NAME: Muhamad Nur Yusri Bin Yunus
AGE: 21
Date Of Birth: 11 July 1994
Nationality: Brunei Darussalam
Race: Malay
Institution: Cosmopolitan College of Commerce and Technology
Course: Diploma in Information Technology
Sunday, 10 July 2016
SET THEORY
INTRODUCTION
Understudies discover that a set is a gathering of items (components) that have something in like manner. We characterize a set by posting or depicting its components.
DEFINITION
set is an accumulation of particular items, considered as an article in its own particular right. For instance, the numbers 2, 4, and 6 are particular items when considered independently, however when they are considered all in all they frame a solitary arrangement of size three, composed {2,4,6}
SYMBOLS:
EXAMPLE:
(http://www.mathgoodies.com/glossary/term.asp?term=Venn%20diagram)
(https://teachbytes.files.wordpress.com/2013/02/venn-diagram.jpg)
(https://i.ytimg.com/vi/kLlFeVRL0v4/maxresdefault.jpg)
(http://i.stack.imgur.com/wpfy4.png)
Understudies discover that a set is a gathering of items (components) that have something in like manner. We characterize a set by posting or depicting its components.
DEFINITION
set is an accumulation of particular items, considered as an article in its own particular right. For instance, the numbers 2, 4, and 6 are particular items when considered independently, however when they are considered all in all they frame a solitary arrangement of size three, composed {2,4,6}
SYMBOLS:
VENN DIAGRAM
DEFINITION
In a Venn outline sets are spoken to by shapes; generally circles or ovals. The components of a set are marked inside the circle. Venn outlines are particularly valuable for indicating connections between sets.
SETS OF VENN DIAGRAM
EXAMPLES:
VIDEO
REFERENCES
(https://cdn.kastatic.org/KA-youtube-converted/jAfNg3ylZAI.mp4/jAfNg3ylZAI.png)(https://s-media-cache-ak0.pinimg.com/564x/f7/ba/64/f7ba6400664fd639142bf81bf43d70d3.jpg)(https://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/PolygonsSetIntersection.svg/220px-PolygonsSetIntersection.svg.png)
(http://www.mathgoodies.com/lessons/toc_unit15.html)(http://www.mathgoodies.com/glossary/term.asp?term=Venn%20diagram)
(https://teachbytes.files.wordpress.com/2013/02/venn-diagram.jpg)
(https://i.ytimg.com/vi/kLlFeVRL0v4/maxresdefault.jpg)
(http://i.stack.imgur.com/wpfy4.png)
STEM AND LEAF PLOT
INTRODUCTION
A Stem and Leaf Plot is a unique table where every information quality is part into a "stem" (the principal digit or digits) and a "leaf" (more often than not the last digit)
DEFINITION
A plot where every information quality is part into a "leaf" (as a rule the last digit) and a "stem" (alternate digits).
EXPLANATION
Stem-and-leaf plots are a strategy for demonstrating the recurrence with which certain classes of qualities happen. You could make a recurrence conveyance table or a histogram for the qualities, or you can utilize a stem-and-leaf plot and let the numbers themselves to indicate essentially the same data.
FORMULA
SYMBOL
EXAMPLE:
VIDEO
REFENCES
(https://www.youtube.com/watch?v=OaJXJduRiIE) (https://i.ytimg.com/vi/8ooKmIIb0Yo/maxresdefault.jpg)
(http://www.bbc.co.uk/staticarchive/9e1d43fdc0891fc3ff696e6e49fbcf6f959ae0d9.gif)
(https://www.mathsisfun.com/data/stem-leaf-plots.html)
A Stem and Leaf Plot is a unique table where every information quality is part into a "stem" (the principal digit or digits) and a "leaf" (more often than not the last digit)
DEFINITION
A plot where every information quality is part into a "leaf" (as a rule the last digit) and a "stem" (alternate digits).
EXPLANATION
Stem-and-leaf plots are a strategy for demonstrating the recurrence with which certain classes of qualities happen. You could make a recurrence conveyance table or a histogram for the qualities, or you can utilize a stem-and-leaf plot and let the numbers themselves to indicate essentially the same data.
FORMULA
SYMBOL
EXAMPLE:
VIDEO
REFENCES
(https://www.youtube.com/watch?v=OaJXJduRiIE) (https://i.ytimg.com/vi/8ooKmIIb0Yo/maxresdefault.jpg)
(http://www.bbc.co.uk/staticarchive/9e1d43fdc0891fc3ff696e6e49fbcf6f959ae0d9.gif)
(https://www.mathsisfun.com/data/stem-leaf-plots.html)
COMBINATION
What is Combination?
