Differentiation questions look easy to mark — until you try to do it the way an examiner does. The final answer is rarely the whole story: most of the marks sit in the method, and students lose accuracy marks to slips that have nothing to do with whether they understand calculus. Here's how the marks are actually awarded, and where they leak.
Take a standard "differentiate and find the stationary points" question. A typical Edexcel/AQA mark scheme breaks down like this:
x^n → nx^(n-1)). This is awarded for the attempt, even if a coefficient is wrong.The key examiner principle: method first, accuracy second. A student who differentiates with a slip but then correctly sets it to zero and solves still earns the method marks — and often a follow-through accuracy mark on their (wrong) derivative.
Differentiating 3x^4 − 2x^2 + 7, students write 12x^3 − 4x + 7 — carrying the constant through. The method mark survives (a power was reduced), but the final A1 is lost because the derivative isn't fully correct.
Negative and fractional powers are where accuracy marks vanish: x^(−1) → −x^(−2) trips many students. The M1 holds; the A1 goes.
"Find the coordinates of the stationary point" needs both. Giving only x throws away the final A1 — pure exam technique, not maths.
Work through each script as a decision chain: was a valid method attempted (award M)? Is the result exactly right (then, and only then, award the dependent A)? Did an earlier slip get used correctly later (allow follow-through)? Marking this way means your feedback matches what the exam board would actually say — and students learn that showing method protects most of the marks.
Mark differentiation (and the whole paper) point by point, against your board's scheme.
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