Algebra Textbook Volume 1 Student Edition wc

1.9EE Earthquake Fault Lines – Exponent Real World Application (optional)

According to Homeland Security,
“Earthquakes are sudden violent shakings
of the earth’s crust. They are caused when
the earth’s tectonic plates move, rub,
collide or break apart.”

http://www.in.gov/dhs/2792.htm

The fault line refers to the break, fracture,
or splinter that occurs in the earth; where
fault lines exist, earthquake activity is more likely. Below is a map of the tectonic
plates around the world.

Thermal heat from the earth’s interior is the number one
cause for the movement of tectonic plates. Fault line
movement can be measured using GPS instruments such a
seismometer. Seismometers measure ground motion,
including the seismic waves motion that earthquakes
produce. Seismographs record this information in a form you
have probably seen (wiggly lines):

In 1935, a mathematician named Charles Richter developed a
scale with which the size of an earthquake could be
measured. This scale is called the Richter scale. The Richter
scale is based on an exponential function, meaning that an
increase of 1 on the Richter scale indicates a ten-fold increase
in the magnitude of the earthquake. The destruction caused

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by an earthquake is approximately described as 10 to a power (10x). So an
earthquake of 1 on the Richter scale can be thought of as having a strength of 101.
Likewise, an earthquake meaning 2 on the Richter scale can be thought of as having
a strength of 102. When referring to earthquake magnitude, the exponent is noted
(without the base 10), so a rating of 1 is equivalent to a 101 and an earthquake of
magnitude 6 is approximately 106. The strength of an earthquake is determined by
the magnitude of the destruction it causes. It is generally accepted that a minor
earthquake felt at around magnitude 4 (104) equates to approximately a 1 cm plate
movement. Damage begins to be felt around 4 or 6.
(http://www.sdgs.usd.edu/publications/maps/earthquakes/rscale.htm).

The largest earthquakes ever recorded happened in the early 1960s. The largest US
earthquake occurred in Prince William Sound Alaska (1964), registering 9.2,, and
the largest worldwide earthquake occurred in Valdivia, Chili (1960), registering 9.5
on the Richter scale (https://en.wikipedia.org/wiki/Lists_of_earthquakes).

Earthquake fault Lines – Internet Project
 Choose a country from Wikipedia’s list of earthquakes by country (above).

 Look up at least 4 earthquakes and record each of their strengths on the
Richter scale and the year they occurred.
o Record the Richter scale in two forms, decimal and round to whole
numbers. The answer will be an approximate.
o Find at least two facts regarding each of the earthquake’s effects, such
as duration, location, death count, property damage, etc.
o Find pictures of the damage done for the strongest and weakest
earthquakes that were chosen. Print these pictures.

 Graph your magnitudes [x=year, y=magnitude]; draw a line of best fit. Put
BOTH forms (example 4 and 104) on your graph!

 From your graph, determine the magnitude of the earthquake predicted five
years after the last one on your graph.
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1.9EE Earthquake Fault Lines (cont.)

 Determine how many times stronger the strongest earthquake is from the

weakest earthquake. For example, one earthquake is 102 and another

earthquake is 106 . To determine the relative magnitude, divide the

expressions – this will mean that you’ll divide the exponents. [Remember to
106
put your largest magnitude on top = 102 = 104=10,000 times stronger.]

 Make a poster to present your findings. Be ready to share your poster with
the class.

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1.10A Negative Exponents Name_________________________________

Negative exponents mean that the number is ______________________ and the exponent
is made _________________________. To move a number it goes from the ____________________
to the _____________________________. All answers should only have ____________________
exponents. The first one has been done for you.

Simplify:

1) x3y−2 = x3  1 = x3
1 y2 y2

2) 495−7 ____________________________________________________________________________________
3) 656−3____________________________________________________________________________________
4) 7−8714___________________________________________________________________________________
5) M15M−12_________________________________________________________________________________
6) C−6C13___________________________________________________________________________________
7) A4B−6A−2B8_____________________________________________________________________________
8) 623−2_____________________________________________________________________________________
9) 844−4_____________________________________________________________________________________
10) 505−2422−3__________________________________________________________________________
11) 822−35−2102__________________________________________________________________________
12) 92223−26−2___________________________________________________________________________
13) 33A−29−1A5__________________________________________________________________________
14) 43M−38−2M7_________________________________________________________________________

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Practice 1.10 B Name_________________________________
Simplify: (8) 244−2
(9) 349−2
(1) 868−4 (10) 405−2186−210
(11) 633−2217−2
(2) . 657−5 (12) 183−2322−3
(13). 24M−48−1M6
(3) A4B−2 14) 102A−35−2A7
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(4) 9−5911

