Estimate the Gradient of a Curve | GCSE Grade 9 Maths | Mr Mathematics

Learn how to estimate the gradient of a curve at a point using a tangent line and interpret the result as an instantaneous rate of change. We use a volume–time graph (water filling a container) and find the gradient at t = 17.5 s by drawing a tangent and computing ΔV/Δt. Then we explain what the gradient means in context: the volume is increasing at about 1 litre per second at that instant. Perfect for GCSE and A‑Level students practicing rates of change and reading gradients from non‑linear graphs. Download the full lesson (notes + worksheet + answers): https://mr-mathematics.com/product/in... What you’ll learn 🟣 How to place a tangent accurately at a given point on a curve 🟣 How to select sensible points on the tangent and calculate gradient m = Δy/Δx 🟣 Interpreting gradient as an instantaneous rate of change with correct units 🟣 Common mistakes to avoid (secant vs tangent, poor scale reading, rounding) Chapters 0:00 Problem setup: volume–time graph 0:27 Where to draw the tangent at t = 17.5 s 0:58 Choosing two clear points on the tangent 1:30 Calculating the gradient ΔV/Δt 2:05 Interpreting “1 litre per second” in context 2:35 Tips to improve accuracy + exam advice 3:00 Where to get the worksheet and further practice Hashtags #Maths #GCSEMaths #ALevelMaths If this helped, please like the video, drop your questions in the comments, and subscribe for more step‑by‑step GCSE and A‑Level tutorials. Share this with a classmate revising rates of change!