Drawing: Challenge & Extension on Tangents to Curves
Mathematics
Grade 8
10 questions
~20 mins
1 views0 downloads
About This Worksheet
This worksheet challenges students to draw and analyze tangents to various curves, developing their procedural and reasoning skills in algebraic graph drawing.
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Drawing: Challenge & Extension on Tangents to Curves
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Practice Questions
Answer all questions carefully. Use the grid to draw and demonstrate your solutions where required.
1.
Construct the tangent to the curve y = x^2 at the point where x = 3. Show your working on the grid.
[3 marks]2.
Plot the graph of y = 2x + 1 and draw the tangent to the parabola y = x^2 at the point where x = 2.
[4 marks]3.
Identify the point of tangency when drawing the tangent to y = x^3 at x = 1. Mark the point clearly on the grid.
[2 marks]4.
Construct the tangent to the curve y = √x at x = 4. Show all steps on the grid.
[3 marks]5.
Draw the curve y = x^2 + 2x + 1 and then sketch the tangent to the curve at x = -1. Use different colors for the curve and the tangent.
[4 marks]6.
Construct the tangent lines to the curve y = x^3 - 3x at x = -2 and x = 2. Compare their slopes visually.
[4 marks]7.
A company designs a ramp modeled by y = 0.5x for x between 0 and 10. Draw the tangent to this ramp at x = 5 and explain its significance in real-world application.
[3 marks]8.
Identify and correct the mistake in the following construction: The tangent to y = x^2 at x=2 is drawn with a slope of 4, but the line is not tangent at the point.
[3 marks]9.
Draw the curve y = x^4 and construct the tangent at the point where x = 1. Use the grid to show the tangent clearly.
[3 marks]10.
Challenge: Given the curve y = x^3 - 6x^2 + 9x, construct the tangent line at the local maximum point and explain how you identified this point.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet