Road width

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Don Shearman

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From users who are members of MfEP Progress Quizzes :

Hanh Vo

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Ready to use

3 years, 4 months ago

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Don Shearman 11 months, 1 week ago

Published this.

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Hanh Vo 3 years, 4 months ago

Gave some feedback: Ready to use

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Don Shearman 3 years, 8 months ago

Created this as a copy of Tunnel diameter.

Name	Status	Author	Last Modified
Tunnel diameter	Ready to use	Don Shearman	14/05/2024 05:30
Road width	Ready to use	Don Shearman	14/05/2024 05:19

There are 4 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

			d	integer	4
			A	integer	60

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(4..9)

JME function reference

Description

Distance from A to B in m in diagram, random integer from 4 to 9

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
"Unnamed part" → "Diameter" - Minimum accepted value
"Unnamed part" → "Diameter" - Maximum accepted value

Parts

Gap-fill
1. Gap Diameter Number entry
  Add

Gap-fill

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

The diagram below shows a circular tunnel with $AB=\var{d}$ metres and angle $BAC=\var{A}^\circ$ . A platform is built in the tunnel from $A$ to $C$ . Assume that angle $BAZ=$ angle $BCZ=90^\circ$ . Find the width, $AC$ , of the platform in the tunnel. You may also assume that $BZ$ is a diameter and is perpendicular to $AC$ . Write the width in the box below and show your full working on your working paper.

Platform width = Diameter m (give your answer correct to 2 decimal places)

Advice

Let the point of intersection of $AC$ and $BZ$ be $D$ . Since $BZ$ is a diameter of the circle, the distance $AD$ will be half of $AC$ . Further triangle $ADB$ is a right angled triangle and we have

$\begin{align}\cos A &=\frac{AD}{AB}\\\cos\var{A}^\circ&=\frac{AD}{\var{d}}\end{align}$

Hence

$\begin{align}AD&=\var{d}\cos\var{A}^\circ\\&\approx \var{precround(d*cos(pi*A/180),3)}\text{ m}\end{align}$

Thus $AC=2\times AD\approx\var{precround(2*d*cos(pi*A/180),2)}\text{ m}$ .

The length of the platform is approximately $\var{precround(2*d*cos(pi*A/180),2)}\text{ m.}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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Number entry
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This question is used in the following exams:

SCC Class Test 1 by Hanh Vo in SCC PrelimMaths.
Don's copy of Class Test 1 for testing by Don Shearman in Don's workspace.
SCC Final Exam by Hanh Vo in SCC PrelimMaths.
Deferred Exam by Don Shearman in MfEP Progress Quizzes.
Final Exam by Don Shearman in MfEP Progress Quizzes.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 11 months, 1 week ago

Hanh Vo 3 years, 4 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Road width

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 11 months, 1 week ago

Hanh Vo 3 years, 4 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`