Monday, September 27, 2021

Sample of Essays for Reading and Writing Test for Revalida Batch 2020-2021 |English Proficiency Test

Bilang bahagi ng pagtatasa upang malaman kung ipapasa ang isang ALS completer, maliban sa kanyang Presentation Portfolio, siya ay isasabak din sa English Proficiency Test kung saan tatasahin ang kanyang kakayahang bumasa at sumulat (reading and writing) sa wikang Ingles.

Ang nasa ibaba ay ilan lamang sa mga sanaysay o essays na maaaring gamitin sa Reading and Writing sa panahon ng Revalida para sa Batch 2020-2021 para sa Elementary o Junior High School Level:


Adapting to Survive

                                   (Image from https://www.centennialparklands.com.au)


Living things adapt to their environment so they can survive. An organism adapts when it develops a behavior that makes it more likely to survive. It can also adapt by forming a physical characteristic or body part that helps it survive.

In a forest biome, some trees grow taller than the other plants around them. This lets them reach the sunlight. Growing taller is an adaptation that helps trees survive. Shorter plants have adapted with their behavior. They have learned to live in the shade with less sunlight. 

Animals in the forest have a wide variety of adaptations. Monkeys have long tails. They can use them almost like another hand. This helps them swing quickly through the tops of trees. They can even do this while holding their babies or gathering food. Giraffes need to reach leaves at the tops of tall trees. Having a long neck is an adaptation that allows them to do this.

Some animals’ adaptations prevent other animals from wanting to eat them. A skunk’s horrible smell makes larger animals choose something else to eat. Even plants sometimes protect themselves in this way. Roses and acacia trees both have dangerous thorns. The thorns prevent animals from eating their leaves.




        Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers. The sample answers are guides only. The answer should be a complete sentence.

1) What are the two main ways that an organism adapts?

by changing its behavior or its physical characteristics

2) What is one animal adaptation you read about in the passage?

a monkey’s tail or a giraffe’s neck or a skunk’s smell

3) Is the animal adaptation you chose a physical or behavioral adaptation?

trees grow tall or short plants learn to live with less sunlight or roses and acacia trees grow thorns

4) What is one plant adaptation you read about in the passage?

trees - physical; short plants - behavioral; roses and acacia trees - physical

5) Is the plant adaptation you chose a physical or behavioral adaptation?

answer depends on student’s choice


Competing for Resources


The resources of any one environment are limited. Depending on which plants and animals share the environment, there may not be enough of everything to go around. All organisms need water, food, and shelter to stay alive. These resources are beneficial, which means they are good for the organisms. When an environment is low on any of these things, organisms must compete for them. Those who get to the resources first have the best chance of survival. Being without water, food, or shelter for very long is detrimental, which means it is harmful to organisms.

The resources in an area determine how big the plant and animal populations can be. Sometimes there are too many living things in an area. The weakest of the populations will not be able to get the resources they need. As the weak die out, the populations get smaller. Finally, the area’s resources recover and can support them again. Sometimes people will capture members of large animal populations and move them. They take them to another location with less competition. This helps them the animals survive.

Sometimes the government will allow the hunting of large animal populations. Deer and rabbits can be good food sources for people. When there are too many of these animals in an area, they sometimes come into the cities looking for food. They often cause trouble. Hunting keeps the number of animals under control.


        Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers. The sample answers are guides only. The answer should be a complete sentence.

1) Why do organisms sometimes have to compete for resources?

because an environment may not have enough resources

2) What kinds of things are beneficial for organisms?

food, water, and shelter

3) What kinds of things are detrimental for organisms?

being without food, water and shelter

4) What happens when populations grow too large for an area?

The weaker ones can’t compete for resources and die out

5) Do you think hunting or relocation is a better solution for over-sized animal populations? Why?

Answer depends on student’s choice


Ecosystems


(Image from https://eschooltoday.com)

An ecosystem is all the things that interact in a specific area, whether they are living or non-living. Some examples of non-living things that support life in an ecosystem are light, air, soil, and water. Living things are the plants and animals, called organisms, that use those resources.

Each of the specific ecosystems in the world has its own conditions created by non-living things. These conditions determine what kinds of living things will be able to thrive there. Organisms can only thrive where their needs are being met. Everything in an organism’s environment has an effect on it. One ecosystem that allows many different kinds of organisms to thrive is a temperate zone. It is an area where the conditions never become too hot or too cold.

All the living things in an ecosystem are called a community. All of one specific kind of organism living in a community is called a population. All the tree frogs in a rainforest community are one population within the community. All the white birch trees are another population within the same community. All the jaguars are yet another rainforest community population.

All living organisms perform certain life processes. They take in nutrients like air, sunlight, water, and food. They use energy from those nutrients to grow and develop. They release energy by doing work and moving. They release waste products. They react to things in their environment. They reproduce, producing offspring, or babies, that are similar to themselves.


        Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers. The sample answers are guides only. The answer should be a complete sentence.

1) What is one example of a non-living thing in an ecosystem?

light, air, water, or soil

2) What are some of the life processes that living organisms do?

take in nutrients, use energy to grow, release energy, release waste, react to their environment or reproduce

3) What does population mean in a community?

one specific type of organism living in a community

4) When does an organism thrive?

when its needs are met

5) Why does a temperate zone support many varieties of organisms

because the conditions are not too hot and not too cold


Food Is Our Fuel


(Image from https://ualr.edu)

Everything that is alive needs energy. All animals get the energy they need from food.    People are animals. You can think about the human body as an amazing machine. It can do all kinds of wonderful things for us. Food is the fuel that helps keep the amazing machine running.

Plants use sunlight to make their own food. Animals are not able to do that. Some animals eat plants. Some animals eat other animals as meat. Some animals, like people, eat both plants and animals.

Since plants make their own food using sunlight, the sun’s energy is found in plants.  The sun’s energy is very strong. It loses a lot of its strength by the time it goes into a plant. 

When we eat plants, we get more of the sun’s energy than when we eat animals. That’s why it is good to eat fruits and vegetables. When an animal eats a plant, the energy is less strong. The animal also used its energy to find the plant to eat. When a second animal eats the first animal, it gets even less energy than the first animal got. The second animal used a lot of energy to find and chase its prey.

Like a car that has to be filled with gasoline, living things have to eat again and again. Instead of gasoline, living things use food as fuel.


        Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers. The sample answers are guides only. The answer should be a complete sentence. 

1) Where do all animals get their energy?

from food

2) Where do plants get their energy?

from sunlight

3) If our bodies are amazing machines, then food is our ______.

fuel

4) Why do we get more energy from eating vegetables than we get from eating meat?

because the sun’s energy is less strong in meat

5) If a third animal eats the second animal,  will it get more or less energy?

less energy

 

Have You Got The Time


(Image from https://stevekeating.me)

People today are always thinking about the time. There never seems to be enough time to do all the things we want to do. Believe it or not, there was a time before time was so important. It was enough to know that the sun was out. That meant it was daytime. During these days when the clock seems to control us, doesn’t that sound kind of nice?

Time can mean a lot of different things. That’s one way we know how important it is for us. We have so many words about it! The smallest amount of time we can measure is called a second. When you put 60 seconds together, you get one minute. If you take 60 minutes, you get one hour. The hands of the clock go all the way around twice in 24 hours, giving us one day.

If you want to look at time beyond one day, you leave the clock and look at a calendar instead. There are about 30 days in one month. Some months have an extra day; February has a couple less. There are 12 months in one year. Time never stops.


        Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers. The sample answers are guides only. The answer should be a complete sentence.

1) What are people always thinking about these days?

time

2) We have lots of different words about time. What does that show?

that it is important

3) How many hours are in one day?

24

4) How many seconds are in one minute?

60

5) How many months are in one year?

12

 

Magnetic Attraction

 


An object that attracts metals, especially iron, is called a magnet. The area near the magnet where it has enough power to attract things is called its magnetic field. The farther away from the magnet an item is, the weaker the magnetic fi eld is. When it is weak, it is less likely an object will become attracted to the magnet.

Magnets can be either permanent or temporary. A permanent magnet stays magnetized for a long time. A temporary magnet loses its magnetism after only a short time. You can even turn something made out of iron into a temporary magnet by rubbing it against a permanent magnet. The more you rub, the stronger your temporary magnet gets. However, the effects will wear off over time.

The two ends of the magnets are called magnetic poles. The poles are found at the ends of bar magnets and the tips of the horseshoe magnets. They are the strongest parts of the magnet. Each magnet has a north pole and a south pole. Opposite poles attract, or pull  toward each other. Poles that are the same repel, or push away from each other. A north pole and a south pole will pull toward each other. Two north poles will push away from each other. The same happens with two south poles. When you hold magnets, you can actually feel the push and pull effects of magnetism.

A special kind of temporary magnet uses electricity to create a magnetic field. It is called an electromagnet. An electromagnet can be an extremely strong magnet. However, it only acts like a magnet when it has electricity. A stronger electrical current will produce a stronger magnet. Unlike other magnets, an electromagnet can be controlled by a switch. When the switch turns the electrical current off the electromagnet loses its magnetism. Whatever the electromagnet was holding drops to the ground. We use this technology to operate large cranes that lift heavy metal objects, such as cars. Electromagnets are also used to make motors run in small appliances. Combining regular magnets and electromagnets makes it possible for electrical energy to be turned into energy of motion.


        Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers. The sample answers are guides only. The answer should be a complete sentence.

1) Explain the difference between a temporary magnet and a permanent magnet

A permanent magnet stays magnetized for a long time. A temporary magnet loses its magnetism in a short time

2) Would two north poles attract each other or push away from each other?

Push away

3) What is different about an electromagnet?

It uses an electrical current and can be turned off and on.

4) What do we use electromagnets for?

lifting heavy objects like cars

5) What does attract mean when speaking about magnets? _

pull toward each other

 

Plant Life Cycle


(Image from https://www.youtube.com/watch?v=XyT153p2uag by MNSB inward)

Every living thing goes through changes. Living things grow through different stages. Then they reach the end of their life cycles and die. There are many kinds of plants. Each kind has its own life cycle.

Many plants start their life cycles as a seed. The seed needs certain things or it will not grow into a plant. Sometimes seeds wait in the ground until they can get the things they need. They wait for warmth from the sun. They wait for water. When they have what they need, they start to grow. A tiny little sprout will push out of each seed. The sprouts stretch up until they poke through the dirt and into the air.

The plants continue to grow when they get sunshine and water. The stems grow taller and leaves unfold. More leaves and stems grow on the main stems. The adult plants grow flowers. The flowers of many plants make fruit. The fruit has seeds inside it so more new plants can grow.

New plants look like their parent plants. Seeds from a parent plant will grow into the same kind of plant as the parent. When a seed begins to grow, it is the beginning of another plant life cycle.

 

        Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm your answers. The sample answers are guides only. The answer should be a complete sentence.

1) What is the process of living, growing, changing, and dying called?

life cycle

2) How do many plants begin?

As seeds

3) What two things does a seed need to have with it in the ground to be able to grow?

Sunshine and water

4) Where can you usually find seeds in an adult plant?

In the fruit

5) What kind of plant will a seed grow into?

the same kind as the parent plant


The Philippine Eagle 

Philippine Eagle

The Philippine Eagle has replaced the maya as our national bird. It is one of the three ln strongest eagles in the world. But it is in danger of extinction. Hunting and deforestation have number of Philippine Eagles to dwindle. Scientists have tried to increase their number by breedi captivity. The first eagle to be bred in captivity is Pag-asa. At 25 years old, Pag-asa is not yet released to the wild as she has developed dependency on her human keeper. 


Answer the following questions based on the reading passage.

1. The Philippine Eagle is in danger of extinction. It means this type of eagle will eventually _______.

A. disappear 
B. increase 
C. migrate
D. starve 

2. When birds are bred in captivity, they are _______.

A. allowed to freely fly in the wide forest
B. cared for in a safe environment
C. caught and sold as pets
D. given a diet of bread

3. What is responsible for the decrease in the number of Philippine Eagles? 

A. their migration to cooler countries
B. their transfer to warmer places
C. the activities of humans
D. lack of available food

4. Pag-asa is the name of the first eagle which ________.

A. was discovered first in our country.
B. was born in captivity.
C. was kept in the wild
D. was given as a gift.

5. What is the problem posed in the selection?  The Philippine Eagles _______.

A. are in danger of being gone forever
B. are dying because of a disease
C. migrate to other countries
D. are not growing fast

6.The purpose for writing the selection is to _________.

A. invite researchers to study the Philippine eagle.
B. make the reader proud of the Philippine eagle.
C. warn the hunters not to harm the Philippine eagle.
D. raise an alarm about the possible disappearance of the Philippine Eagle.

7. A good title for this selection is _________.

A. Help Save the Philippine Eagle
B. See the Rare Philippine Eagle
C. Breeding the Philippine Eagle
D. The Effects of Deforestation


Home to Millions of Fish

Coral Reefs

Coral reefs are found in shallow areas of tropical ocean waters. They are like beautiful underground gardens that grow in salty waters. Millions of fish and sea plants make their home in the reefs as these provide a safe sanctuary for them. They always allow small fish to hide from large predator fish. 

But many coral reefs are in trouble. Water pollution is destroying many reefs. Tourism likewise harms them. If reefs are damaged, we will lose many of our most beautiful fish.

Coral reefs are described as underground gardens because __________.

A. they are full of flowers
B. there are many sea plants
C. they have many enormous fish
D. there are many types of pebbles


DREAMS


We often say "Sweet dreams." but have you ever wondered why we dream? Some say that dreaming is our brain's way of exercising. While we sleep, our brain may be testing the connections and pathways to see if they are working well. Others believe that dreaming is our brain's way of sorting out problems. Problems that have not been addressed during the day are sometimes resolved in our sleep. Yet another explanation is that dreaming is our brain's way of fixing and organizing all the information we have. While sleeping, our brains have a chance to sort out the information that we want to keep from the stuff we no longer want. Still another idea is that dreams are just another form of thinking. Will we ever get to know the answer to this question? Maybe we should sleep on it.

