Pure · Algebra & functions
Chapter 1 · 3
The idea
Sketching curves
Sketching standard curves from their key features — intercepts, repeated-root behaviour, and the asymptotes of reciprocals — and finding where curves meet.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
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Pure · Algebra & functions
Sketching curves
Sketching standard curves from their key features — intercepts, repeated-root behaviour, and the asymptotes of reciprocals — and finding where curves meet.
Why it works
Shape, not points
"Sketch the curve" is not an invitation to plot points — a sketch earns its marks by telling the curve's story: where it cuts, where it touches, which way its ends run, where it blows up. Sketching is capturing the shape and the few features that pin a curve down. Start with the intercepts: the -intercept is the value at ; the -intercepts (roots) are where . For a factorised curve the roots are read straight off — — and gives .Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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