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 30 Minutes
80 Marks
Calculator is allowed
IB MATH AI SL, Paper 1, May, 2022, TZ2, Solved Past Paper
Master the 2022 IB May for Paper 1 Mathematics AI SL with examiner tailored solutions and comments for TZ2
Question 1 [Explained]
This question involves the motion of a windscreen wiper on a car, which rotates in a circular path. The wiper arm pivots at a point labeled O and sweeps through an angle of 140°. The wiper blade, which is responsible for clearing the windscreen, is attached to the arm between points A and B. The length of the blade is 46 cm, and the total length of the wiper arm from the pivot point O to the end point B is 56 cm. The question requires calculating the length of the arc traced by point B as the wiper moves, as well as determining the area of the windscreen that is cleared by the blade. The unshaded area in the accompanying diagram represents the portion of the windscreen cleared by the blade.
Question 1 [a] [Explanation]
This part of the question asks you to calculate the length of the arc formed by point B, which is the end of the rubber blade. The arc length is a segment of the circumference of a circle, and it can be calculated using the formula for arc length, which involves the radius of the circle and the angle in radians.
Question 1 [b] [Explanation]
This part of the question requires you to determine the area of the windscreen that is cleared by the rubber blade. The area cleared by the blade can be found by calculating the area of the sector formed by the blade's motion and then subtracting the area of the sector that is not cleared (the area from the pivot to point A).
Question 2 [Explained]
This question involves analyzing the outcomes of applications to a university's Arts and Sciences programmes. A total of 130 applicants applied, and their acceptance or rejection is summarized in a table. The task is to determine probabilities related to these outcomes, using the data provided.
Accepted | Rejected | |
|---|---|---|
Arts programme | 17 | 24 |
Sciences programme | 25 | 64 |
Question 2 [a] [Explanation]
This part of the question asks you to calculate the probability that a randomly selected applicant from the group was accepted by the university. This involves determining the total number of accepted applicants and dividing it by the total number of applicants.
Question 2 [b] [Explanation]
This part of the question asks you to find the probability that an applicant who was accepted applied for the Arts programme. This involves determining the number of accepted applicants in the Arts programme and dividing it by the total number of accepted applicants.