What is the definition of 'rate' in the context of Cambridge IGCSE Mathematics?

In Cambridge IGCSE Mathematics, 'rate' refers to a ratio that compares two different quantities measured in different units. It is often used to describe how one quantity changes in relation to another, such as speed (distance per time) or density (mass per volume).

How do you calculate the rate of speed in a mathematical problem?

To calculate the rate of speed, you divide the total distance traveled by the total time taken. The formula is speed = distance ÷ time. This calculation helps determine how fast an object is moving, and the units are typically expressed as kilometers per hour (km/h) or meters per second (m/s).

What is the difference between 'rate' and 'ratio' in mathematics?

While both 'rate' and 'ratio' involve comparisons between quantities, a 'rate' specifically compares two quantities with different units, such as kilometers per hour. A 'ratio', on the other hand, compares two quantities with the same unit, such as the ratio of boys to girls in a class.

Can you provide an example of a real-world application of rates?

A common real-world application of rates is in calculating fuel efficiency for vehicles, often expressed as miles per gallon (mpg) or liters per 100 kilometers (L/100 km). This rate helps drivers understand how much fuel their vehicle consumes over a certain distance, aiding in cost estimation and environmental impact assessment.

How are rates used in solving problems involving proportional relationships in IGCSE Mathematics?

In IGCSE Mathematics, rates are used to solve problems involving proportional relationships by setting up equations that relate the quantities involved. For example, if a car travels 300 kilometers in 5 hours, the rate of speed can be used to find how far it would travel in 8 hours by setting up a proportion: (300 km / 5 hours) = (x km / 8 hours), and solving for x.

Why is "Comparing rates in different units" a common mistake in Rate?

Why it happens: 750\,ml vs 1.2\,L — students compute the price-per-something without converting. How to avoid it: Convert to the same unit first. Source: 0580/22 best-buy questions

Why is "Inverting the rate (e.g. computing $\dfrac{V}{m}$ for density)" a common mistake in Rate?

Why it happens: Rearranging the formula incorrectly under pressure. How to avoid it: Always write the formula with units: is in g/cm^3 — mass on top.

Why is "Omitting units in the final answer" a common mistake in Rate?

Why it happens: Students focus on the number and forget the unit. How to avoid it: Mark schemes require units for full marks. Always include them.

Cambridge IGCSE Mathematics (0580)

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Short Notes - Rate

Detailed Study Notes

Detailed notes on Number for Cambridge IGCSE Mathematics, covering key concepts, explanations, examples, and exam-focused revision points.

Rates — Cambridge IGCSE 0580 Maths Extended (2026)

A rate is a ratio with units — distance per hour, dollars per day, litres per minute. Recognise the keyword 'per' and the rest is unit conversion plus careful arithmetic.

At a glance

A rate compares two quantities with different units, written as one PER the other.
Common rates: km/h, $/day, m³/min, beats per minute,$ /m², L/100km.
Find a rate by dividing: total $\div$ time (or other base unit).
Use a rate by multiplying: rate $\times$ time gives total.
Always convert to consistent units before computing.
Best-buy / unit-rate questions: divide cost by quantity to compare "price per unit".
Rate of FLOW: volume / time. e.g. $20\,\text{L/min}$ .

What you’ll learn

Mapped to the Cambridge IGCSE 0580 syllabus (2025-2027).

Use rates to model and solve real-world problems involving constant rates of change.
Compare quantities by computing a unit rate.
Convert between rates expressed in different units.

What a rate is

A rate links two different units. Read 'per' as 'divided by'.

A rate is a ratio of two quantities measured in different units. The word "per" signals a rate.

Rate	Units
Speed	km per hour, m per second
Wage	dollars per hour, dollars per day
Flow	litres per minute, m³ per second
Population growth	people per year
Heart rate	beats per minute
Fuel efficiency	km per litre, miles per gallon

Computing a rate from two known quantities: $\text{rate} = \dfrac{\text{quantity}}{\text{time (or base unit)}}.$

Cover a cell: quantity = rate × time, rate = quantity ÷ time, time = quantity ÷ rate.

