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Tutorial 1: (Number Systems)

Total: 30

1. Simplify:

1.1 100 36 size 12{ sqrt {"100"` - `"36"} } {} [1]

1.2 25 49 size 12{ sqrt { { {"25"} over {"49"} } } } {} [1]

1.3 2 6 3 15 size 12{ sqrt {2 rSup { size 8{6} } 3 rSup { size 8{"15"} } } } {} [2]

1.4 9 ( 9 + 16 ) size 12{ sqrt {9} ` \( sqrt {9} `+` sqrt {"16"} \) } {} [3]

1.5 9² [1]

1.6 a = 4, a = size 12{ sqrt {a} `=`"4,"~a`=`} {} [1]

1.7 a 3 = 5, a = size 12{ nroot { size 8{3} } {a} `=`"5,"~a`={}} {} [1] [10]

2. Use the 324, and answer the following questions:

2.1 Is 324 divisible by 3? Give a reason for your answer. [2]

2.2 Write 324 as the product of its prime factors [3]

324

2.3 Now determine 324 size 12{ sqrt {"324"} } {} [2]

2.4 Is 324 a perfect square? Give a reason for your answer. [2] [9]

3. Determine each of the following without using your calculator.

3.1 81 size 12{ sqrt {"81"} } {} [1]

3.2 36 4 size 12{ sqrt { { {"36"} over {4} } } } {} [2]

3.3 3 2 + 4 2 size 12{ sqrt {3 rSup { size 8{2} } `+`4 rSup { size 8{2} } } } {} [2]

3.4 16 x 16 size 12{ sqrt {"16"x rSup { size 8{"16"} } } } {} [2]

4. If x = 3, determine:

4.1 4 x size 12{4 rSup { size 8{x} } } {} [2]

4.2 27 x size 12{ nroot { size 8{x} } {"27"} } {} [2] [11]

Tutorial

I demonstrate knowledge and understanding of: Learning outcomes 0000 000 00 0
1. natural numbers ( N ) and whole numbers ( N 0 ) 1.1
2. the identification of the different types of numbers; 1.1
3. compound numbers; 1.2.6
4. divisibility rules; 1.2.6
5. the multiples of a number; 1.2.6
6. the factors of a number; 1.2.6
7. prime numbers; 1.1
8. prime factors; 1.2.6
9. expressing a number as the product of its prime factors; 1.2.6; 1.2.3
10. expressing prime factors in exponent notation; 1.2.3
11. even and odd numbers; 1.1
12. square roots of a number; 1.2.7
13. cube roots of a number; 1.2.7
14. the smallest common factor (LCM); 1.2.6
15. the biggest common divider (BCD). 1.2.6
The learner’s … 1 2 3 4
work is… Not done.. Partially done. Mostly complete. Complete.
layout of the work is… Not understandable. Difficult to follow. Sometimes easy to follow. Easy to follow.
accuracy of calculations… Are mathematically incorrect. Contain major errors. Contain minor errors. Are correct.
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Test 1: (Number Systems)

Total: 30

1. Tabulate the following:

1.1 All the prime numbers between 20 and 30. [2]

1.2 All the factors of 12. [2]

1.3 All factors of 12 which are compound numbers [2] [6]

2. Determine the smallest natural number for * so that the following number is divisible by 3. (Give a reason for your answer)

1213156*3 [2]

3. Determine the following without using your calculator.

3.1 36 + 64 size 12{ sqrt {"36"`+`"64"} } {} [2]

3.2 2 9 3 size 12{ nroot { size 8{3} } {2 rSup { size 8{9} } } } {} [2]

3.3 2 7 9 size 12{ sqrt {2 { { size 8{7} } over { size 8{9} } } } } {} [3]

3.4 0,04 size 12{ sqrt {"0,04"} } {} [2]

3.5 100 36 size 12{ sqrt {"100"`-`" 36"} } {} [2]

3.6 8 × 27 3 size 12{ nroot { size 8{3} } {8 times "27"} } {} [2]

3.7 ( 9 ) 2 size 12{ \( sqrt {9} \) rSup { size 8{2} } } {} [2]

3.8 64 1 3 size 12{ nroot { size 8{3} } {"64"` - `1} } {} [2] [17]

4. Determine 1 728 3 size 12{ nroot { size 8{3} } {"1 728"} } {} using prime factors, without using a calculator.

[5]

5. Bonus question

If (n) means n n what is the value of ((2)) ? [2]

Enrichment Exercise for the quick learner

(Learning unit 1)

Each question has five possible answers. Only one answer is correct. Place a cross (X) over the letter that indicates the correct answer.

1. If n and p are both odd, which of the following will be even?

a) np b) n ² p + 2 c) n + p +1 d) 2 n +3 p +5 e) 2 n + p

2. R 120 is divided amongst three men in the ratio 3 : 4: 9. The one with the smallest share will receive ...

a) R16 b) R20 c) R22,50 d) R24,50 e) R40

3. How many triangles are there in the figure?

a) 8 b) 12 c) 14 d) 16 e) 20

4. A decagon has 2 interior angles of 120° each. If all the remaining angles are of the same size, each angle will be equal to ...

a) 15° b) 30° c) 120° d) 150° e) 165°

5. The last digit of the number 3 1993 is ....

a) 1 b) 3 c) 6 d) 7 e) 9

6. The figure below has 5 squares. If AB = 6, the area of the figure is...

a) 12 b) 20 c) 24 d) 36 e) impossible

Assessment

Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment standards(ASs)
We know this when the learner :
1.1 describes and illustrates the historical and cultural development of numbers;
1.2 recognises, classifies and represents the following numbers in order to describe and compare them:1.2.3 numbers written in exponent form; including squares and cubes of natural numbers and their square roots and cube roots;1.2.6 multiples and factors;1.2.7 irrational numbers in the context of measurement (e.g. square and cube roots on non-perfect squares and cubes);
1.6 estimates and calculates by selecting suitable steps for solving problems that involve the following:1.6.2 multiple steps with rational numbers (including division with fractions and decimals);1.6.3 exponents.

Memorandum

Class assignment 2

1.1 48 = 2 4 × 3; 60 = 2² × 3 × 5; 450 = 2 x 3² x 5²;

P 48 = {2, 3}; P 60 = {2, 3, 5}; P 450 = {2, 3, 5};

2.1 i)== (2 10 )

= 2 5

= 32

ii)== (2³ x 5³)

= 2 x 5

= 10

2.2 a) 36

b) 192

c) 1

d) 1

e) 2

f) 17

g) 63

h) 9

i) 10

j) 4

k) 27

l) 8 x 6

Homework assignment 2

1.1= (2 12 )

= 2 4

= 16

1.2= (2 4 x 3 4 )

= 2 x 3

= 6

2.1= 3² = 9

2.2 5a²b 5

2.3=x 3 =

= 1,2

2.4: 4 + 64 = 68

  • :2(8) = 16
  • :13

2.7 () 2 = 54

2.8= 36

  • :2(9) = 18
  • :9 - 27 = -18

Class assignment 3

21. LCM : Lowest common multiple

LCM of 2, 6, 12 :

24 HCF : Highest common factor

HCF of 24 and 48 :

2. 38 = 2 x 19

57 = 3 x 19

95 = 5 x 19

HCF = 19

LCM = 19 x 2 x 3 x 5

= 570

TUTORIAL 1

1.1= 8

1.2

  • 2³ . 3 7,5
  • :3(3 + 4) = 21
  • :81
  • :16

1.7 :125

2.1 :3 + 2 + 4 = 9

9 ÷ 3 = 3 Yes!

2.2: 324 = 2² x 3 4

2.3:= (2² x 3 4 )

= 2 x 3²

= 18

2.4: Yes! 18 x 18 = 324 /18² = 324

  • :9
  • : 6 2 size 12{ { {6} over {2} } } {} = 3

3.3: 9 + 16 size 12{ sqrt {9+"16"} } {} = 25 size 12{ sqrt {"25"} } {} = 5

3.4: 4 x 8 size 12{x rSup { size 8{8} } } {}

  • :4 3 = 64
  • :3

Enrichment exercise

1. d

2. c

3. d

4. 180 ( 10 2 ) 10 size 12{ { {"180" \( "10" - 2 \) } over {"10"} } } {} = 144º (one angle) (1 440 – 240) ÷ 8 = 150 ( d )

5. b 3 1992 ends on 1

6. d AB = 6

(2 x ) 2 + x 2 = 36

4 x 2 + x 2 = 36

5 x 2 = 36

TEST 1

  • :23, 29
  • :1, 2, 3, 6, 12
  • :4, 6, 12

2. :* 2 1 + 2 + 1 + 3 + 1 + 5 + 6 + 3 = 22

3.1 100 size 12{ sqrt {"100"} } {} = 10

3.2 2 3 = 8

3.3 25 9 size 12{ sqrt { { {"25"} over {9} } } } {} = 5 3 size 12{ { {5} over {3} } } {} = 1 2 3 size 12{ { {2} over {3} } } {}

3.4 4 100 size 12{ sqrt { { {4} over {"100"} } } } {} = 2 10 size 12{ { {2} over {"10"} } } {} = 0,2 / 1 5 size 12{ { {1} over {5} } } {}

3.5 64 size 12{ sqrt {"64"} } {} = 8

  • :2 x 3 = 6
  • :9
  • :4 – 1 = 3

4. 2 6 x3 3 3 size 12{ nroot { size 8{3} } {2 rSup { size 8{6} } x3 rSup { size 8{3} } } } {} = 2 2 x 3

= 4 x 3

= 12

5. (2) = 2 2 = 4

(4) = 4 4 = 256

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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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