This cheat sheet covers three important compound measures: speed, density, and pressure. Students need these formulas to solve real-world problems involving travel, materials, fluids, gases, and forces. It helps connect units clearly so calculations are easier to set up and check.
The layout is designed as a printable reference with clear sections for quick revision.
The main ideas are based on dividing one quantity by another, such as distance divided by time, mass divided by volume, or force divided by area. The core formulas are , , and . Each formula can be rearranged to find any missing quantity.
Correct units are essential because compound measures depend on both the numbers and the units used.
Key Facts
- Speed is calculated using , where is speed, is distance, and is time.
- Distance is calculated using when speed and time are known.
- Time is calculated using when distance and speed are known.
- Density is calculated using , where is density, is mass, and is volume.
- Mass is calculated using , and volume is calculated using .
- Pressure is calculated using , where is pressure, is force, and is area.
- Force is calculated using , and area is calculated using .
- Units must match the formula, such as for speed, for density, and or for pressure.
Vocabulary
- Speed
- Speed is the distance traveled per unit of time, usually calculated with .
- Distance
- Distance is the length of the path traveled, often found using .
- Density
- Density is the mass per unit volume of a substance, calculated with .
- Pressure
- Pressure is the force applied per unit area, calculated with .
- Compound Measure
- A compound measure combines two different units, such as , , or .
- Rearranging a Formula
- Rearranging a formula means changing its subject so a different unknown can be calculated.
Common Mistakes to Avoid
- Using mismatched time units, such as distance in kilometers and time in minutes, gives a speed in rather than unless the time is converted.
- Multiplying instead of dividing for compound measures is wrong when the formula requires a rate, such as , , or .
- Forgetting to square area units is incorrect because pressure uses area, so must be used for in pascals.
- Confusing mass and weight leads to incorrect pressure calculations because pressure uses force in newtons, not mass in kilograms.
- Rounding too early can change the final answer, so keep extra digits during working and round only at the end.
Practice Questions
- 1 A cyclist travels in . Find the cyclist's average speed in .
- 2 A metal block has mass and volume . Find its density in .
- 3 A force of acts on an area of . Find the pressure in pascals.
- 4 Two boxes have the same force pressing down, but one has a smaller contact area. Explain which box creates greater pressure and why.
Understanding Speed Distance Time and Compound Measures
A compound measure compares two linked quantities. It tells more than either quantity on its own. A journey of sixty kilometres sounds long, but its meaning changes when the travel time is known.
A material with a mass of one kilogram may feel heavy or light depending on how much space it fills. This is why these measures are useful.
They describe rates, packing, or spreading. In each case, the result depends on a relationship between measurements rather than a single measurement.
Unit conversion is often the hardest part of these problems. A calculator cannot fix units that do not match. For speed, students commonly need to change hours into seconds or kilometres into metres before calculating.
One hour contains three thousand six hundred seconds. One kilometre contains one thousand metres. If a speed is given in kilometres per hour but time is in seconds, convert one of them first.
Write the units beside every number during working. At the end, check whether the final unit makes sense for the situation. Walking speeds are often given in kilometres per hour, while scientific experiments often use metres per second.
Density helps explain why equal sized objects can have very different masses. A small metal block can weigh more than a large piece of foam because its particles are packed more closely. Density is important in material choice.
Engineers consider it when making bicycles, aircraft, boats, buildings, and packaging. It can help identify a substance when its mass and volume are measured carefully. Water has a density close to one thousand kilograms per cubic metre.
Objects less dense than water can float if their overall shape gives them enough volume. A steel ship floats because its hull contains air, making the average density of the whole ship lower than water.
Pressure depends strongly on contact area. The same force produces greater pressure when it acts over a smaller area. A drawing pin enters a noticeboard because the sharp tip has a tiny area.
Snowshoes reduce pressure on snow by spreading a person's weight over a larger area. This idea appears in tyres, foundations, cutting tools, and high heeled shoes. Students should separate force from pressure in their thinking.
Force is a push or pull, measured in newtons. Pressure describes how concentrated that force is on a surface. In calculations, sketch the situation first and label the quantity being found.
Then choose a rearranged relationship that places the unknown on its own. Estimate the answer before calculating. A larger area should give lower pressure for the same force, so an answer showing the opposite may reveal an error.