Year 10 Maths • AC9M10M02 • Authored homework
Logarithmic scales in context
Interpret and use logarithmic scales in applied contexts involving very small and very large quantities, such as pH, sound intensity, earthquakes and scientific measurement. Show working, use correct units and check reasonableness.
Part A
Short-answer questions
Explain why logarithmic scales are useful for very large ranges of values.
What does one unit increase on a base-10 logarithmic scale usually represent?
On the Richter-style earthquake scale, what does a difference of 1 magnitude suggest about scale size?
State whether pH 3 is more acidic or less acidic than pH 5.
How many times greater is 10^6 than 10^4?
Write 1000 as a power of 10.
Write 0.001 as a power of 10.
Explain why equal spacing on a logarithmic graph does not mean equal additive increases.
Name one real logarithmic scale.
Correct this misconception: “A logarithmic scale increases by adding the same amount each step.”
Part B
Long-answer questions
Compare values of 10^2, 10^4 and 10^6 and explain how they would appear on a logarithmic scale.
Explain why pH 4 is ten times more acidic than pH 5, using the idea of powers of ten.
A sound is 100 times more intense than another. Express this as a difference of powers of ten.
A graph uses a logarithmic vertical scale for population. Explain why this may make exponential growth easier to compare.
Compare an earthquake of magnitude 6 with magnitude 4 in terms of scale steps, stating any assumptions.
Create a small table of values from 10^-3 to 10^3 and describe their spacing on a logarithmic axis.
Explain the difference between multiplying by 10 and adding 10 on an ordinary scale.
A student reads a logarithmic graph as if it were linear. Describe the mistake and its likely effect on interpretation.
Choose an applied context where data varies over many powers of ten and justify why a logarithmic scale helps.
Write a full explanation of a logarithmic scale using one applied example, including powers of ten and interpretation.
Part C
Research and understanding task
Research one logarithmic scale, such as pH, decibels, earthquake magnitude or astronomical brightness. Explain what each step means, give two example values, and describe why a linear scale would be less useful.