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CXC CAPE · · Pure Mathematics

Applications of differentiation
Practice Questions

40 CXC CAPE Pure Mathematics questions on Applications of differentiation, each with instant feedback and a full examiner-style mark scheme.

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Try 2 sample questions on Applications of differentiation

Question 1 · 1 mark · Difficulty 1/3

What is a stationary point of a curve?

  1. A point at which the gradient is zero
  2. A point at which the curve crosses the x-axis
  3. A point at which the curve is steepest
  4. A point at which the curve is undefined
Show answer & explanation
✓ Answer: A — A point at which the gradient is zero
Award 1 mark. The tangent there is horizontal.
Question 2 · 1 mark · Difficulty 1/3

How is the gradient of the tangent to a curve at a point found?

  1. By substituting the point into the equation of the curve
  2. By evaluating the derivative at that point
  3. By integrating the function
  4. By finding the second derivative
Show answer & explanation
✓ Answer: B — By evaluating the derivative at that point
Award 1 mark. The derivative gives the gradient as a function of x.
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20 questions · 25 min · free

CXC CAPE Pure Mathematics: Applications of differentiation FAQ

Is Kramizo free for CXC CAPE students preparing for Pure Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Applications of differentiation practice with other Pure Mathematics topics or even switch to a totally different CXC CAPE subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Applications of differentiation questions aligned to the official CXC CAPE Pure Mathematics syllabus?
Every question is written against the published CXC CAPE Pure Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CXC CAPE paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from CXC CAPE.
How is Applications of differentiation typically tested on CXC CAPE Pure Mathematics papers?
Applications of differentiation appears across multiple question types on real CXC CAPE Pure Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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