# 1.2 Algebra

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## 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 $x$ ² (the number immediately before $x$ ²): 3
• Coefficient of $x$ (the number immediately before $x$ ): - $\frac{1}{4}$
• Constant: 5
• The degree of expression (highest power of $x$ ): 2
• The expression is arranged in descending powers of $x$ .
• 3 $x$ ² means 3 x $x$ ² (3 multiplied by $x$ ²)
• $x$ ² means ( $x$ ) x ( $x$ ) ( $x$ multiplied by $x$ )
• 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:

$\frac{\left(\frac{1}{4}{x}^{2}-x\right)}{4}+6$

• Indicate the following:

1.1 number of terms

1.2 coefficient of $x$

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.

 $x$ 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 = ……………………………………………………

 $x$ 2 5 8 9 12 20 y 10 16 22

1.2 formula: y = ……………………………………………………

 $x$ 3 7 10 9 12 20 y 12 32 47

1.3 formula: y = ……………………………………………………

 $x$ 1 3 4 9 12 20 y 1 9 16

1.4 formula: y = ……………………………………………………

 $x$ 1 2 3 6 7 10 y 1 8 27

1.5 formula: y = ……………………………………………………

 $x$ 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 ( $x$ ) 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:

$-\frac{1}{4}a+\frac{{a}^{2}}{5}+7+{3a}^{3}$

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

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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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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