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Lessons 3 and 4 of a SAT prep. Basic explanations and explained word problems. 

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Study note

Alie Hernan

United States of America

DEFAULT (US)

Math (SAT®)

SAT Prep- Lesson 3-4 Simplifying Expressions & Conversions

Overview

lesson 3: Simpliying Expression S
1
The law of Substitution -
-- if two things are equal, you can
always Substitute one for the other
ex: If x and
.:.Y.
numbers such that.
what is the value of 2y + 7.
?
6x
are positive
3x-2y=7₁
2y and 7 appear in both
equations and expressions
given equation :
add 2y to both sides!
x 9
3x-2y = 7
2
3x-2y = 7
+ 2% +2Y.
appears in
Since 2x + 7
the fraction,
we may remplace it with 3 y and
simplify:
2y + 7
3x
3x = 2y + 7
6 X
2
we can just plug in values for x and y
that satisfy the equation.
x = 3 and y = I are solutions because
3 (3) - 2 ( 1 )= 7
we can evaluate the fraction by plugging
in these numbers: (2 (1) + 7) / 6 (3) = 9/18
= 1/2 or 0.5
-Simplifying Percent Problems -
to increase a number by a/..,
Just multiply by (100 + a)%, and to
decrease a number by a% Just.
mutiply by (100-9.)%.
The population of sea urchins
in a particular reef has been
decreasing by 10% per year
for the last 3 years. What is the total
percent decrease. In this population
over the past 3 years?
explanation to decrease the
quantify by 10%, we must multiply
by 0.90.
if the original population is n
then the population after 3 years is
(0.90) (0.90) (0.90) n = 0.729n.
Since this is 72.9% of the original
population, the total
15
foo 72.9 = 27.1%.
Apparently it's not 30% ? - Simplifying Operations.
+ Every Operation can be expressed in terms of its inverse
increasing a positive number by 25%
and then decreasing this result by
50% is equivalent to dividing the.
number by
A) 1.33
B) 1.50
(21.60
D) 1.65
explanation: If
1.25n
will
we increase positive number n by 25%, we
I we are adding 100%. + 25%. = 125%).
If we decrease this we get 0.50.1.25n = 0.625.n.
get
multiplying by 0.625 is the same as dividing by the
reciprocal.
0.625
= 1.60
- Important Factoring Identities -
q² + b ² =
(a+b) (a−b)
a ² + 2ab + b ² = (a+b) (a+b)
9² -2 ab + b² = (a-b) (a−b)
Explanation: we must simplify any complicated
looking expressions. Here we must
Find m+n not the values of
Im and n individually.
Correct Answer is
(m²_n ²) is the
Simplified version of
(m+n) (m-n). If we
were to use the box
method to simplify we'
I would once again get
(m²-n²)
If m and n are real numbers
Such that
2-n²
m
2m-2n
m² -n²
2m-2n
こ
(m/n).
'(m+n) (m/
x (m/n).
.9.
z
=
O|N
с
2
what is the
value of
min
m+n = 9
Que can cancel
out like terms
when the equation
gets like this. - look for Patterns.
- look for simple patterns that help you simplify with the law of substitution.
explanation: (x+2) ² = x² + 4x +4
allows for a more clever
Substitution.
if x² + 4x + 5 = Y and Z = x + 2,
which of the following expresses y.
in terms of 2?
A) Y = 2² +1
B) Y = 2 (2+3)
c)y=z²+5
0) Y = (2+2²) +)
x² + 4x +5=Y
-1 -1
x²+4+4=y=1
(x+2)² = Y-1
22=
=y-!
41
+1
2² = y lesson 4: conversions
Conversion Factors
-- A conversion factor is a fraction in which the numerator and the
denominator are equal.
Ex:
I mile.
1.609 kilometers
-Using Conversion Factors -
→ when converting quantities, make sure that the units cancel properly
like common factors.
this a conversion factor
for converting kilometers
to miles..
Ex: If you run 10-km and want to know how many.
miles you ran the conversion is:
10 kilometers
Niko is 27 inches shorter than his
father who is S ft. 10 in tall.
How tall is niko? (1 ft = 12 in)
A) 3 ft 4in
B) 3ft 6in
()3ft 71
D) 3 ft 10 in
I mile
(1.609 Kilometers) = 6.215 miles
5 ft 10in = 70
5x12=60+10= 70
70-27=43
43=12= 3.7
3 ft 7 in - Universal vs. Problem - Specific" Conversions
- Sometimes the conversion factors are Universal (Ex: Ipound = 16 ounces )
always!
or some times
it is problem specific
(Ex: machine pumps 3 gallons per Inr)
I hour: 3 gallons
If a factory can manufacture
b computer screens in n days.
at a cost of c dollars per
Screen, then which of the
following reapresents
total cost, in dollars, of the
computer Screens that can be
manufactured, at that rate
in m days?
the
A) bcm
B) bmn
с
c) mc
bn
D). b.c
mn
converting days to dollars
m days (
A
1
gallons
depend on time.
H
b screens
n days
bcm
n
-) (f
dollars
dollars
Screen

SAT Prep- Lesson 3-4 Simplifying Expressions & Conversions

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SAT Prep- Lesson 3-4 Simplifying Expressions & Conversions

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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13 M

#1

950 K+

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I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying