Bounds with area

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Simon Thomas

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Simon Thomas 5 years, 2 months ago

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Simon Thomas 5 years, 2 months ago

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Question statement

Give all answers to 2 decimal places:

Give any introductory information the student needs.

			Name	Type	Generated Value

width	number	3.6
length	number	5.8
minarea	number	20.4125
maxarea	number	21.3525
width2	integer	26
area	integer	350
minlength	number	13.0188679245
maxlength	number	13.9215686275

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random (2..4#0.1)

JME function reference

Description

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

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Generated value: `number`

3.6

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

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

A rectangle has a width of $\var{width}$ cm and length of $\var{length}$ cm, each rounded to the nearest mm.

What is:

(i) the minimum possible area of the rectangle in cm $^2$ Gap 0.

(ii) the maximum possible area of the rectangle in cm $^2$ Gap 1.

Advice

(a)

The given width = $\var{width}$ cm and length = $\var{length}$ cm are each rounded to the nearest 0.1cm. To find the upper and lower bounds we must add/subtract half of this value.

Since half of 0.1cm is 0.05cm we obtain:

Lower bound for width $= \var{width}-0.05=\var{width-0.05}$

Upper bound for width $= \var{width}+0.05=\var{width+0.05}$

Lower bound for length $= \var{length}-0.05=\var{length-0.05}$

Upper bound for length $= \var{length}+0.05=\var{length+0.05}$

Since area = length $\times$ width, we have:

lower bound area = lower bound length $\times$ lower bound width $=\var{length-0.05} \times \var{width-0.05} = \var{minarea}$ cm $^2=\var{precround(minarea,2)}$ cm $^2$ to 2d.p.

and

upper bound area = upper bound length $\times$ upper bound width $=\var{length+0.05} \times\var{width+0.05} = \var{maxarea}$ cm $^2=\var{precround(maxarea,2)}$ cm $^2$ to 2d.p.

(b)

The given width = $\var{width2}$ cm is rounded to the nearest 1cm. To find the upper and lower bounds we must add/subtract half of this value.

Since half of 1cm is 0.5cm we obtain:

Lower bound for width $= \var{width2}-0.5=\var{width2-0.5}$

Upper bound for width $= \var{width2}+0.5=\var{width2+0.5}$

The given area = $\var{area}$ cm is rounded to the nearest 10cm $^2$ . To find the upper and lower bounds we must add/subtract half of this value.

Since half of 10cm $^2$ is 5cm $^2$ we obtain:

Lower bound for area $= \var{area}-5=\var{area-5}$

Upper bound for area $= \var{area}+5=\var{area+5}$

Since length = area $\div$ width, we have:

lower bound length= lower bound area $\div$ upper bound width (to get a small answer we want to be dividing a small number by a big number)

$=\var{area-5} \div \var{width2+0.5} = \var{minlength}$ cm $=\var{precround(minlength,2)}$ cm to 2d.p.

and

upper bound length = upper bound area $\div$ lower bound width (to get a large answer we want to be dividing a large number by a small number)

$=\var{area+5} \div \var{width2-0.5} = \var{maxlength}$ cm $=\var{precround(maxlength,2)}$ cm to 2d.p.

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Part	Test	Passed?
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Number entry
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Number entry
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Gap-fill
Gap-fill		Hasn't run yet
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Number entry
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This question is used in the following exam:

Working with Bounds by Simon Thomas in Maths support.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Simon Thomas 5 years, 2 months ago

Simon Thomas 5 years, 2 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

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Error

Bounds with area

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 2 months ago

Simon Thomas 5 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`