This deep dive covers Step-by-Step Process within Area Under Curves for GCSE Mathematics. Revise Area Under Curves in Graphs for GCSE Mathematics with 9 exam-style questions and 10 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 11
Practice
9 questions
Recall
10 flashcards
Step-by-Step Process
- Identify the strip width h and the number of strips n
- List the x-values at each strip boundary: x₀, x₁, x₂, ..., xₙ
- Calculate (or read from the graph) the y-value at each x-value
- Identify: first y-value = y₀, last y-value = yₙ, middle values = y₁ to yₙ₋₁
- Apply the formula: Area ≈ h/2 × (y₀ + yₙ + 2(y₁ + y₂ + ... + yₙ₋₁))
- Include units in your answer (e.g. m, km, litres)
Alternative approach: calculate each individual trapezium using Area = ½(a + b)h, then add them all up. This gives the same answer.
Keep building this topic
Read this section alongside the surrounding pages in Area Under Curves. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Area Under Curves
On a velocity-time graph, what does the area under the curve represent?
Explain whether the trapezium rule gives an overestimate or underestimate for the area under the curve y = x² between x = 0 and x = 3. Justify your answer.
Quick Recall Flashcards
9 questions on Area Under Curves — practise free
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