# GRADE 9 MATH MODULE PDF ANSWER KEY

Grade 9 mathematics (10F): a course for independent study. isBN Module 1 Learning Activity Answer Keys. Module 2: Number Sense. Mathematics Grade 9 Module - Ebook download as PDF File .pdf), Text File .txt) letter that you think best answers the question. which is the quadratic term?. A mathematics study guide and revision book for Grade 9 Module 2-D . can read or download Grade 9 Science Module Unit 2 Answer Key in PDF format.

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TEACHING GUIDE Module 1: Quadratic Equations and Inequalities A. Learning Outcomes .. DRAFT Answer Key Part I Part II (Use the rubric to rate students' 1. . This lesson had been taken up by the students in their Grade 7 mathematics. 1: DRAFT March 24, 1 LEARNING MODULE MATH 9 MODULE NO. .. Find out the answers to these questions and determine the vast . Mrs. Villareal was asked by her principal to transfer her Grade 9 class to a new classroom that was recently built. .. ebra-handouts/cittadelmonte.info; DRAFT. Mathematics Learner's Material 9 This instructional material was regarding simplifying radicals Let us consolidate your answers: In The lesson Beam Learning Guide, Year 2 – Mathematics, Module Radicals Expressions in cittadelmonte.info Radical Equations in One Variable.

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For sure you were able to identify the situations that can be represented by quadratic equations. In the next activity, you will write quadratic equations in standard form. Set Me To Your Standard! Answer the questions that follow.

How did you write each quadratic equation in standard form? What mathematics concepts or principles did you apply to write each quadratic equation in standard form? Discuss how you applied these mathematics concepts or principles. Which quadratic equations did you find difficult to write in standard form? Compare your work with those of your classmates. Did you arrive at the same answers? If NOT, explain. How was the activity you have just done? Was it easy for you to write quadratic equations in standard form?

It was easy for sure! In this section, the discussion was about quadratic equations, their forms and how they are illustrated in real life. Go back to the previous section and compare your initial ideas with the discussion. How much of your initial ideas are found in the discussion? Which ideas are different and need revision? Activity 7: Dig Deeper!

Answer the following questions.

## cittadelmonte.info: Workbook - Grade 9 Math with Answer Key (): Eran I. Levin: Books

How are quadratic equations different from linear equations? How do you write quadratic equations in standard form? Give at least 3 examples. How are you going to represent the number of Mathematics Club members? What expression represents the amount each member will share? If there were 25 members more in the club, what expression would represent the amount each would share? What mathematical sentence would represent the given situation?

Write this in standard form then describe. Your goal in this section is to take a closer look at some aspects of the topic.

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You are going to think deeper and test further your understanding of quadratic equations. After doing the following activities, you should be able to answer this important question: How are quadratic equations used in solving real-life problems and in making decisions? If there had been 25 members more in the club, each would have contributed Php50 less. Activity 8: Where in the Real World? Give 5 examples of quadratic equations written in standard form.

Identify the values of a, b, and c in each equation. Name some objects or cite situations in real life where quadratic equations are illustrated. Formulate quadratic equations out of these objects or situations then describe each.

This lesson was about quadratic equations and how they are illustrated in real life. The lesson provided you with opportunities to describe quadratic equations using practical situations and their mathematical representations. Moreover, you were given the chance to formulate quadratic equations as illustrated in some real-life situations. Your understanding of this lesson and other previously learned mathematics concepts and principles will facilitate your learning of the next lesson, Solving Quadratic Equations.

Your goal in this section is to apply your learning to real-life situations. You will be given a practical task which will demonstrate your understanding of quadratic equations. In this section, the discussion was about your understanding of quadratic equations and how they are illustrated in real life. What new realizations do you have about quadratic equations? How would you connect this to real life?

How would you use this in making decisions? In this section, your task was to give examples of quadratic equations written in standard form and name some objects or cite real-life situations where quadratic equations are illustrated. How did you find the performance task? How did the task help you realize the importance of the topic in real life? Now that you have a deeper understanding of the topic, you are ready to do the tasks in the next section. Find My Roots!!! Find the following square roots.

