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 AI HL, Paper 3, May, 2022, TZ1, Solved Past Paper
Master the 2022 IB May for Paper 3 Mathematics AI HL with examiner tailored solutions and comments for TZ1
Question 1 [Explained]
Let's think about how a computer virus spreads through a city's computers, and how we can use math to guess how many will get hit by this digital bug.
Imagine a clock starting the moment the first computer gets infected. We count every day that passes as t.
Now, think of a running total, Q(t), which adds up all the computers that have caught the virus by the end of each day t. A smart person, like a systems analyst, has already figured out these details and collected some numbers to help us understand the spread.
To put it simply, t is our day counter since the virus started its journey, and Q(t) keeps a tally of all the unlucky computers that have been ambushed by the virus up to that point. With these two things, we can start to sketch out the virus's path through the city and make some educated guesses on what might happen next.
t | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
Q(t) | 20 | 90 | 403 | 1806 | 8070 | 32667 | 120146 |
Question 1 [a] [i] [Explanation]
Let's determine the formula for a line that best fits a set of data points given by a function (Q(t) ). This line is going to show us the overall trend of the function's values over time, specifically on the time interval (t).
Now, to frame this in more formal mathematical language, we are seeking the equation for the linear regression of the function (Q(t)). It's a way to find a straight line that most closely approximates the function's behavior on the interval (t).
Question 1 [a] [ii] [Explanation]
Consider the formula for calculating the strength of the relationship between two variables. This formula, denoted as (r), is commonly known as the Pearson correlation coefficient. What would be its numerical value?
In simpler terms, if we were to measure how two types of data are connected, what number would we use to describe this connection using Pearson's method?
Question 1 [a] [iii] [Explanation]
Explain why conducting a hypothesis test on the value of r found in part (a)(ii) would be inappropriate.
The question asks you to discuss the reasons why it is not suitable to perform a hypothesis test on the r value calculated in section (a)(ii). R typically represents the correlation coefficient in statistics, which measures the strength and direction of a linear relationship between two variables.