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 (C)</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. (C)</p> Signup and view all the answers

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

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

Which process is commonly associated with metamorphism?

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

Which transformation is an example of metamorphism?

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

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

<p>$22$ (A)</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 (D)</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 (B)</p> Signup and view all the answers

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

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

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

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

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

<p>$-20$ (A)</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 $y = x$ (B)</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 (A)</p> Signup and view all the answers

What is neocrystallization?

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

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

<p>Phyllite (A)</p> Signup and view all the answers

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

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

What is the result of directed stress on rocks?

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

What characterizes plastic deformation in mineral grains?

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

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

<p>Compression (D)</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. (A)</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 (D)</p> Signup and view all the answers

How is the interest rate expressed?

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

What is simple interest?

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

What happens to temperature as depth increases in the Earth?

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

What does the maturity date refer to?

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

What does the Law of Original Horizontality state?

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

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

<p>Absolute dating (B)</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 (D)</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. (C)</p> Signup and view all the answers

Which type of dating relies on radioactive decay?

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

Which of the following describes isotopes?

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

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

<p>Ductile (A)</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 (D)</p> Signup and view all the answers

Who proposed the seafloor spreading hypothesis?

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

What are black smokers?

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

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

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

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

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

Why are fossils primarily found in sedimentary rocks?

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

What are transform faults in the context of seafloor spreading?

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

Flashcards

Magma

Molten rock material formed by partial melting of the mantle and crust, containing liquids, gases, crystals, and rock fragments.

Adiabatic decompression

Process where decreasing pressure leads to a drop in melting temperature of materials.

Volatiles

Substances that easily evaporate and exist as gases near the Earth's surface, like water and carbon dioxide.

Geothermal gradient

The increasing temperature with depth within the Earth.

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Simple interest

Interest calculated on the original principal amount throughout the borrowing period.

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Interest

Amount paid or earned on top of the original investment or loan.

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Principal

Original amount of money lent or deposited.

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Interest rate

Percentage charged for using money over a period.

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Inverse of a Function

The inverse of a function is the function that reverses the input and output values of the original function.

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Graphing Inverse Functions

To graph an inverse function, create a table of values using the original function and switch the x and y values in the table, then plot the new pairs.

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Maturity Value

Maturity value is the total amount owed on a loan (or earned from an investment) at the end of a specified length of time.

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Addition

Combining numbers to find a sum.

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Subtraction

Finding the difference between two numbers.

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Order of Operations

A set of rules to follow when evaluating expressions that involve multiple arithmetic operations.

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Metamorphism

The process of changing the characteristics of a rock due to changes in temperature, pressure, or reactions with hot fluids.

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Protolith

The original rock before undergoing metamorphism. It can be any type of rock.

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Recrystallization

The process of growing the size of mineral grains in pre-existing materials.

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Flux Melting

Lowering a substance's melting point by introducing impurities.

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Magmatism

The process of magma formation and movement within the Earth's crust.

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Tholeiitic Magmas

Magmas produced by a large degree of melting, usually found near divergent plate boundaries.

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Calc-alkaline Basalts

Basalts formed along convergent plate boundaries above subduction zones.

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Alkaline Basalts

Basalts formed from smaller degree of partial melting, resulting in alkali-rich magma.

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Phase Change (In Minerals)

A transformation in the mineral structure while preserving the chemical formula. For example, andalusite changing to kyanite.

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Pressure Solution

A process where minerals dissolve in areas of high pressure and recrystallize in areas of low pressure. This can occur when rocks are subjected to uneven pressure.

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Plastic Deformation

The deformation of mineral grains at high temperatures, causing them to soften and flow without fracturing.

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Confining Stress

Stress that acts uniformly in all directions on a rock or sediment. This commonly occurs when rocks are buried deep underground.

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Directed Stress

Stress that acts only in one direction. It's often linked to tectonic activity, where forces push or pull on the Earth's crust.

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Compression (Stress)

A type of directed stress that squeezes a rock, causing folding or faulting.

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Tension (Stress)

A type of directed stress that pulls a rock apart, leading to stretching or thinning.

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Law of Original Horizontality

States that sedimentary layers are originally deposited in a horizontal position.

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Law of Lateral Continuity

States that sedimentary layers extend laterally in all directions until they thin out or change into a different type of sediment.

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Law of Superposition

States that in undisturbed rock layers, the oldest layers are at the bottom and the youngest layers are at the top.

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Cross-Cutting Relationships

States that geologic features that cut across other layers of rock are younger than the layers they cut through.

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Relative Dating

Determining the age of rocks and fossils in relation to each other, without giving a specific numerical age.

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Absolute Dating

Determining the exact numerical age of rocks and fossils using radioactive decay.

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Isotopes

Atoms of the same element with the same number of protons but a different number of neutrons.

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Half-life

The time it takes for half of a radioactive isotope to decay into a stable element.

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What causes rocks to deform?

Stress on rocks, like pressure or tension, can cause them to change shape or break. The type of deformation depends on the rock type, stress intensity, and direction.

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What is elastic deformation?

Elastic deformation is when a rock returns to its original shape after the stress is removed. Imagine a rubber band stretching and then bouncing back.

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What is ductile deformation?

Ductile deformation is when a rock changes shape permanently without breaking. Think of a piece of clay being molded.

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What is brittle deformation?

Brittle deformation is when a rock breaks or fractures under stress. Imagine a glass breaking when dropped.

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What is a fault?

A fault is a crack or fracture in the Earth's crust where rocks have moved past each other. It's like a big crack in the ground where the land has shifted.

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What is seafloor spreading?

Seafloor spreading is the process where new oceanic crust is formed at mid-ocean ridges and then moves away from the ridge.

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What is the Mid-Oceanic Ridge?

The Mid-Oceanic Ridge is a vast underwater mountain range where new oceanic crust is formed. It's like a giant underwater volcano.

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What are fossils?

Fossils are the preserved remains or traces of ancient organisms. They are typically found in sedimentary rocks.

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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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General Mathematics & Earth Science - Assessment 2 (Reviewer)

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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