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HomeCXC CSEC MathematicsGraphs: Gradients of curves — estimation of gradient using tangent at a point
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Graphs: Gradients of curves — estimation of gradient using tangent at a point
Practice Questions

20 CXC CSEC Mathematics questions on Graphs: Gradients of curves — estimation of gradient using tangent at a point, each with instant feedback and a full examiner-style mark scheme.

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Try 2 sample questions on Graphs: Gradients of curves — estimation of gradient using tangent at a point

Question 1 · 1 mark · Difficulty 2/3

A graph shows the temperature (T °C) of rum during distillation in Trinidad plotted against time (t minutes). At t = 15 minutes, a tangent is drawn to the curve. The tangent passes through points (10, 65) and (20, 85). What is the gradient of the curve at t = 15 minutes?

  1. 1.5 °C per minute
  2. 2.0 °C per minute
  3. 3.0 °C per minute
  4. 4.0 °C per minute
Show answer & explanation
✓ Answer: B2.0 °C per minute
Award 1 mark for calculating gradient = (85 - 65)/(20 - 10) = 20/10 = 2.0 °C per minute. A is incorrect due to arithmetic error. C is incorrect, likely from calculating 20 - 10 = 10 but using 30 as rise. D is incorrect from calculation error.
Question 2 · 1 mark · Difficulty 2/3

The diagram shows the distance (d km) traveled by a fishing boat in Grenada against time (t hours). A tangent is drawn at t = 2.5 hours passing through (1, 8) and (4, 23). Calculate the speed of the boat at t = 2.5 hours.

  1. 3 km/h
  2. 5 km/h
  3. 7.5 km/h
  4. 15 km/h
Show answer & explanation
✓ Answer: B5 km/h
Award 1 mark for gradient = (23 - 8)/(4 - 1) = 15/3 = 5 km/h. Speed is the rate of change of distance with time, which is the gradient. A is incorrect from calculation error. C is incorrect, possibly from (23-8)/2. D is incorrect from using only the rise (23-8).
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CXC CSEC Mathematics: Graphs: Gradients of curves — estimation of gradient using tangent at a point FAQ

How many CXC CSEC Mathematics questions on Graphs: Gradients of curves — estimation of gradient using tangent at a point are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Graphs: Gradients of curves — estimation of gradient using tangent at a point for CXC CSEC 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 CXC 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 CXC CSEC 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 Graphs: Gradients of curves — estimation of gradient using tangent at a point practice with other Mathematics topics or even switch to a totally different CXC 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 Graphs: Gradients of curves — estimation of gradient using tangent at a point questions aligned to the official CXC CSEC Mathematics syllabus?
Every question is written against the published CXC CSEC 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 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.
How is Graphs: Gradients of curves — estimation of gradient using tangent at a point typically tested on CXC CSEC Mathematics papers?
Graphs: Gradients of curves — estimation of gradient using tangent at a point appears across multiple question types on real CXC CSEC 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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