David's copy of Straight line equation application: measuring sunflower height

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David Rickard 6 years, 5 months ago

Created this as a copy of Straight line equation application: measuring sunflower height.

Name	Status	Author	Last Modified
Find the equation of a line through two points - positive gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Find the equation of a line through two points - negative gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Find the equation of a line through two points - zero gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Straight line equation application: measuring sunflower height	Ready to use	Bradley Bush	03/02/2021 13:59
Louise's copy of Find the equation of a line through two points - positive gradient	draft	Louise Lynch	26/01/2022 19:48
Find the equation of a line through two points - positive gradient	draft	Mark Hodds	03/02/2021 13:59
Ida's copy of Find the equation of a line through two points - positive gradient	draft	Ida Landgärds	03/02/2021 13:59
Spørsmål 1	draft	Ida Landgärds	03/02/2021 13:59
Marte's copy of Find the equation of a line through two points - positive gradient	draft	Marte Bråtalien	03/02/2021 13:59
Thomas's copy of Find the equation of a line through two points - negative gradient	draft	Thomas Strasser	03/02/2021 13:59
Equation de droite	Needs to be tested	Alain Virouleau	30/05/2019 18:52
Linear Equations - Find the equation of a line through two points	draft	Paul Hancock	03/02/2021 13:59
Find the equation of a line through two points - positive gradient [L3]	Needs to be tested	Matthew James Sykes	03/02/2021 13:59
Beer Lambert Law	Doesn't work	Matthew James Sykes	03/02/2021 13:59
Beer Lambert Law Working Back up	Should not be used	Matthew James Sykes	03/02/2021 13:59
Joël's copy of Find the equation of a line through two points - positive gradient	draft	Jo Cohen	03/02/2021 13:59
Beer Lambert Law Working Back up	Should not be used	Matthew James Sykes	03/02/2021 13:59
Ida's copy of Spørsmål 1	draft	Ida Landgärds	09/01/2023 10:54
David's copy of Straight line equation application: measuring sunflower height	draft	David Rickard	03/02/2021 13:59
equation of a line through two points	draft	heike hoffmann	03/02/2021 13:59
Luis's copy of Find the equation of a line through two points - zero gradient	draft	Luis Hernandez	03/02/2021 13:59
Simon's copy of Equation of a line through two points - positive gradient	draft	Simon Thomas	03/02/2021 13:59
Maria's copy of Simon's copy of Equation of a line through two points - positive gradient	draft	Maria Aneiros	03/02/2021 13:59
Maria's copy of Find the equation of a line through two points - negative gradient	draft	Maria Aneiros	03/02/2021 13:59
Heather's copy of Find the equation of a line through two points - positive gradient	draft	Heather Driscoll	03/02/2021 13:59
Equation of a line through two points - positive gradient	draft	Heather Driscoll	03/02/2021 13:59
Equation of a line through two points	draft	Philip Charlton	03/02/2021 13:59
Find the equation of a line through two points - zero gradient	draft	Xiaodan Leng	03/02/2021 13:59
Equation of a line through two points - positive gradient	draft	Xiaodan Leng	03/02/2021 13:59
Straight line equation application: measuring sunflower height	draft	Adelle Colbourn	03/02/2021 13:59
Musa's copy of Find the equation of a line through two points	draft	Musa Mammadov	01/08/2022 08:15
Find the equation of a line through two points - positive gradient	Ready to use	Simon Vaughan	03/02/2021 13:59

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Question statement

{person['name']} is given a sunflower seedling for {person['pronouns']['their']} 30th birthday (day $0$ ) and observes its height. {capitalise(person['pronouns']['they'])} make{s} the following observations later that week:

Observation	A	B
Day	$\var{xa}$	$\var{xb}$
height (cm)	$\var{ya}$	$\var{yb}$

{person['name']} plots the 2 points:

{plotPoints()}

Give any introductory information the student needs.

			Name	Type	Generated Value

xa	integer	4
xb	integer	5
ya	integer	11
yb	integer	13

			Name	Type	Generated Value

			person	dict	Dictionary with 3 entries
			s	string	s

			Name	Type	Generated Value

m	integer	2
c	integer	3
d	integer	20

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..5)

JME function reference

Description

x coordinate of point a

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:

Statement
Advice

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Choose one from a list
Part e) Gap-fill
1. Gap Number entry
  Add
Part f) Gap-fill
1. Gap Number entry
  Add
Part g) Choose several from a list

Gap-fill

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

What is the gradient, $m$, of the straight line between the two points?

$m =$ Unnamed gap

Advice

a)

The gradient is the ratio of vertical change ($y_2-y_1$) to horizontal change ($x_2-x_1$).

\[ m = \frac{y_2-y_1}{x_2-x_1}=\frac{\simplify[!collectNumbers]{{yb}-{ya}}}{\simplify[!collectNumbers]{{xb}-{xa}}}=\frac{\simplify{{yb}-{ya}}}{\simplify{{xb}-{xa}}}=\simplify[simplifyFractions,unitDenominator]{({yb-ya})/({xb-xa})}\text{.}\]

b)

Rearranging the equation $y=mx+c$ for $c$ and using point A:

\[ c = y_1-mx_1 = \var{ya}-\var{m}\times\var{xa}=\simplify{{ya-m*xa}}\text{.}\]

We then check this against point $B$:

\[ y_2 = mx_2 + c = \simplify[fractionNumbers]{{m}{xb}+{c}}=\simplify{{m}*{xb}+{c}}\text{.}\]

b)

We now substitute the values for $m$ and $c$ into the equation of a straight line, $y=mx+c$,

\[y=\simplify[!noLeadingMinus,unitFactor]{{m} x+ {c}}\text{.}\]

{advicePoints()}

c)

The gradient represents the vertical change (height in cm) per unit of the horizontal axis (days): the change in height of the sunflower per day.

d)

Substituting $x=\var{d}$ into the straight line equation, the height $y$ after $\var{d}$ days is

\begin{align}
y&=\simplify{{m}}x+\var{c}\\
&=\simplify[]{{m}{d}}+\var{c}\\
&=\var{m*d+c}\text{cm.}
\end{align}

e)

Substituting $x=\var{1826}$ into the straight line equation, the height $y$ after $1826$ days is

\begin{align}
y&=\simplify{{m}}x+\var{c}\\
&=\simplify[]{{m}1826} + \var{c}\\
&=\var{m*1826+c}\text{cm.}
\end{align}

Note that this is $\var{(m*1826+c)/100}$ metres. In 2014, a sunflower of $9.17$ metres was entered into the Guinness World Records as tallest sunflower.

f)

Possible reasons that the prediction will not be accurate are:

from everyday observations and basic biology that a sunflower cannot keep growing forever, but our straight line equation would predict otherwise.
the set of observations are limited in their time frame. In particular another relationship could easily fit the 2 data points.

Invalid reasons that the prediction will not be accurate are:

There can only be one straight line between two points; only one equation describes this.
Based on common sense, we know that sunflowers do grow over time.

Give a worked solution to the whole question.

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
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Choose several from a list
Choose several from a list		Hasn't run yet

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David's copy of Straight line equation application: measuring sunflower height

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

David Rickard 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

b)

c)

d)

e)

f)

Loading...

Error

David's copy of Straight line equation application: measuring sunflower height

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

David Rickard 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

b)

c)

d)

e)

f)

Generated value: `integer`