Unit 4

In unit 4 we learned about geometry. In this unit we studied geometry using graph papers to draw the figures.

In chapter 8 we were learning about coordinates. Using graph papers, we determined the point and location of a point. 

*The image below is a coordinate plane that we use to determine a point, location, and coordinate.

To find the coordinate we need to order it by X then Y (x,y). After we get the coordinates we name it with a capital letter.

In chapter 10 we were learning about reasoning in geometry. So every answer that we put must be with reason. We were thought about alternate angle (Z-Angle), co-interior (C-Angle), and corresponding angle (F-Angle).

There are some terminologies in geometry:

Terminologies in geometry

• Point
• The basic element of geometric figure
• all geometric figure are made up of points
• use upper case letter
• no length and no width
• Line
• The connection between two or more points
• No endpoints
• Use lowercase letter
• Line segment 
• Part of line with endpoint
• It has two endpoints
• use uppercase letter
• Identified by points at the end
• Ray
• Part of line with endpoint
• has 1 endpoint
• can be name by saying the endpoint first
• Use lowercase letter
• Collinear points
• Points that lie in a straight line
• Angle
• When two line meet each other in 1 point

An alternate angle is when a pair of parallel lines are cross by a transversal line and the angles (the blue angles in the picture) are equal.

                                                     

a co-interior angle is when a pair of parallel lines are cross by a transversal line and form angles (as shown in the picture) where the sum of angles red area is 180 degrees.

                                                          

    

Corresponding angles are when two parallel lines are crossed by a transversal line and form angles that are equal to the other as shown in the picture:

Worked example:

Not only that, we also learned about types of angles like opposite, complimentary, supplementary, obtuse, acute, etc. angles.

Opposite angle

Opposite angles are angles that are opposite. Both angles were made with the same two lines and is always equal.

Opposite angle:

The angle b and a are equal.

Complimentary angle

Complimentary angles are angles that add up to a total of 90⁰.

Example:

Supplementary angle

Supplementary angles are angles that add up to a total of 180^o.

Example:

Obtuse angle

Obtuse angles are angles that are more than 90^o.

Examples:

Acute angle

Acute angles are angles that less than 90^o.

Examples:

Circle

- Parts of circle

- Area of Circle

     A=

How to find the perimeter/circumference of a circle?

So we need to multiply the diameter of the circle with the pi

Introduction

Hello

My name is Muhammad Faishal Fadhlurahman you can call me Fais
I'm a student from SVP.
This blog is an assignment from our maths teacher so please enjoy it and may it help with your study.

Unit 1 (Numbers)

 In this unit we have learned about whole number, fraction, decimal, ratio, Rates, scale drawing and percentage and also the concepts of each topic. 

In the first chapter we studied about whole numbers. We learned about basic roman numerals, number order and structure, fractions, decimals, percentage, and reviewing on last year lesson.

Roman Numerals

• 1   = I
• 2   = II
• 3   = III
• 4   = IV
• 5   = V
• 6   = VI
• 7   = VII
• 8   = VIII
• 9   = XI
• 10 = X

*I as in 1 for Roman Numerals can only be used 3 times in a numerals. For example is when we write 4, for 4 we use subtraction (-) not addition (+) so it will be IV (5-1) instead of IIII (1+1+1+1)

Fractions
In fraction we learned about how to add, subtract, multiply, and divide fractions. We also learned to change fraction into mix numbers and vice versa.

To add and subtract fraction we firstly need to match the denominator so that it will be the same number. After that will be the same as normal subtraction.

*The way to match the denominator is by finding the lowest common multiple of both denominator. Then divide the LCM with the denominators and multiply it with the existing numerator to get the new numerator.

This process is only used for fractions with different denominator. However if the denominators are the same just do it like normally. Example below.

To multiply fractions just multiply the numerator with the other numerator and denominator with the other denominator.

*The process in which you simplify the fractions you are multiplying by dividing either the first fraction's numerator with the second fraction's denominator or vice versa is called cancelation.

To divide a fractions you just need to make one of the fraction reversed or upside down then change it into multiplication. After that multiply and simplify them. 

Examples below:

Decimals
In decimals, we learned about adding, subtracting, multiplying, and dividing decimals. We also learned about converting decimals to fraction or percentage.

To add and subtract decimals we can just do it directly like usual. But pay attention to the dot because they should be on top of each other. 

To multiply decimals we need to see the numbers behind the dots. But first forget about the decimal. points/ dots,If the sum of numbers in both or all decimals is 3 digits so later move the dot 3 times.

To divide decimals we need to make all decimals become whole numbers. we can do it by multiplying them with 10, 100, 1000, 10000, 100000, and so on as long as it is the multiple of 10. However, don't forget if one decimal is multiplied the other decimal must also be multiplied so that they will be balanced. 