Questions

1. Based on the selection, what does our brain exercise through sleeping?

a. the connections and pathways
c the content and concepts
b. the left and right hemispheres
d. the gray matter

2. Which of the statements does NOT show how dreams fix our problems?

a. As we dream, we constantly think about what we have learned or experienced
b. Our dreams help us focus on things we are unable to notice during the day
c. Our brain comes up with solutions in our sleep.
d. Our brain sorts and files information.

3. How does a brain-through dreams - perform the function of an office clerk?

a. It sorts information we need from what we don't need.
b. It files what we know into fixed categories.
c. It clears the board to store new information
d. It functions alone

4. Based on how it is used in the selection, which of the following words is a synonym for the word "resolved?"

a. accommodated 
b. reflected 
c. decided 
d. fixed

5. Which of the following statements is NOT true about the brain?

a. Our brain makes connections
b. Our brain never stops thinking.
c. Sleeping is our brain's way of shutting down
d. Our brain replays our experiences as we sleep.

6. Which question is the selection trying to answer?

a. What are the types of dreams?
b. What are our reasons for dreaming?
c. Are all dreams sweet?
d. How can we stop from dreaming?

7. In the selection, what does it mean to "sleep on it?"
a. ignore it
b. take a nap
c. think about it
d. forget about it

8. Which could be a good title for this selection?

a. Dreaming: Explained
b. Preventing Our Dreams
c. Interpreting One's Dream
d. Finding Solutions to Dreaming

Good Luck to your REVALIDA!


Lesson 4 - Problem-Solving Using Pythagorean Theorem: Introduction to Trigonometry in Taglish

LESSON 4 – SOLVING REAL-LIFE PROBLEMS USING THE PYTHAGOREAN THEOREM

Matapos nating mapag-aralan ang mga uri ng linya, salikop o anggulo, complementary at supplementary angle gayundin ang katuturan ng Pythagorean Theorem, sa leksyon 4 ay susubukin naman nating mabigyang solusyon ang mga halimbawa ng mga problema sa tunay na buhay gamit ang bisa ng Pythagorean Theorem ni Pythagoras.




Dapat lamang nating tandaan na ang Pythagorean Theorem ay ginagamit lamang kung may mabubuo tayong right angle o right triangle.

STEPS in solving problems involving RIGHT TRIANGLES:

Nasa ibaba ang mga hakbang upang masolusyonan ang isang Math problem na kinassangkutan ng Right Triangle:


STEP 1 Identify the hypotenuse and the legs of the triangle. (Tukuyin ang hypotenuse at mga legs ng triangle.)

STEP 2 Use the formula derived from the Pythagorean theorem. (Gamitin ang formula ng Pythagorean theorem: c2 = a2 + b2)

STEP 3 Substitute the given values to the variables in the formula and solve for the unknown. (Ilagay ang mga values na ibinigay sa problema at hanapin ang unknown.)

STEP 4 Simplify to get the final answer. (Gawing simple ang sagot)



[Problem 1 to 4 from ALS Junior High School Module Trigonometric Functions 1]

Problem 1

Jake was performing his favorite billiard trick shot. He hit the cue ball and it went to one corner of the table, rolled to the other corner, hit the exact center of the back cushion and hit the eighth ball causing it to drop into one of the holes before returning to its original position. If the dimensions of the table are 6 ft. by 8 ft., how far did the cue ball travel?



Problem 2

Alice, a landscape architect, designed a flowerbed for a very important client. The flowerbed will take the shape of a right triangle with legs equal to 12 ft. and 9 ft. She wants to place some decorative stones along the hypotenuse of the flowerbed 1 ft. apart. How many stones does she need?




Problem 3

Two cars start traveling perpendicularly away from each other from the same place. If one travels 6 km and the other 8 km, how far apart will they be from each other using their bumpers as points of reference? 





Problem 4

A pendulum travelled 30 cm away from a center line. The center line is 40 cm long. What is the distance between the pendulum and one end of the center line?



Problem 5

A ladder 13 m long is placed on the ground in such a way that it touches the top of a vertical wall 12 m high. Find the distance of the foot of the ladder from the bottom of the wall. 
(Source: https://www.math-only-math.com)




TANDAAN

1. Magagamit lamang ang Pythagorean Theorem sa  mga right angles o right triangles.

2. Hindi lang sukat ng hypotenuse ang mahahanap sa Pythagorean Theorem kundi maging ang iba pang sukat/haba ng mga sides/legs (opposite and adjacent sides) kung ang 2 sukat ay ibinigay.

