# 1.2 Algebra

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3.2.5 the value of the expression if a = -2

4. Write an algebraic expression for each of the following.

4.1 the product of a and p , multiplied by the sum of a and p .

4.2 the sum of a and p , multiplied by 3

4.3 the quotient of a and p multiplied by 3

4.4 the cost of a bus trip is p rand per km. Calculate the cost of the entire, trip if the distance travelled is 45 km.

4.5 5 is added to the product of 3 and a , and the answer is reduced by the sum of 9 and b

5. You rent a car at Cape Town International airport at R 125,50 per day.

5.1 Compile a table to indicate how much it will cost you in hire for the following periods: 6; 7; ..... 12 days.

5.2 Determine a formula for representing the data with y (total cost) and $x$ (number of days).

5.3 What will the total hiring costs for 2½ months come to?

6. How many terms in each of the following expressions?

6.1 a b + m / n - 2( a + b )

6.2 ( p + q + r )3 - 4 r ²

6.3 m / n + 7 m ² ÷ 5 x p - q x r

6.4 (6 x q ) ÷ ( r x 7)

6.5 $\frac{\text{mn - pr - a}}{5}$

Assessment

 Assessment of myself: by myself: Assessment by Teacher: I can…    1 2 3 4 Critical Outcomes 1 2 3 4 distinguish between the terms of a polynomial; (Lo 2.4; 2.8.2; 2.9) Critical and creative thinking identify the coefficient of an unknown; (Lo 2.4; 2.9) Collaborating identify the constant in a polynomial; (Lo 2.4; 2.9) Organising en managing determine the degree of an expression; (Lo 2.4; 2.9; 2.8.1) Processing of information arrange the expression in a descending order; (Lo 2.4; 2.9) Communication accurately multiply and divide the signs (+ / -); (Lo 2.4; 2.8.4) Problem solving write algebraic expressions; (Lo 2.4; 2.2; 2.8.4) Independence determine the formulas for flow diagrams and tables. (Lo 2.1; 2.3; 2.4; 2.7)

good average not so good

 Comments by the learner: My plan of action: My marks: I am very satisfied with the standard of my work. < Date : I am satisfied with the steady progress I have made. Out of: I have worked hard, but my achievement is not satisfactory. Learner : I did not give my best. >
 Comments by parents: Comments by teacher: Parent signature: Date : Signature: Date :

## Assessment

 Learning outcomes(LOs) LO 2 Patterns Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems, using algebraic language and skills. We know this when the learner : 2.1 investigates and extends numerical and geometrical patterns to find relationships and rules, including patterns that:2.1.1 are presented in physical or diagrammatic form;2.1.2 are not limited to series with constant difference or ratio;2.1.3 occur in natural and cultural contexts; 2.1.4 are created by the learner him/herself;2.1.5 are presented in tables;2.1.6 are presented algebraically; 2.2 describes, explains and justifies observed relationships or rules in own words or in algebra; 2.3 represents and uses relationships between variables to determine input an output values in a variety of ways by making use of:2.3.1 verbal descriptions;2.3.2 flow diagrams;2.3.3 tables;2.3.4 formulas and equations; 2.4 builds mathematical models that represent, describe and provide solutions to problem situations, thereby revealing responsibility towards the environment and the health of other people (including problems in the contexts of human rights, social, economic, cultural and environmental issues); 2.7 is able to determine, analyse and interpret the equivalence of different descriptions of the same relationship or rule which can be represented:2.7.1 verbally;2.7.2 by means of flow diagrams;2.7.3 in tables;2.7.4 by means of equations or expressions to thereby select the most practical representation of a given situation; 2.8 is able to use conventions of algebraic notation and the variable, reconcilable and distributive laws to:2.8.1 classify terms like even and odd and to account for the classification;2.8.2 assemble equal terms;2.8.3 multiply or divide an algebraic expression with one, two, or three terms by a monomial; 2.8.4 simplify algebraic expressions in bracketed notation using one or two sets of brackets and two types of operation;2.8.5 compare different versions of algebraic expressions having one or two operations, select those that are equivalent and motivate the selected examples;2.8.6 rewrite algebraic expressions, formulas or equations in context in simpler or more usable form; 2.9 is able to interpret and use the following algebraic ideas in context: term, expression, coefficient, exponent (or index), basis, constant, variable, equation, formula (or rule).

## Class assignment 1

• 2
• $-\frac{1}{4}$
• 6
• 2

2.1 x + 7

2.2 x + 7

2.3 a – b

• ( x + 7) – 6

= x – 13

• x x $b$ = x $b$
• $\frac{x}{7}$
• $a$ 2
• $\sqrt{a}$

2.9 $\text{ab}$ – ( $a$ $b$ )

3.1 a c

7 -4

3.2 a c

9 $-\frac{1}{2}$

4. 21; 31; 95; $y=2x+1$

## Homework assignment 1

• y = 2 x + 6
• y = 5 x – 3
• y = x 2
• y = x 3
• y = x 2 + 1
• Sketch: (3 x 4) + 1 = 13
• y = 3 x + 1
• y = 3(110) + 1 = 331
• (2 005 – 1) ÷ 3 = 668
• 7 – $\frac{1}{4}a$ + $\frac{{a}^{2}}{5}$ + 3 ${a}^{3}$
• 4
• $\frac{1}{5}$
• 3
• 7
• $-\frac{1}{4}\left(-\frac{2}{1}\right)$ + ${\left(\frac{-2}{5}\right)}^{2}$ + 7 3(-2) 3

= $\frac{1}{2}$ + $\frac{4}{5}$ + 7 – 24

= $\frac{5+8+\text{70}-\text{240}}{\text{10}}$

= $\frac{-\text{157}}{\text{10}}$ = -15,7

• ap + ( a + p )
• 3( a + p )
• $\frac{a}{p}$ + 3
• 45 p
• (3 a + 5) – (9 + b )

5.1

 Days 6 7 8 9 10 11 12 R 753 878,50 1 004 1 629,50 1 255 1 380,50 1 506
• y = 125,5 x
• 2 $\frac{1}{2}$ months (2 x 30 ) + 15 75 x R125,50 = R9 412,50

or (30 + 31 + 15) 76 x R125,50 = R9 538,00

• 3
• 2
• 3
• 1
• 1

#### Questions & Answers

what does nano mean?
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?
absolutely yes
Daniel
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it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
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Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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