General Mathematics: Inverse Functions & Interest
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Questions and Answers

What is the process called when the melting point of a substance is reduced by introducing impurities?

  • Partial melting
  • Recrystallization
  • Flux melting (correct)
  • Metamorphism

    • What characterizes magmatism?

  • It involves only the melting of rocks.
  • It can occur along plate boundaries or within the plate. (correct)
  • It only occurs within the Earth's crust.
  • It solely results in the formation of metamorphic rocks.

    • What happens to the protolith during metamorphism?

  • It is always melted entirely.
  • Its texture and mineralogy change. (correct)
  • It retains its characteristics unchanged.
  • It becomes completely transformed into new rock types.

    • Which of the following is NOT a classification of plate boundaries?

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

    What is recrystallization in the context of metamorphism?

    <p>Growth in size of mineral grains from pre-existing materials.</p> Signup and view all the answers

    Which type of magma is produced by a large degree of melting?

    <p>Tholeiitic magmas</p> Signup and view all the answers

    Which process is commonly associated with metamorphism?

    <p>Recrystallization of mineral grains</p> Signup and view all the answers

    Which transformation is an example of metamorphism?

    <p>Limestone to marble</p> Signup and view all the answers

    What is the result of the equation $8 + 14$?

    <p>$22$</p> Signup and view all the answers

    What operation is performed to isolate $x$ in the equation $8 - 4 = -6 - 14$?

    <p>Add $14$ to both sides</p> Signup and view all the answers

    What is the first step to solve the inverse equation $y = 8 + 14$?

    <p>Subtract $8$ from both sides</p> Signup and view all the answers

    If $f(x) = 8 + 14$, what would be $f^{-1}(y)$ if $y = 22$?

    <p>$14$</p> Signup and view all the answers

    Which expression correctly simplifies to $-1 (4 - 2)$?

    <p>$-2$</p> Signup and view all the answers

    What is the outcome of the expression $2(-3 - 7)$?

    <p>$-20$</p> Signup and view all the answers

    What does graphing the inverse function derive from the equation $y = 8 + 14$?

    <p>A reflection across the line $y = x$</p> Signup and view all the answers

    What is the primary operation used in finding the maturity value in simple interest calculations?

    <p>Addition of principal and interest</p> Signup and view all the answers

    What is neocrystallization?

    <p>The formation of new minerals from pre-existing minerals due to heat.</p> Signup and view all the answers

    Which of the following is an example of a rock that undergoes neocrystallization?

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

    What type of stress acts uniformly in all directions on a rock?

    <p>Confining stress</p> Signup and view all the answers

    What is the result of directed stress on rocks?

    <p>It results in folding and faulting.</p> Signup and view all the answers

    Which of the following is true about phase change in minerals?

    <p>It can lead to the formation of polymorphs.</p> Signup and view all the answers

    What characterizes plastic deformation in mineral grains?

    <p>It involves softening and deformation at high temperatures.</p> Signup and view all the answers

    Which type of stress is associated with the squeezing of rocks?

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

    What type of evidence supports the theory of ocean floor spreading?

    <p>Magnetic orientation of the oceanic crust.</p> Signup and view all the answers

    What does the term 'principal' refer to in financial context?

    <p>The amount of money extended for credit or deposited in a bank</p> Signup and view all the answers

    How is the interest rate expressed?

    <p>In percent, but may be converted to decimal</p> Signup and view all the answers

    What is the effect of decreasing pressure on magma formation?

    <p>It causes adiabatic decompression leading to melting</p> Signup and view all the answers

    Which of the following accurately defines volatiles in the context of magma formation?

    <p>Substances that can easily evaporate and exist in gaseous form</p> Signup and view all the answers

    What is simple interest?

    <p>Interest calculated only on the borrowed amount over the entire loan duration</p> Signup and view all the answers

    What happens to temperature as depth increases in the Earth?

    <p>It increases with depth</p> Signup and view all the answers

    What does the maturity date refer to?

    <p>The final date for repaying the principal amount</p> Signup and view all the answers

    What is the primary result of introducing volatiles like water to hot mantle rock?

    <p>It induces flux melting</p> Signup and view all the answers

    What does the Law of Original Horizontality state?

    <p>Sediments are deposited in a horizontal manner.</p> Signup and view all the answers

    Which principle indicates that sediment layers thin out at the edges of the depositional basin?

    <p>Law of Lateral Continuity</p> Signup and view all the answers

    What does the Law of Superposition describe?

    <p>The youngest rocks are at the top of undisturbed layers.</p> Signup and view all the answers

    Which method allows for determining the exact numerical age of rocks?

    <p>Absolute dating</p> Signup and view all the answers

    What principle states that geologic features that cut across rocks are younger than the rocks they cut through?

    <p>Principles of Cross-Cutting Relationships</p> Signup and view all the answers

    What is half-life in the context of isotopes?

    <p>The time it takes for half of an isotope to decay.</p> Signup and view all the answers

    Which type of dating relies on radioactive decay?