A combination is an arrangement of objects (numbers, letters, words, etc...) where order doesn't matter for example: 1, 2 is the same as 2, 1.
Formula:
EXAMPLE:
Evaluate 7c2:
7c2 = 7!/2!(7 - 2)! = 7*6*5*4*3*2*1 / 2*1 (5*4*3*2*1) = 7*6 / 2 * 1 = 42 / 2 = 21 (Answer)
There are 12 boys and 14 girls in Mrs. Schultzkie 's math class. Find the number of ways Mrs. Schultzkie can select a team of 3 students from the class of to work on a group project. The team is to consist of 1 girl and 2 boys.
Order , or position, is not important. Using the multiplication continuing principle
12 C 2 (BOYS) * 14 C 1 (GIRLS) 12 * 11 / 2 * 1 * * 14 / 1 = 66 * 14 = 924
VIDEO
REFERENCES
(http://www.800score.com/content/gre/nCr1.gif)
(https://www.youtube.com/results?search_query=combination+in+mathematics)
(https://www.youtube.com/results?search_query=combination+in+mathematics)
PERMUTATION
INTRODUCTION
A set V comprises of n components if its components can be tallied 1, 2,..., n. As it were, the set V can be carried into a 1-1 correspondence with the set {1, 2, ..., n}. Frequently it's more advantageous to begin numbering from 0. At that point we get the set {0, 1, 2, ..., n-1}.
DEFINITION
The quantity of changes of an arrangement of n components is signified n! (affirmed n factorial.)
Ways:
1! = 1 ways
2! = 2 ways
3! = 6 ways
4! = 24 ways
5! = 120 ways
6! = 720 ways
7! = 5,040 ways
8! = 40,320 ways
EXPLANATION
i'm going to pick number 8 and why 8! the answer is 40,320?
It is simple, you just have to expand it for example 8*7*6*5*4*3*2*1* and the answer will be 40,320.
Symbols:
P! = Permutation
N! = Number selected
R! = Object from total
EXAMPLES:
VIDEO
REFERENCES
(https://www.youtube.com/watch?v=DROZVHObeko)
(http://www.careerarm.com/wp-content/uploads/2015/07/p-and-c-1.png)
(https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKQMGTR0WnThQumZXMKd_aqnres05DhFGFdfvKjBAQkTJu8vBDOA0qBAAW9FUkmHAe6DXGZqlAnj4OxUf7Qud5Wd29CR5-q2-FGYS7-jTsIFgEEq4XQw_0lvWRmIfDoEebeltFDFEoMXk/s1600/permutation%201.JPG)
(https://i.ytimg.com/vi/0WDUWCtxM1U/maxresdefault.jpg) (http://www.cut-the-knot.org/do_you_know/permutation.shtml)
A set V comprises of n components if its components can be tallied 1, 2,..., n. As it were, the set V can be carried into a 1-1 correspondence with the set {1, 2, ..., n}. Frequently it's more advantageous to begin numbering from 0. At that point we get the set {0, 1, 2, ..., n-1}.
DEFINITION
The quantity of changes of an arrangement of n components is signified n! (affirmed n factorial.)
Ways:
1! = 1 ways
2! = 2 ways
3! = 6 ways
4! = 24 ways
5! = 120 ways
6! = 720 ways
7! = 5,040 ways
8! = 40,320 ways
EXPLANATION
i'm going to pick number 8 and why 8! the answer is 40,320?
It is simple, you just have to expand it for example 8*7*6*5*4*3*2*1* and the answer will be 40,320.
Symbols:
P! = Permutation
N! = Number selected
R! = Object from total
EXAMPLES:
REFERENCES
(https://www.youtube.com/watch?v=DROZVHObeko)
(http://www.careerarm.com/wp-content/uploads/2015/07/p-and-c-1.png)
(https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKQMGTR0WnThQumZXMKd_aqnres05DhFGFdfvKjBAQkTJu8vBDOA0qBAAW9FUkmHAe6DXGZqlAnj4OxUf7Qud5Wd29CR5-q2-FGYS7-jTsIFgEEq4XQw_0lvWRmIfDoEebeltFDFEoMXk/s1600/permutation%201.JPG)
(https://i.ytimg.com/vi/0WDUWCtxM1U/maxresdefault.jpg) (http://www.cut-the-knot.org/do_you_know/permutation.shtml)
GEOMETRIC PROGRESSION
INTRODUCTION
A geometric grouping is an arrangement such that any component after the first is acquired by duplicating the former component by a consistent called the normal proportion which is signified by ratio. The regular proportion (r) is acquired by partitioning any term by the previous term.