3. Mag-drawing kung hindi ma-imagine ang larawang isinasaad ng problem.

4. Tandaan ang square root ng ilang bilang tulad ng:

1 = square root ng 1 dahil 1 x 1 or 12 = 1
2 = square root ng 4 dahil 2 x 2 or 22 = 4
3 = square root ng 9 dahil 3 x 3 or 32 = 9
4 = square root ng 16 dahil 4 x 4 or 42 = 16
5 = square root ng 25 dahil 5 x 5 or 52 = 25
6 = square root ng 36 dahil 6 x 6 or 62 = 36
        7 = square root ng 49 dahil 7 x 7 or 72 = 49
8 = square root ng 64 dahil 8 x 8 or 82 = 64
9 = square root ng 81 dahil 9 x 9 or 92 = 81
10 = square root ng 100 dahil 10 x 10 or 102 = 100
11 = square root ng 121 dahil 11 x 11 or 112 = 121
12 = square root ng 144 dahil 12 x 12 or 122 = 144
13 = square root ng 169 dahil 13 x 13 or 132 = 169
14 = square root ng 196 dahil 14 x 14 or 142 = 196
15 = square root ng 225 dahil 15 x 15 or 152 = 225

Alalahanin na ang 
A = square root ng Y dahil A x A (A times A) or A2 = Y

A square root of a number (Y) is one of the factors (Aof Y such that when you multiply it TWO (2) times (A x A) or you square it (A2), you will get that number Y.







Lesson 3 - Pythagorean Theorem: Introduction to Trigonometry | Trigonometry in Taglish

LESSON 3 – PYTHAGOREAN THEOREM

Sa unang dalawang leksyon ay napag-aralan natin ang tungkol sa mga uri ng linya at mga uri ng anggulo o salikop. Ngayon naman, nakatakda nating alamin ang Pythagorean Theorem at paano ito makatutulong upang lalo pa nating maunawaan ang Trigonometry.


Bago ito, alamin muna natin kung ano ang sinasabing complementary at supplementary angles.

Complementary angles = ang dalawang anggulo ay complementary kung ang suma o total ng kanilang mga angles ay 90 degrees (90o).

Ibig sabihin, ∠A  +  ∠B = 90o

If ∠XYZ  = 36o     and  ∠ 345 = 54o, then we can say that ∠XYZ is a complement of ∠345  (and vice versa) because their sum is 90o.  We can also say that because the sum of their angles is 90o, ∠XYZ and ∠345 are complementary angles.

Supplementary angles = ang dalawang anggulo ay supplementary kung ang suma o total ng kanilang mga angles ay 180 degrees (180o).

Ibig sabihin, ∠V  +  ∠W = 180o

If ∠DEF  = 45o     and  ∠ 123 = 135o, then we can say that ∠DEF is a supplement of ∠123  (and vice versa) because their sum is 180o.  We can also say that because the sum of their angles is 180o, ∠DEF and ∠123 are supplementary angles.

Base sa kanilang depinisyon, ang angle na mabubuo ng dalawang complementary angles ay right angle (dahil ang sukat nito ay 90 degrees).  Straight angle naman ang mabubuo ng dalawang supplementary angles (dahil ang sukat nito ay 180 degrees).





PAGSASANAY

1. Give the complement of  ∠ABC if its measure is 37o.

A. 153o
B. 143o
C.  53o
D. 43o

2. If two angles are right angles, then they are ___.

A. complementary
B. supplementary
C. straight angles
D. obtuse angles 

3. Tukuyin ang mga complementary angles sa larawan:

        A. ∠AXB at ∠BXD
B. ∠BXC at ∠CXD
C. ∠AXC at ∠CXD
D. ∠AXB at ∠BXC

4. Ano ang supplementary angle ng ∠AXB sa larawan?


        A. ∠BXC only
B. ∠AXD only
C. Both ∠BXC at ∠AXD
D. ∠DXC

5. If ∠PUJ is 25o, then the measure of its supplement is ________?

        A. 20o
B. 65o
C. 155o
D. 335o


Ang aralin sa Pythagorean Theorem ay mahalaga sapagkat ito ay magtuturo sa iyo kung paano malutas ang mga problema sa totoong buhay na may kinalaman sa mga anggulo. Ngunit kailangan mo munang magkaroon ng kaalaman tungkol sa square root ng isang numero upang maunawaan nang mabuti ang araling ito.

Ano ang SQUARE ROOT?

Sa Matematika, ang square root ay isang factor ng isang numero na, kapag minultiply sa kanyang  sarili, ay nagbibigay ng orihinal na numero. 

Halimbawa, ang 3 at –3 ay parehong factor ng 9. Kapag minultiply ang 3 sa kanyang sarili, 3 x 3 o 32, makukuha ang 9 dahil 3 x 3 = 9 o 32 = 9.  Gayundin, kapag minultiply ang -3 sa kanyang sarili, (-3) x  (-3)  o (-32), makukuha ang 9 dahil (-3) x (-3) = 9 o (-32) = 9. Kung ganoon, masasabi na ang square root ng 9 ay 3 at (-3) [negative 9].