How did you find each square root? How many square roots does a number have? Explain your answer. Does a negative number have a square root? Describe the following numbers: These knowledge and skills will help you in solving quadratic equations by extracting square roots. You may check your answers with your teacher. How do you describe rational numbers? How about numbers that are irrational? Solve each of the following equations in as many ways as you can. How did you solve each equation? What mathematics concepts or principles did you apply to come up with the solution of each equation?

Explain how you applied these. Compare the solutions you got with those of your classmates. If not, why? Which equations did you find difficult to solve? Were you able to find the square roots of some numbers? Did the activity provide you with an opportunity to strengthen your understanding of rational and irrational numbers? In the next activity, you will be solving linear equations. Just like finding square roots of numbers, solving linear equations is also a skill which you need to develop further in order for you understand the new lesson.

How did you find the activity? Were you able to recall and apply the different mathematics concepts or principles in solving linear equations? In the next activity, you will be representing a situation using a mathematical sentence. Such mathematical sentence will be used to satisfy the conditions of the given situation. Air Out!!! Draw a diagram to illustrate the given situation. How are you going to represent the length of a side of the square-shaped wall? How about its area?

Suppose the area of the remaining part of the wall after the carpenter has made the square opening is 6 m2. What equation would describe the area of the remaining part of the wall? How will you find the length of a side of the wall? Activity 4: Learn to Solve Quadratic Equations!!!

Use the quadratic equations below to answer the questions that follow. Describe and compare the given equations. What statements can you make? Solve each equation in as many ways as you can. Determine the values of each variable to make each equation true.

He asked a carpenter to make a square opening on the wall where the exhaust fan will be installed. The square opening must have an area of 0. The activity you have just done shows how a real-life situation can be represented by a mathematical sentence. Were you able to represent the given situation by an equation?

Do you now have an idea on how to use the equation in finding the length of a side of the wall? To further give you ideas in solving the equation or other similar equations, perform the next activity. How did you know that the values of the variable really satisfy the equation? Aside from the procedures that you followed in solving each equation, do you think there are other ways of solving it? Describe these ways if there are any.

Activity 5: Anything Real or Nothing Real? Find the solutions of each of the following quadratic equations, then answer the questions that follow. How did you determine the solutions of each equation? How many solutions does each equation have? What can you say about each quadratic equation based on the solutions obtained? Are you ready to learn about solving quadratic equations by extracting square roots? From the activities done, you were able to find the square roots of numbers, solve linear equations, represent a real-life situation by a mathematical sentence, and use different ways of solving a quadratic equation.

But how does finding solutions of quadratic equations facilitate in solving real-life problems and in making decisions? Before doing these activities, read and understand first some important notes on solving quadratic equations by extracting square roots and the examples presented.

Were you able to determine the values of the variable that make each equation true? Were you able to find other ways of solving each equation? Let us extend your understanding of quadratic equations and learn more about their solutions by performing the next activity. Both values of x satisfy the given equation. Since t2 equals 0, then the equation has only one solution.

To check: There is no real number when squared gives - 9. Example 4: Solve the resulting equation. Check the obtained values of x against the original equation. Activity 6: Extract Me!!! Solve the following quadratic equations by extracting square roots. How did you find the solutions of each equation? What mathematics concepts or principles did you apply in finding the solutions? Compare your answers with those of your classmates. Did you arrive at the same solutions?

Your goal in this section is to apply previously learned mathematics concepts and principles in solving quadratic equations by extracting square roots. What Does a Square Have? Write a quadratic equation that represents the area of each square. Then find the length of its side using the equation formulated.

How did you come up with the equation that represents the area of each shaded region? How did you find the length of side of each square? Do all solutions to each equation represent the length of side of the square? Was it easy for you to find the solutions of quadratic equations by extracting square roots?

Did you apply the different mathematics concepts and principles in finding the solutions of each equation? I know you did! In this section, the discussion was about solving quadratic equations by extracting square roots. Extract Then Describe Me! Solve each of the following quadratic equations by extracting square roots. How did you find the roots of each equation? Which equation did you find difficult to solve by extracting square roots?

Which roots are rational? Which are not? How will you approximate those roots that are irrational? Activity 9: Intensify Your Understanding! Answer the following. Do you agree that a quadratic equation has at most two solutions? Justify your answer and give examples.

Give examples of quadratic equations with a two real solutions, b one real solution, and c no real solution. Do you agree with Sheryl? You are going to think deeper and test further your understanding of solving quadratic equations by extracting square roots.

How does finding solutions of quadratic equations facilitate in solving real-life problems and in making decisions? Were you able to find and describe the roots of each equation? Were you able to approximate the roots that are irrational?

Deepen further your understanding of solving quadratic equations by extracting square roots by doing the next activity. Cruz asked Emilio to construct a square table such that its area is 3 m2. Is it possible for Emilio to construct such table using an ordinary tape measure? If the total area of the border is 3.

In this section, the discussion was about your understanding of solving quadratic equations by extracting square roots. What new realizations do you have about solving quadratic equations by extracting square roots? Activity What More Can I Do? Describe quadratic equations with 2 solutions, 1 solution, and no solution.

Give at least two examples for each. Give at least five quadratic equations which can be solved by extracting square roots, then solve. You will be given a practical task in which you will demonstrate your understanding of solving quadratic equations by extracting square roots. How did the task help you see the real world use of the topic?

Collect square tiles of different sizes. Using these tiles, formulate quadratic equations that can be solved by extracting square roots. Find the solutions or roots of these equations. This lesson was about solving quadratic equations by extracting square roots. The lesson provided you with opportunities to describe quadratic equations and solve these by extracting square roots. You were also able to find out how such equations are illustrated in real life.

Moreover, you were given the chance to demonstrate your understanding of the lesson by doing a practical task. Your understanding of this lesson and other previously learned mathematics concepts and principles will enable you to learn about the wide applications of quadratic equations in real life. What Made Me? Factor each of the following polynomials. How did you factor each polynomial? What factoring technique did you use to come up with the factors of each polynomial?

Explain how you used this technique.

How would you know if the factors you got are the correct ones? Which of the polynomials did you find difficult to factor? Start Lesson 2B of this module by assessing your knowledge of the different mathematics concepts previously studied and your skills in performing mathematical operations. These knowledge and skills will help you in understanding solving quadratic equations by factoring. The Manhole Directions: How are you going to represent the length and the width of the pathway?

What expression would represent the area of the cemented portion of the pathway? Suppose the area of the cemented portion of the pathway is What equation would describe its area?

How will you find the length and the width of the pathway? Were you able to recall and apply the different mathematics concepts or principles in factoring polynomials? This mathematical sentence will be used to satisfy the conditions of the given situation. A rectangular metal manhole with an area of 0. The length of the pathway is 8 m longer than its width.

Do you now have an idea on how to use the equation in finding the length and the width of the pathway? Why is the Product Zero? Use the equations below to answer the following questions. How would you compare the three equations? What value s of x would make each equation true? How would you know if the value of x that you got satisfies each equation? Compare the solutions of the given equations. What statement can you make? Some quadratic equations can be solved easily by factoring. To solve such quadratic equations, the following procedure can be followed.

Transform the quadratic equation into standard form if necessary. Factor the quadratic expression. Apply the zero product property by setting each factor of the quadratic expression equal to 0.

Are you ready to learn about solving quadratic equations by factoring? From the activities done, you were able to find the factors of polynomials, represent a real-life situation by a mathematical statement, and interpret zero product. Before doing these activities, read and understand first some important notes on solving quadratic equations by factoring and the examples presented.

Solve each resulting equation. Check the values of the variable obtained by substituting each in the original equation. To solve the equation, factor the quadratic expression 9x2 — 4.

