Ida's copy of Cumulative percent decrease

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Ida Landgärds

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Ida Landgärds 6 years, 11 months ago

Created this as a copy of Cumulative percent decrease.

Name	Status	Author	Last Modified
Simple interest	Ready to use	Stanislav Duris	20/11/2019 14:42
Cumulative percent decrease	Ready to use	Stanislav Duris	20/11/2019 14:36
Exponential increase	Ready to use	Stanislav Duris	20/11/2019 14:38
Ida's copy of Cumulative percent decrease	draft	Ida Landgärds	12/04/2018 10:54
Spørsmål 4	draft	Ida Landgärds	02/12/2020 15:42
haifa's copy of Cumulative percent decrease	draft	haifa abd	01/05/2018 14:20
Consumer Arithmetic - Simple Interest	draft	Paul Hancock	24/07/2018 03:08

There are 9 other versions that do you not have access to.

Question statement

En smartphones verdi minsker hver måned med $\var{perc}$ %. Når den lanseres koster den $\var{price}$ kr.

Give any introductory information the student needs.

			Name	Type	Generated Value

			price	integer	7600
			perc	number	4

			Name	Type	Generated Value

threshold	number	5300
pricee1	number	5263.26
pricee2	number	5482.56
pricee3	number	5711.00
testn	integer	9
test	number	5263.26
price2	number	5263.26
n	integer	9
person	dict	Dictionary with 3 entries

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(6000..8000 #100) 

JME function reference

Description

The original price.

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`

7600

→ Used by:

pricee1
pricee2
pricee3
test

Statement
Advice
"Part a)" → "Unnamed gap" - Minimum accepted value
"Part a)" → "Unnamed gap" - Maximum accepted value
"Part a)" → "Unnamed step" - prompt
"Part a)" → "Step 1." - Minimum accepted value
"Part a)" → "Step 1." - Maximum accepted value
"Part b)" → "Unnamed gap" - Minimum accepted value
"Part b)" → "Unnamed gap" - Maximum accepted value
"Part b)" → "Unnamed step" - prompt
"Part b)" → "Step 1." - Minimum accepted value
"Part b)" → "Step 1." - Maximum accepted value
"Part b)" → "Step 2." - Minimum accepted value
"Part b)" → "Step 2." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

Hvor mye koster smartphonen etter $1$ måned?

Svar: Unnamed gap

Advice

a)

We can use the multiplier method to calculate the new price. If the price decreases by {perc}%, this its value is {100-perc}% of the original value after 1 month. The decimal multiplier for {100-perc}% is

\[\frac{\var{100-perc}}{100} = \var{(100-perc)/100} \text{.}\]

Each month our smartphone's value can be found by multiplying the previous month's value by the decimal multiplier. For example, after the first month, the value is

\[ \var{(100-perc)/100} \times\mathrm{£}\var{price} = \mathrm{£}\var{dpformat(price*(100-perc)/100,2)}\text{.} \]

To calculate the price after 5 months, we multiply the original price of the smartphone by our multiplier 5 times:

\[ \begin{align} \text{Final worth} &= \var{price} \times \var{(100-perc)/100} \times \var{(100-perc)/100} \times \var{(100-perc)/100} \times \var{(100-perc)/100} \times \var{(100-perc)/100} \\&= \var{price} \times \var{(100-perc)/100}^{5} \\&= £\var{precround(price*((100-perc)/100)^5, 2)} {.} \end{align}\]

b)

From part a), the value after 5 months is £$\var{precround(price*((100-perc)/100)^5, 2)}$. Continuing to multiply the price by the decimal multiplier,

\[£\var{precround(price*((100-perc)/100)^5, 2)} \times \var{(100-perc)/100} = £\var{precround(precround(price*((100-perc)/100)^5, 2)*(100-perc)/100, 2)}\]

\[£\var{precround(price*((100-perc)/100)^5, 2)} \times \var{(100-perc)/100}^2 = £\var{precround(precround(price*((100-perc)/100)^6, 2)*(100-perc)/100, 2)}\]

\[£\var{precround(price*((100-perc)/100)^5, 2)} \times \var{(100-perc)/100}^3 = £\var{precround(precround(price*((100-perc)/100)^7, 2)*(100-perc)/100, 2)}\]

\[£\var{precround(price*((100-perc)/100)^5, 2)} \times \var{(100-perc)/100}^4 = £\var{precround(precround(price*((100-perc)/100)^8, 2)*(100-perc)/100, 2)}\]

The smartphone's value will be below $£\var{threshold}$ after {n-5} more months ({n} months in total since its release).

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
Information only
Number entry
Number entry		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
Information only
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is not used in any exams.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Ida Landgärds 6 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

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Ida's copy of Cumulative percent decrease

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Ida Landgärds 6 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`