Sa iba pang paliwanag, ang square root ng isang bilang na kinakatawan ng x ay isang bilang na kinakatawan ng y tulad ng y² = x; sa madaling salita, ang bilang y ay ang square root ng  x. Halimbawa, ang 5 at −5 ay square root ng 25, dahil 5² =(-5²)= 25.

Paano makukuha ang square root ng isang numero?

Isang paraan upang makuha ang square root ng isang bilang ay isipin lamang ang mga factors ng bilang na iyon. Kapag minultiply mo ng 2 beses ang factor na iyong napili at lumabas ang bilang na iyon, ang factor na iyong napili ay ang square root ng bilang na iyon.

Halimbawa:

Ano ang square root ng 64?

Step 1: Isulat ang mga factors ng 64.

Ano ang factors ng isang bilang?

Ang mga ito ay ang mga numero na kapag minultiply mo ay makukuha mo ang bilang na binanggit. 

Ano –ano ang factors ng 64?

Ang mga factors ng 64 ay 1, 2, 4, 8, 16, 32, at 64 dahil:

1 x 64 = 64 2 x 32 = 64
4 x 16 = 64 8 x 8 = 64

        Step 2: Piliin ang numero na inulit ng 2 beses para makuha ang 64.

Sa mga numerong nasa itaas, mapapansin na ang square root ng 64 ay 8 dahil 82 =64. Gayunman, malalaman din natin sa susunod na mga lesson na 2 ang square root ng isang bilang, isang positive at isang negative. Kaya, square root din ng 64 ang -8 (negative 8) dahil (-82) = 64.

Matapos nating malaman kung ano ang square root ng isang bilang at kung paano ito makukuha, handa na tayong pag-aralan ang Pythagorean Theorem. Pero bago ito, kilalanin muna natin si Pythagoras na siyang pinagmulan ng teoryang ito.

Sino si Pythagoras?

Si Pythagoras ng Samos (c. 570 - c. 495 BC) ay isang sinaunang pilosopong Greek na Ionian at ang eponymous na nagtatag ng Pythagoreanism. Ang kanyang mga katuruang pampulitika at pangrelihiyon ay kilalang kilala sa Magna Graecia at naiimpluwensyahan ang mga pilosopiya ni Plato, Aristotle, at, sa pamamagitan nila, pilosopiya sa Kanluranin. Ang kaalaman sa kanyang buhay ay nalilimutan ng alamat, ngunit lumilitaw na siya ay anak ni Mnesarchus, isang mang-uukit ng mutya sa isla ng Samos. (Wikipedia)



Ano ang Pythagorean Theorem o Pythagoras’ Theorem ?

Sa Matematika, ang teorya ng Pythagorean, o teorya ng Pythagoras, ay isang pangunahing kaugnayan sa Euclidean Geometry sa mga tatlong panig/gilid ng isang right triangle. Nakasaad dito na ang area ng parisukat na ang panig ay ang hypotenuse (ang gilid sa tapat ng right angle) ay katumbas ng kabuuan ng mga area ng mga parisukat sa iba pang dalawang panig. Ang teoryang ito ay maaaring nakasulat bilang isang equation na nauugnay sa haba ng mga gilid ng a, b at c, na madalas na tinatawag na Pythagorean equation:

a2 + b2 = c2 

kung saan kumakatawan sa c ang haba ng hypotenuse at a at b ang haba ng iba pang dalawang panig/gilid ng tatsulok.


Upang maunawaan natin nang lubusan ang kahalagahan ng Pythagorean Theorem, magbigay tayo ng halimbawa sa tunay na buhay.

Masdan natin ang larawan sa ibaba:




Anong anggulo ang nabuo ng hagdan at ng lupa?

Kung ang sagot mo ay right angle, tama ka.

Ano ang distansya mula sa lupa hanggang sa tuktok ng slide (o haba ng hagdan)? 

Kung ang sagot mo ay 3 units, magaling!

Gaano kalayo ang ibabang bahagi ng hagdan hanggang sa ibabang bahagi ng slide?

Tama ka kung 4 units ang iyong sagot.

Ngunit paano natin makalkula ang haba ng slide? Magagawa natin ito sa pamamagitan ng paggamit ng Pythagorean theorem base sa ibinigay na haba ng hagdan at ang distansya mula sa ibabang dulo ng slide hanggang sa ibabang dulo ng hagdan.

Sa ating aktibidad, ang hagdan at ang lupa ay bumuo ng isang right angle. Kaya, isang right triangle ay nabuo kasama ang slide.

