Border area

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Don Shearman 2 years ago

Created this.

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

width	integer	8
breadth	integer	9
area	integer	47
space	string	decorative floor
border	number	1.21
negativeRoot	number	-9.71

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..12)

JME function reference

Description

width of rectangular area in question

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`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
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Gap-fill

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

A rectangular {space} {width} metres by {breadth} metres is to have a border built around it. The border is to be rectangular with the {space} in the middle. You have {area} square metres of material for the border. How wide will the border need to be? Give your answer correct to 2 decimal palces and show full working on your hand written notes.

Note that the area, $A$ , of the border is given by the formula

$A=4x^2+\var{2*(width+breadth)}x$

where $x$ is the width of the border.

The border will be Unnamed gap metres wide.

Advice

We are told that the area of the border is

$A=4x^2+\var{2*(width+breadth)}x$ where

$x$ is the required width of the border. Hence we need to solve

$\var{area}=4x^2+\var{2*(width+breadth)}x$ for

$x$ .

Rearranging this equation we have

$4x^2+\var{2*(width+breadth)}x-\var{area}=0$ which can be solved using the quadratic formula as

$\begin{align}x&=\frac{\var{-2*(width+breadth)}\pm\sqrt{\var{2*(width+breadth)}^2-4\times 4\times \var{area}}}{2\times 4}\\&=\frac{\var{-2*(width+breadth)}\pm\sqrt{\var{(2*(width+breadth))^2-16*area}}}{8}\\&\approx \var{border}\text{ or }\var{negativeRoot}\end{align}$

Since the border cannot have negative width, we can ignore the negative solution and conclude that the width of the border will be approximately $\var{border}$ metres wide.

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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 ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Border area

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 1 year ago

Don Shearman 2 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`