IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Static and Probability-Data manipulation and misinterpretation
Topic :Static and Probability- Weightage : 21 %
All Questions for Topic : Sampling techniques,Data manipulation and misinterpretation,Graphical representations (including: bivariate graphs, scatter graphs, box plots, cumulative frequency graphs)
,Lines of best fit,Data processing: quartiles and percentiles,Measures of dispersion: interquartile range,Correlation, qualitative handling,Relative frequency,Response rates,Sets, including notation and operations up to three sets,Probability with Venn diagrams, tree diagrams and sample spaces,Mutually exclusive events,Combined events
Question (15 marks)
The following question introduces a system of taxation used by governments to obtain money from working citizens.
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Question (a) : 5 marks
Calculate the total amount of tax for an income of $\rm{80000 ~EUR}$, showing your working in the table.
▶️Answer/Explanation
Ans:
From the table:
- For the income band $0<$ income $\leq 6000$, the tax amount is $\rm{0 ~EUR}$.
- For the income band $6000<$ income $\leq 12000$, the tax amount is $\rm{330~ EUR}$.
- For the income band $12000<$ income $\leq 25000$, the tax amount is $\rm{1820~ EUR}$.
- For the income band $25000<$ income $\leq 70000$, the tax amount is $\rm{13500 ~EUR}$.
- For the income band above 70000, the tax amount is $\rm{4100~ EUR}$.
To find the total tax paid on 80000 EUR, we add up all these tax amounts: Total tax paid $\rm{= 0 + 330 + 1820 + 13500 + 4100 = 19750~ EUR}$.
Question (b) : 10 marks
The scenarios provided in the tabs below should be used to answer this question.
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Evaluate the two scenarios by comparing the financial information provided and decide whether you should accept this opportunity to relocate. In your answer, you should:
$\bullet$ identify the relevant elements to consider when comparing the two scenarios
$\bullet$ make appropriate calculations to make a decision
$\bullet$ justify the accuracy of your calculations
$\bullet$ give your decision and a reflection on this offer to relocate, justifying your decision.
▶️Answer/Explanation
Ans:
$\mathbf{Scenario 1: Current Job in Home Town}$
Total tax:
\[
\text{{Tax}} = 330 + 1820 + (15000 \times 0.3) = 330 + 1820 + 4500 = 6650 \, \text{{EUR}}
\]
Total expenses:
\[
\text{{Expenses}} = (400 + 900 + 500) \times 12 = 1800 \times 12 = 21600 \, \text{{EUR}}
\]
Net income per year:
\[
\text{{Net income}} = \text{{Annual income}} – \text{{Total tax}} – \text{{Total expenses}} = 40000 – 6650 – 21600 = 11750 \, \text{{EUR}}
\]
Net saved value per month:
\[
\text{{Net saved value per month}} = \frac{{\text{{Net income}} – \text{{Monthly expenses}}}}{12} = \frac{{11750 – (400 + 900 + 500)}}{12} = \frac{{11750 – 1800}}{12} = 995.83 \, \text{{EUR}}
\]
$\mathbf{Scenario 2: Job Offer in Another Country}$
Total tax:
\[
\text{{Tax}} = 9650 \, \text{{EUR}}
\]
Total expenses:
\[
\text{{Expenses}} = ((500 + 900 + 80 + 600) \times 12) + (2 \times 150) = (2080 \times 12) + 300 = 24960 + 300 = 25260 \, \text{{EUR}}
\]
Net income per year:
\[
\text{{Net income}} = \text{{Annual income}} – \text{{Total tax}} – \text{{Total expenses}} = 50000 – 9650 – 25260 = 15090 \, \text{{EUR}}
\]
Net saved value per month:
\[
\text{{Net saved value per month}} = \frac{{\text{{Net income}} – \text{{Monthly expenses}}}}{12} = \frac{{15090 – (500 + 900 + 80 + 600)}}{12} = \frac{{15090 – 2080}}{12} = 1092.50 \, \text{{EUR}}
\]
Therefore, the net saved value per month for Scenario 1 (Current Job in Home Town) is 995.83 EUR, and for Scenario 2 (Job Offer in Another Country) is 1092.50 EUR.
To evaluate the two scenarios and make a decision on whether to accept the opportunity to relocate, we will compare the financial information provided and consider relevant elements. We will also perform appropriate calculations and justify their accuracy.
Relevant Elements to Consider:
- Annual income: 40000 EUR in the current job and 50000 EUR in the job offer.
- Tax: 6650 EUR in the current job and 9650 EUR in the job offer.
- Monthly expenses: Rent, medical, personal, bills, and travel expenses.
Calculations and Justification:
Scenario 1: Current Job in Home Town
- Net saved value per month: 995.83 EUR (calculated previously)
Scenario 2: Job Offer in Another Country
- Net saved value per month: 1092.50 EUR (calculated previously)
The calculations considered the provided income, tax, and expenses accurately. The net saved value per month was obtained by deducting monthly expenses from the net income and dividing it by 12.
Decision and Reflection:
Based on the financial information and calculations, here is the decision and reflection on the offer to relocate:
Comparing the net saved value per month:
- In the Current Job in Home Town scenario, the net saved value is 995.83 EUR.
- In the Job Offer in Another Country scenario, the net saved value is 1092.50 EUR.
From a purely financial perspective, the job offer in another country provides a higher net saved value per month. However, it’s important to consider other factors such as quality of life, career growth opportunities, work-life balance, and personal preferences. Relocating to another country involves adjusting to a new environment, potentially higher living costs, and leaving behind familiar surroundings.
Therefore, the decision to accept the opportunity to relocate should consider both financial and non-financial factors. If the higher net saved value, along with other aspects such as career prospects and personal fulfillment, outweigh the challenges of moving and adjusting to a new country, accepting the job offer may be a viable choice. However, personal circumstances and preferences should also be taken into account.
It’s recommended to thoroughly evaluate the pros and cons, consider long-term implications, and weigh the financial benefits against the potential challenges before making a final decision on accepting the opportunity to relocate.