DEFINITION
A sequence, such as the numbers 1, 3, 9, 27, 81, in which each term is multiplied by the same factor in order to obtain the following term. Also called geometric sequence.
EXPLANATION AND EXAMPLES
The formula and calculation are the same as Arithmetic Progression, only the different is we have to find the common ratio, not the common difference. for example:
OTHER FORMULA AND EXAMPLES
VIDEO
REFERENCES
(http://pad3.whstatic.com/images/thumb/5/54/Find-the-Sum-of-a-Geometric-Sequence-Step-2Bullet1.jpg/aid591689-728px-Find-the-Sum-of-a-Geometric-Sequence-Step-2Bullet1.jpg)
(http://pad3.whstatic.com/images/thumb/0/0a/Find-the-Sum-of-a-Geometric-Sequence-Step-1Bullet1.jpg/aid591689-728px-Find-the-Sum-of-a-Geometric-Sequence-Step-1Bullet1.jpg)
(http://www.mathsisfun.com/algebra/images/sequence.gif)
(http://mathematics.laerd.com/maths/geometric-progression-intro.php)
(http://www.thefreedictionary.com/geometric+progression)
(http://www.regentsprep.org/regents/math/algtrig/atp2/ArithG12.gif)
(http://pad3.whstatic.com/images/thumb/e/ef/Find-the-Sum-of-a-Geometric-Sequence-Step-4.jpg/670px-Find-the-Sum-of-a-Geometric-Sequence-Step-4.jpg)
(http://www.wikihow.com/images/4/4d/Find-Any-Term-of-a-Geometric-Sequence-Step-4.jpg)
A geometric grouping is an arrangement such that any component after the first is acquired by duplicating the former component by a consistent called the normal proportion which is signified by ratio. The regular proportion (r) is acquired by partitioning any term by the previous term.
DEFINITION
A sequence, such as the numbers 1, 3, 9, 27, 81, in which each term is multiplied by the same factor in order to obtain the following term. Also called geometric sequence.
EXPLANATION AND EXAMPLES
The formula and calculation are the same as Arithmetic Progression, only the different is we have to find the common ratio, not the common difference. for example:
OTHER FORMULA AND EXAMPLES
VIDEO
REFERENCES
(http://pad3.whstatic.com/images/thumb/5/54/Find-the-Sum-of-a-Geometric-Sequence-Step-2Bullet1.jpg/aid591689-728px-Find-the-Sum-of-a-Geometric-Sequence-Step-2Bullet1.jpg)
(http://pad3.whstatic.com/images/thumb/0/0a/Find-the-Sum-of-a-Geometric-Sequence-Step-1Bullet1.jpg/aid591689-728px-Find-the-Sum-of-a-Geometric-Sequence-Step-1Bullet1.jpg)
(http://www.mathsisfun.com/algebra/images/sequence.gif)
(http://mathematics.laerd.com/maths/geometric-progression-intro.php)
(http://www.thefreedictionary.com/geometric+progression)
(http://www.regentsprep.org/regents/math/algtrig/atp2/ArithG12.gif)
(http://pad3.whstatic.com/images/thumb/e/ef/Find-the-Sum-of-a-Geometric-Sequence-Step-4.jpg/670px-Find-the-Sum-of-a-Geometric-Sequence-Step-4.jpg)
(http://www.wikihow.com/images/4/4d/Find-Any-Term-of-a-Geometric-Sequence-Step-4.jpg)
Saturday, 9 July 2016
INEQUALITIES
INTRODUCTION
explanations that demonstrate the relationship between two (or more) expressions with one of the accompanying five signs: < , ≤ , > , ≥ , ≠ and presents the idea of disparities with variables, and demonstrates to discover an answer set for an in balance, given a substitution set.
SYMBOL OF INEQUALITIES
EXPLANATION
EXAMPLES:
VIDEO
REFERENCES
(https://www.google.com.bn/search?biw=1536&bih=731&tbm=isch&sa=1&q=examples+of+inequalities&oq=examples+of+inequalities&gs_l=img.3..0i19l3j0i5i30i19j0i8i30i19l4.239438.243814.0.244026.26.18.1.7.7.0.112.1477.16j2.18.0....0...1c.1.64.img..0.26.1492...0j0i10i19j0i30i19.9Hcl2YKM--8#imgrc=ZDF3ELcMFG-xQM%3A)
(http://deeringmath.com/precalc/precalcbook/ch4graphics/chapter4__24.png)
explanations that demonstrate the relationship between two (or more) expressions with one of the accompanying five signs: < , ≤ , > , ≥ , ≠ and presents the idea of disparities with variables, and demonstrates to discover an answer set for an in balance, given a substitution set.