Worked. "A car uses $42\,\text{L}$ of petrol to travel $588\,\text{km}$ . Find the fuel efficiency in km per litre."

$\dfrac{588}{42} = 14\,\text{km/L}$ .

Using a rate to scale up or down: $\text{quantity} = \text{rate} \times \text{time}.$

Worked. "A printer prints at $24$ pages per minute. How many pages in $7$ minutes?"

$24 \times 7 = 168$ pages.

Converting between rate units. Same trick as speed: convert each part separately.

$20\,\text{L/min} = 20 \times 60 = 1200\,\text{L/h}$ .
$15 per hour: $15 \div 60 = 0.25$ , so $0.25 per minute.

'Per' means divided by.
Compute: total / base = rate.
Use: rate × time = total.
Convert each part of the rate (numerator / denominator) separately.

Best buy — comparing unit rates

Convert each option to 'price per unit' and compare. The smallest unit price wins.

When two products come in different sizes/prices, compute the unit rate for each — usually "price per unit quantity" — and pick the smallest.

Worked. Pack A: $4.50 for $750\,\text{g}$ . Pack B: $6.20 for $1\,\text{kg}$ . Which is better value?

A: $4.50 / 750 = 0.006$ , so $0.006 per gram = $6.00 per kg.
B: $6.20 / 1000 = 0.0062$ , so $0.0062 per gram = $6.20 per kg.

A is cheaper per kg ($6.00 vs $6.20).

Convert both to $/kg: Pack A at $6.00 beats Pack B at $6.20.

State the answer in context. Examiners want a sentence that names the cheaper pack AND quotes the unit price for both.

Reverse direction. Sometimes you compare "quantity per dollar" instead — the LARGER value wins. For Pack A: $750/4.50 = 166.7$ g per $. Pack B: $1000/6.20 = 161.3$ g per $. A again. The choice of direction doesn't matter as long as you stay consistent.

Compute price per unit for each option.
Smaller price-per-unit wins.
OR compute units-per-dollar; larger wins.
State the answer with both unit prices for full credit.

Flow rate and time-to-fill

Flow rates work the same way: volume / time. Time to fill = volume / flow rate.

Flow problems give you a flow rate (e.g. $20\,\text{L/min}$ ) and ask either how much fills in a given time, or how long to fill a given volume.

Volume from rate and time: $V = R \times t$ . Time from volume and rate: $t = V / R$ .

Worked. A tap fills a $240\,\text{L}$ tank at $20\,\text{L/min}$ . How long?

$t = 240 / 20 = 12\,\text{min}$ .

Two taps. When two taps fill the same tank, the combined rate is the SUM of the individual rates. (Same idea as workers in inverse-proportion problems.)

Worked. Tap A fills at $30\,\text{L/min}$ , tap B at $20\,\text{L/min}$ . Both running, how long to fill $300\,\text{L}$ ?

Combined rate: $30 + 20 = 50\,\text{L/min}$ .
Time: $300 / 50 = 6\,\text{min}$ .

Filling AND draining. If a drain operates at $10\,\text{L/min}$ alongside the two taps, net rate is $50 - 10 = 40\,\text{L/min}$ . Time = $300 / 40 = 7.5\,\text{min}$ .

Net rate = inflow − outflow: 30 + 20 − 10 = 40 L/min.

Volume = rate × time. Time = volume / rate.
Two filling taps: ADD their rates.
A drain SUBTRACTS from the net rate.
Always check the units (L/min vs L/h).

Rate vs ratio — they're not the same

Ratios compare two quantities of the SAME unit. Rates compare two quantities of DIFFERENT units.

Both ratios and rates use division — and it's easy to slip from one into the other. The distinction:

Ratio — same units. e.g. "$50 to $30" simplifies to $5 : 3$ . The unit cancels.
Rate — different units. e.g. "$50 per $30\,\text{kg}$ " is $1.67 per kg, NOT a ratio of $50 to 30.

If the unit cancels it's a ratio; if the unit must stay it's a rate.

A useful rule of thumb: if you can drop the unit safely, it's a ratio. If you'd lose meaning by dropping it, it's a rate.

Ratio: same unit, compares parts.
Rate: different units, compares change.
Both use division.
If dropping the unit destroys meaning → rate.

Quick recap

Rate = quantity per base unit. 'Per' means divide.
Compute: total ÷ base = rate. Use: rate × time = total.
Best buy: compute price per unit; smallest wins.
Flow: V = R × t. Two taps add rates; a drain subtracts.
Rate ≠ ratio: rate compares DIFFERENT units; ratio compares SAME units.
Always check units match before substituting.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

Rate — a ratio of two quantities of different units, expressed using "per".
Unit rate — the rate written so the denominator equals one (e.g. price per kg, miles per hour).
Flow rate — the volume of fluid passing per unit time (e.g. L/min).
Best buy — the option with the lowest price per unit (or highest quantity per dollar).

How it’s examined

Rate questions usually appear as a 2-3 mark Paper 2 item — find a rate from totals, then use it. Best-buy questions show up most years on Paper 2 as 3 marks. Paper 4 wraps rates inside multi-step problems involving currency, fuel, or flow. Examiner reports flag failing to convert units (e.g. forgetting to switch L/min to L/h) and stating only the unit-rate without naming the cheaper option.

Sources: Cambridge IGCSE Mathematics 0580 syllabus 2025-2027 (E1.12); 0580/22 May/Jun 2024 — Q8 (best buy); 0580/42 Oct/Nov 2024 — Q7 (flow rate, multi-tap); 0580 Examiner Reports 2022-2024. Last reviewed 2026-05-05.

Take this whole topic with you

Step-by-step worked examples — Rate

Step-by-step solutions to past-paper-style questions on rate, written exactly the way a tutor would explain them at the board.

Question type:

Question patterns to master — Rate

Almost every rate exam question is one of these shapes. Learn to spot each one and you will always know how to start.

Direct calculation

Recognise it by

A single instruction — find the density/pressure/rate — with the two quantities supplied and one formula to apply.

How to approach it

Quote the rate formula ( $\rho=\frac{m}{V}$ , $P=\frac{F}{A}$ , $\text{rate}=\frac{\text{change}}{\text{time}}$ ), substitute, and state the answer with its compound unit.

Common trap

Examiner reports flag inverting the rate (computing $\frac{V}{m}$ for density) and omitting the unit from the final answer.

Word problem

Recognise it by

A real-world context — pipes draining a tank, workers sharing a job, more people on a task — with no formula stated.

How to approach it

Express each contributor as a rate (job or volume per unit time), add the rates when they act together, then take the reciprocal for the combined time; for workforce scaling use person-days.

Common trap

Examiner reports flag candidates averaging individual rates or times instead of adding the rates — the lowest-scoring error on combined-rate questions.

Multi-step problem

Recognise it by

Several pieces chained — a volume found first then a mass, or standard pay plus a separate overtime calculation.

How to approach it

Work through each stage in turn, keeping full precision until the end: find the intermediate quantity, apply the rate, then convert units or combine totals.

Common trap

Examiner reports flag premature rounding of an intermediate value and lumping standard and overtime pay together so overtime hours are miscounted.

Show that / prove

Recognise it by

An instruction to show that two values are equal, or to decide and justify which purchase is the better value.

How to approach it

Derive the conversion factor in full (showing the unit change), or compute the comparable unit price for each option and state the conclusion explicitly.

Common trap

Examiner reports flag stating a conversion factor without deriving it, and giving a 'best buy' choice with no supporting comparison.

