Podcast
Questions and Answers
What is the volume of a rectangular prism with dimensions 2 cm, 4 cm, and 5 cm?
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.
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?
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.
The formula for calculating mass is _____ x Volume.
Match the following unit conversions with their values:
Match the following unit conversions with their values:
What does 'direct proportion' mean?
What does 'direct proportion' mean?
In a direct proportion, y is expressed as _____x, where k is the multiplier.
In a direct proportion, y is expressed as _____x, where k is the multiplier.
A direct proportion graph can be represented as a curve.
A direct proportion graph can be represented as a curve.
What is the percentage increase when an amount is increased first by 10% and then by 12%?
What is the percentage increase when an amount is increased first by 10% and then by 12%?
The multiplier to increase an amount by 12% is 1.12.
The multiplier to increase an amount by 12% is 1.12.
What formula is used to calculate speed?
What formula is used to calculate speed?
Density is calculated using the formula _____ = Mass ÷ Volume.
Density is calculated using the formula _____ = Mass ÷ Volume.
Match the following measurements with their formulas:
Match the following measurements with their formulas:
If a piece of metal weighs 40g and has a volume of 4cm³, what is its density?
If a piece of metal weighs 40g and has a volume of 4cm³, what is its density?
45 minutes is equal to 0.75 hours.
45 minutes is equal to 0.75 hours.
Calculate the volume of a block of ice that measures 5cm by 2cm by 4cm.
Calculate the volume of a block of ice that measures 5cm by 2cm by 4cm.
What is the relationship between y and x given that y is proportional to $x^2$?
What is the relationship between y and x given that y is proportional to $x^2$?
For directly proportional relationships, k remains constant.
For directly proportional relationships, k remains constant.
If when x = 2, y = 16, what is the value of k in the equation $y = kx^2$?
If when x = 2, y = 16, what is the value of k in the equation $y = kx^2$?
The equation representing an inverse relationship between y and x is $y = \frac{k}{x}$, where k = _____ when x = 4 and y = 25.
The equation representing an inverse relationship between y and x is $y = \frac{k}{x}$, where k = _____ when x = 4 and y = 25.
Match the following relationships with their equations:
Match the following relationships with their equations:
Which equation correctly represents g in terms of f when g is proportional to the square root of f?
Which equation correctly represents g in terms of f when g is proportional to the square root of f?
If x decreases, y increases in an inversely proportional relationship.
If x decreases, y increases in an inversely proportional relationship.
What is the value of y when x = 2, given the equation for inverse proportionality with k = 100?
What is the value of y when x = 2, given the equation for inverse proportionality with k = 100?
Flashcards
Percentage Multiplier
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
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
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
Speed
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Density
Density
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Volume
Volume
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Mass
Mass
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Compound Interest
Compound Interest
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Pressure
Pressure
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Direct Proportion
Direct Proportion
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Pressure Formula
Pressure Formula
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Direct Proportion Formula
Direct Proportion Formula
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Direct Proportion Graph
Direct Proportion Graph
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Finding the Multiplier (k)
Finding the Multiplier (k)
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Converting Units
Converting Units
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Common Multiplier in Direct Proportion
Common Multiplier in Direct Proportion
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Inverse Proportion
Inverse Proportion
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Multiplier (k)
Multiplier (k)
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Direct Proportion with Powers
Direct Proportion with Powers
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Direct Proportion with Square Root
Direct Proportion with Square Root
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Equation for Direct/ Inverse Proportion
Equation for Direct/ Inverse Proportion
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Proportionality Factor
Proportionality Factor
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Writing an Equation for Direct/Inverse Proportion
Writing an Equation for Direct/Inverse Proportion
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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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