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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

Application of nanotechnology in medicine
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
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
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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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