PrepWisePrepWiseArea Under Curves
GraphsDeep Dive

Step-by-Step Process

Part of Area Under Curves — GCSE Mathematics

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

  1. Identify the strip width h and the number of strips n
  2. List the x-values at each strip boundary: x₀, x₁, x₂, ..., xₙ
  3. Calculate (or read from the graph) the y-value at each x-value
  4. Identify: first y-value = y₀, last y-value = yₙ, middle values = y₁ to yₙ₋₁
  5. Apply the formula: Area ≈ h/2 × (y₀ + yₙ + 2(y₁ + y₂ + ... + yₙ₋₁))
  6. 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.

The Trapezium Rule FormulaOverestimate or Underestimate?Measuring What You Cannot Calculate DirectlyArea Under a Curve — Core Principles

Practice Questions for Area Under Curves

On a velocity-time graph, what does the area under the curve represent?

  • A. The acceleration
  • B. The average velocity
  • C. The distance (or displacement) travelled
  • D. The speed at a given moment
1 markfoundation

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.

2 markshigher

Quick Recall Flashcards

What is the trapezium rule used for?
Estimating the area under a curve by dividing it into trapezium-shaped strips. Each strip is a trapezium (not a rectangle or triangle). The more strips used, the more accurate the estimate. It is an approximation — the actual area is slightly different because the tops of the strips are straight lines, not curves.
What does the area under a speed-time graph represent?
Distance travelled. Area under a speed-time graph = distance travelled This works for any speed-time or velocity-time graph. Even if the graph is curved, the area still represents distance. Units: if speed is m/s and time is s, then area has units of metres (m).

Want to test your knowledge?

PrepWise has 9 exam-style questions and 10 flashcards for Area Under Curves — with adaptive difficulty and instant feedback.

Join Alpha

Previous

The Trapezium Rule Formula

Next

Overestimate or Underestimate?