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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 30 Minutes

 

80 Marks

 

Calculator is allowed

IB MATH AI SL, Paper 1, November, 2022, TZ0, Solved Past Paper

Master the 2022 IB November for Paper 1 Mathematics AI SL with examiner tailored solutions and comments for TZ0

Question 1 [Explained]

This question involves a real-world scenario where Kacheena is standing at the top of a 218-meter vertical cliff, represented by point K. The base of the cliff is denoted as point B, and a ship is positioned at point S, 1200 meters away from Kacheena. The task is to analyze the geometric relationships between these points, which are illustrated in a diagram. The problem requires using trigonometric concepts to find specific angles and distances related to the ship's position relative to Kacheena and the cliff.

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

This part of the question asks you to determine the angle of elevation from the ship, located at point S, to Kacheena, who is standing at the top of the cliff at point K. The angle of elevation is the angle formed between the horizontal line from the ship and the line of sight from the ship to Kacheena. This requires the application of trigonometric functions to calculate the angle based on the given distances.

Question 1 [b] [Explanation]

This part of the question requires finding the horizontal distance from the base of the cliff, point B, to the ship, point S. This involves using trigonometric relationships in the right triangle formed by the cliff, the horizontal distance, and the line of sight from the ship to Kacheena.

Question 1 [c] [Explanation]

This part of the question asks you to express the horizontal distance found in part (b) in scientific notation, in the form a×10k, where 1≤a<10 and k is an integer. This involves converting the numerical value into a standardized format used for representing large or small numbers.

Question 2 [Explained]

The town of Neerim has initiated a reforestation program where they plan to plant trees over several months. In the first month, they plant 85 trees. Each month thereafter, the number of trees planted increases by 30. This pattern of planting forms an arithmetic sequence, where the first term is 85 and the common difference is 30. The task is to analyze this sequence to determine specific values related to the number of trees planted over a period of time.


Question 2 [a] [Explanation]

This part of the question asks you to find the number of trees that will be planted in the 15th month of the program. Given the arithmetic nature of the sequence, you need to determine the 15th term using the formula for the nth term of an arithmetic sequence.


Question 2 [b] [Explanation]

This part of the question requires you to calculate the total number of trees planted over the first 15 months of the program. This involves finding the sum of the first 15 terms of the arithmetic sequence.