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6. Laat n enige natuurlike getal wees. As 3 die tienesyfer in n² is, bepaal die enesyfer in n².

7. Die gemiddelde van drie heelgetalle is 86. As een van hulle 70 is, wat is die gemiddelde van die ander twee?

8. Saretha het ’n R10- en R20-noot by ABSA omgeruil vir ’n gelyke aantal 50c-, 20c-, en 5c-stukke. Hoeveel muntstukke het Saretha gekry?

Assessering

Leeruitkomstes(LUs)
LU 1
Getalle, Verwerkings en VerwantskappeDie leerder is in staat om getalle en die verwantskappe daarvan te herken, te beskryf en voor te stel, en om tydens probleemoplossing bevoeg en met selfvertroue te tel, te skat, te bereken en te kontroleer.
Assesseringstandaarde(ASe)
Dit word bewys as die leerder:
1.2 die volgende getalle kan herken, klassifiseer en voorstel om hulle te beskryf en te vergelyk:
  • heelgetalle;
  • desimale breuke en persentasies;
1.2.5 optelling- en vermenigvuldiginginverses;
1.7 ’n reeks tegnieke gebruik om berekeninge te doen, wat die volgende insluit:1.7.1 die gebruik van kommutatiewe, assosiatiewe en distributiewe eienskappe met rasionale getalle;1.7.2 die gebruik van ’n sakrekenaar;
1.8 ’n reeks strategieë gebruik om oplossings te kontroleer, en die korrektheid van oplossings beoordeel.
LU 2
Patrone, Funksies en AlgebraDie leerder is in staat om patrone en verwantskappe te herken, te beskryf en voor te stel, en probleme op te los deur algebraïese taal en vaardighede te gebruik.
Dit word bewys as die leerder:
2.5 vergelykings oplos deur inspeksie, toets-en-verbeter- of algebraïese prosesse (optelling- en vermenigvuldiginginverses) en die oplossings deur vervanging toets;
2.8 konvensies van algebraïese noterings en die wisselbare, verenigbare en verspreibare wette gebruik om:2.8.4 algebraïese uitdrukkings wat in hakienotasie met een of twee stelle hakies en twee tipe bewerkings gegee word, te vereenvoudig;2.8.6 algebraïese uitdrukkings, formules of vergelykings binne konteks in eenvoudiger of meer bruikbare vorms te skryf.

Memorandum

1. - 5. Algemeen

6.1 1 – a = 7 a = –6

  • a = 10
  • 42 = a
  • a = 11
  • –30 = a
  • a = 6
  • 5 – 12 + 3 a = 5 a + 5 + 2

3 a – 5 a = 5 + 2 + 12 – 5

–2 a = 14

a = –7

  • 2 a – 3 A = 24

a = 24

size 12{∴} {} a = –24

8.3 a 4 size 12{ { {a} over {4} } } {} = 5 1 size 12{ { {5} over {1} } } {} a = 20

8.4 2 a = 16

a = 8

  • a = –9
  • 9 + 3 a + 3 = 8 – 8 a

11 a = –4

size 12{∴} {} a = 4 11 size 12{ { { - 4} over {"11"} } } {} (–2 3 8 size 12{ { {3} over {8} } } {} )

8.7 12 a size 12{ { { - "12"} over {a} } } {} = 24 1 size 12{ { { - "24"} over {1} } } {} –24 a = –12

a = 1 2 size 12{ { {1} over {2} } } {}

  • 10 a + 5 = 8 a + 12

2 a = 7

a = 3 1 2 size 12{ { {1} over {2} } } {}

8.9 –6 a + 6 = 6 a + 24

–12 a = 18

a = 18 12 size 12{ { { - "18"} over {"12"} } } {} 3 2 size 12{ { { - 3} over {2} } } {} (–1 1 2 size 12{ { {1} over {2} } } {} )

  • Eie keuse

KLASWERKOPDRAG 2

  1. 20: 1. Nommer 1: x

Nommer 2: 15 – x

2. Kinders: x 20 x

Grootmense: (140 – x ) 45(140 – x )

