Solve equations which include a single root (e.g. \sqrt{x}=blah)

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Xiaodan Leng 5 years, 8 months ago

Created this as a copy of Solve equations which include a single root (e.g. \sqrt{x}=blah).

Name	Status	Author	Last Modified
Solve equations which include a single odd power (e.g. x^odd=blah)	Ready to use	Ben Brawn	20/03/2025 04:05
Solve equations which include a single even power (e.g. x^even=blah)	Ready to use	Ben Brawn	20/03/2025 04:14
Solve equations which include a single root (e.g. \sqrt{x}=blah)	Ready to use	Ben Brawn	21/02/2025 08:07
Eirik's copy of Solve equations which include a single root (e.g. \sqrt{x}=blah)	draft	Eirik Heen	14/06/2017 09:28
Hannah's copy of Solve equations which include a single root (e.g. \sqrt{x}=blah)	draft	Hannah Bartholomew	26/06/2018 17:17
Solve equations which include a single odd power (e.g. x^odd=blah)	draft	Xiaodan Leng	11/07/2019 02:28
Solve equations which include a single root (e.g. \sqrt{x}=blah)	draft	Xiaodan Leng	11/07/2019 02:28
Solve equations which include a single even power (e.g. x^even=blah)	draft	Xiaodan Leng	11/07/2019 02:29
Leonardo's copy of Solve equations which include a single odd power (e.g. x^odd=blah)	draft	Leonardo Juliano	30/08/2019 13:59

There are 3 other versions that do you not have access to.

Question statement

Please complete the following.

Give any introductory information the student needs.

			Name	Type	Generated Value

intpower	integer	9
intrhs	integer	2
intsoln	number	512

			Name	Type	Generated Value

bpower	integer	4
bnice	integer	-2
bsoln	number	16
bxcoeff	integer	-1
bb	integer	56
bc	integer	58

			Name	Type	Generated Value

dpower	integer	7
dc	integer	62
db	integer	33
ddenom	integer	7

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..9)

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`

→ Used by:

intrhs
intsoln

Advice
"Part a)" - prompt

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

If $\sqrt[\var{intpower}]{x}=\var{intrhs}$ , then $x=$ Unnamed gap.

Advice

a) Given $\sqrt[\var{intpower}]{x}=\var{intrhs}$ , we raise both sides to the power of $\var{intpower}$ to get $x$ by itself.

$\sqrt[\var{intpower}]{x}$	$=$	$\var{intrhs}$

$\left(\sqrt[\var{intpower}]{x}\right)^{\var{intpower}}$	$=$	$\simplify[basic]{({intrhs})^{intpower}}$

$x$	$=$	$\var{intsoln}$

b) Given $\simplify{{bxcoeff}y^(1/{bpower})+{bb}}=\var{bc}$ , we can rearrange the equation to get $y^\frac{1}{\var{bpower}}$ by itself and then we can raise both sides to the power of $\var{bpower}$ to get $y$ by itself.

$\simplify{{bxcoeff}y^(1/{bpower})+{bb}}$	$=$	$\var{bc}$

$\simplify{{bxcoeff}y^(1/{bpower})}$	$=$	$\simplify[basic]{{bc}-{bb}}$

$\simplify{{bxcoeff}y^(1/{bpower})}$	$=$	$\simplify{{bc-bb}}$

$y^\frac{1}{\var{bpower}}$	$=$	$\simplify[!basic]{{bc-bb}/{bxcoeff}}$

$y^\frac{1}{\var{bpower}}$	$=$	$\simplify{{bc-bb}/{bxcoeff}}$

$\left(y^\frac{1}{\var{bpower}}\right)^{\var{bpower}}$	$=$	$\simplify[basic]{({(bc-bb)/bxcoeff})^{bpower}}$

$y$	$=$	$\var{bsoln}$

c) Given $\displaystyle{\simplify{(root(z+{db},{dpower}))/{ddenom}}}=\var{dc}$ , we can rearrange the equation to get $\simplify{(root(z+{db},{dpower}))}$ by itself, then we can raise both sides to the power of $\var{dpower}$ , and finally rearrange to get $z$ by itself.

$\displaystyle{\simplify{(root(z+{db},{dpower}))/{ddenom}}}$	$=$	$\var{dc}$

$\displaystyle{\simplify{(root(z+{db},{dpower}))}}$	$=$	$\simplify[basic]{{dc}*{ddenom}}$

$\displaystyle{\simplify{(root(z+{db},{dpower}))}}$	$=$	$\var{dc*ddenom}$

$\left(\sqrt[\var{dpower}]{\simplify{z+{db}}}\right)^\var{dpower}$	$=$	$\simplify[basic]{({dc*ddenom})^{dpower}}$

$\simplify{z+{db}}$	$=$	$\simplify[basic]{-{abs(dcddenom)}^{dpower}}$ $\simplify[basic]{({abs(dcddenom)})^{dpower}}$ $\simplify[basic]{({(dc*ddenom)})^{dpower}}$

$z$	$=$	$\simplify[basic]{-{abs(dcddenom)}^{dpower}-{db}}$ $\simplify[basic]{({abs(dcddenom)})^{dpower}-{db}}$ $\simplify[basic]{({(dc*ddenom)})^{dpower}-{db}}$

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Mathematical expression
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Solve equations which include a single root (e.g. \sqrt{x}=blah)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Solve equations which include a single root (e.g. \sqrt{x}=blah)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`