(5) N−12N21

(6) E16E−9

(7) x−3y5x9y−2

Practice 1.10 C Name_________________________________
Simplify: (8) 822−5
(1) 5−668 (9) 2−262
(10) 305−22−220
(2) A7B−3 (11). 50223−25−2622−3
(12) 183−2322−4276−2
(3) 7−476 (13) 25w94−2w−5
(14) 92A−73−3A11
(4) 9169−9 105 | P a g e

(5) N−11N16

(6) F13F−8

(7) x5y−9x−4y11

Practice 1.10 D Name_________________________________
Simplify: (8) 633−3
(1) w−7w12 (9) 8−243
(10) 822−3422−5
(2) z14z−6 (11) 182−4823−3212−3
(12) 1022−6243−2455−2
(3) 393−7 (13) 152w135−2w−83−2
(14) 122A113−2A−94−2
(4) 4−5411 106 | P a g e

(5) A−3B4

(6) 759−2

(7) M6N−5M−3N9

1.11A Combining Like Terms Name_________________________________

The separate parts of an expression in math are called the ___________________________.
These ____________________________ are separated by ______________________ and
__________________________ signs.

Examples:

4A+7B+(−3C)+(−9D) has ____________ terms.

−3u+5v+(−7w)+2x+y+−(8z) has ___________ terms.

6x2−2x+11 has _____________ terms.

Most terms have several parts. There will usually be a ________________ raised to a
_________________ or ___________________. If the variable has no exponent, the exponent is a
_________________. The number in front of the variable is called the _____________________.
If there is no number in front of the variable, it is assumed to be a ________________.

Terms are called ________________ or __________________ if the variable portions of the two

terms are identical. Identify like terms in the blanks to the right:

−6x 9y2 4x 1) ________ ________ _________

4z3 15A2 6A 2) ________ ________ _________

3A 8z3 y2 3) ________ ________ _________
2y 12y −5A2 4) ________ ________

2z3 4A2 −7y 5) ________ ________

6) ________ ________

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1.11 A cont’d Name_________________________________

Six pencils and four pencils are equal to ten pencils.

6x2+4x2 is the same problem. It means 6 of these (________) and 4 of these
(________) equal 10 of these (________). Two terms can be combined only if the variable
portions are ______________________ ______________________. When _______________________
terms are combined, the ________________________________________________ are combined
and the _____________________ ______________________ stays the same. 6x2+4x2=10x2

Terms must be written in the proper __________________. Terms with variables that are
different letters are written so that the letters are in ___________________________ order.

Example:________________________________________

Terms with the same variable raised to different power have the powers arranged
so that they are ______________________________.

Example:_________________________________________

Examples: Combine like terms
(1) 4xc8y+12z+6x+3y−2z=__________________________________

(2) 3A+5−A2+8A−4A2−10=___________________________________

(3) 7M+14N+M−20N+2M=__________________________________

(4) −6C3+5C2+9C−15C−11C2=________________________________

(5) x+x2+8+7x2−9x+6=______________________________________

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Practice 1.11 B Name_________________________________
Combine like terms:

(1) 8A+11B−C+2A−15B−4C=________________________________

(2) 4x−6y+10z−8x+2y−6z=__________________________________

(3) 5x2−10x−15−4x2+7x−5=__________________________________

(4) 12P−14R−20P−7Q−6R+13Q=______________________________

(5) −9A3+7A+5A2−A3+3A−15A2=_______________________________

(6) −6A−8C−2C−10B+4A+7B=___________________________________

(7) 9y−8x−7z+5z−x−12y=_____________________________________

(8) 7x2−6x−9+3x2−4x−1=_______________________________________

(9) −8Q+6P−4R+9R−P+3Q=____________________________________

(10) 12−10A2−8A+7A2−15+12A=_______________________________

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Practice 1.11 C Name_________________________________

Combine like terms:

(1) 7Q−5P+3R−9Q−2P+7R=________________________________

(2) 9A+10B−8C+A−12B−4C=_______________________________

(3) −4x2−5x−8+2x2−7x+3=___________________________________

(4) 6x−4y+2z−10x+8y+6z=__________________________________

(5) 6A+4−8A2+A−10+A2=_____________________________________

(6) 10y−9x+8z−10z−8y+7x=_________________________________

(7) 4x2−12x−14x3−10x3+2x−6x2=____________________________

(8) 4C+3B−2A−8B−3A−9C=___________________________________

(9) 15−13A2−11A+5+3A2+A=________________________________

(10) 16P+14Q−12R−18P−4Q−8R=____________________________

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