Estimating Gradients: Real-world Applications
Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on estimating gradients of curves through real-world applications and procedural practice, aimed at Grade 8 students.
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Estimating Gradients: Real-world Applications
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Use the grid to estimate gradients and show your working.
1.
Estimate the gradient of the curve y = x^2 at the point where x = 2 by drawing a tangent line using the grid.
[2 marks]2.
On the grid, draw two points close to x=3 on the curve y = 2x + 1. Estimate the gradient of the tangent at x=3.
[3 marks]3.
Using the points (1,3) and (3,7) on the curve, calculate the approximate gradient.
[3 marks]B
Targeted Practice
Estimate the gradient at specific points on various curves and justify your reasoning.
1.
Estimate the gradient of y = √x at x=4 by drawing the tangent line.
[3 marks]2.
At what approximate gradient is the curve y = x^3 changing at x=1? Draw your tangent.
[3 marks]3.
Estimate the gradient of the curve y = 5x - x^2 at x=2 and explain your method.
[4 marks]C
Real-world Applications
Use the grid to estimate gradients in real-life contexts and interpret their meaning.
1.
A car’s speed over time is represented by the curve s(t). Estimate the rate of change of distance at t=5 hours, assuming the curve is y = 3t + 2.
[4 marks]2.
A cyclist’s speed is decreasing along a curved path. Using the grid, estimate the gradient of the tangent to the speed curve at a specific point to determine if the cyclist is accelerating or decelerating.
[4 marks]D
Challenge & Extension
Tackle these advanced problems involving estimation methods and reasoning.
1.
Given the curve y = x^3 + 2x, estimate the gradient at x=2 using tangent drawing on the grid, and compare it with the exact derivative.
[4 marks]2.
Construct the tangent to y=4x - x^2 at x=3. Estimate the gradient and discuss any discrepancies with the exact gradient.
[4 marks]E
Mixed Review & Error Analysis
Attempt a variety of questions and analyze common mistakes.
1.
Estimate the gradient of y = 2x + 5 at x=0 using the grid. What mistake might lead to an incorrect estimate? How can it be fixed?
[3 marks]2.
Calculate the gradient between points (2,7) and (4,15) on y=3x+1. How close is this to the gradient at x=3? Explain your reasoning.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet