Applied y-intercepts: Investing in boats

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Christian Lawson-Perfect	said	Ready to use	7 years, 7 months ago
Bradley Bush	said	Needs to be tested	7 years, 8 months ago

History

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Christian Lawson-Perfect 7 years, 7 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 7 years, 7 months ago

Saved a checkpoint:

I've reworded a few things, replace the list of (all-male) famous people with the random names extension, and put the "identify the constant term" part above the "write down the constant term" part.

Restore this checkpoint

○

Christian Lawson-Perfect commented 7 years, 7 months ago

I don't like how the graph works - why drag a slider and not the line itself?

The label on the slider says "p = ..." - what's p?

○

Elliott Fletcher 7 years, 8 months ago

Published this.

○

Bradley Bush 7 years, 8 months ago

Gave some feedback: Needs to be tested

○

Bradley Bush 7 years, 8 months ago

Created this.

There is only one version of this question that you have access to.

There are 3 other versions that do you not have access to.

Question statement

You are a forgetful investor set on saving enough money to buy a new fishing boat for when you retire.

Your savings account manager tells you your savings account is worth £{formatnumber(bal,"en")}.

You have forgotten the principal amount you started with the account with; however you do know that you have been saving for exactly nine years now and your manager informs you that the bank has been paying you a premium of £{m} per year.

Your account manager shows you this graph, which plots account balance over time for a given principal amount.

The line on the graph below can be repositioned by dragging the slider.

{geogebra_applet('HtnCWSSQ',[["p",p],["m",m],["c",c]])}

Give any introductory information the student needs.

			Name	Type	Generated Value

p	integer	1100
friend	dict	Dictionary with 3 entries
m	integer	15
c	integer	1020
bal	integer	1155

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
1100

JME function reference

Description

not intercept, starting intercept

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`

1100

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Choose one from a list
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Choose several from a list

Gap-fill

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

With $y$ representing the account balance and $x$ the number of years the account has been open, give an expression for the balance in the form $y=mx+c$ .

$y=$ Unnamed gap

Advice

a)

The balance increases by £{m} each year, so $m = \var{m}$.

We know that at $x = 9$ years, $y = \var{bal}$. Substituting these values into the equation, we obtain

\[ \var{bal} = \var{m} \times 9 + c \]

Rearrange this to find $c$:

\begin{align}
c &= \var{bal} - \var{m} \times 9 \\
&= \var{bal} - \var{m*9} \\
&= \var{c}
\end{align}

So the formula for the account balance is

\[y = \var{m}x+\var{c}\text{.}\]

b)

The constant term $\var{c}$ determines the point at which the line crosses the $y$-axis. This point is called the $y$-intercept.

c)

The initial investment is the value of $y$ at $x = 0$, so it's £{c}$.

d)

It is useful to plot the graph of {friend['name']}'s savings account against your own for comparison ({friend['name']}'s balance is shown as a dashed line):

{geogebra_applet('gpFmg3Ex',[["p",p],["m",m],["c",c]])}

Using this graph, we can see that only two of the statements are true:

The two lines are parallel. This is because they both increase by £{m} each year.
The plot of {friend['name']}'s balance has a higher $y$-intercept because {friend['pronouns']['their']} initial balance is higher.

As the gradients of the two lines on the graph are the same, we can eliminate the other two statements about the lines converging and about having a higher gradient.

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
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
Mathematical expression
Mathematical expression		Hasn't run yet
Choose several from a list
Choose several from a list		Hasn't run yet

This question is used in the following exams:

Money by Christian Lawson-Perfect in Transition to university.
maths practice-revision by David Martin in David's workspace.
Questions using the random person extension by Christian Lawson-Perfect in Christian's workspace.
Test SCORM Export by Iain Bruce in Iain's workspace.
Module 3 by Niharika Singh in Niharika's workspace.
All the good stuff by Chris Templet in Chris's workspace.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect commented 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

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Error

Applied y-intercepts: Investing in boats

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect 7 years, 7 months ago

Christian Lawson-Perfect commented 7 years, 7 months ago

Elliott Fletcher 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

Generated value: `integer`