20 x + 45(140 – x ) = 5 580

20 x + 6 300 – 45 x = 5 580

–25 x = –720

x = 28,8 28 / 29

Grootmense: 140 – 28 = 112

of 140 – 29 = 111

HUISWERKOPDRAG 1 EN 2

  • –3 a = 3

a = –1

  • a = –4
  • 8 x – 21 x + 10 = 28

8(3) – 2(3) + 10 = 28

– 6 + 10 = 28 √

2.2 5 x – 10 = 10 x – 10

5 x – 10 x = –10 + 10

–5 x = 0

x = 0

x size 12{ in } {} 1R √

3.1 1 z size 12{ { {1} over {z} } } {} = 1 18 size 12{ { {1} over {"18"} } } {} z size 12{z} {} = 18

3.2 1 – 5 z = 11

–5 z = 10

z = –2

3.2.1 Geen oplossing

3.2.2 z = –2

3.3 z + 3[ z + 2 z – 12] = 45

z + 3[3 z – 12] = 45

z + 9 z – 36] = 45

10 z = 81

z = 8,1

3.4 24 z – 32 – 2 z – 14 = 37

22 z = 83

z size 12{ approx } {} 3,77

3.5 z – 5 z + 40 = 48

–7 z = –88

z = 22

  • 6 x – 8 = 55

6 x = 63

x = 10 1 2 size 12{ { {1} over {2} } } {} (10,5)

4.2 x + 9 x = –64

10 x = –64

x = –6,4

4.3 x + x 1 x + 2 = –90

3 x = –93

x = –31 –31; –30; 29

4.4 Lemoene: 3 x x 45 36

Piesangs: x x 18 12

18 x + 135 x = 1 836

153 x = 1 836

x = 12

  • Nou –6

Cameron: x + 8 [ 18 ]; x + 8 –6

Liam: x [ 10 ]; x – 6

3( x – 6) = x + 2

3 x – 18 = x + 2

2 x = 20

x = 10

4.6 Seëls: R1,20 : x 50 – x

R2,40 : 50 – x of x

120 x + 240(50 – x ) = 5 880 1,20(50 – x ) + 2,40 x = 58,8

120 x + 12 000 – 240 x ) = 5 880 60 – 1,20 x ) + 2,40 x = 58,8

–120 x = –6 120 of 1,20 x = 1,20

x = 51 x = 1

R1,20 4

4.7 Een gedeelte: x

Ander gedeelte: x + 550

x + 2( x + 550) = 18 000

x 2 x + 1 100 = 18 000

3 x = 16 900

4.8 Massa

3 792 kgVrouens: 18 3 x

Dogters: 25 x

25 x + 3 x (18) = 3 792

25 x + 54 x = 3 792

79 x = 3 792

x = 48

Dogters: 48 kg elk

Vrouens: 144 kg elk

Nommer12 x 4.9 Ene: 2 x 8

Tiene x x 10 4

omgeruil: 21 x

2 x – 36 = 12 x

9 x = 36

x = 4

4.10 Gr. 8: x + 3 2 257

Gr. 9: x 225

Gr. 10: x + 25 250

x + 32 + x + x + 25 = 732

3 x = 675

x = 225

TUTORIAAL 2

  • Ya √ = Kan x se waarde uitwerk

[5 x = 5 0 . x = 0]

  • x = 0 √
  • a = 12 √√
  • a = 7 √√
  • a = 7 3 size 12{ { {7} over {3} } } {} (2 1 3 size 12{ { {1} over {3} } } {} ) √√
  • a = 3 √√
  • a = 4 √√
  • 32 = 4(2(9) – p ) √

32 = 4(18 – p )

8 = 18 – p

p = 10 √

  • 45,67 = p 21 , 3 size 12{ { {p} over {"21",3} } } {}

p = 972,771 √

4.1 7a 1 size 12{ { {7a} over {1} } } {} + a 3 size 12{ { {a} over {3} } } {} = 30

22 a 3 size 12{ { {"22"a} over {3} } } {} = 30 1 size 12{ { {"30"} over {1} } } {}

22 a = 90 √

a = 90 22 size 12{ { {"90"} over {"22"} } } {}

= 4 2 22 size 12{ { {2} over {"22"} } } {} = 4 1 11 size 12{ { {1} over {"11"} } } {}

4 a 2 – 3 a = 4 a 2 √

0 = 3 a

  1. = a
  2. –4 a + 8 = 3 a – 12 √

–7 a = –20 √

a = 20 7 size 12{ { {"20"} over {7} } } {} = 2 6 7 size 12{ { {6} over {7} } } {} (of size 12{ approx } {} 2,86) √

  • 5 a + 15 + 4 a + 5 = 2 a – 14 √

7 a = –34 √

a = 4,9 √

  • 5 a = –2 a + 6 √

7 a = 6 √

a = 6 7 size 12{ { {6} over {7} } } {} (0,86) √

  • 9 x – 28 = 5 x

4 x = 28

x = 7 √

5.2.1 x + 4 2 x + 2( x + 4) = 108 √

2 x + 2 x + 8 = 108

4 x = 100

x = 25√

√ √

size 12{∴} {} l = 29 cm b = 25 cm

5.2.2 A = 29 x 25 √

= 725 cm 2

6. x + x + 2 + x + 4 + x + 6 = 112 √

4 x = 112 – 12

4 x = 100

x = 25 √

size 12{∴} {} Nommers: 25; 27; 29; 31 √√

7. 6162 size 12{ sqrt {"6162"} } {} size 12{ approx } {} 78 √

size 12{∴} {} 6 162 ÷ 78 = 79

size 12{∴} {} 78; 79 √√

TOETS 1

1.11 x = 34

1.12 –3 x = 1

–3 x = –6

size 12{∴} {} x = 2

1.13 2 x + 10 = 18

2 x = 8

size 12{∴} {} x = 4

1.14 2 x = 40 – 8

2 x = 32

size 12{∴} {} x = 16

  • x – 6 – x – 1 = 5 x – 4

2 x x – 5 x = –4 + 1 + 6

–4 x = 3

x = 3 4 size 12{ { { - 3} over {4} } } {}

  • 3 x = 15 – 6

3 x = 9

size 12{∴} {} x = 3

1.7 x = 4 x 2 = 8

1.8 6 x + 48 = 114

6 x = 66

size 12{∴} {} x = 11

1.9 x – 7 x = 30 – 9

3 x = 21

size 12{∴} {} x = 7

1.10 x – 2 – 2 x 3 = 7

x = 7 + 3 + 2

x = 12

size 12{∴} {} x = –12

  • x 5 3 size 12{ left ( { {x - 5} over {3} } right )} {} = 4

x = (4 × 3) + 5

= 17

  • x + x 1 + x + 2 = 66

3 x = 63

x = 21

  • 2 x + 2( x + 5,5) = 27

2 x + 2 x + 11 = 27

4 x = 16 x 4 cm

x = 4 x + 5,5 9,5 cm

2.4 Jonte: 5 x 50 5 x + x = 60

Dogters: x 10 6 x = 60

x = 10

2.5 Nou +5

Gareth 5 x 5 x + 5

Seun x x + 5

size 12{∴} {} Gareth: 25

size 12{∴} {} Seun: 5 x + 5 = 3( x + 5)

5 x + 5 = 3 x + 15

2 x = 10

x = 5

3. ( 1 2a size 12{\( { {1} over {2a} } } {} + 2 a ) size 12{a\)} {} 2 = 7 2

1 4a 2 size 12{ { {1} over {4a rSup { size 8{2} } } } } {} + 2 + 4 a size 12{a} {} 2 = 49

1 4a 2 size 12{ { {1} over {4a rSup { size 8{2} } } } } {} + 4 a size 12{a} {} 2 = 47

Questions & Answers

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
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
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
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 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11033/1.1
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