Study Notes - Mathematics

 Today, in Mathematics we are making study notes of Number for our topic test on Friday. Now, I go to Mathematics site and we are talking about Number, Order of Operation, Rounding, Standard Form, Percentage "of mean times", Percentage increase/decrease, 

Number

• Multiples - Multiples are set of numbers that correspond to a base number that has been mulitplied by other numbers. A Multiple is formed by multiplying a given number by the counting numbers. 

Multiples: 3, 6, 9, 12...

• Factor - Factor is a number or algebraic expression that divides another number or expression evenly. Factors are the numbers you mulitply together to get a product.

Factor: 15 - 1, 3, 5, 15

• Prime Number - A Prime Number are numbers that have only 2 factors. A Prime Number is a number that can only be divided evenly (no remainders) by itself and the number 1.

• HCF (Highest Common Factor) - Highest Common Factor is found by finding all common factors of two numbers and selecting the largest one.

Highest Common Factor is 4.

8: 1, 2, 4, 8

12: 1, 2, 4, 6, 12

• LCM (Lowest Common Factor) - Lowest Common Factor is a multiple number you get when you multiply a number by a whole number. 

Lowest Common Factor is 24

6: 6, 12, 18, 24, 30, 36 ...

8: 8, 16, 24, 32, 40 ...

Order of Operation 

Here is what we did to solve problems and it's called BEDMAS: 

• B - stands for brackets.
• E - stands for exponents.
• D - stands for division.
• M - stands for multiplication.
• A - stands for addition.
• S - stands for subtraction.

Rounding 

Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation.

 Example:

Replacing $23.4476 with $23.45, the fraction 312/937 with 1/3 or the expression √2 with 1.414.

Number	1dp	2dp	3dp
34.3565	34.4	34.36	34.357

Standard Form

Standard form allows us to write numbers without using as many digits. A number is standard form is written in two parts: Number from 1 to 9 x power of 10

Example: 

35 946 (first number must be from 1 - 9)

followed by power of 10

Answer: 3.5946 x 10 power of 4

Percentage (of mean times)

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

3/5 of 400 = 240

10% of 600 = 60

Increase/Decrease:

To Increase/Decrease an amount by a percentage, first calculate the percentage of the amount and then either add this answer on to increase the quantity, or subtract this answer to decrease the quantity.

Example:

Question	Working	Answer
Increase 60 by 10% Decrease 200 by 5%	60 + 10% * 60 200 - 5% * 200	66 190

Smart Goal

 "SMART GOAL"

For me, the meaning of SMART GOAL are Specific, Measurable, Achievable, Realistic and Time. It is important to us students to learn the Smart Goal so that we can help our parents and achieve our dreams in the right time. Smart Goal set us up for success by mkaing it Specific, Measurable, Achievable, Realistic and Time. The Smart method helps us to push further and gives us a sense of direction and helps us organize and to reach our goals.

What are SMART GOAL Example?

Smart Goal have different examples:

S = Specific

Specific is a clear and specific as possible with what you want to achieve. The more narrow your goal, the more you’ll understand the steps necessary to achieve it.

Example: “I want to earn a position managing a development team for a startup tech company.”

M = Measurable

Measurable is what evidence will prove you’re making progress toward your goal? For example, if your goal is to earn a position managing a development team for a startup tech company, you might measure progress by the number of management positions you’ve applied for and the number of interviews you’ve completed. Setting milestones along the way will give you the opportunity to re-evaluate and course-correct as needed. When you achieve your milestones, remember to reward yourself in small but meaningful ways.

Example: “I will apply to three open positions for the manager of a development team at a tech startup.”

A = Achievable

Achievable have you set an achievable goal? Setting goals you can reasonably accomplish within a certain time-frame will help keep you motivated and focused. Using the above example of earning a job managing a development team, you should know the credentials, experience and skills necessary to earn a leadership position. Before you begin working toward a goal, decide whether it’s something you can achieve now or whether there are additional preliminary steps you should take to become better prepared.

Example: “I will update my resume with relevant qualifications, so I can apply to three open positions for the manager of a development team at a tech startup.”

R = Realistic

Relevant is when setting goals for yourself, consider whether or not they are relevant. Each of your goals should align with your values and larger, long-term goals. If a goal doesn’t contribute toward your broader objectives, you might rethink it. Ask yourself why the goal is important to you, how achieving it will help you and how it will contribute toward your long-term goals.

Example: “To achieve my goal of being in leadership, I will update my resume with relevant qualifications so I can apply to three open positions for the manager of a development team at a tech startup.”

T = Time

Time-based is what your goal time-frame? An end-date can help provide motivation and help you prioritize. For example, if your goal is to earn a promotion to a more senior position, you might give yourself six months. If you haven’t achieved your goal in that time-frame, take time to consider why. Your time-frame might have been unrealistic, you might have run into unexpected roadblocks or your goal might have been unachievable.

Example: “To achieve my goal of being in leadership, I will update my resume with relevant qualifications so I can apply to three open positions for the manager of a development team at a tech startup this week.”