Math Chapter: Percentages and Measures

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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)

50 cm³

30 cm³

60 cm³

Pressure can be calculated by multiplying force and area.

False

What is the formula for pressure?

Pressure = Force ÷ Area

To convert 8 km/h to mph, you multiply by ______ miles.

1.6 Signup and view all the answers

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

0.5 N/cm² Signup and view all the answers

Define direct proportion.

Two sets of values are in direct proportion if they have a common multiplier. Signup and view all the answers

The formula for y in terms of x when y is in direct proportion to x is y = ______ x.

k Signup and view all the answers

Match the following conversions:

8 km/h = 5 mph 70 mph = 31.29 m/s 1 km = 0.621 miles 18 km/h = 0.005 m/s Signup and view all the answers

What is the multiplier to increase an amount by 12%?

1.12 Signup and view all the answers

If you increase an amount by 10% and then by another 12%, the overall percentage increase is 122%.

False Signup and view all the answers

Calculate the density of a piece of metal that weighs 40g and has a volume of 4cm³.

10 g/cm³ Signup and view all the answers

Speed is calculated using the formula __________.

Distance ÷ Time Signup and view all the answers

Match the following measurements with their formulas:

Speed = Distance ÷ Time Density = Mass ÷ Volume Volume = Length × Width × Height Time = Distance ÷ Speed Signup and view all the answers

A block of ice measures 5 cm by 2 cm by 4 cm. What is the volume of the cube?

40 cm³ Signup and view all the answers

To find the mass of an object, you can multiply its density by its volume.

True Signup and view all the answers

To convert 45 minutes into hours, you would write it as __________.

0.75 Signup and view all the answers

What is the equation for y in terms of x when y is proportional to $x^2$?

y = 4x^2 Signup and view all the answers

In direct proportion, if one value increases, the other value must increase as well.

True Signup and view all the answers

What is the value of k when x = 4 and y = 25 in an inverse proportion scenario?

100 Signup and view all the answers

The multiplier in the inverse proportion relationship is represented by _____ .

k Signup and view all the answers

Match the following equations with their type of proportion:

y = kx^2 = Direct Proportion y = k/x = Inverse Proportion g = k√f = Direct Proportion k = yx = Inverse Proportion Signup and view all the answers

When f = 9 and g = 30, how can g be expressed in terms of f?

g = k√f Signup and view all the answers

If y and x are inversely proportional, then when x increases, y must also increase.

False Signup and view all the answers

If x = 2, find the value of y given that k = 100 and y is inversely proportional to x.

50 Signup and view all the answers

Study Notes

Repeated Percentages

To increase a value by 10%, multiply by 1.10
To increase a value by 12%, multiply by 1.12
To find the overall percentage increase from multiple percentage increases, multiply the individual multipliers together

Compound Percentages

Compound Interest: Calculate the future value of an amount that earns interest over time, where the interest is added to the principal each period.
- Formula: Amount x (Multiplier)^Time
Compound Depreciation: Calculate the future value of an amount that loses value over time, where the depreciation is subtracted from the principal each period.
- Formula: Amount x (Decreasing Multiplier)^Time

Compound Measures

Compound measures combine two or more units of measurement
Density: Mass / Volume. Measured in g/cm³, kg/m³ or kg/l
Speed: Distance / Time. Units include m/s, km/h or mph
Pressure: Force / Area. Units include N/m² or N/cm²
Fuel Consumption: Distance / Volume. Units include km/l or mpg

Compound Measure - Speed

Speed = Distance / Time
Time = Distance / Speed
Distance = Speed x Time
Convert minutes to hours to calculate speed

Compound Measure - Density

Density = Mass / Volume
Volume = Mass / Density
Mass = Density x Volume
Used to determine how tightly matter is packed within a given volume

Compound Measure - Pressure

Pressure = Force / Area
Area = Force / Pressure
Force = Pressure x Area
Measured in N/m², N/cm², N/km²

Compound Measure - Converting Measurements

Conversion factors will vary
Examples include converting km/h to mph, km/h to km/s, and mph to m/s

What is Direct Proportion?

Two sets of values are in direct proportion if they have a common multiplier.
Direct proportion graphs are straight lines that pass through the origin (0,0).

Direct Proportion - without powers

If y is directly proportional to x, then y = kx, where k is the constant of proportionality (multiplier).
Find the multiplier (k) by dividing a y value by its corresponding x value.
Use the multiplier (k) to generate more calculations for the same relationship.

Direct Proportion - with powers

If y is directly proportional to x², then y = kx².
If y is directly proportional to x³, then y = kx³.

Inverse Proportion

Two sets of values are inversely proportional if one value increases while the other decreases at the same rate.
To write an equation for inverse proportionality: y= k/x where k is the constant of proportionality (k = yx).

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Description

This quiz covers the concepts of repeated percentages, compound percentages, and compound measures. You will learn how to calculate percentage increases, compound interest, and various measurements such as density, speed, and pressure. Test your knowledge and enhance your understanding of these essential mathematical topics.