Ang  right triangle ay tatsulok na may right angle. Ang gilid na katapat ng right angle ay tinatawag na hypotenuse. Ang dalawang gilid naman ay tinatawag na legs.

Mapapansin sa larawan na ang pinakamahabang side o gilid ay ang hypotenuse.


Ang dalawang legs ay maaaring tawaging adjacent at opposite side depende kung anong anggulo ang pinagbabatayan. Ang opposite side ay katapat ng anggulong batayan. Adjacent side naman ang tawag sa gilid ng angle na binabanggit.

Tulad nang nabanggit sa itaas, upang makalkula ang haba ng isang gilid ng isang tatsulok, magagamit natin ang teorya ng Pythagorean na nagsasaad na:

Sa isang right triangle, ang square ng hypotenuse ay katumbas ng square ng isang gilid (opposite side) kasama ang square ng isa pang gilid (adjacent side).

Ang ibig sabihin ng square ng hypotenuse ay i-multiply ang sukat ng hypotenuse sa kanyang sarili.

Kung ang sukat ng hypotenuse ay kinakatawan ng titik c, ang square ng hypotenuse ay c x c  or c2.

Gayundin ang paglalarawan nito sa dalawa pang gilid.

Square ng opposite side = a x a or a2
Square ng adjacent side = b x b or b2

Pagsamahin natin ang lahat ng mga gilid upang mabuo natin ang Pythaghorean formula:

c2 = a2 + b2   or a2 + b2  = c2

Balikan natin ang larawan sa itaas at kalkulahin natin ang sukat ng slide, gamit ang formula sa itaas.

I-presenta natin ang sukat ng hagdan bilang titik a, at tiktik b naman ang distanya mula sa ibaba ng hagdan hanggang ibaba ng slide. Ang sukat naman ng slide ay titik c. 

Base sa larawan, lagyan natin ng value ang mga titik:

a = 3
b = 4
c =  ?

Gamit ang formula sa ibaba, kalkulahin natin ang sukat ng slide:

c2 = a2 + b2
c2 = 32 + 42
c2 = 9 + 16
c2 = 25
c =  251/2  or √𝟐𝟓
c = 5 at (-5)  [Disregard -5 because we are only interested in positive value]
c = 5 units  final answer

Upang lubos na maunawaan pa ang tungkol sa Pythagorean Theorem, sasagutin natin sa susunod na leksyon ang ilang pagsasanay na problema na may kinalaman sa tunay na buhay na kinasasangkutan ng right triangles.

Dapat natin tandaan sa ngayon na ang Pythagorean Theorem ay akma lamang kung ang tatsulok o triangle ay right triangle. Hindi ito angkop sa iba pang uri ng tatsulok tulad ng  isosceles, equilateral, scalene, obtuse, at acute triangle.

May iba pang mga paraan upang makuha ang square root ng isang bilang. Ito ay tatalakayin sa ibang leksyon.

Mga sagot sa pagsasanay:
1. C
2. B
3. B
4. C
5. C

 

Lesson 2 - Angles: Introduction to Trigonometry | Trigonometry in Taglish

LESSON 2 – ANGLES (Mga SALIKOP O ANGGULO)

Sa araling ito, malalaman mo kung ano ang anggulo o salikop. Malalaman mo rin ang iba't ibang mga uri ng mga anggulo at kung paano ito sinusukat.


Ang pag-alam tungkol sa mga anggulo ay napakahalaga sapagkat may mga problemang maaari nating harapin na nangangailangan ng kaalaman sa mga anggulo at kanilang mga sukat. Ang kaalamang ito ay kapaki-pakinabang din sa paggawa ng ating pang-araw-araw na gawain tulad ng pagsasabi ng oras. 

Isang paraan upang maunawaan ang iba’t ibang uri ng angles ay ang pagmamasid sa isang orasan. Mapapansin na ang isang ordinaryong orasan ay may dalawang kamay, isang maliit at isang malaki. (Huwag muna nating pansinin ang ikatlong maliit na kamay na para sa segundo.) Ang dalawang kamay na ito o ray ay may iisang endpoint. Ang endpoint na ito ay tinatawag ding vertex. Ang angle o salikop ay nalilikha kapag ang dalawang linya ay nagsalubong o nag-intersect sa iisang point.



Paano bibigyan ng pangalan ang isang angle?

Ang isang angle ay maaaring pangalanan sa pamamagitang ng tatlong magkakaibang malalaking titik. Masdan ang larawan sa ibaba. Tatlong anggulo ang nakalarawan dito:
∠ABC (Pagbasa: Angle ABC),    ∠BCA,   at   ∠BAC. Dapat nating tandaan na sa pagbibigay pangalan sa isang salikop, ang ikalawa o gitnang titik ay para sa vertex o ang intersecting point.


Maliban sa 3 malalaking titik, maaari ring pangalanan ang isang angle ng isang titik lamang o isang numero, tulad ng nasa ibabang larawan.
Ilang angles ang nakita mo sa larawan?

                                            



The PROTRACTOR

Ang nakalarawan sa ibaba ay tinatawag na protractor. Ito ay isang aparato na ginagamit upang sukatin ang isang anggulo.


Mag-ingat sa pagbasa ng tamang hanay ng mga numero dahil ang isang protractor ay may dalawang hanay ng mga numero: ang isang hanay ay nagmula sa 0 hanggang 180, ang isa pang hanay ay mula 180 hanggang 0. Alin man sa iyong nabasa ay nakasalalay sa kung paano mo inilalagay ang protractor: ilagay ito upang ang isang gilid ng anggulo ay nakahanay  sa  isa sa mga zero, at basahin ang hanay ng mga numerong iyon upang masukat ang tamang anggulo.

Paano Gumamit ng Protractor?

Upang masukat ang isang anggulo gamit ang isang protractor, sundin ang mga hakbang sa ibaba.

1. I-line up ang vertex ng anggulo gamit ang tuldok sa gitna ng protractor.
2. I-line up ang isang gilid ng anggulo na may 0 degree sa protractor.
3. Basahin ang protractor upang makita kung saan ang isa pang gilid ng anggulo ay tumumbok sa number scale.


    This angle measures 120 degrees, or 120°.


This angle measures 35 degrees, or 35°.

Degree ( ° ) is the unit of measurement for angle.

Pagmasdan ang mga larawan sa ibaba at isulat kung ano ang sukat na anggulo base sa protractor.





Mga Uri ng Anggulo

1. Acute angle  -  ang tawag sa isang salikop kung ang sukat nito ay lampas sa zero degree nguni’t mas mababa sa 90 degrees, 






2. Right angle  -  ang tawag sa isang salikop kung ang sukat nito ay eksaktong 90 degrees.


3. Obtuse angle  -  ang tawag sa isang salikop kung ang sukat nito ay mas malaki sa 90 degrees subali’t mas mababa sa 180 degrees.



4. Straight angle  -  ang tawag sa isang salikop kung ang sukat nito ay eksaktong180 degrees.


5. Reflex angle  -  ang tawag sa isang salikop kung ang sukat nito ay mas malaki sa 180 degrees subali’t mas mababa sa 360 degrees.





6. Complete  or full angle  -  ang tawag sa isang salikop kung ang sukat nito ay eksaktong 360 degrees.


PAGTATASA (Assessment) : Lines and Angles

1. Kung ang dalawang linya ay hindi maaaring makagawa ng isang anggulo, ito ay tinatawag na _______.

A. Intersecting lines
B. Parallel lines
C. Perpendicular lines
D. Straight lines

2. Dalawang linya na makalilikha ng apat na right angles.

A. Intersecting lines
B. Parallel lines
C. Perpendicular lines
D. Straight lines

3. Anong mga anggulo ang malilikha ng dalawang intersecting lines?

A. 2 right at 2 acute angles
B. 4 na acute angles
C. 2 acute at 2 obtuse angles
D. 1 acute, 1 right, at 2 obtuse angles

4. Sa larawan, anong uri ng anggulo ang nilikha ng dalawang kamay ng orasan?


A. Acute angle
B. Right angle
C. Reflex angle
D. Obtuse angle

5. Sa larawan, anong uri ng anggulo ang nilikha ng dalawang kamay ng orasan?


A. Acute angle
B. Right angle
C. Obtuse angle
D. Reflex angle

6. Sa larawan, alin ang obtuse angle?
∠CEG II. ∠CEF
III. ∠BEF IV. BEG


A. I
B.  II and  III
C. II and IV
D. I and IV

7. Alin sa mga sukat ang halimbawa ng isang acute angle?

A. 170 degrees
B.  115 degrees
C.  90 degrees
D. 37 degrees

8. Ano ang sukat ng anggulo na sinukat ng protractor?




A. 60 degrees
B.  65 degrees
C.  120 degrees
D. 180 degrees


9. Ilang obtuse angle ang maaaring kapalooban ng isang straight angle?

A. 0
B.  1
C.  2
D. 4


10. Kung ang isang angle ay may sukat na 18 degrees, anong sukat ang kailangan nito upang maging right angle?

A. 12 degrees
B.  42 degrees
C.  72 degrees
D. 162 degrees

Sa susunod na leksyon ay tatalakayin naman natin ang tungkol sa complementary at supplementary anglesPythagorean Theorem at kung paano ito magagamit sa paglutas ng mga tunay na  suliranin  na kinasasangkutan ng mga anggulo.

Mga Sagot sa Pagtatasa: