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, TZ2, Solved Past Paper
Master the 2023 IB May for Paper 3 Mathematics AI HL with examiner tailored solutions and comments for TZ2
Question 1 [Explained]
This problem involves determining the optimal route between two points, H and S, which are separated by regions with different travel speeds. Huw lives in a house, H, and attends a school, S. The school is located 1.2 km south and 4 km east of his house.
There is a boundary, [MN], that runs from west to east, 0.4 km south of Huw's house. North of this boundary is a field where Huw can run at 15 km h-1. South of the boundary is rough ground where Huw walks at 5 km h-1.
The task is to find the optimal route for Huw to take from his house to his school, considering the different speeds in the two regions.
In simpler terms, Huw needs to get from his house to his school. There are two areas he can travel through: one where he can run faster and another where he has to walk slower. The question asks for the best path he should take to minimize his travel time.
Question 1 [a] [Explanation]
Calculate the total time it takes for Huw to travel directly from point 'H' to point 'S'. Express the duration in minutes and round the result to the nearest minute.
The question is asking for the time it takes for Huw to travel from point 'H' to point 'S' without any detours, using the most direct route possible. The final answer should be given in minutes, and you should round the number to the nearest minute for simplicity.
Video Solution by an IB Examiner - Coming soon
Question 1 [b] [Explanation]
Huw has discovered that he could spend less time traveling by choosing an alternative, less direct route.
He identifies a new point, 'P', along the 'MN' track, situated precisely 'x' kilometers east of 'M'.
Opting for this detour, Huw decides to run from point 'H' to point 'P', and then proceed to walk from 'P' to his final destination, 'S'.
The duration, represented by 'T(x)', denotes the total number of hours Huw takes to complete his journey following this new path.
Huw wants to reduce his travel time by choosing a different path.
He selects a new point 'P' on the MN track, located 'x' kilometers to the east of point 'M'.
He then runs from 'H' to 'P' and walks from 'P' to 'S'.
The function 'T(x)' represents the total travel time in hours for this new route.
Video Solution by an IB Examiner - Coming soon
Question 1 [b] [i] [Explanation]
Given the function (T(x)), we need to show that it is defined as:
In simple terms, we want to verify that (T(x)) is equal to this expression. The function (T(x)) involves a combination of square roots and quadratic terms in the numerator, and a constant divisor in the denominator.
Question 1 [b] [ii] [Explanation]
Illustrate the graph of ( y = T(x)).
This question asks you to draw the graph of the function (T(x)). Essentially, you need to visualize how the function ( y = T(x)) behaves by plotting its curve on a graph.