C)
42% ofk(D)250% ofk(E)
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If 12 percent ofkequals 30 percent ofj, which of the following expresses
jin terms ofk?
3.6% ofk(A)
18% ofk(B)
40% ofk(C)
42% ofk(D)250% ofk(E)
When plugging in numbers for percentages, use 100.
12% of 100 = 12
Multiple-Choice
k= 100
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If 12 percent ofkequals 30 percent ofj, which of the following expresses
jin terms ofk?
3.6% ofk(A)
18% ofk(B)
40% ofk(C)
42% ofk(D)250% ofk(E)
When plugging in numbers for percentages, use 100.
12 = 0.3j
40 = j(Divide both sides by 0.3)
40 is our Goal Number.
Multiple-Choice
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If 12 percent ofkequals 30 percent ofj, which of the following expresses
jin terms ofk?
3.6% ofk(A)
18% ofk(B)
40% ofk(C)
42% ofk(D)250% ofk(E)
40 is our Goal Number.
k= 100
3.6
18
40
42250
Multiple-Choice
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More Applications
of PIN
Pl i I N b
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Given that xis a positive integer...
If 5 < y, then what is the
Plugging In Numbers
On the SAT, you can choose to work with numbers rather than
with variables.
When the SAT gives you Variable Rules, you can PIN.
Just remember to PIN with a number that obeys the rules!
If the product ab is odd...
M lti l Ch i
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Multiple-Choice
If -1 < a < 0, which of the following gives the correct ordering ofa, a2, and a3
from least to greatest?
a < a2 < a3(A)
a < a3 < a2(B)
a2 < a < a3(C)
a2
< a3
< a(D)a3 < a < a2(E)
M lti l Ch i
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ALWAYS
REMEMBER
Use parentheses when entering
negative numbers in a calculator.
Multiple-Choice
If -1 < a < 0, which of the following gives the correct ordering ofa, a2, and a3
from least to greatest?
a < a2 < a3(A)
a < a3 < a2(B)
a2 < a < a3(C)
a2
< a3
< a(D)a3 < a < a2(E)
(-.5)^2
.25
Lets pick a= (-.5)
Pick any number for a...
a2 = (.25)
...as long as it obeys the Variable Rules.
M lti l Ch i
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(-.5)^3
Multiple-Choice
If -1 < a < 0, which of the following gives the correct ordering ofa, a2, and a3
from least to greatest?
a < a2 < a3(A)
a < a3 < a2(B)
a2 < a < a3(C)
a2
< a3
< a(D)a3 < a < a2(E)
Lets pick a= (-.5)
Pick any number for a...
a2 = (.25)
a3 = (-.125)
-.125
-.5 < -.125 < .25
...as long as it obeys the Variable Rules.
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Plugging in
Answer Choices
Pl i I A
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Often the SAT asks you to find the value of a variable.
If you are asked to find the value of a variable and the SAT gives
you numbers for the answer choices, plug them in.
ifx2 + 7 = 88, then x could be
8(A)9(B)
10(C)
11(D)
12(E)
If x2 + 7 = 88 then, x could be...
What is y when...
Plugging In Answers
M ltiple Choice
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Multiple-Choice
Ifxis an integer and 2 is the remainder when 3x+ 11 is divided by 5,
thenxcould be
4(A)
5(B)
6(C)
7(D)
8(E)
Multiple Choice
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Ifxis an integer and 2 is the remainder when 3x+ 11 is divided by 5,
thenxcould be
4(A)
5(B)
6(C)
7(D)
8(E)
ALWAYS
REMEMBER
If youre looking for the value of a variable, you
can almost always plug in the answer choices!
Multiple-Choice
Multiple Choice
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Ifxis an integer and 2 is the remainder when 3x+ 11 is divided by 5,
thenxcould be
4(A)
5(B)
6(C)
7(D)
8(E)
One of these answer choices must work for x.
Plug in x = 4
3(4) + 11
5=
23
5= 4 R3
Multiple-Choice
Multiple Choice
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Ifxis an integer and 2 is the remainder when 3x+ 11 is divided by 5,
thenxcould be
4(A)
5(B)
6(C)
7(D)
8(E)
Plug in x = 7
3(7) + 11
5=
32
5= 6 R2
ALWAYS
REMEMBER
When Plugging in Answers, stop once you find a value
that works.
Multiple-Choice
Multiple Choice
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$5(A)
$7(B)
$8(C)
$10(D)
$11(E)
A ticket to a baseball game costs c dollars. Five friends buy tickets for the
game, and they each buy a hot dog for $3. If the total the five friends
spent was $55, then what is c ?
Multiple-Choice
Multiple Choice
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A ticket to a baseball game costs c dollars. Five friends buy tickets for the
game, and they each buy a hot dog for $3. If the total the five friends
spent was $55, then what is c ?
$5(A)
$7(B)
$8(C)
$10(D)
$11(E)
Plug in Answers when you are asked to find the value of avariable and there are numbers in the answer choices.
Multiple-Choice
Multiple Choice
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$5(A)
$7(B)
$8(C)
$10(D)
$11(E)
A ticket to a baseball game costs c dollars. Five friends buy tickets for the
game, and they each buy a hot dog for $3. If the total the five friends
spent was $55, then what is c ?
(5 tickets$8) + (5 hot dogs$3) = $55
Multiple-Choice
Multiple Choice
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$5(A)
$7(B)
$8(C)
$10(D)
$11(E)
A ticket to a baseball game costs c dollars. Five friends buy tickets for the
game, and they each buy a hot dog for $3. If the total the five friends
spent was $55, then what is c ?
5c + 5(3) = 55
We also could have used algebra.
5c + 15= 55
5c = 40
c = 8
ALWAYS
REMEMBER
Plugging in Answers is often safer than algebra,
especially when you arent sure how to begin.
Multiple-Choice
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Recap
Recap
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Recap
Make sure to obey the variable rules!
Plug inANSWERS if youre trying to find the value of a variable.
Plug in NUMBERS if you see variables in the answers.
Use a Goal Number when you can!
Recap
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Recap
ALWAYS
REMEMBER
When Plugging in Numbers to find a Goal Number, you must test all five
answer choices. Its possible more than one will yield the Goal Number.
ALWAYS
REMEMBERWhen 2 answer choices yield the Goal Number, you need to Re-PIN.
ALWAYS
REMEMBER
When you see the phrase in terms of you can always plug in for that
variable.
ALWAYS
REMEMBERUse parentheses when entering negative numbers in a calculator
ALWAYS
REMEMBER
If youre looking for the value of a variable, you can almost always plug
in the answer choices!
ALWAYS
REMEMBERWhen Plugging in Answers, stop once you find a value that works.
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CORE WORK
Whats next?
From your homepage, click the links
under Core Homework to complete
your assignments.
Do your
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