2.6.2 Task 1

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Merryn Horrocks

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Merryn Horrocks

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Ready to use

10 months ago

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Merryn Horrocks 10 months ago

Published this.

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Merryn Horrocks 10 months ago

Gave some feedback: Ready to use

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Merryn Horrocks 10 months ago

Created this as a copy of 2.6.2 Annuli between circles.

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Question statement

Draw the annulus defined by the inequalities

$\var{R12}<(\var{simplify(expression("x-"+Cx),"all")})^2+(\var{simplify(expression("y-"+Cy),"all")})^2<\var{R22}$

Give any introductory information the student needs.

			Name	Type	Generated Value

R1	integer	4
R12	integer	16
R2	integer	9
R22	integer	81
Cx	integer	0
Cy	integer	1

			Name	Type	Generated Value

correctGraph	jsxgraphboard	HTML node
xmin	integer	-10
ymin	integer	-9
xmaxtemp	integer	10
ymaxtemp	integer	11
xmax	integer	10
ymax	integer	11
graph	jsxgraphboard	HTML node

			Name	Type	Generated Value

expr

expression

x^2 + (y - 1)^2

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..5)

JME function reference

Description

The inner radius

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

R12
R2
correctGraph

This variable doesn't seem to be used anywhere.

Parts

Extension

Extension

Ask the student a question, and give any hints about how they should answer this part.

Drag the blue point to move the centre of the circles.

Then drag the red point to set the radius for the inner circle.

Finally drag the black point to set the radius for the outer circle.

{graph}

Advice

The quantity $\var{expr}$ is the square of the distance of a point $(x, y)$ from the point $(\var{Cx},\var{Cy})$.

Hence, as we saw earlier, the left-hand inequality

$\var{R12} < \var{expr}\qquad$ which is the same as $\qquad \var{expr} > \var{R12}$

is the region exterior to the circle $C_1$ centre $(\var{Cx}, \var{Cy})$ radius $\var{R1}$.

Similarly the right-hand inequality

$\var{expr} < \var{R22}$

defines the interior of the circle $C_2$ centre $(\var{Cx}, \var{Cy})$ radius $\var{R2}$. Hence the double inequality holds for any point in the annulus between $C_1$ and $C_2$.

{correctGraph}

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Merryn Horrocks 10 months ago

Merryn Horrocks 10 months ago

Merryn Horrocks 10 months ago

Error in variable testing condition

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Generated value: `integer`

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2.6.2 Task 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 10 months ago

Merryn Horrocks 10 months ago

Merryn Horrocks 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Extension

Generated value: `integer`