    <p>Absolute dating</p> Signup and view all the answers

    Which of the following describes isotopes?

    <p>Elements that have a different number of neutrons.</p> Signup and view all the answers

    What type of rock deformation involves the rock reshaping without breaking?

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

    Which of the following best describes a fault?

    <p>A discernible displacement where rocks grind or slide past each other</p> Signup and view all the answers

    Who proposed the seafloor spreading hypothesis?

    <p>Harry Hess and Robert Dietz</p> Signup and view all the answers

    What are black smokers?

    <p>Vents that spew dark, mineral-rich fluids</p> Signup and view all the answers

    Which type of sedimentary structures results from the process of stratification?

    <p>Rock layers</p> Signup and view all the answers

    What feature comprises 20% of the ocean floor’s surface?

    <p>Mid-Oceanic Ridge</p> Signup and view all the answers

    Why are fossils primarily found in sedimentary rocks?

    <p>Organisms' remains sink and are covered by sediments.</p> Signup and view all the answers

    What are transform faults in the context of seafloor spreading?

    <p>Segments that divide the seafloor</p> Signup and view all the answers

    Study Notes

    General Mathematics

    • Inverse Functions: A function g is the inverse of f if the ordered pairs of g are the ordered pairs of f written in reversed order.
    • One-to-One Function: A function is one-to-one if every second element is paired with only one first element, and a function has an inverse if and only if it is one-to-one.
    • Steps to Find Inverse Function:
      • Change f(x) to y
      • Interchange the variables x and y
      • Solve for y in terms of x
      • Change y to f⁻¹(x)
    • Example: Find the inverse function of f(x) = 2x - 1.
      • Step 1: y = 2x - 1
      • Step 2: x = 2y - 1
      • Step 3: x + 1 = 2y, y = (x + 1)/2
      • Step 4: f⁻¹(x) = (x + 1)/2

    Unit 12: Simple and Compound Interest

    • Interest: The amount a person earns or pays on top of the initial investment or loan.
    • Lender/Creditor: Party lending money or extending loans.
    • Borrower/Debtor: Party using the money or credit.
    • Principal: The amount of money borrowed or deposited.
    • Interest Rate: The charged amount for the use of money, usually expressed in percent.
    • Time of Interest: The period from borrowing to due date.
    • Maturity Date: The due date for loan payment.
    • Simple Interest: Calculated on the original principal over the entire borrowing period.
      • Formula: I = Prt (Interest = Principal × Rate × Time)
    • Maturity Value: The total sum of principal and interest.
      • Formula: M = P + I or M = P(1 + rt)

    Magmatism

    • Magma: Molten rock from the mantle and crust, containing liquids, gases, crystals, and rock fragments.
    • Pressure: Decrease in pressure leads to adiabatic decompression, decreasing material melting temperatures.
    • Volatiles: Substances (e.g., water, carbon dioxide) that easily evaporate and can exist as gases. Volatiles mix with hot mantle rock to form magma.
    • Temperature: Temperature increases with depth (geothermal gradient) causing melting.

    Metamorphism

    • Metamorphism: A process changing rock characteristics due to temperature, pressure, or reactions with hot fluids; the original rock is called a protolith.
    • Recrystallization: Mineral grains grow in size due to pre-existing material.
    • Neocrystallization: Formation of new minerals from pre-existing minerals due to heat.

    Stress in Rocks

    • Rock Deformation: Rocks change shape due to different types of stress.
    • Types of Stress:
      • Confining stress: Uniform pressure in all directions.
      • Directed stress: Pressure exerted in one direction (compression, tension, shear).
    • Types of deformation:
      • Elastic: Rock returns to original shape.
      • Ductile: Rock reshapes without breaking.
      • Brittle: Rock fractures.
    • Faults: Fractures where rocks break and shift.

    The Seafloor Spreading Hypothesis

    • Proposed by Harry Hess and Robert Dietz, it explains the formation of oceanic crust.
    • Paleomagnetic Evidence: Magnetic orientation of oceanic crust and the age of rocks support the idea that the ocean floor is spreading.

    How Layers of Rocks Are Formed

    • Fossils: Remains of organisms who lived before the last glacial period.
    • Stratification: The formation of sedimentary rock layers caused by the deposition of sediments.

    Relative and Absolute Dating

    • Relative dating: Determines the sequence of rock layers without a precise age.
    • Absolute dating: Determines the precise numerical age of rocks using radioactive decay.
    • Laws of Stratigraphy:
      • Law of Lateral Continuity: Layers extend laterally unless they thin out.
      • Law of Superposition: Younger layers lie above older layers in undistributed sequences.
      • Cross-Cutting Relationships: A geologic feature that cuts across another feature is younger than the one it cuts through.

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    Description

    This quiz covers key concepts in general mathematics, focusing on inverse functions and the basics of simple and compound interest. You will learn how to determine the inverse of a function and the essential terms related to interest calculations. Test your understanding of these foundational topics essential for higher mathematics.

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