Factor Then Solve! Solve the following quadratic equations by factoring. Your goal in this section is to apply previously learned mathematics concepts and principles in solving quadratic equations by factoring.

The quadratic equation given describes the area of the shaded region of each figure.

Use the equation to find the length and width of the figure. How did you find the length and width of each figure? Can all solutions to each equation be used to determine the length and width of each figure?

You are going to think deeper and test further your understanding of solving quadratic equations by factoring. Was it easy for you to find the solutions of quadratic equations by factoring? In this section, the discussion was about solving quadratic equations by factoring. How Well Did I Understand?

Answer each of the following. Which of the following quadratic equations may be solved more appropriately by factoring? Do you agree with Patricia? Do you agree that not all quadratic equations can be solved by factoring? Justify your answer by giving examples.

Find the solutions of each of the following quadratic equations by factoring. Explain how you arrived at you answer. A computer manufacturing company would like to come up with a new laptop computer such that its monitor is 80 square inches smaller than the present ones.

Suppose the length of the monitor of the larger computer is 5 inches longer than its width and the area of the smaller computer is 70 square inches. What are the dimensions of the monitor of the larger computer? In this section, the discussion was about your understanding of solving quadratic equations by factoring. What new insights do you have about solving quadratic equations by factoring?

Meet My Demands!!! Lakandula would like to increase his production of milkfish bangus due to its high demand in the market. He is thinking of making a larger fishpond in his sq m lot near a river. Help Mr. Lakandula by making a sketch plan of the fishpond to be made. Out of the given situation and the sketch plan made, formulate as many quadratic equations then solve by factoring.

You may use the rubric in the next page to rate your work. Rubric for Sketch Plan and Equations Formulated and Solved 4 3 2 1 The sketch plan is accurately made, presentable, and appropriate. The sketch plan is accurately made and appropriate.

The sketch plan is not accurately made but appropriate. The sketch plan is made but not appropriate. Quadratic equations are accurately formulated and solved correctly. Quadratic equations are accurately formulated but not all are solved correctly. Quadratic equations are accurately formulated but are not solved correctly. Quadratic equations are accurately formulated but are not solved. You will be given a practical task which will demonstrate your understanding of solving quadratic equations by factoring.

This lesson was about solving quadratic equations by factoring. The lesson provided you with opportunities to describe quadratic equations and solve these by factoring. You were able to find out also how such equations are illustrated in real life.

Your understanding of this lesson and other previously learned mathematics concepts and principles will facilitate your learning of the wide applications of quadratic equations in real life. These knowledge and skills will help you in understanding Solving Quadratic Equations by Completing the Square. How did you find the solution s of each equation?

Which of the equations has only one solution? Which of the equations has two solutions? Which of the equations has solutions that are irrational? Were you able to simplify those solutions that are irrational? How did you write those irrational solutions? Express each of the following perfect square trinomials as a square of a binomial.

In the next activity, you will be expressing a perfect square trinomial as a square of a binomial. I know that you already have an idea on how to do this. This activity will help you in solving quadratic equations by completing the square. How do you describe a perfect square trinomial? How did you express each perfect square trinomial as the square of a binomial? What mathematics concepts or principles did you apply to come up with your answer?

Compare your answer with those of your classmates. Did you get the same answer? Observe the terms of each trinomial. How is the third term related to the coefficient of the middle term? Is there an easy way of expressing a perfect square trinomial as a square of a binomial? If there is any, explain how.

Make It Perfect!!! Determine a number that must be added to make each of the following a perfect square trinomial. Explain how you arrived at your answer. Let us further strengthen your knowledge and skills in mathematics particularly in writing perfect square trinomials by doing the next activity.

Was it easy for you to determine the number that must be added to the terms of a polynomial to make it a perfect square trinomial?

Were you able to figure out how it can be easily done? Such a mathematical sentence will be used to satisfy the conditions of the given situation.

Finish the Contract! Another method of solving quadratic equation is by completing the square. Can you tell why the value of k should be positive? Divide both sides of the equation by a then simplify. Write the equation such that the terms with variables are on the left side of the equation and the constant term is on the right side.

