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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket 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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