Tunnel diameter

Error

There was an error loading the page.

Contributors

Don Shearman

Feedback

From users who are members of MfEP Progress Quizzes :

Hanh Vo

said

Ready to use

3 years, 4 months ago

History

○

Don Shearman 11 months, 1 week ago

Published this.

○

Hanh Vo 3 years, 4 months ago

Gave some feedback: Ready to use

○

Don Shearman 3 years, 8 months ago

Created this.

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	8
			A	integer	75

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 car tunnel with $AB=\var{d}$ metres and angle $BAC=\var{A}^\circ$ . Assume that angle $BAZ=$ angle $BCZ=90^\circ$ and that $BZ$ is perpendicular to $AC$ . Find the diameter, $BZ$ , of the tunnel. Write the diameter in the box below and show your full working on your working paper.

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

Advice

Let $D$ be the point at the intersection of $AC$ and $BZ$ . We have that angle $BDA=90^\circ$ and hence angle $ABD=\var{90-A}^\circ$ .

Since angle $BAZ=90^\circ$ we have

$\cos\var{90-A}^\circ=\frac{\var{d}}{BZ}$ and hence

$\begin{align}BZ&=\frac{\var{d}}{\cos\var{90-A}^\circ}\\&\approx\var{precround(d/sin(pi*A/180),2)}\end{align}$

Hence the diameter of the tunnel is approximately $\var{precround(d/sin(pi*A/180),2)}$ metres.

Give a worked solution to the whole question.

URL

Text alternative

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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 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.

Loading...

Error

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

Tunnel diameter

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`