sat math 1 notes

8/8/2019 SAT Math 1 Notes

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When Shrugging, Try Plugging

Math 1Plugging in Numbers


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WHEN SHRUGGING, TRY PLUGGING

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


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.


7/47WHEN SHRUGGING, TRY PLUGGING

(6 + 4)2? (6 + 4x)2? (6 + 4)2x?


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!



x + 6(A)

2x + 6(C)

4x + 3(D)

4x + 6(E)

2x + 3(B)

Multiple-Choice







x + 6(A)

2x + 6(C)

4x + 3(D)

4x + 6(E)

2x + 3(B)

Multiple-Choice





Pick any number for x...



x + 6(A)

2x + 6(C)

4x + 3(D)

4x + 6(E)

2x + 3(B)

Multiple-Choice



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.



5 + 6(A)

2(5) + 6(C)

4(5) + 3(D)

4(5) + 6(E)

2(5) + 3(B)

Multiple-Choice




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.



Multiple-Choice





x + 6(A)

2x + 6(C)

4x + 3(D)

4x + 6(E)

2x + 3(B)


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The Goal Number



The Goal Number




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.



3 + 6(A)

2(3) + 6(C)

4(3) + 3(D)

4(3) + 6(E)

2(3) + 3(B)

The Goal Number




there, in terms ofx?


3

3

18

15

12

9

9

ALWAYS

REMEMBERWhen 2 answer choices yield the Goal Number, you need to Re-PIN.



x + 6(A)

2x + 6(C)

4x + 3(D)

4x + 6(E)

2x + 3(B)

The Goal Number





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!



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)


(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)


(C)8a

(D)a

8

(E)a

4

a = 8

2b = 8

b = 4(b/4) = 1


Multiple-Choice


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a

4

2a(A)

8a(B)


(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)


(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)


(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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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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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)


Multiple-Choice


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jin terms ofk?

3.6% ofk(A)

18% ofk(B)

40% ofk(C)

42% ofk(D)250% ofk(E)


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



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



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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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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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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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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$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)




(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)




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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