Another way:

To convert decimal to fractions you need to see how many digits behind the dots.

1 = /10

2 = /100

3 =/1000

To convert decimal to percentage just multiply them by 100%.

Percentage  

To convert percentage to decimals, we need to divide them with 100 %. So they will be a decimal.

To convert percentage to fraction we need to make it become over 100 (/100) then simplify.

Example:

To find a percentage of a quantity we need to multiply the quantity with the percentage over 100. Like this:

Work Example from our book:

Ratio

In ratio, we learned about how to use ratio for word problems. We also learned equivalent ratio, and dividing a quantity with a given ratio. 

First of all, ratio can be expressed by :(double dots or colon), / and "to" 

In using ratio to solve word problem, we must know the question and understand them. First, we need to find 1 first. After that, we just need to multiply the 1 with each given ratio. 

For equivalent ratio, we can multiply both or more numbers with the same numbers. You can also simplify them by dividing them with the same number.

For dividing a quantity with the given ratio, this concept is related with the first concept. We can find I first.

These are several questions and its solution:

Rates

In rates we learned about distances, time, simplifying rate, writing numbers as rate, and many more. Here you will see examples, solution, and the how it works.

Observe this as an example:

Write each of the following as a rate in simplest form.

8 KM in 2h 

To write this as a rate we need to use the symbol / or per.

It will become

8 Km/2H

But in rate you must make it as simplest form

So it will become 

4km/h

This just one example of rate that I have learned.

Scale Drawing

In scale drawing, we still apply the concept of ratio. Scale drawing of an object is the same shape as the object but a different size.

Scale = length on drawing : real length

A scale can be written in two ways, as 1 cm: 1 m or 1cm :100cm (1m)

If the scale drawing is larger than the real length, then the scale drawing is called anenlargement and the first term of the scale would be the larger.

For example:

A real distance of a line 10 m. But the scale drawing is only 5 m.

It should be 5 : 10 but its not the simplest form so you must simplify them become 1m for the scale per 2m for the real distance.

Unit 2 (Algebra)

In unit 2 we learned about algebra.

-Terminologies in algebra:

• Variables - the letters such as a,b,c,x,y
• Coefficient - number in front of the variable
• Constant - number without variable
• Monomials - Algebraic expression containing one term
• Binomials - Algebraic expression containing two terms
• Trinomials - Algebraic expression consist of three terms
• Polynomials - Algebraic expression which have two or more terms
• Like terms - have the same pro-numerals/variable/letter
• Unlike terms - have different pro-numerals/variable/letter

   *In algebra,term of the same kind is called like terms can be combined into a single terms.

Algebraic operations:

- Addition and subtraction of like terms.
With like terms we can just immediately add or subtract a pro-numeral with another pro-numeral

Example: 9a+12a = 21a         10a-29a = -19a

 But if they are unlike terms you should simplify them first. 

Example:

12X + 5Y + 2X + 76B = 76B +14X+ 5Y

The way simplify the equations is by using like terms operations. 
Like so

- Multiplication of pro-numerals. 
For multiplication of pro-numerals we need to do it separately between the coefficient and the variable.

Example: 16x X 5y=
                16 X 5    = 80
                 x X y     = xy
                 answer= 14 ab
-Division of pro-numerals. 
To do division between pro-numerals we can convert it into a fraction and do it separately between coefficient and variables. Using that way, we can simply divide the pro-numerals.

Example: 20x/ 5x = 4( we can cancel the variables by crossing them)

Using algebra

-Using algebra we can use algebra to solve problems like the ones below

When a pro-numeral is multiplied by itself, we can express them using index notation.

example: a x a x a x a x a x a x a x a = a

Worked example:

Not only that, in algebra there are equations and in-equations.

Equations

Algebra equation = Algebraic expression that use equal sign

Example of algebraic equation = 3x + 7 =  4x + 4

To solve the problem above we need to group them (monomials with monomials and the constant with the other constant). To group them we should change the sign.We change sign only if the numbers move above the equal sign.

*the sign in front of the numbers stay with the numbers

After the process, the algebra will look like this =
 3x-4x =7+4
-x =11
x = -11

In Equations

In Equation = Algebraic expression that dont use equal sign.

Inequalty sign :

Example:

Note= the way use the changing sign concepts/magic door.

When multiplying/dividing an inequation by a negative number, the sign must be change.  

                  
Worked example:

The way above is using another method which is balancing methods. To answer the inequation problem you must answer it in a curly bracket or number line.

We also learned about algebraic fractions.

To solve algebraic fractions, you just need to apply the same concept of fraction. For addition and subtraction we need the same denominator. In multiplying and dividing, we need to do it separately between variables and the coefficients.
Worked example for addition and subtraction:

Worked example for multiplication and division: