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Desmos graphs

The sine graph

Here is the graph of y=sin( x). Drag the large orange point to move it along the graph. Click on any orange point to toggle a label showing its coordinates.

The cosine graph

Here is the graph of y=cos( x). Drag the large orange point to move it along the graph. Click on any orange point to toggle a label showing its coordinates.

The tan graph

Here is the graph of y=tan( x) with dashed lines showing the asymptotes.

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A12c - Graphs of trigonometric functions

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Here is the graph of y=sin( x). Drag the large orange point to move it along the graph. Click on any orange point to toggle a label showing its coordinates. Here is the graph of y=cos( x). Drag the large orange point to move it along the graph.

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https://padlet.com/rdownes/Algebra1
https://padlet.com/rdownes/Algebra2
https://padlet.com/rdownes/Algebra3
https://padlet.com/rdownes/Algebra4
https://padlet.com/rdownes/Algebra5
https://padlet.com/rdownes/Algebra6
https://padlet.com/rdownes/Algebra7
https://padlet.com/rdownes/Algebra8
https://padlet.com/rdownes/Algebra9
https://padlet.com/rdownes/Algebra10
https://padlet.com/rdownes/Algebra11
https://padlet.com/rdownes/Algebra12

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Teachers: log in to access the following:

Slides in PPTX (with click-to-reveal answers)

Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Further resources on external sites (log in to see links):

Links to past exam questions

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A11b - Identifying turning points of quadratic functions by completing the square

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Teachers: log in to access the following: Slides in PPTX (with click-to-reveal answers) Slides in PDF (one slide per page, suitable for importing into IWB software) Worksheet (with space for student work) Handout (slides with exercises only; 4 per page for reduced printing) Further resources on external sites (log in to see links): Links to past exam questions Teachers: log in to access these.

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Before sketching quadratics, make sure that you can identify the equations of quadratic curves given a sketch, as covered in lessons A11a and A11b.

Interactive GeoGebra Activity: sketching quadratics

Generate new questions by clicking the "New question" button. Change the style of the question by adjusting the horizontal slider. To see what your sketch should look like, simply drag down the vertical slider. You can move the labels of the key points around a little to aid visibility.

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Before sketching quadratics, make sure that you can identify the equations of quadratic curves given a sketch, as covered in lessons A11a and A11b. Generate new questions by clicking the "New question" button. Change the style of the question by adjusting the horizontal slider.

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Note: linear graphs are covered in lesson A9a, so this lesson focuses on quadratic, cubic and reciprocal graphs.

Links to past exam questions

Interactive GeoGebra activity: the general quadratic and cubic curves

The general quadratic in \(x\) may be expressed in the form \(ax^{2}+bx+c\) and the general cubic in \(x \) may be expressed in the form \(ax^{3}+bx^{2}+cx+d\), where \(a, b, c,\) and \(d\) (in the case of the cubic) are constants. Adjust the sliders to see how changing each of \(a, b, c,\) and \(d\) impacts the shape of the curve. Use your mouse's scroll function to zoom in and out. Hit the reset button in the top corner to return the activity to its original state.

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A12a - Graphs of linear functions, quadratic functions, simple cubic functions, and the reciprocal function

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Note: linear graphs are covered in lesson A9a, so this lesson focuses on quadratic, cubic and reciprocal graphs. Links to past exam questions The general quadratic in \(x\) may be expressed in the form \(ax^{2}+bx+c\) and the general cubic in \(x \) may be expressed in the form \(ax^{3}+bx^{2}+cx+d\), where \(a, b, c,\) and \(d\) (in the case of the cubic) are constants.

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Plotting graphs using a table of values is a helpful skill for this lesson. This is covered in: The Gamma exercise and subsequent slides assume knowledge of index laws, transformations of functions, and arithmetic with decimals. These are covered in:

Teachers: log in to access the following:

Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Links to past exam questions

Teachers: log in to access these.

Teachers: log in to view this content.

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Plotting graphs using a table of values is a helpful skill for this lesson. This is covered in: The Gamma exercise and subsequent slides assume knowledge of index laws, transformations of functions, and arithmetic with decimals.

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Teachers: log in to access the following:

Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Links to past exam questions

Teachers: log in to access these.

Teachers: log in to view this content.

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A13a - Sketch translations and reflections of a given function

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Teachers: log in to access the following: Slides in PDF (one slide per page, suitable for importing into IWB software) Worksheet (with space for student work) Handout (slides with exercises only; 4 per page for reduced printing) Links to past exam questions Teachers: log in to access these.

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Moore's Law Is Ending... So, What's Next?

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Synthesizing Obama: Learning Lip Sync from Audio