Transpose rational formula

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Merryn Horrocks

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Ready to use

1 year, 2 months ago

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Merryn Horrocks 1 year, 2 months ago

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Merryn Horrocks 1 year, 2 months ago

Gave some feedback: Ready to use

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Don Shearman 3 years, 8 months ago

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Question statement

Make $x$ the subject of $\displaystyle{y=\var{formula[select]}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

formula	list	List of 2 items
answer	list	List of 2 items
select	integer	0

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[latex("\\frac\{r+x\}\{1-rx\}"),latex("\\sqrt\{\\frac\{x-1\}\{x+1\}\}")]

JME function reference

Description

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

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Generated value: `list`

[ latex("\\frac\{r+x\}\{1-rx\}"), latex("\\sqrt\{\\frac\{x-1\}\{x+1\}\}") ]

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
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Gap-fill

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$x=$ Unnamed gap

Advice

$\begin{align}y&=\frac{r+x}{1-rx}\\ y(1-rx) &= r+x\qquad\text{multiply both sides by }(1-rx)\\y-ryx &= r+x\qquad\textrm{expand LHS}\\y-r &=x+ryx\qquad\text{rearrange}\\y-r&=x(1+ry)\qquad\text{factorise RHS}\\\frac{y-r}{1+ry}&=x\qquad\text{divide by }(1+ry)\\x&=\frac{y-r}{1+ry} \end{align}$

$\begin{align} y&=\sqrt{\frac{x-1}{x+1}}\\y^2&=\frac{x-1}{x+1}\qquad\text{square}\\y^2(x+1)&=x-1\qquad\text{multiply by }(x+1)\\y^2x+y^2&=x-1\qquad\text{expand LHS}\\y^2x-x&=-y^2-1\qquad\text{rearrange}\\x(y^2-1)&=-y^2-1\qquad\text{factorise LHS}\\x&=\frac{-y^2-1}{y^2-1} \end{align}$

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This question is used in the following exams:

Formulae and Transposition by Don Shearman in HELM books.
HELM Book 1.5 exercises by Merryn Horrocks in HELM books.

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Merryn Horrocks 1 year, 2 months ago

Merryn Horrocks 1 year, 2 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

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Generated value: `list`

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Transpose rational formula

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year, 2 months ago

Merryn Horrocks 1 year, 2 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`