Standard graph shapes
Edexcel 1MA1 routinely tests sketch-and-recognise on Paper 1 (non-calculator), particularly Higher. Pupils need to know the shape, key features, and where the graph crosses the axes.
Linear: y = mx + c
A straight line. Gradient m, y-intercept c. Slope upward if m > 0, downward if m < 0.
Quadratic: y = ax² + bx + c
A parabola. Opens upward if a > 0, downward if a < 0. One turning point. Has 0, 1, or 2 real roots.
Cubic: y = ax³ + bx² + cx + d
S-shaped curve. If a > 0, comes from bottom-left to top-right; if a < 0, top-left to bottom-right. Up to 2 turning points and up to 3 real roots.
Reciprocal: y = a/x (a ≠ 0)
Two branches in opposite quadrants — Q1+Q3 if a > 0, Q2+Q4 if a < 0. Asymptotes along the x-axis and y-axis. The graph never touches them.
Exponential: y = a^x (a > 0, a ≠ 1)
If a > 1: increasing, passes through (0, 1), asymptote y = 0 as x → −∞. If 0 < a < 1: decreasing, passes through (0, 1), asymptote y = 0 as x → +∞.
Trigonometric (Higher only)
- y = sin(x): wave from −1 to 1, period 360°, sin(0) = 0.
- y = cos(x): wave from −1 to 1, period 360°, cos(0) = 1.
- y = tan(x): repeating period 180°, asymptotes at 90° + 180°n.
Common Edexcel mark-scheme phrasing
- B1 for correct general shape.
- B1 for axis intercepts shown.
- B1 for asymptotes drawn (reciprocal/exponential) or correct period (trig).
⚠Common mistakes— Common errors
- Drawing a quadratic as a "V" (that's a modulus graph, not a parabola).
- Forgetting the reciprocal has two branches.
- Drawing exponential touching the x-axis (it approaches but never reaches).
- Sketching cosine starting at 0 (it starts at 1 — that's sine starting at 0).
AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves