Maths:Topic Eight: "Probability"

Topic Eight: "Probability" 

Definition: 

Mathematicians use the words “experiment” and “outcome” in a very wide sense.

Any process of observation or measurement is called an experiment. Noting down whether a

newborn baby is male or female, tossing a coin, picking up a ball from a bag containing balls

of different colours and observing the number of accidents at a particular place in a day are

some examples of experiments.

A random experiment is one in which the exact outcome cannot be predicted

before conducting the experiment. However, one can list out all possible outcomes of the

experiment.

The set of all possible outcomes of a random experiment is called its sample space and

it is denoted by the letter S. Each repetition of the experiment is called a trial.

A subset of the sample space S is called an event.

Let A be a subset of S. If the experiment, when conducted, results in an outcome that

belongs to A, then we say that the event A has occurred.

Examples:

Let us illustrate random experiment, sample space, events with the help of some

examples.

Reference:

www.textbooksonline.tn.nic.in/books/std10/std10-maths-em-2.pdf

Maths:Topic Seven: "Geometric Progression"

Topic Seven: "Geometric Progression"

Definition:

Examples:

1.

Note:

2.

Reference:

www.textbooksonline.tn.nic.in/Books/Std10/Std10-Maths-EM-1.pdf

Maths:Topic Six: "Arithmetic Progression"

Topic Six: "Arithmetic Progression"

Definition:

Examples:

Here's some example of "Arithmetic Progression"

1.

(i) 2, 5, 8, 11, 14, g is an A.P. because a1 = 2 and the common difference d = 3.

(ii) -4, -4, -4, -4, g is an A.P. because a1 = -4 and d = 0.

(iii) 2, 1.5, 1, 0.5, 0, - 0.5, - 1.0, - 1.5,g is an A.P. because a1 = 2 and d = -0.5.

Note:

2. 

Reference:

www.textbooksonline.tn.nic.in/Books/Std10/Std10-Maths-EM-1.pdf

Maths:Topic Five: "Inequality"

Topic Five: "Inequality"

Introduction:

The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an
arrowhead. It is an example of an inequality.

This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3. We
will be interested in finding the values of x for which the inequality is true.

We use four symbols to denote inequalities:

Key Point

>  is greater than

> is greater than or equal to

<  is less than

< is less than or equal to

Notice that the arrowhead always points to the smaller expression

EXAMPLES:

1. We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.
Inequalities can be represented on a number line such as that shown in Figure 1. The solid line
shows the range of values that x can take. We put an open circle at −1 to show that although
the solid line goes from −1, x cannot actually equal −1.

Figure 1. A number line showing x > −1.

2. Suppose we wish to solve the inequality

4x + 6 > 3x + 7.

First we subtract 6 from both sides to give

4x > 3x + 1

Now we subtract 3x from both sides:

x > 1

This is the solution. It can be represented on the number line as shown in Figure 2.

Figure 2. A number line showing x > 1.

REFERENCE:

www.mathcentre.ac.uk/resources/uploaded/mc-ty-inequalities-2009-1.pdf 

Maths:Topic Four: "Measures of dispersion : Part 3"

TOPIC FOUR: "MEASURES OF DISPERSION : PART 3" 

Definition:

What is MODE? 

Mode is many, Repeating and etc. Other definition is a number that appears most often in set of numbers. 

The first step to find Mode is ARRANGE THE NUMBER IN ASCENDING ORDER (if possible), second, you just need to find the that appears most often. 

Examples:

1. {1, 2, 2, 3, 4, 5, 2, 6, 7, 8, 2, 9, 0}

Here the mode is the number " 2 ". Because it is the number that appear often.

2.{1, 2, 1, 2, 3, 4, 1, 5, 2, 6, 7, 8, 2, 9, 0}

Here, there's around two numbers that are repeating: "1", (around 3 times) "2" (around 4 times). therefor, the mode is number 2. 

3.{1, 2, 1, 2, 3, 4, 1, 5, 2, 6, 7, 8, 1, 2, 9, 0}

Here, there's around two numbers that are repeating: "1", (around 4 times) "2" (around 4 times). therefor, the mode is number 1 and 2. Because both number appears often (Same times). 

KEY-POINTS 

1. Arrange the numbers in ascending order, but if the numbers is to many, you can just skip.

2. Find the numbers that appears most often (Mark them if possible so that you can count them.)

Maths:Topic Four: "Measures of dispersion : Part 2"

Topic Four: "Measures of dispersion : Part 2"

 Definition:

What Is Median? Median means "MIDDLE". Here the median of values are the number which are located in the middle of its sequences. But it all dependence on the values and the the total of the values itself. 

