Rectangular Hyperbola 2

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Jon Stammers

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Jon Stammers 8 years, 5 months ago

Created this as a copy of Rectangular Hyperbola.

Name	Status	Author	Last Modified
Rectangular Hyperbola	draft	Jon Stammers	17/11/2016 13:59
Rectangular Hyperbola 2	draft	Jon Stammers	17/11/2016 14:01
Rectangular Hyperbola 3	draft	Jon Stammers	17/11/2016 14:03

Question statement

You are given the equation

$\simplify[all]{y({c}x+{d})=({a}x+{b})}.$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	9
b	integer	11
c	integer	-9
d	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-12..12 except 0)

JME function reference

Description

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`

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

Where does the asymptote that is parallel to the $x-axis$ intersect the $y-axis$ ?

Unnamed gap

Advice

Don't forget the following when trying to find asymptotes:

The asyptote that is parallel to the $x$ -axis is found by equating the coefficient of the highest order of $y$ to zero.
Similarly, the asyptote that is parallel to the $y$ -axis is found by equating the coefficient of the highest order of $x$ to zero.
Transposition is almost always required!

Steps:

Transpose to eliminate the fraction: $y(\var{c}x+\var{d}) = \var{a}x+\var{b}$
At this stage we have a coefficient for the highest order of $y$ .

Equate this to zero: $\var{c}x+\var{d}=0$
Transpose and solve for $x$ : $x=-\var{d}/\var{c}$
This is where our asymptote parallel to the $y$ -axis crosses the $x$ -axis.

Going back to step 1, multiply out the bracket: $\var{c}xy+\var{d}y = \var{a}x+\var{b}$
Collect $x$ terms together: $\var{c}xy-\var{a}x+\var{d}y-\var{b} = 0$
Factorise for $x$ : $x(\var{c}y-\var{a})+\var{d}y-\var{b} = 0$
Equate the coefficient of $x$ to zero:

\var{c}y-\var{a}=0
Transpose and solve for $y$ : $y=\var{a}/\var{c}$
This is where our asymptote parallel to the $x$ -axis crosses the $y$ -axis.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Number entry
Number entry		Hasn't run yet
Gap-fill
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Number entry
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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Jon Stammers 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Rectangular Hyperbola 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Jon Stammers 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`