SYMBOL OF INEQUALITIES
EXPLANATION
EXAMPLES:
VIDEO
REFERENCES
(https://www.google.com.bn/search?biw=1536&bih=731&tbm=isch&sa=1&q=examples+of+inequalities&oq=examples+of+inequalities&gs_l=img.3..0i19l3j0i5i30i19j0i8i30i19l4.239438.243814.0.244026.26.18.1.7.7.0.112.1477.16j2.18.0....0...1c.1.64.img..0.26.1492...0j0i10i19j0i30i19.9Hcl2YKM--8#imgrc=ZDF3ELcMFG-xQM%3A)
(http://deeringmath.com/precalc/precalcbook/ch4graphics/chapter4__24.png)
Tuesday, 5 July 2016
LOGARITHMS
INTRODUCTION
One of my normal reporters, Yousuf, as of late turned out to be extremely confounded over what "log" implied. He'd missed a little, however basic bit of data − that if the base is overlooked, it's expected we are discussing log base 10
REFERENCES
One of my normal reporters, Yousuf, as of late turned out to be extremely confounded over what "log" implied. He'd missed a little, however basic bit of data − that if the base is overlooked, it's expected we are discussing log base 10
Calculator Showing "log" and "In" Buttons
So "log" (as written in math course readings and on number crunchers) signifies "log10" and talked as "log to the base 10". These are known as the normal logarithms.
We utilize "ln" in math course books and on number crunchers to signify "loge", which we say as "log to the base e". These are known as the common logarithms.
DEFINITION
In mathematics, the logarithm is the reverse operation to exponentiation. That implies the logarithm of a number is the type to which another settled worth, the base, must be raised to deliver that number
EXPLANATION
A logarithm is simply an exponent that is written in a special way.
For example ,we know that the following exponential equation is true:
32 = 9
In this case, the base is 3 and the exponent is 2. We can write this equation in logarithm form (with identical meaning) as follows:
log 3 9 = 2
We say this as "the logarithm of 9 to the base 3 is 2". What we have viably done is to move the type down on to the primary line. This was done generally to make duplications and divisions less demanding, however logarithms are still extremely convenient in mathematics
EXAMPLES
1.
2.
VIDEO
REFERENCES
(https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_5m8qSfUh84wKhRhCoU2_5t3xmwKMLvd8X5z9k__xHAd6c4Nf_0JdUcOEGC1QyXoAhEZY7fb85AXgcmUBd70aYrD_2VU3rO19xr3sqrynw241spJIiceDEv5qx_XPtT2GSEXfSkNq9xU/s1600/ex07.PNG)
(http://www.intmath.com/exponential-logarithmic-functions/1-definitions-exp-log-fns.php)
(http://www.intmath.com/blog/mathematics/logarithms-a-visual-introduction-4526)
(https://en.wikipedia.org/wiki/Logarithm)
(https://www.youtube.com/results?search_query=mathematics+logarithms)
LINEAR PROGRAMMING
INTRODUCTION
Direct Programming is a speculation of Linear Algebra. It is fit for taking care of an assortment of issues, running from discovering plans for aircrafts or films in a theater to circulating oil from refineries to business sectors. The purpose behind this extraordinary flexibility is the straightforwardness at which requirements can be joined into the model. To see this, in the accompanying segment we portray a particular issue in awesome point of interest, and in §3 we talk about how some quadratic (or higher request) limitations can be taken care of also.
DEFINITION
Linear Programming is the process of finding the extreme values (maximum and minimum values) of a function for a region defined by inequalities.
WHAT ARE LINEAR PROGRAMMING?
Straight writing computer programs is a technique that is utilized to locate a base or most extreme worth for a capacity. That quality is going to fulfill a known arrangement of conditions imperatives. Imperatives are the imbalances in the direct programming issue. Their answer is charted as an achievable district, which is an arrangement of focuses. These focuses are the place the diagrams of the disparities converge. Furthermore, the locale is said to be limited when the diagram of an arrangement of imperatives is a polygonal district.
There are 7 stages that are utilized when taking care of an issue utilizing straight programming which is:
1. Define the variables
2. Writes a system of inequalities
3. Graph the system of inequalities
4. Find the coordinates of the vertices of feasible region
5. Write a function to be maximized or minimized
6. Substitute the coordinates of the vertices into the function
7. Select the greatest or least result. Answer the problem.
EXAMPLES:
REFERENCES
(https://web.williams.edu/Mathematics/sjmiller/public_html/BrownClasses/54/handouts/LinearProgramming.pdf)
(https://en.wikibooks.org/wiki/Applicable_Mathematics/Linear_Programming_and_Graphical_Solutions)
(http://images.slideplayer.com/5/1493045/slides/slide_6.jpg)
(http://www.shelovesmath.com/wp-content/uploads/2012/11/Jewelry-Graph1.png)
Direct Programming is a speculation of Linear Algebra. It is fit for taking care of an assortment of issues, running from discovering plans for aircrafts or films in a theater to circulating oil from refineries to business sectors. The purpose behind this extraordinary flexibility is the straightforwardness at which requirements can be joined into the model. To see this, in the accompanying segment we portray a particular issue in awesome point of interest, and in §3 we talk about how some quadratic (or higher request) limitations can be taken care of also.
DEFINITION
Linear Programming is the process of finding the extreme values (maximum and minimum values) of a function for a region defined by inequalities.
WHAT ARE LINEAR PROGRAMMING?
Straight writing computer programs is a technique that is utilized to locate a base or most extreme worth for a capacity. That quality is going to fulfill a known arrangement of conditions imperatives. Imperatives are the imbalances in the direct programming issue. Their answer is charted as an achievable district, which is an arrangement of focuses. These focuses are the place the diagrams of the disparities converge. Furthermore, the locale is said to be limited when the diagram of an arrangement of imperatives is a polygonal district.
There are 7 stages that are utilized when taking care of an issue utilizing straight programming which is:
1. Define the variables
2. Writes a system of inequalities
3. Graph the system of inequalities
4. Find the coordinates of the vertices of feasible region
5. Write a function to be maximized or minimized
6. Substitute the coordinates of the vertices into the function
7. Select the greatest or least result. Answer the problem.
EXAMPLES:
REFERENCES
(https://web.williams.edu/Mathematics/sjmiller/public_html/BrownClasses/54/handouts/LinearProgramming.pdf)
(https://en.wikibooks.org/wiki/Applicable_Mathematics/Linear_Programming_and_Graphical_Solutions)
(http://images.slideplayer.com/5/1493045/slides/slide_6.jpg)
(http://www.shelovesmath.com/wp-content/uploads/2012/11/Jewelry-Graph1.png)
Friday, 1 July 2016
INDICES
INTRODUCTION
Records are a helpful method for all the more basically communicating substantial numbers. They additionally give us a numerous valuable properties for controlling them utilizing what are know as the Law of Indices.
DEFINITION
The records of a number says how often to utilize the number in a duplication and it is composed as a little number to one side or more the base number.
WHAT ARE INDICES?
Records are a helpful method for all the more basically communicating substantial numbers. They additionally give us a numerous valuable properties for controlling them utilizing what are know as the Law of Indices.
DEFINITION
The records of a number says how often to utilize the number in a duplication and it is composed as a little number to one side or more the base number.
WHAT ARE INDICES?
The expression 25 is defined as follows:
35 = 3 x 3 x 3 x 3 x 3
we call "3" the base and "5" the index.
LAW OF INDICES
To control expression, we can consider utilizing the Law of Indices. These laws just apply to expressions with the same base, for instance, 34 and 32 can be controlled utilizing the Law of Indices, yet we can't utilize the Law of Indices to control the expressions 35 and 57 as their base contrasts (their bases are 3 and 5, individually.
RULE 1:
To multiply expressions with the same base, copy the base and add the indices.
An example:
simplify 4 x 43 (note: 4 = 41)
41 x 43 = 41+ 3
= 44
= 4 x 4 x 4 x 4
= 256
RULE 2:
To divide expressions with the same base, copy the base and subtract the indices.
An example:
Simplify: 5(y9 / y5):
5(y9 / y5) = 5 (y9-5)
= 5y4
REFERENCES
(http://mathematics.laerd.com/maths/indices-intro.php)
(https://www.youtube.com/watch?v=LrvKAMgcipo)
An example:
simplify 4 x 43 (note: 4 = 41)
41 x 43 = 41+ 3
= 44
= 4 x 4 x 4 x 4
= 256
RULE 2:
To divide expressions with the same base, copy the base and subtract the indices.
An example:
Simplify: 5(y9 / y5):
5(y9 / y5) = 5 (y9-5)
= 5y4
REFERENCES
(http://mathematics.laerd.com/maths/indices-intro.php)
(https://www.youtube.com/watch?v=LrvKAMgcipo)
Subscribe to:
Posts (Atom)