I will show you how to find the median and I will try the best that I can to help you understand its concepts, with my own formula (Based on my understanding).

The first step of finding median is to "ARRANGE THE NUMBERS IN ASCENDING ORDER". Second Step is to cancel out or stroke out the numbers from the first sequence and last sequence, then the second sequence and the second last sequence, you need to to do this until you reach the middle number(Whether its consist of 1 number or 2 numbers: It all dependence on the sequence.).    

Here's few examples for "Median":

1. Find the median of the following sequence below:

3, 5, 2, 1, 8, 7, 6, 0, 4 

Okay, the first step is to arrange it into "ASCENDING" order.

0, 1, 2, 3, 4, 5, 6, 7, 8

Then, you need to cross out or stoke out the number(As mention before).

0, 1, 2, 3, 4, 5, 6, 7, 8

0, 1, 2, 3, 4, 5, 6, 7, 8

0, 1, 2, 3, 4, 5, 6, 7, 8

0, 1, 2, 3, 4, 5, 6, 7, 8

From the number sequence: you can see that the median is the number "4".

2. Find the median of the following sequence below:

3, 5, 2, 1, 8, 7, 6, 0, 4, 9

Just like the previous procedures:

Arrange in ascending order:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Stroke out or cross out the numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

 Here as you can see: there is around 2 numbers in the middle: which are "4, 5". If you come across something like this, all you need to do is to:

First: Find the SUM of the numbers : 4 + 5 = 9

Second: DIVIDE the SUM by 2: 9 / 2 = 4.5 

Therefor: The median is 4.5. 

KEY-POINTS: 

1. ARRANGE THE NUMBERS FIRST IN ASCENDING ORDER.
2. STROKE OR CROSS OUT THE NUMBERS.
3. THE MEDIAN WILL BE LOCATED IN THE MIDDLE.
4. IF THE MIDDLE NUMBERS IS MORE THAN 1:
1. FIND THE SUM OF THE NUMBERS
2. DIVIDE THE SUM BY 2

To Be Continue....

Maths:Topic Four: "Measures of dispersion : Part 1"

Topic Four: "Measures of dispersion : Part 1"

The first part of "Measures Of Dispersion" is: "Average".

"Average"

Average consist of 3:

1. Mean
2. Median
3. Mode

1. Mean

Mean is where you need to find the average. For example:

1,2,3,4,5,6,7,8

The the steps for finding Mean is:

• To find the total or sum of the number:
• SUM= 1+2+3+4+5+6+7+8 
• SUM= 36 

• Then, you just need to divide the SUM by the values of the number:

• 1,2,3,4,5,6,7,8 = the total number of this values are : 8
•  So, 36/8 = 4.5 

• The Mean is equal to : "4.5"

Here is another example:

10,2,8,7,11,9,5

• First Step: Find the SUM; 
• SUM= 10+2+8+7+11+9+5
• SUM= 52

• Second Step: Divide by total number of of the values
• 10,2,8,7,11,9,5 = the total number of values: 7
• So, 52 / 7 = 7.43

• The Mean is equal to : "7.43"

Here is another example: but this time with specific request:

• Find the MEAN of the following numbers below. Give your answer in 2 DECIMAL PLACES.  

28,1,9,56,100.3,2,1,2 

• SUM = 28+1+9+56+100+3+2+1+2
• SUM = 202

• Total number of values: 9
• MEAN = 202 / 9
• MEAN = 22.44444444......(Original)
• MEAN = 22.44 (2 Decimal Places)

KEY-POINTS: 

 First you need to find the SUM of the values. Then, you DIVIDE the SUM by the NUMBER OF VALUES.  

TO BE CONTINUE...

Maths: Topic Three: "Sequence"

Topic Three: "Sequence"

What is a sequence? 

A list of numbers or objects in a special order.

Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.

Examples:

Reference:

https://www.mathsisfun.com/numberpatterns.html

Maths: Topic Two: "Logarithm"

Topic Two: "Logarithm"

Definition:

A logarithm is the power to which a number must be raised in order to get some other number

 For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:

log 100 = 2

because

10² = 100

The Laws Of Logarithms:

 

Examples:

References:

https://www.mathsisfun.com/algebra/logarithms.html

Maths: Topic One: "Indices"

Topic One: "Indices"

Introduction

Indices are a useful way of more simply expressing large numbers. They also present us with many useful properties for manipulating them using what are called the Law of Indices.

The Laws of Indices:

Example:

Taken From http://mathematics.laerd.com/maths/indices-4.php

Taken From http://mathematics.laerd.com/maths/indices-1.php