Energy use

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Don Shearman 1 year ago

Published this.

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Don Shearman 2 years, 1 month ago

Created this.

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	10
b	integer	-55
energy	integer	900

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(10..90 #5)

JME function reference

Description

Negative root of quadratic, random between 10 and 90 in steps of 5

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:

Advice
"Unnamed part" - prompt

Parts

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.

In order to produce a quantity $x$ of a certain electronic component an amount of energy, $E$ is required where

$E=\simplify{x^2+{b+a}x+{a*b+energy}}\text{ Joules}$

If the energy used during a production run of this component was $\var{energy}$ Joules, how many of the components were produced?

Unnamed gap components were produced. Show full working on your handwritten notes.

Advice

We are told that the energy used by the process is given by

$E=\simplify{x^2+{b+a}x+{a*b+energy}}\text{ Joules}$ and that

$E=\var{energy}$ joules. Hence we need to solve

$\var{energy}=\simplify{x^2+{b+a}x+{a*b+energy}}$ or

$\simplify{x^2+{b+a}x+{a*b}}=0$

This equation can be factorised as

$(x+\var{a})(x-\var{-b})=0$ which has solutions

$x=\var{-a}\quad\text{or}\quad x=\var{-b}.$

Since the process will produce a positive number of components we can ignore the negative root and conclude that $\var{-b}$ components were produced.

Note that the quadratic formula could also be used to find the roots of this equation.

Give a worked solution to the whole question.

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

This question is used in the following exam:

Class Test 1 by Don Shearman in MfEP Progress Quizzes.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 1 year ago

Don Shearman 2 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Energy use

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 1 year ago

Don Shearman 2 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`