Grade 9 Mathematics Module Quarter 2

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Questions and Answers

What does the equation y = kx represent?

Direct variation

What is the relationship between the area of a circle and the square of its radius?

Direct square variation

What is the relationship between the number of workers and the time it takes to complete a job, assuming they all work at the same pace?

Inverse variation

What is the formula for calculating the volume of a cylinder?

<p>V = πr²h</p> Signup and view all the answers

An expression has an ______ exponent if the exponent is either positive or negative integers.

<p>integral</p> Signup and view all the answers

For any non-zero number a, a⁰ is equal to ______.

<p>1</p> Signup and view all the answers

What is the simplified form of the expression x⁴/x²?

<p>x²</p> Signup and view all the answers

What is the simplified form of the expression (8²)⁻¹?

<p>1/64</p> Signup and view all the answers

What is the simplified form of the expression 1/a⁻²?

<p>a²</p> Signup and view all the answers

What is the simplified form of the expression √a^m?

<p>a^(m/n)</p> Signup and view all the answers

Flashcards

Direct Variation

Two quantities vary directly if as one increases, the other increases by the same factor.

Inverse Variation

Two quantities vary inversely if as one increases, the other decreases by the same factor.

Constant of Variation

A constant value that relates two quantities in a direct or inverse variation.

Zero Exponent

Any non-zero number raised to the power of zero equals 1.

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Integral Exponent

An exponent that is a positive or negative integer

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Product of Powers

When multiplying powers with the same base, add the exponents.

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Quotient of Powers

When dividing powers with the same base, subtract the exponents.

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Power of a Power

When raising a power to another power, multiply the exponents.

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Power of a Product

When raising a product to a power, raise each factor to the power.

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Power of a Quotient

When raising a quotient to a power, raise both the numerator and denominator to the power

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Negative Exponent

A negative exponent indicates reciprocal.

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Joint Variation

One quantity varies directly with the product of other quantities.

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Combined Variation

One quantity varies directly with one quantity and inversely with another.

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Radical

An expression involving a root (square root, cube root, etc).

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Radical Expression

An expression with a radical sign.

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Simplest Form of a Radical

A radical expression where the radicand has no perfect nth power factors, there is no radical in the denominator, and the index is the lowest possible.

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Rationalizing the Denominator

Multiplying the numerator and denominator by a radical to eliminate all radicals from the denominator.

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Similar Radicals

Radicals with the same index and radicand.

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Dissimilar Radicals

Radicals with different indices or radicands.

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Addition/Subtraction of Radicals

You can only add/subtract radicals with the same index and radicand. Add/subtract their coefficients.

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Multiplication of Radicals

Multiply coefficients and radicands separately.

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Conjugate of a Radical Expression

Same terms, but with opposite sign between terms.

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Study Notes

PIVOT 4A Learner's Material

  • This is a learner's material for Grade 9 Mathematics, Quarter 2
  • It is based on the Most Essential Learning Competencies (MELCs)
  • The material is designed for independent learning, suitable for the new normal
  • It uses an IDEA instructional process
  • Activities are in graduated levels of difficulty (simple to complex)
  • The work is of the Government of the Philippines
  • No copyright shall subsist
  • Prior approval of the government agency is necessary for use for profit
  • Copyright holders for borrowed materials are acknowledged
  • The publisher and authors claim no ownership over these borrowed materials

Module Information

  • The module was assessed and revised by DepEd Regional Office 4A and CLMD CALABARZON
  • It accords with the standards prescribed by DepEd
  • Ensures no Intellectual Property Rights are violated

Authors and Contributors

  • List of authors and their roles (instructional design lead, content writers, internal reviewers, etc.)

Guide for Using PIVOT 4A Learner's Material

  • For Parents/Guardians:
    • Provide support, knowledge and activities to learners in the new normal
  • For Learners:
    • Answer all activities on separate sheets of paper
    • Complete the PIVOT Assessment Card
    • Submit the completed work to the teacher
  • Use the K-12 Learning Module Delivery Process

Parts of PIVOT 4A Learner's Material

  • Introduction: Describes learning competencies, lesson objectives, and relevant samples
  • Development: Activities, tasks, and content to learn concepts
  • Engagement: Task designed to use knowledge, skills and values
  • Assimilation: Activities to connect previous knowledge and make critical analysis of concepts

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