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Mathematics

Grade 8

The number system

(natural and whole numbers)

Module 3

Algebra

ALGEBRA

CLASS ASSIGNMENT 1

  • Discover ALGEBRA step by step...
  • In Algebra, we make use of letters in the place of unknowns (numbers that we do not know).
  • Letters represent variables (values that may vary) and numbers are the constants (the values remain the same).

Look at the polynomial, for example

From the above, you will be able to recognise the following:

  • The number of terms (terms are separated by + and - signs): 3 terms
  • Coefficient of x size 12{x} {} ² (the number immediately before x size 12{x} {} ²): 3
  • Coefficient of x size 12{x} {} (the number immediately before x size 12{x} {} ): - 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}
  • Constant: 5
  • The degree of expression (highest power of x size 12{x} {} ): 2
  • The expression is arranged in descending powers of x size 12{x} {} .
  • 3 x size 12{x} {} ² means 3 x x size 12{x} {} ² (3 multiplied by x size 12{x} {} ²)
  • x size 12{x} {} ² means ( x size 12{x} {} ) x ( x size 12{x} {} ) ( x size 12{x} {} multiplied by x size 12{x} {} )
  • What happens to ( + )and ( - ) signs during multiplication and division?

Here you have it:

  • ( + ) x of ÷ ( + ) = ( + )
  • ( - ) x of ÷ ( - ) = ( + )
  • ( + ) x of ÷ ( - ) = ( - )

1. Study the following in your groups and supply the answers:

( 1 4 x 2 x ) 4 + 6 size 12{ { { \( { { size 8{1} } over { size 8{4} } } x rSup { size 8{2} } ` - `x \) } over {4} } `+`6} {}

  • Indicate the following:

1.1 number of terms

1.2 coefficient of x size 12{x} {}

1.3 constant

1.4 degree of the expression

2. Now we can use variables to define the following with the magical language of mathematics --- i.e. algebraic expressions.

See if you can define these in the form of algebraic expressions:

Given Algebraic Expression

2.1 The sum of a number and 9

2.2 A number multiplied by 7

2.3 The difference between a and b

2.4 6 less than a number reduced by 7

2.5 The product of a number and b

2.6 Quotient of a number and 7

2.7 Square of a

2.8 Square root of a

2.9 Subtract the difference between a and b from their product

3. The following are referred to as flow diagrams – They consist ofa) inputb) formula in which the input number is substitutedc) output

Complete (a), (b) and (c)

4. See if you can determine a formula for the following and complete the table.

x size 12{x} {} 2 5 8 10 15 47
y 7 11 17

formula: y =

HOMEWORK ASSIGNMENT 1

1. Determine a formula for each of the following and complete the table.

1.1 formula: y = ……………………………………………………

x size 12{x} {} 2 5 8 9 12 20
y 10 16 22

1.2 formula: y = ……………………………………………………

x size 12{x} {} 3 7 10 9 12 20
y 12 32 47

1.3 formula: y = ……………………………………………………

x size 12{x} {} 1 3 4 9 12 20
y 1 9 16

1.4 formula: y = ……………………………………………………

x size 12{x} {} 1 2 3 6 7 10
y 1 8 27

1.5 formula: y = ……………………………………………………

x size 12{x} {} 1 2 4 9 12 20
y 2 5 17

2. The sketch shows matches arranged to form squares and combinations of squares.

2.1 Make a sketch to show four squares and indicate how many matches were used.

Matches? …………………………

2.2 Can you determine a formula that will provide a quick way for determining how many matches you will need to form ( x size 12{x} {} ) number of squares?

y = ………………………………… (with y representing the number of matches)

2.3 Now make use of your formula to determine how many matches you will need to form 110 squares.

2.4 Determine how many squares you will be able to form with 2 005 matches.

3. Examine the following expression and answer the questions that follow:

1 4 a + a 2 5 + 7 + 3a 3 size 12{ - { {1} over {4} } a``+`` { {a rSup { size 8{2} } } over {5`} } ``+`7`+3a rSup { size 8{3} } } {}

3.1 Arrange the expression in ascending powers of a.

3.2 Determine:

3.2.1 number of terms

3.2.2 coefficient of a ²

3.2.3 degree of the expression

3.2.4 constant term

Questions & Answers

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Damian Reply
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Daniel
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Akash Reply
it is a goid question and i want to know the answer as well
Maciej
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Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
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I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
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Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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