Implicit 1

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Violeta CIT

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Violeta CIT 8 years, 6 months ago

Created this as a copy of SFY0004 Implicit 1.

Name	Status	Author	Last Modified
SFY0004 Implicit 1	Ready to use	Bill Foster	01/06/2016 09:47
Implicit Differentiation	draft	Clare Lundon	16/01/2018 13:19
Implicit 1	draft	Violeta CIT	26/09/2016 15:15
Simon's copy of SFY0004 Implicit 1	draft	Simon Thomas	11/03/2019 14:41
Harder implicit differentiation	draft	Simon Thomas	11/03/2019 15:41
Implicit 1	draft	Xiaodan Leng	11/07/2019 06:39

There are 16 other versions that do you not have access to.

Question statement

Given the following relation between $x$ and $y$

$\simplify[all,!collectNumbers]{x^2+y^2+{a}x+{b}y}=\var{c}$
answer the following question.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-4
c	integer	9
b	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
-random(1..9)

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Description

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

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Generated value: `integer`

-4

→ Used by:

Statement
Advice
"Unnamed part" → "Unnamed gap" - Correct answer

Parts

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.

Using implicit differentiation find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$ .

Input your answer here:

$\displaystyle \frac{dy}{dx}=$ Unnamed gap

Advice

On differentiating both sides of the equation implicitly we get

$2x + \simplify[all,!collectNumbers]{2y*Diff(y,x,1) + {a} + {b} *Diff(y,x,1)} = 0$
Collecting terms in

$\displaystyle\frac{dy}{dx}$ and rearranging the equation we get

$(\var{b} + 2y) \frac{dy}{dx} = \simplify[all,!collectNumbers]{{ -a} -2x}$ and hence on further rearranging:

$\frac{dy}{dx} = \simplify[all,!collectNumbers]{({ - a} - 2 * x) / ({b} + (2 * y))}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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Mathematical expression
Mathematical expression		Hasn't run yet

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Violeta CIT 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Implicit 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Violeta CIT 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`