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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.

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IB MATH AA HL, Paper 3, May, 2022, TZ2, Solved Past Paper

Master the 2022 IB May for Paper 3 Mathematics AA HL with examiner tailored solutions and comments for TZ2

Question 1 [Explained]

This question involves analyzing a set of quadratic curves defined by the equation (y² = x² + ax + b). You're asked to investigate how these curves behave as the parameters (a) and (b) change, with both (a) and (b) being natural numbers.

Question 1 [a] [Explanation]

Please create a graph on the same coordinate plane for the curves described by the inequalities $(- 2 \leq x \leq 2)$ and $(- 2 \leq y \leq 2)$ . Ensure that any points where the curves intersect with the coordinate axes are distinctly marked.

This task involves plotting two specific ranges for (x) and (y) and highlighting their intersection points with the axes, providing a clear visualization of these linear constraints within the given bounds.

Video Solution by an IB Examiner - Coming soon

Question 1 [a] [i] [Explanation]

Consider the scenario where the square of a variable (y) is equal to the cube of another variable (x). Furthermore, this relationship holds true only when (x) is zero or a positive number.

Expressed mathematically:

$y^{2} = x^{3}, x \geq 0$

Question 1 [a] [ii] [Explanation]

Consider the equation (y² = x³ + 1) for all values of (x) that are greater than or equal to (-1). The task is to explore the relationship between (y) and (x) under these conditions.

Video Solution by an IB Examiner - Coming soon

Question 1 [b] [i] [Explanation]

Identify the coordinates of the points where the curvature of the curve defined by the equation (y² = x³ + 1) changes. These points are known as inflection points.