Estimating Gradients: Problem Solving & Reasoning
Mathematics
Year 9
11 questions
~22 mins
3 views0 downloads
About This Worksheet
A worksheet focused on estimating gradients of curves by drawing tangents and calculating their slopes. Designed to develop procedural skills and reasoning for Year 9 students.
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Estimating Gradients: Problem Solving & Reasoning
Subject: MathematicsGrade: Year 9
Name:
Date:
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Untitled Worksheet
Grade Year 9
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Using the graph of y = x^2, estimate the gradient of the curve at x = 2 by drawing a tangent and calculating the slope between two points on the tangent.
[3 marks]2.
Estimate the gradient of y = 3x + 2 at the point where x = 1. Use the grid to draw a tangent near x=1 and calculate the slope.
[3 marks]3.
On the graph of y = √x, draw a tangent at a point near x = 4. Estimate the gradient by drawing two points on the tangent and calculating the slope.
[3 marks]4.
Explain why estimating the gradient from a graph can sometimes lead to inaccuracies. Give an example scenario.
[4 marks]5.
Estimate the gradient at x = -1 for the curve y = x^3 by drawing a tangent and calculating the slope.
[3 marks]6.
Given the function y = 2x - 5, estimate the gradient at x = 0 by drawing a tangent. How does the estimated gradient compare to the actual gradient?
[4 marks]7.
On the graph of y = x^2, estimate the gradient at x = 3. Draw the tangent and note down the approximate gradient.
[3 marks]8.
A student estimates the gradient at x=2 for y= x^2 as 2. Do you agree? Explain your reasoning.
[4 marks]9.
Estimate the gradient at x = 0.5 for y = x^3 using the grid. Use two points on the tangent to find the slope.
[3 marks]10.
Challenge: For y = x^4, estimate the gradient at x=1 by drawing a tangent. How does the gradient change as x increases?
[4 marks]11.
Estimate the gradient at x = 2 for y = x^2 + 3x. Draw the tangent and note the estimated slope.
[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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet