Car window 2

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Don Shearman

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From users who are members of MfEP Progress Quizzes :

Hanh Vo

said

Ready to use

3 years, 2 months ago

History

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Don Shearman 11 months, 4 weeks ago

Published this.

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Hanh Vo 3 years, 2 months ago

Gave some feedback: Ready to use

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Don Shearman 3 years, 5 months ago

Created this as a copy of Car window (sample).

Name	Status	Author	Last Modified
Car window	Ready to use	Don Shearman	16/04/2024 06:13
Car window 2	Ready to use	Don Shearman	16/04/2024 06:16

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

c	integer	20
a	integer	10
b	integer	11
angle	number	18.6481553056

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(20..27)

JME function reference

Description

length of side c of triangle

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:

angle

Parts

Gap-fill
1. Gap C 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 part of a car window with side $AC=\var{a}$ cm, side $BC=\var{c}$ cm and side $AB=\var{b}$ cm. Find the size of the angle $C$ to the nearest degree. Give your answer in the box below and show full working on your handwritten notes.

$C=$ C $^\circ$

Advice

Since we know the lengths of all 3 sides, we will use the cosine rule to find the required angle.

We have that $a=\var{c}$ cm, $b=\var{a}$ cm and $c=\var{b}$ cm. Using the cosine rule $c^2=a^2+b^2-2ab\cos C$ we have"

$\begin{align} \var{b}^2&=\var{c}^2+\var{a}^2-2\times \var{c}\times \var{a}\times\cos C\\\var{b^2}&=\var{c^2}+\var{a^2}-\var{2*c*a}\cos C\\\cos C&=\frac{\var{c^2}+\var{a^2}-\var{b^2}}{\var{2*c*a}}\\C&=\cos^{-1}\frac{\simplify{{c^2}+{a^2}-{b^2}}}{\var{2*c*a}}\\&\approx \var{precround({angle},0)}^\circ\end{align}$

Give a worked solution to the whole question.

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

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, 4 weeks ago

Hanh Vo 3 years, 2 months ago

Don Shearman 3 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Car window 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 11 months, 4 weeks ago

Hanh Vo 3 years, 2 months ago

Don Shearman 3 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`