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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.

 

01 Hours

 

55 Marks

 

Calculator is allowed

IB MATH AI HL, Paper 3, May, 2021, TZ1, Solved Past Paper

Master the 2021 IB May for Paper 3 Mathematics AI HL with examiner tailored solutions and comments for TZ1

Question 1 [Explained]

A potential landing site for a spacecraft on Mars has been located at point A. The task is to calculate the minimum time from sunrise to sunset at this point.

 

Use radians for all calculations in this question. Consider all given values as exact. This means you should not round off the values and should use the most precise measurements available.

 

Mars completes a full orbit around the Sun in 669 Martian days, which makes up one Martian year. This information is crucial for understanding the planet's rotational and orbital dynamics.

 

On day (t), where (t∈Z) (meaning (t) is an integer), the length of time in hours from the start of the Martian day until sunrise at point A can be modeled by a function (R(t)). This function is defined as:

 

(R(t) = a sin(bt) + c), with (t∈R) (meaning (t) is a real number). This function represents the variation in sunrise times over different days, with (a), (b), and (c) being constants.

 

The graph of (R) is provided for one Martian year, which helps visualize how sunrise times change throughout the year.

Question 1 (Figure)
Question 1 [a] [Explanation]

Demonstrate that the value of b closely approximates 0.00939.

 

This question is asking you to verify that the variable b has a value that is approximately equal to 0.00939, suggesting a minor difference might exist, but for practical purposes, they can be considered as nearly the same.

Video Solution by an IB Examiner - Coming soon

Question 1 [b] [Explanation]

Mars takes 24 hours and 40 minutes to complete one full rotation on its axis.

 

Determine the angle that Mars rotates through each hour.

 

This question asks us to find out how many degrees Mars rotates on its axis in one hour. Since a full rotation is 360 degrees and we know the time it takes for a complete rotation, we need to calculate the angle for each hour by dividing the total rotation angle by the total time in hours.

Video Solution by an IB Examiner - Coming soon