Compound and Repeated Percentages Quiz
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Questions and Answers

What is the volume of a rectangular prism with dimensions 2 cm, 4 cm, and 5 cm?

  • 40 cm³ (correct)
  • 60 cm³
  • 30 cm³
  • 50 cm³
  • Pressure is calculated using the formula Force ÷ Area.

    True (A)

    If a force of 10 Newtons is applied to an area of 20 cm², what is the pressure produced?

    0.5 N/cm²

    The formula for calculating mass is _____ x Volume.

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

    Match the following unit conversions with their values:

    <p>8 km/h = 5 mph 18 km/h = 0.005 km/s 70 mph = 31.29 m/s 1 km = 1.6 miles</p> Signup and view all the answers

    What does 'direct proportion' mean?

    <p>Values increase or decrease together. (A)</p> Signup and view all the answers

    In a direct proportion, y is expressed as _____x, where k is the multiplier.

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

    A direct proportion graph can be represented as a curve.

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

    What is the percentage increase when an amount is increased first by 10% and then by 12%?

    <p>23.2% (A)</p> Signup and view all the answers

    The multiplier to increase an amount by 12% is 1.12.

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

    What formula is used to calculate speed?

    <p>Speed = Distance ÷ Time</p> Signup and view all the answers

    Density is calculated using the formula _____ = Mass ÷ Volume.

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

    Match the following measurements with their formulas:

    <p>Speed = Distance ÷ Time Density = Mass ÷ Volume Distance = Speed x Time Time = Distance ÷ Speed</p> Signup and view all the answers

    If a piece of metal weighs 40g and has a volume of 4cm³, what is its density?

    <p>10 g/cm³ (B)</p> Signup and view all the answers

    45 minutes is equal to 0.75 hours.

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

    Calculate the volume of a block of ice that measures 5cm by 2cm by 4cm.

    <p>40 cm³</p> Signup and view all the answers

    What is the relationship between y and x given that y is proportional to $x^2$?

    <p>y increases as x increases (A)</p> Signup and view all the answers

    For directly proportional relationships, k remains constant.

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

    If when x = 2, y = 16, what is the value of k in the equation $y = kx^2$?

    <p>4</p> Signup and view all the answers

    The equation representing an inverse relationship between y and x is $y = \frac{k}{x}$, where k = _____ when x = 4 and y = 25.

    <p>100</p> Signup and view all the answers

    Match the following relationships with their equations:

    <p>Direct Proportion = y = kx^2 Inverse Proportion = y = k/x Direct Proportion with powers = y = kx Square Root Proportion = g = k√f</p> Signup and view all the answers

    Which equation correctly represents g in terms of f when g is proportional to the square root of f?

    <p>g = k√f (B)</p> Signup and view all the answers

    If x decreases, y increases in an inversely proportional relationship.

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

    What is the value of y when x = 2, given the equation for inverse proportionality with k = 100?

    <p>50</p> Signup and view all the answers

    Flashcards

    Percentage Multiplier

    The multiplier used to increase a value by a certain percentage. For example, the multiplier for a 10% increase is 1.10, which is obtained by dividing 110% by 100.

    Overall Percentage Increase

    The overall percentage increase when multiple percentage increases are applied consecutively. It is calculated by multiplying the individual multipliers together.

    Compound Measure

    A measure that combines two different units, often used to describe quantities such as speed, density, and pressure. It is expressed as a ratio of two units.

    Speed

    The rate at which an object moves, calculated by dividing the distance traveled by the time taken.

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    Density

    The amount of matter contained in a given volume. It is a measure of how tightly packed matter is in a substance. It can be calculated by dividing mass by volume.

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    Volume

    The space occupied by a three-dimensional object, calculated by multiplying its length, width, and height. It is often expressed in cubic units (cm3, m3).

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    Mass

    The amount of matter in an object, often expressed in grams (g).

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    Compound Interest

    A type of interest that is calculated on the principal amount plus any accumulated interest from previous periods. It leads to exponential growth over time.

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    Pressure

    Pressure is defined as the force applied per unit area.

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    Direct Proportion

    Direct proportion means that as one quantity increases, the other quantity increases at the same rate, and their ratio remains constant.

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    Pressure Formula

    The formula for pressure is Pressure = Force / Area.

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    Direct Proportion Formula

    Direct proportion can be represented by the formula y = kx, where k is the constant of proportionality.

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    Direct Proportion Graph

    Direct Proportion graphs are always straight lines passing through the origin (0,0).

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    Finding the Multiplier (k)

    To find the multiplier (k) in a direct proportion, divide the value of y by the corresponding value of x.

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    Converting Units

    To convert units, use the relationship between the two units.

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    Common Multiplier in Direct Proportion

    When two quantities are directly proportional, they have a common multiplier which is a constant.

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    Inverse Proportion

    A relationship where one variable increases as another variable decreases at a constant rate. For example, if the speed of a car increases, the time it takes to travel a certain distance decreases proportionally.

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    Multiplier (k)

    The constant factor that relates two variables in a direct proportion. It represents the ratio of change between the variables.

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    Direct Proportion with Powers

    A type of direct proportion where one variable is proportional to the square of another variable. For example, the area of a square is proportional to the square of its side length.

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    Direct Proportion with Square Root

    A type of direct proportion where one variable is proportional to the square root of another variable. For example, the time it takes for a pendulum to swing back and forth is proportional to the square root of its length.

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    Equation for Direct/ Inverse Proportion

    The equation that represents the relationship between two variables in a direct or inverse proportion. It typically includes the multiplier (k) and the variables involved.

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    Proportionality Factor

    In direct proportion, if one variable increases by a factor, the other variable increases by the same factor. In inverse proportion, if one variable increases by a factor, the other variable decreases by the same factor.

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    Writing an Equation for Direct/Inverse Proportion

    To write down an equation representing the relationship between two variables in direct or inverse proportion. It requires identifying the type of proportion, the multiplier (k), and the variables involved.

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    Study Notes

    Repeated Percentages

    • To increase a quantity by 10%, multiply by 1.10
    • To increase a quantity by 12%, multiply by 1.12
    • To find the overall percentage increase when increasing by multiple percentages, multiply the individual multipliers.

    Compound Percentages

    • Compound interest calculates interest on both the original principal and the accumulated interest from prior periods.
    • If an amount increases by 10% each year, multiply the initial amount by 1.10 a 3 year period to determine the final amount.
    • Alternatively, if an amount depreciates by 10% each year, multiply the initial amount by 0.90 for a 3 year period to determine the final amount.

    Compound Measures - Units

    • Compound measures are units that consist of two measurements.
    • Examples:
      • Density: mass/volume (g/cm³, kg/m³ kg/L)
      • Speed: distance/time (m/s, km/h, mph)
      • Pressure: force/area (N/m², N/cm²)
      • Fuel consumption: distance/volume (km/L, mpg)

    Compound Measures - Speed

    • Speed = Distance / Time
    • Time = Distance / Speed
    • Distance = Speed x Time
    • Convert minutes to hours to use in speed calculations.

    Compound Measures - Density

    • Density = Mass / Volume
    • Volume = Mass / Density
    • Mass = Density x Volume
    • Use formulas to calculate missing parameters regarding density, mass and volume.

    Compound Measures - Pressure

    • Pressure = Force / Area
    • Area = Force / Pressure
    • Force = Pressure x Area
    • Pressure units: N/cm², N/m², N/km²

    Compound Measures - Converting Measurements

    • Use conversion factors to change units of measurement.
    • Example conversions: km/h to mph, km/h to km/s, mph to m/s

    Direct Proportion

    • Two sets of values are directly proportional if they have a common multiplier.
    • In a direct proportion graph, the line passes through the origin (0,0)
    • Direct proportion equations are of the form y = kx, where k is the constant of proportionality.
    • To find k, use the given x and y values. Examples include find a constant k is known in relation to x and y when x is known

    Direct Proportion - Without Powers

    • The formula y=kx represents direct proportion, where k is the constant of proportionality.
    • To find the constant, divide a value of y by its corresponding value of x.

    Direct Proportion - With Powers

    • If y is directly proportional to the square of x, the equation is y = kx².
    • If y is directly proportional to the cube of x, the equation is y = kx³.
    • Use given values to solve for the constant k and form the correct equation.

    Inverse Proportion

    • Two values are inversely proportional if one value increases as the other decreases.
    • The formula representing inverse proportion is y=k/x.
    • To find the constant k, multiply a value of x and its corresponding value of y.

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    Description

    Test your understanding of repeated and compound percentages, including how to calculate percentage increases and understand compound measures like density and speed. This quiz covers essential mathematical concepts that are fundamental for various applications in finance and science.

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