1Calculate density from mass and volume
CoreDirect calculation• density
Question
A metal block has mass $480\,\text{g}$ and volume $60\,\text{cm}^{3}$ . Find its density.
Step-by-step solution
1. Step 1
  Density $= \dfrac{\text{mass}}{\text{volume}}$ .
  $\rho = \dfrac{480}{60} = 8\,\text{g/cm}^{3}$
Answer
$8\,\text{g/cm}^{3}$
2Compare two purchase options (best buy)
CoreShow that / prove• Adapted from 0580/22 Oct/Nov 2023 Q7• best buy, unit price
Question
Pack A: $750\,\text{ml}$ for $3.20. Pack B: $1.2\,\text{L}$ for $4.80. Which is better value?
Step-by-step solution
1. Step 1
  Convert to common units: A is $750\,\text{ml}$ , B is $1200\,\text{ml}$ .
2. Step 2
  Price per ml: A = $\dfrac{3.20}{750} = 0.00427$ ; B = $\dfrac{4.80}{1200} = 0.00400$ .
3. Step 3
  B is cheaper per ml, so Pack B is better value.
Answer
Pack B (cheaper per ml)
Examiner tip
Always state your reasoning. "Pack B" alone, without showing the comparison, scores zero marks.
3Calculate pressure from force and area
ExtendedDirect calculation• pressure
Question
A force of $250\,\text{N}$ is applied to an area of $0.05\,\text{m}^{2}$ . Find the pressure.
Step-by-step solution
1. Step 1
  Pressure $= \dfrac{\text{force}}{\text{area}}$ .
  $P = \dfrac{250}{0.05} = 5000\,\text{N/m}^{2}$
Answer
$5000\,\text{N/m}^{2}$ (Pa)
4Solve a flow-rate problem with mixed units
ExtendedDirect calculation• flow rate, unit conversion
Question
Water flows at $1.5\,\text{L/s}$ . How long, in hours, to fill a $5400\,\text{L}$ tank?
Step-by-step solution
1. Step 1
  Time in seconds: $\dfrac{5400}{1.5} = 3600\,\text{s}$ .
2. Step 2
  Convert to hours: $\dfrac{3600}{3600} = 1$ hour.
Answer
$1$ hour
5Find mass given density and volume
ExtendedMulti-step problem• Adapted from 0580/22 May/Jun 2024 Q11• density, mass
Question
A cylindrical block of copper has radius $4\,\text{cm}$ and height $10\,\text{cm}$ . The density of copper is $8.96\,\text{g/cm}^{3}$ . Find the mass of the block, giving your answer in kilograms to 3 significant figures.
Step-by-step solution
1. Step 1
  Volume of the cylinder.
  $V = \pi r^{2} h = \pi \times 16 \times 10 = 160\pi \approx 502.655\,\text{cm}^{3}$
2. Step 2
  Rearrange $\rho = \dfrac{m}{V}$ to get $m = \rho V$ .
  $m = 8.96 \times 502.655 \approx 4503.79\,\text{g}$
3. Step 3
  Convert to kilograms: $4503.79 \div 1000 = 4.50\,\text{kg}$ (3 s.f.).
Answer
$4.50\,\text{kg}$
Examiner tip
The 2024 mark scheme awards a method mark for $V = \pi r^{2} h$ and a separate method mark for $m = \rho V$ . Keep full calculator precision until the final rounding step — examiner reports flag premature rounding as the top error here.
6Calculate weekly pay including overtime
ExtendedMulti-step problem• Adapted from 0580/42 Oct/Nov 2022 Q4• rate of pay, applied
Question
Asha is paid $12.50 per hour for a standard $35$ -hour week. Any additional hours are paid at time-and-a-half. One week she works $42$ hours. Find her total pay for that week.
Step-by-step solution
1. Step 1
  Standard pay: $35 \times 12.50 = \$ 437.50$.
2. Step 2
  Overtime hours: $42 - 35 = 7$ hours.
3. Step 3
  Overtime rate: $12.50 \times 1.5 = \$ 18.75$/h.
4. Step 4
  Overtime pay.
  $7 \times 18.75 = 131.25$
5. Step 5
  Total: $\$ 437.50 + $131.25 = $568.75$.
Answer
$568.75
Examiner tip
Examiners reward showing standard pay and overtime pay separately. Candidates who lump everything together and miscount overtime hours typically lose 2 of 4 marks.
7Average rate of cooling
ExtendedDirect calculation• Adapted from 0580/42 May/Jun 2023 Q9• rate of change, applied
Question
A cup of coffee cools from $84^{\circ}\text{C}$ to $36^{\circ}\text{C}$ in $12$ minutes. Find the average rate of cooling in degrees per minute.
Step-by-step solution
1. Step 1
  Temperature drop: $84 - 36 = 48^{\circ}\text{C}$ .
2. Step 2
  Average rate.
  $\text{rate} = \dfrac{48}{12} = 4^{\circ}\text{C/min}$
Answer
$4^{\circ}\text{C/min}$
Examiner tip
