Compound and Repeated Percentages Quiz

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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).

Signup and view all the flashcards

Mass

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

Signup and view all the flashcards

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.

Signup and view all the flashcards

Pressure

Pressure is defined as the force applied per unit area.

Signup and view all the flashcards

Direct Proportion

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

Signup and view all the flashcards

Pressure Formula

The formula for pressure is Pressure = Force / Area.

Signup and view all the flashcards

Direct Proportion Formula

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

Signup and view all the flashcards

Direct Proportion Graph

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

Signup and view all the flashcards

Finding the Multiplier (k)

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

Signup and view all the flashcards

Converting Units

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

Signup and view all the flashcards

Common Multiplier in Direct Proportion

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

Signup and view all the flashcards

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.

Signup and view all the flashcards

Multiplier (k)

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

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Signup and view all the flashcards

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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

More Like This

Mathematics: Integers
10 questions
Arithmetic - 1 Quiz
24 questions

Arithmetic - 1 Quiz

ThriftyFoxglove9282 avatar
ThriftyFoxglove9282
Math Chapter: Percentages and Measures
24 questions
Use Quizgecko on...
Browser
Browser