These are explanations and solutions for IB past papers, not the official version. For official papers, you can go to IB Follet or access them through your school.
These are explanations and solutions for IB past papers, not the official version. For official papers, you can go to IB Follet or access them through your school.
These are explanations and solutions for IB past papers, not the official version. For official papers, you can go to IB Follet or access them through your school.
These are explanations and solutions for IB past papers, not the official version. For official papers, you can go to IB Follet or access them through your school.
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IB MATH AI HL, Paper 3, May, 2023, TZ1, Solved Past Paper
Master the 2023 IB May for Paper 3 Mathematics AI HL with examiner tailored solutions and comments for TZ1
Question 1 [Explained]
The question involves finding the most cost-effective barrel shape for storing wine based on a historic measurement method. This method was used in 17th century Austria, where the price of a wine barrel was estimated by inserting a stick through a hole in the barrel's side to measure the depth of the wine. The depth was represented by the stick's length from the entry point to the wine's surface, denoted as SD.
The longer the SD, the more the customer would pay. The relationship between the stick's length, SD (in meters), and the cost, C (in guilders), was direct. For instance, a length of 0.5 meters for SD meant the wine cost 0.80 guilders.
This question asks you to apply this historic pricing method to determine the most economical barrel design for wine storage.
In simple terms, the task is to figure out the best shape for a wine barrel that would cost the least amount of money based on how deep a stick can measure the wine inside. The deeper the stick goes, the higher the price of the wine. The goal is to find a barrel shape that provides the best value for the money.
Question 1 [a] [Explanation]
The problem addresses the relationship between two variables, (C) and (d), where (C) is directly proportional to (d).
This means that as (d) changes, (C) changes in a consistent way, maintaining a constant ratio between them.
To solve the problem, you need to find an equation that expresses (C) in terms of (d).
This requires identifying a constant (k) such that
In simple terms, your task is to determine the value of (k) that links (C) and (d) through a multiplication.
Question 1 [b] [Explanation]
A specific barrel of wine is priced at 0.96 guldens.
Your task is to confirm that the variable d is equivalent to 0.6. This involves demonstrating, likely through calculation or logical deduction, that d aligns with this value based on the given price or other contextual factors provided earlier in the problem.
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