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 AA HL, Paper 3, May, 2021, TZ2, Solved Past Paper
Master the 2021 IB May for Paper 3 Mathematics AA HL with examiner tailored solutions and comments for TZ2
Question 1 [Explained]
The task is to examine the characteristics and some primary attributes of the function (fn(x) = xn(a - x)n ), where (a) is a positive real number and (n) is a positive integer.
Specifically, for the parts of the task labeled (a) and (b), the value of (a) is set to 2.
We will be looking at the particular function (f1(x) = x(2 - x)).
Question 1 [a] [Explanation]
Create a visual representation of the function (y = f1(x)). In your depiction, please indicate where the graph crosses the horizontal and vertical axes. Additionally, identify the precise points on the graph where it reaches the highest or lowest values within a local region.
Keep an eye out for any points where the graph either peaks or dips, noting these coordinates specifically.
Video Solution by an IB Examiner - Coming soon
Question 1 [b] [Explanation]
Consider the function (fn(x) = x2 (2- xn)}), where (n) belongs to the set of positive integers greater than 1.
Explore the function (y = fn(x)) for specific values of (n), particularly:
- For odd values like (n = 3) and (n = 5);
- For even values such as (n = 2) and (n = 4).
Then, proceed to fill in the following table with your findings.
| Number of local maximum points | Number of local minimum points | Number of points of inflexion with zero gradient | |
|---|---|---|---|
n = 3 and n = 5 | |||
n = 2 and n = 4 |
(n) | Number of local maximum points | Number of local minimum points | Number of points of inflexion with zero gradient |
|---|---|---|---|
(n = 3) and (n = 5) | 1 | 0 | 2 |
(n = 2) and (n = 4) | 1 | 2 | 0 |