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Wiskunde

Graad 9

Algebra en meetkunde

Module 6

Algebra van die vier basiese operasies

Aktiwiteit 1

Om die optelling– en aftrekkingsreëls van algebra te hersien

[lu 1.2, 1.6]

A Onthou jy nog wat terme is?

  • Terme word deur + of – geskei. Sê in elk van die volgende hoeveel terme daar is:

1. a + 5

2. 2a 2

3. 5a(a+1)

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

  • Versamel die gelyksoortige terme om elk van die volgende uitdrukkings te vereenvoudig:

1. 5a + 2a

2. 2a 2 + 3a – a 2

3. 3x – 6 + x + 11

4. 2a(a–1) – 2a 2

B Optel van uitdrukkings

  • Voorbeeld:

Tel 3x + 4 by x + 5. (x + 5) + (3x + 4) Skryf as som, met hakies.

x + 5 + 3x + 4 Verwyder hakies versigtig.

4x + 9 Versamel gelyksoortige terme.

Tel die twee gegewe uitdrukkings bymekaar:

1. 7a + 3 en a + 2

2. 5x – 2 en 6 – 3x

3. x + ½ en 4x – 3½

4. a 2 + 2a + 6 en a – 3 + a 2

5. 4a 2 – a – 3 en 1 + 3a – 5a 2

C Aftrek van uitdrukkings

  • Bestudeer die volgende voorbeelde sorgvuldig:

Trek 3x – 5 van 7x + 2 af.

(7x + 2) – (3x – 5) Let op: 3x – 5 is in tweede posisie, na die minus.

7x + 2 – 3x + 5 Die minus voor die hakie maak ‘n verskil!

4x + 7 Versamel gelyksoortige terme.

Bereken 5a – 1 minus 7a + 12: (5a – 1) – (7a + 12)

5a – 1 – 7a – 12

–2a – 13

D Gemengde probleme

  • Onthou om jou antwoorde volledig te vereenvoudig in die volgende oefening:

1. Tel 2a – 1 by 5a + 2.

2. Vind die som van 6x + 5 en 2 – 3x.

3. Wat is 3a – 2a 2 plus a 2 – 6a?

4. (x 2 + x) + (x + x 2 ) = . . .

5. Bereken (3a – 5) – (a – 2).

6. Trek 12a + 2 van 1 + 7a af.

7. Hoeveel is 4x 2 + 4x minder as 6x 2 – 13x?

8. Hoeveel is 4x 2 + 4x meer as 6x 2 – 13x?

9. Wat is die verskil tussen 8x + 3 en 2x +1?

  • Gebruik geskikte tegnieke om die volgende uitdrukkings te vereenvoudig:

1. x 2 + 5x 2 – 3x + 7x – 2 + 8

2. 7a 2 – 12a + 2a 2 – 5 + a – 3

3. (a 2 – 4) + (5a + 3) + (7a 2 + 4a)

4. (2x – x 2 ) – (4x 2 – 12) – (3x – 5)

5. (x 2 + 5x 2 – 3x) + (7x – 2 + 8)

6. 7a 2 – (12a + 2a 2 – 5) + a – 3

7. (a 2 – 4) + 5a + 3 + (7a 2 + 4a)

8. (2x – x 2 ) – 4x 2 – 12 – (3x – 5)

9. x 2 + 5x 2 – 3x + (7x – 2 + 8)

10. 7a 2 – 12a + 2a 2 – (5 + a – 3)

11. a 2 – 4 + 5a + 3 + 7a 2 + 4a

12. (2x – x 2 ) – [(4x 2 – 12) – (3x – 5)]

  • Hier is die antwoorde op die vorige 12 probleme:

1. 6x 2 + 4x + 6

2. 9a 2 – 11a – 8

3. 8a 2 + 9a – 1

4. – 5x 2 – x + 17

5. 6x 2 + 4x + 6

6. 5a 2 – 11a + 2

7. 8a 2 + 9a – 1

8. – 5x 2 – x – 7

9. 6x 2 + 4x + 6

10. 9a 2 – 13a – 2

11. 8a 2 + 9a – 1

12. – 5x 2 + 5x + 7

Aktiwiteit 2

Om sekere polinome (veelterme) te vermenigvuldig deur hakies en die distributiewe wet te gebruik

[lu 1.2, 1.6, 2.7]

‘n Mono miaal het een term; ‘n bi nomiaal het twee terme; ‘n tri nomiaal het drie terme. Ons noem hulle dikwels eenterme, tweeterme en drieterme.

A Vermenigvuldiging van eenterme .

Ons gebruik dikwels hakies.

  • Voorbeelde:

2a × 5a = 10a 2

3a 3 × 2a × 4a 2 = 24 a 6

4ab × 9a 2 × (–2a) × b = –36a 4 b 2

a × 2a × 4 × (3a 2 ) 3 = a × 2a × 4 × 3a 2 × 3a 2 × 3a 2 = 126a 8

(2ab 2 ) 3 × (a 2 bc) 2 × (2bc) 2 = (2ab 2 ) (2ab 2 ) (2ab 2 ) × (a 2 bc) (a 2 bc) × (2bc) (2bc) = 32a 7 b 10 c 4

Maak altyd seker dat jou antwoord in die eenvoudigste vorm is.

Oefening:

1. (3x) (5x 2 )

  1. (x 3 ) (–2x)
  2. (2x) 2 (4)
  3. (ax) 2 (bx 2 ) (cx 2 ) 2

B Eenterm × tweeterm

Hakies is noodsaaklik.

  • Voorbeelde:

5(2a + 1) beteken: vermenigvuldig 5 met 2a en ook met 1. 5 (2a + 1) = 10a + 5

Wees baie versigtig om nie tekenfoute te maak nie.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
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
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
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
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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