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, TZ1, Solved Past Paper
Master the 2021 IB May for Paper 3 Mathematics AA HL with examiner tailored solutions and comments for TZ1
Question 1 [Explained]
The question invites you to explore the characteristics and key behaviors of cubic polynomials, specifically those of the form (x3 - 3cx + 2) where (x) is a real number and (c) is a parameter that can vary within the real numbers. You are asked to consider how the function behaves as (c) changes.
Two specific cases are given for analysis: when (c = -1) and (c = 0). You are to examine how the graph of the function, represented as ( y = f (x)), changes between these two scenarios. This exploration helps in understanding the impact of the parameter (c) on the shape and position of the cubic polynomial's graph.
Overall, this analysis is crucial for understanding how changes in the coefficient (c) influence the graph's properties, such as its roots and turning points.
Question 1 [a] [Explanation]
Draw the graph of ( y = f (x)) on separate axes, indicating the y-intercept and marking the points where the gradient is zero. Provide details such as the y-intercept value and the coordinates of stationary points where the slope of the tangent is zero.
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Question 1 [a] [i] [Explanation]
Let's consider a situation where the value of a particular constant, c, is established to be exactly 1.
Question 1 [a] [ii] [Explanation]
If we're examining a certain situation mathematically and we come to find out that a particular variable, let's refer to it as c, equates to the number 2.
Question 1 [b] [Explanation]
Consider a function, denoted by f (x), that maps each input (x) to a corresponding output. What would be the mathematical expression for the rate at which the output changes with respect to a small change in input, precisely at a point (x)?
This is essentially asking for the derivative of the function ( f ) with respect to its variable (x), which gives us the slope of the tangent line to the function's graph at any point (x).
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Question 1 [c] [Explanation]
Determine the possible values for the parameter c which ensure that the function y = f (x) is graphically represented with specific characteristics. This is a follow-up task that may relate to previously established contexts or functions.
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