Solve an equation in algebraic fractions

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Bill Foster

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6 years, 4 months ago

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Bill Foster 6 years, 4 months ago

Gave some feedback: Ready to use

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Solve an equation in algebraic fractions	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Solve an equation in algebraic fractions	draft	Luis Hernandez	30/11/2018 00:45
Auflösen einer Gleichung	Ready to use	Ulrich Görtz	26/11/2020 10:28

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Question statement

Solve the following equation for $x$ .

Input your answer as a fraction or an integer as appropriate and not as a decimal.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	5
c	number	10
b	integer	-2
d	integer	3
g	number	1
m	integer	2
q	number	2
p	integer	1
s	integer	-3
r	number	-4.6
t	integer	-1
an2	number	-18
an1	integer	11

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..5 except [p,abs(b)])

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`

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only

Gap-fill

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

$\simplify{({p}*x+{s}) / ({a} * x + {b}) = ({q}*x+{t}) / ({c} * x + {d})}$

$x=\;$ Unnamed gap

If you want help in solving the equation, click on Show steps. If you do so then you will lose 1 mark.

Advice

Cross-multiply to get:

$\simplify{({p}*x+{s})*({c} * x + {d})=({q}*x+{t})*({a} * x + {b})}$
Multiplying out we get

$\simplify{{p*c}x^2 +{p*d+c*s}x+{s*d}={q*a}x^2 +{q*b+t*a}x+{t*b}}$ Subtracting

${\var{a*q}}x^2$ from each side we are left with

$\simplify{{p*d+c*s}x+{s*d}={q*b+t*a}x+{t*b}}$ which we solve as a linear equation:

$\simplify{{p*d+c*s-q*b-t*a}x={t*b-s*d}}$ and so

$\simplify{x={an1}/{an2}}.$

Give a worked solution to the whole question.

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Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Solve an equation in algebraic fractions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`