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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.

02 Hours

110 Marks

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IB MATH AA HL, Paper 1, November, 2021, TZ0, Solved Past Paper

Master the 2021 IB November for Paper 1 Mathematics AA HL with examiner tailored solutions and comments for TZ0

Question 1 [Explained]

The task involves finding the original function (y(x)) based on its derivative. We're given that the derivative of (y) with respect to (x), denoted as $(\frac{d y}{d x})$ , equals the cosine of $(x - \frac{π}{4})$ . Additionally, there's a specific condition given where (y) is 2 at $(x = \frac{3 π}{4})$ . Using this information, we need to calculate the formula for (y) that will give us the value of (y) for any (x).

To break it down: We have a rate of change of (y) expressed through a trigonometric function, and we want to reverse-engineer the original equation for (y) given this rate of change and one point on the curve. The challenge is to integrate the rate of change and apply the initial condition to find the exact function.

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Question 2 [Explained]

Let's explore a mathematical function named (f), crafted with the rule $(\frac{2 x + 4}{3 - x})$ , valid for every real number except (x = 3). The exclusion of 3 is essential since it would make the denominator zero, and division by zero is undefined.

Question 2 [a] [Explanation]

Consider presenting the mathematical formula that encapsulates the relationship between the critical variables under examination.

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Question 2 [a] [i] [Explanation]

Identify the line that the graph of the function (f) cannot cross vertically.

Question 2 [a] [ii] [Explanation]

Consider a function ( f ). We are interested in understanding if there's a line that the graph of ( f ) approaches but never actually reaches as we move far to the right or left along the x-axis. This special line is called a horizontal asymptote. What is this line for the function ( f )?

Question 2 [b] [Explanation]

Determine the precise points on the coordinate plane where the curve represented by the function ( f ) intersects the horizontal axis.

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Question 2 [b] [i] [Explanation]

Consider the point where a curve intersects the x-axis. This specific point is where the curve's height is zero. Now, let's move along the curve, away from this intersection point, such that we proceed to the right for a certain distance, measured along the x-axis. Then, from our new position, we draw a vertical line up to meet the curve again.

What we want to determine is the length of this vertical line. In other words, we're interested in finding out the height of the curve at this new point on the x-axis, a certain distance away from the original intersection.