Understanding Angles

An angle is formed by two rays that meet at the same endpoint. Angles are denoted by the symbol $\angle$. In an angle, we recognize the angle arms, the vertex, and the angle region.

In the picture, the arms of the angle are rays $OA$ and $OB$. Point $O$ is the vertex, while the shaded area is the angle region.

Introduction

Data is essential in everyday life. Clear data helps us make decisions, compare information, and explain a situation more accurately. To make data easier to read, it is usually presented in the form of tables or diagrams.

Collecting Data

In general, data can be divided into two main types:

Introduction

Al-Khwarizmi is widely known as one of the major figures in the history of algebra. In school mathematics, algebraic forms are used to represent unknown quantities with letters or variables.

Simple examples:

• the square of $3$ is $3^2 = 9$
• the square root of $9$ is $\sqrt{9} = 3$

A Problem Involving Algebraic Forms

A traveler rides for 3 hours at an average speed of $(2x-5)$ km/h, then continues for 4 hours at an average speed of $(4x+8)$ km/h. If the total distance traveled is 346 km, the value of $x$ can be found using algebraic expressions.

Introduction

In the previous post, I wrote about Definition of Set

, Presenting Relationships Between Sets Using Venn Diagrams

, And Presenting Set Operations in a Venn Diagram

. Now, I will give a quiz related to the set material. This is intended so that readers can measure their understanding in studying material about the set which is divided into these three posts.

Introduction

After the previous post we discussed meaning of set and presenting relationships between sets with a Venn diagram, so on this occasion we will discuss presenting set operations in Venn diagrams, the properties of set operations, and their application in solving everyday problems related to the concept of sets.

Introduction

Sets can be presented in several ways:

1. by description,
2. by set-builder notation,
3. by listing their elements,
4. or by using a Venn diagram.

This diagram is named after the British mathematician John Venn (1834-1923).

Basic guidelines for drawing a Venn diagram:

1. The universal set $S$ is drawn as a rectangle.
2. Each set inside the universal set is shown by a simple closed curve.
3. Each member of a set is represented by a point or written inside its region.
4. If a set has many members, the members do not have to be written one by one.

Example of a Venn diagram:

Introduction

When we shop in a fruit market or supermarket, we see fruits grouped by type, such as grapes, mangoes, and oranges. In mathematics, a collection like this can be called a set if its members are clearly defined.

Not every collection qualifies as a set. The objects in the collection must be identifiable without ambiguity.

Introduction

Consider this example. Naomi buys chicken noodles every 2 days, Uciha every 3 days, and Sakiro every 5 days. If they all buy noodles together today, after how many days will they meet again on the same day?

This kind of problem can be solved using the idea of the Least Common Multiple (LCM).

Introduction

Class VII.A of a junior high school held an election for class president. The candidates were Danang, Fatimah, and Zalfa. After the votes were counted, Danang received $\dfrac{1}{3}$ of Fatimah’s votes, while Fatimah received $\dfrac{3}{4}$ of Zalfa’s votes. If there are 32 students in the class, how many votes did each candidate get?

Introduction

Congratulations to those of you who have graduated from elementary school and entered junior high school. The material you studied before will be very useful at this level, including mathematics. This article summarizes Grade 7 mathematics materials based on the 2013 curriculum revision.