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HomeCIE IGCSE MathematicsAlgebra and Graphs: Gradient of a curve and rate of change (tangents)
CIE · IGCSE · Mathematics

Algebra and Graphs: Gradient of a curve and rate of change (tangents)
Practice Questions

40 CIE IGCSE Mathematics questions on Algebra and Graphs: Gradient of a curve and rate of change (tangents), each with instant feedback and a full examiner-style mark scheme.

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✨ Revision guide includes key terms, worked examples and exam technique for Algebra and Graphs: Gradient of a curve and rate of change (tangents).

Try 2 sample questions on Algebra and Graphs: Gradient of a curve and rate of change (tangents)

Question 1 · 1 mark · Difficulty 1/3

The graph shows the distance travelled by a car over time. A tangent is drawn to the curve at point P. What does the gradient of this tangent represent?

  1. The total distance travelled
  2. The instantaneous speed at point P
  3. The average speed for the whole journey
  4. The acceleration at point P
Show answer & explanation
✓ Answer: BThe instantaneous speed at point P
Award 1 mark for identifying that the gradient of a distance-time curve gives speed/velocity. A is incorrect — the total distance is read from the y-axis, not from a gradient. C is incorrect — average speed would require the gradient of a chord, not a tangent. D is incorrect — acceleration would be the gradient of a speed-time graph, not a distance-time graph.
Question 2 · 1 mark · Difficulty 1/3

The graph shows the distance travelled by a car over time. A tangent is drawn to the curve at point P. What does the gradient of this tangent represent?

  1. The total distance travelled
  2. The instantaneous speed at point P
  3. The average speed for the whole journey
  4. The acceleration at point P
Show answer & explanation
✓ Answer: BThe instantaneous speed at point P
Award 1 mark for identifying that the gradient of a tangent to a distance-time curve gives instantaneous speed. A is incorrect — distance is read from the y-axis, not from the gradient. C is incorrect — average speed would be calculated from total distance ÷ total time, not from a tangent. D is incorrect — acceleration would be the gradient of a speed-time graph, not a distance-time graph.
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CIE IGCSE Mathematics: Algebra and Graphs: Gradient of a curve and rate of change (tangents) FAQ

How many CIE IGCSE Mathematics questions on Algebra and Graphs: Gradient of a curve and rate of change (tangents) are there on Kramizo?
Kramizo currently has 40 exam-board-aligned practice questions on Algebra and Graphs: Gradient of a curve and rate of change (tangents) for CIE IGCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real CIE paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for CIE IGCSE students preparing for 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 Algebra and Graphs: Gradient of a curve and rate of change (tangents) practice with other Mathematics topics or even switch to a totally different CIE 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 Algebra and Graphs: Gradient of a curve and rate of change (tangents) questions aligned to the official CIE IGCSE Mathematics syllabus?
Every question is written against the published CIE IGCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CIE 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 CIE.
How is Algebra and Graphs: Gradient of a curve and rate of change (tangents) typically tested on CIE IGCSE Mathematics papers?
Algebra and Graphs: Gradient of a curve and rate of change (tangents) appears across multiple question types on real CIE IGCSE 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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