Are you ready to learn about solving quadratic equations by completing the square? From the activities done, you were able to solve equations, express a perfect square trinomial as a square of a binomial, write perfect square trinomials, and represent a real-life situation by a mathematical sentence.

Before doing these activities, read and understand first some important notes on Solving Quadratic Equations by Completing the Square and the examples presented. The shaded region of the diagram at the right shows the portion of a square-shaped car park that is already cemented. The area of the cemented part is m2. Use the diagram to answer the following questions.

How would you represent the length of the side of the car park? How about the width of the cemented portion? What equation would represent the area of the cemented part of the car park? Using the equation formulated, how are you going to find the length of a side of the car park? Add the square of one-half of the coefficient of x on both sides of the resulting equation.

The left side of the equation becomes a perfect square trinomial. Express the perfect square trinomial on the left side of the equation as a square of a binomial. Solve the resulting quadratic equation by extracting the square root.

Solve the resulting linear equations. Check the solutions obtained against the original equation. Divide both sides of the equation by 2 then simplify. Add 18 to both sides of the equation then simplify.

Add 41 to both sides of the equation then simplify. Notice that 25 is a perfect square. Your goal in this section is to apply the key concepts of solving quadratic equations by completing the square.

Complete Me! Find the solutions of each of the following quadratic equations by completing the square. Was it easy for you to find the solutions of quadratic equations by completing the square?

Represent then Solve! Using each figure, write a quadratic equation that represents the area of the shaded region.

## Mathematics Grade 9 Module

Then find the solutions to the equation by completing the square. Do all solutions to each equation represent a particular measure of each figure?

Were you able to solve the equations formulated and obtain the appropriate measure that would describe each figure? In this section, the discussion was about solving quadratic equations by completing the square.

Can she use it in finding the solutions of the equation? Explain why or why not. Do you agree that any quadratic equation can be solved by completing the square? If you are to choose between completing the square and factoring in finding the solutions of each of the following equations, which would you choose? Explain and solve the equation using your preferred method. The first few parts of his solution are shown below.

An open box is to be formed out of a rectangular piece of cardboard whose length is 8 cm longer than its width. To form the box, a square of side 4 cm will be removed from each corner of the cardboard. How would you represent the dimensions of the cardboard? What expressions represent the length, width, and height of the box?

You are going to think deeper and test further your understanding of solving quadratic equations by completing the square. If the box is to hold cm3, what mathematical sentence would represent the given situation? Using the mathematical sentence formulated, how are you going to find the dimensions of the rectangular piece of cardboard? What are the dimensions of the rectangular piece of cardboard?

What is the length of the box? How about its width and height? In what year did the average weekly income of an employee become Php Design Packaging Boxes!!! Perform the following. Designing Open Boxes 1. Make sketch plans of 5 rectangular open boxes such that: Write a quadratic equation that would represent the volume of each box.

You will be given a practical task which will demonstrate your understanding of solving quadratic equations by completing the square.

## Follow the Author

In this section, the discussion was about your understanding of solving quadratic equations by completing the square. What new insights do you have about solving quadratic equations by completing the square? Solve each quadratic equation by completing the square to determine the dimensions of the materials to be used in constructing each box.

Designing Covers of the Open Boxes 1. Make sketch plans of covers of the open boxes in Part A such that: This lesson was about solving quadratic equations by completing the square. The lesson provided you with opportunities to describe quadratic equations and solve these by completing the square. Work with a partner in simplifying each of the following expressions.

These knowledge and skills will help you in understanding solving quadratic equations by using the quadratic formula. How would you describe the expressions given? How did you simplify each expression? Which expression did you find difficult to simplify? Did you arrive at the same answer?

Follow the Standards! Then identify the values of a, b, and c. How do you describe a quadratic equation that is written in standard form?

Are there different ways of writing a quadratic equation in standard form? Were you able to simplify the expressions? In the next activity, you will be writing quadratic equations in standard form.

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