The mark scheme accepts the rate as positive ("4°C/min") or signed (" $-4$ °C/min"). State the units explicitly — a bare "4" without °C/min loses the accuracy mark.
8Flow rate — draining a tank with two pipes
ExtendedWord problem• Adapted from 0580/42 Feb/Mar 2024 Q6• flow rate, combined rates
Question
A tank holds $1800\,\text{L}$ . Pipe $A$ drains the tank at $25\,\text{L/min}$ and pipe $B$ at $35\,\text{L/min}$ . (a) If only pipe $A$ is opened, how long does the tank take to empty? (b) If both pipes are opened together, how long does it take?
Step-by-step solution
1. Step 1
  (a) Time with pipe A only.
  $t_A = \dfrac{1800}{25} = 72\,\text{min}$
2. Step 2
  (b) Combined flow rate when both pipes are open: $25 + 35 = 60\,\text{L/min}$ .
3. Step 3
  Combined time.
  $t_{AB} = \dfrac{1800}{60} = 30\,\text{min}$
Answer
(a) $72\,\text{min}$ (b) $30\,\text{min}$
Examiner tip
Examiner reports flag that candidates often try to average the two pipe rates ( $(25+35)/2 = 30$ ) instead of summing them. Rates add when both processes happen simultaneously.
9Show that a density value in g/cm³ matches one in kg/m³
ExtendedShow that / prove• Adapted from 0580/42 May/Jun 2024 Q5• density, show that, unit conversion
Question
Show that a density of $2.7\,\text{g/cm}^{3}$ is the same as $2700\,\text{kg/m}^{3}$ .
Step-by-step solution
1. Step 1
  Convert $1\,\text{g/cm}^{3}$ to $\text{kg/m}^{3}$ .
  $1\,\dfrac{\text{g}}{\text{cm}^{3}} = \dfrac{0.001\,\text{kg}}{10^{-6}\,\text{m}^{3}} = 1000\,\text{kg/m}^{3}$
2. Step 2
  Therefore $2.7\,\text{g/cm}^{3} = 2.7 \times 1000 = 2700\,\text{kg/m}^{3}$ . ✓
Answer
$2.7\,\text{g/cm}^{3} \times 1000 = 2700\,\text{kg/m}^{3}$ , as required.
Examiner tip
The 2024 mark scheme requires the conversion factor of $1000$ to be derived (not just stated). Candidates who write " $\times 1000$ " without showing the volume conversion $\text{cm}^{3} \to \text{m}^{3}$ lose the method mark.
10Combined work rate — three workers painting a fence
ChallengeWord problem• Adapted from 0580/42 Oct/Nov 2023 Q11• combined work rate, stretch, inverse proportion
Question
Alex can paint a fence alone in $6$ hours. Beni can paint the same fence alone in $8$ hours. Chen can paint it alone in $12$ hours. How long do they take to paint the fence working together?
Step-by-step solution
1. Step 1
  Express each worker's rate as a fraction of the job per hour.
  $\text{Alex} = \dfrac{1}{6},\ \text{Beni} = \dfrac{1}{8},\ \text{Chen} = \dfrac{1}{12}$
2. Step 2
  Combined rate (job/hour) — add the rates.
  $\dfrac{1}{6} + \dfrac{1}{8} + \dfrac{1}{12} = \dfrac{4 + 3 + 2}{24} = \dfrac{9}{24} = \dfrac{3}{8}$
3. Step 3
  Time = $\dfrac{1}{\text{rate}}$ .
  $t = \dfrac{1}{3/8} = \dfrac{8}{3}\,\text{h}$
4. Step 4
  Convert: $\dfrac{8}{3}\,\text{h} = 2\,\text{h}\ 40\,\text{min}$ .
Answer
$\dfrac{8}{3}$ hours $= 2$ h $40$ min.
Examiner tip
The 2023 examiner report flags this as one of the lowest-scoring questions on Paper 4: candidates average the times ( $6+8+12 \div 3 = 8.7$ ) instead of adding the rates. Memorise: add rates, take reciprocal for combined time.
11Workforce scaling — more people, less time
ChallengeWord problem• Adapted from 0580/42 May/Jun 2024 Q11• inverse proportion, stretch, person-hours
Question
A construction job takes $15$ workers $24$ days to complete. Assuming every worker contributes equally, how long would the same job take with $20$ workers?
Step-by-step solution
1. Step 1
  Compute total person-days for the job.
  $15 \times 24 = 360\,\text{person-days}$
2. Step 2
  With $20$ workers, days required.
  $t = \dfrac{360}{20} = 18\,\text{days}$
3. Step 3
  Sanity check: more workers $\Rightarrow$ fewer days. $20 > 15$ and $18 < 24$ . ✓
Answer
$18$ days
Examiner tip
The 2024 mark scheme awards a method mark for explicitly computing person-days (or stating that workers and time are in inverse proportion). Candidates who set up a wrong direct-proportion equation often score zero. Always sanity-check that more people gives less time.

Key Formulae — Rate

The formulae you need to memorise for rate on the Cambridge IGCSE 0580 paper, with every variable defined in plain English and a note on when to use it.

Density
$\rho = \dfrac{m}{V}$
$\rho$
density (g/cm $^{3}$ or kg/m $^{3}$ )
$m$
mass
$V$
volume
When to use
Any question about how heavy a substance is per unit volume.
Pressure
$P = \dfrac{F}{A}$
$P$
pressure (Pa = N/m $^{2}$ )
$F$
force (N)
$A$
area (m $^{2}$ )
When to use
Force-area-pressure problems.
General rate
$\text{rate} = \dfrac{\text{quantity changed}}{\text{time taken}}$
When to use
Flow rate, growth rate, fuel consumption, etc.

Key Definitions and Keywords — Rate

Definitions to memorise and the exact keywords mark schemes credit for rate answers — sharpened from recent examiner reports for the 2026 0580 sitting.

Rate
Examiner keyword
A measure comparing two related quantities, usually with different units (e.g. km/h, $/kg).
Density
Examiner keyword
Mass per unit volume.
Pressure
Examiner keyword
Force per unit area.
Unit rate
A rate with denominator $1$ , e.g. $0.30 per ml.

Common Mistakes and Misconceptions — Rate

The traps other students keep falling into on rate questions — taken from recent Cambridge IGCSE 0580 examiner reports and mark schemes — and how to avoid them.

✕Comparing rates in different units
0580/22 best-buy questions
Why it happens
$750\,\text{ml}$ vs $1.2\,\text{L}$ — students compute the price-per-something without converting.
How to avoid it
Convert to the same unit first.
✕Inverting the rate (e.g. computing $\dfrac{V}{m}$ for density)
Why it happens
Rearranging the formula incorrectly under pressure.
How to avoid it
Always write the formula with units: $\rho$ is in $\text{g/cm}^{3}$ — mass on top.
✕Omitting units in the final answer
Why it happens
Students focus on the number and forget the unit.
How to avoid it
Mark schemes require units for full marks. Always include them.

Rate — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Rate

Units

Speed

km per hour, m per second

Wage

dollars per hour, dollars per day

Flow

litres per minute, m³ per second

Population growth

people per year

Heart rate

beats per minute

Fuel efficiency

km per litre, miles per gallon

Flow problems give you a flow rate (e.g. $20\,\text{L/min}$ ) and ask either how much fills in a given time, or how long to fill a given volume.

Volume from rate and time: $V = R \times t$ . Time from volume and rate: $t = V / R$ .

Worked. A tap fills a $240\,\text{L}$ tank at $20\,\text{L/min}$ . How long?

$t = 240 / 20 = 12\,\text{min}$ .

Two taps. When two taps fill the same tank, the combined rate is the SUM of the individual rates. (Same idea as workers in inverse-proportion problems.)

Worked. Tap A fills at $30\,\text{L/min}$ , tap B at $20\,\text{L/min}$ . Both running, how long to fill $300\,\text{L}$ ?

Combined rate: $30 + 20 = 50\,\text{L/min}$ .
Time: $300 / 50 = 6\,\text{min}$ .

Filling AND draining. If a drain operates at $10\,\text{L/min}$ alongside the two taps, net rate is $50 - 10 = 40\,\text{L/min}$ . Time = $300 / 40 = 7.5\,\text{min}$ .

Net rate = inflow − outflow: 30 + 20 − 10 = 40 L/min.

Rate

Short Notes - Rate

Detailed Study Notes

At a glance

What you’ll learn

What a rate is

Best buy — comparing unit rates

Flow rate and time-to-fill

Rate vs ratio — they're not the same

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

Question patterns to master — Rate

1Calculate density from mass and volume

2Compare two purchase options (best buy)

3Calculate pressure from force and area

4Solve a flow-rate problem with mixed units

5Find mass given density and volume

6Calculate weekly pay including overtime

7Average rate of cooling

8Flow rate — draining a tank with two pipes

9Show that a density value in g/cm³ matches one in kg/m³

10Combined work rate — three workers painting a fence

11Workforce scaling — more people, less time

Density

Pressure

General rate

Rate

Density

Pressure

Unit rate

✕Comparing rates in different units

✕Inverting the rate (e.g. computing Vm\dfrac{V}{m}mV​ for density)

✕Omitting units in the final answer

Rate — frequently asked questions

Rate

Short Notes - Rate

Detailed Study Notes

At a glance

What you’ll learn

What a rate is

Best buy — comparing unit rates

Flow rate and time-to-fill

Rate vs ratio — they're not the same

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

Question patterns to master — Rate

1Calculate density from mass and volume

2Compare two purchase options (best buy)

3Calculate pressure from force and area

4Solve a flow-rate problem with mixed units

5Find mass given density and volume

6Calculate weekly pay including overtime

7Average rate of cooling

8Flow rate — draining a tank with two pipes

9Show that a density value in g/cm³ matches one in kg/m³

10Combined work rate — three workers painting a fence

11Workforce scaling — more people, less time

Density

Pressure

General rate

Rate

Density

Pressure

Unit rate

✕Comparing rates in different units

✕Inverting the rate (e.g. computing Vm\dfrac{V}{m}mV​ for density)

✕Omitting units in the final answer

Rate — frequently asked questions

✕Inverting the rate (e.g. computing $\dfrac{V}{m}$ for density)

✕Inverting the rate (e.g. computing $\dfrac{V}{m}$ for density)