The Calculus Project (Classroom)

Sam Waterfield, Nov 10, 2021

Welcome, student, and thank you for visiting. These GeoGebra applets are designed to run alongside your A-level teaching in Year 1 calculus topics. Your teacher will direct you to the appropriate content outside of class but feel free to explore using your earlier calculus knowledge and geometric intuition. You should find a greater appreciation for the applets contained within as you develop your mathematical methods further. Use the extra questions and instructions found within each applet to focus your explorations.

Table of Contents

  1. Phase 1
    1. 1.1 Estimating gradients of curves
    2. 1.2 Try to graph the derivative function
    3. 1.3 Sketching graphs from derivative information
    4. 1.4 Optimisation - Parabola and Rectangle
    5. 1.5 Optimisation - Cuboid
    6. 1.6 Optimisation - Cylinder
  2. Phase 2
    1. 2.1 Areas under curves
    2. 2.2 Accumulated area function
    3. 2.3 Area above and below the x-axis
    4. 2.4 Area above and below the x-axis - further investigation
    5. 2.5 Area between functions
    6. 2.6 Approximating areas

1.

Phase 1

Applets designed to run alongside Y1 Differentiation (applications).

  • 1. 1.1 Estimating gradients of curves
  • 2. 1.2 Try to graph the derivative function
  • 3. 1.3 Sketching graphs from derivative information
  • 4. 1.4 Optimisation - Parabola and Rectangle
  • 5. 1.5 Optimisation - Cuboid
  • 6. 1.6 Optimisation - Cylinder

1.1.

1.1 Estimating gradients of curves

Applet explorations
[b]1)[/b] Consider the steepness of the curve at each of the labelled points. Is it positive/negative, large/small? Are any gradients easier to estimate than others?[br][br][b]2)[/b] You could plot a tangent line to better visualise the gradients. Drag the point across the curve to change where the tangent touches the curve.[br][br][b]3)[/b] Check your answers and refresh the page to change the graph when you are happy with your estimates. What has all this got to do with calculus?[br][br][b]Summarise any key points at the bottom of the page.[/b]
Applet conclusions
Note any key points from this activity. How can this applet be used to develop our understanding of calculus?
– Sam Waterfield

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Phase 2

Applets designed to run alongside Y1 Integration (applications).

  • 1. 2.1 Areas under curves
  • 2. 2.2 Accumulated area function
  • 3. 2.3 Area above and below the x-axis
  • 4. 2.4 Area above and below the x-axis - further investigation
  • 5. 2.5 Area between functions
  • 6. 2.6 Approximating areas

2.1.

2.1 Areas under curves

Applet explorations
[b]1)[/b] Follow the instructions in the GeoGebra applet and carefully consider each of the accompanying questions before moving on. This will outline the fundamental aims for this topic.[br][br][b]2)[/b] Write out a table of findings once you get to Question 5. Can you make any predictions about later values?[br][br][b]3)[/b] Test out your predictions using the applet after clicking ‘Finished!’ Does changing the starting point change your prediction?[br][br][b]Summarise any key points at the bottom of the page.[/b]
Applet conclusions
Note any key points from this activity. How can this applet be used to develop our understanding of calculus?[br]
– Sam Waterfield, Peter Sassman

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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Information