IB Math AI Paper 2

If you're struggling to understand the structure of IB Math AI Paper 2, you've come to the right place! In this post, we will provide a thorough breakdown of IB Math AI Paper 2, ensuring you are familiarised with the structure of the exam and know what type of questions to expect so you can approach the exam with confidence. 

IB Math AI Paper 2

• Paper 2 is made up of extended-reponse questions based on the syllabus.
• Paper 2 may cover all topics of the syllabus. 
• SL students may score up to 80 marks while HL students can obtain a maximum of 110 marks.
• Individual questions may require knowledge of more than one topic.
• Questions may be presented in the form of words, symbols, diagrams or tables, or combinations of these.
• Normally, each question reflects an incline of difficulty, from relatively easy tasks at the start of a question to relatively difficult tasks at the end of a question. The emphasis is upon sustained reasoning.
• For SL, Paper 2 contributes 40% to the overall subject grade, while for HL, it accounts for 30%. 
• SL students have 1 hour 30 minutes, while HL students are given 2 hours to complete Paper 2.
• A calculator is required for this exam. 

A typical SL question may look the following way:

In a college 450 students were surveyed with the following results:

150 have a television 

205 have a computer 

220 have an iPhone 

75 have an iPhone and a computer 

60 have a television and a computer 

70 have a television and an iPhone 

40 have all three. 

(a) Draw a Ven diagram to show this information. Use T to represent the set of students who have a television, C the set of students who have a computer and I the set of students who have an iPhone. [4]

(b) Write down the number of students that 

      (i) have a computer only;

      (ii) have an iPhone and a computer but no television. [2]

(c) Write down n[T  ∩ (C ∪ l)']. [2]

(d) Calculate the number of students who have none of the three. [2]

Two students are chosen at random from the 450 students. Calculate the probability that

(e) 

      (i) neither has an iPhone

      (ii) only one of the students has an iPhone [6]

A typical HL question may look the following way:

A change in grazing habits has resulted in two species of herbivore, X and Y, competing for food on the same grasslands. At time t=0 environmentalists begin to record the sizes of both populations. Let the size of the population of X be x, and the size of Y be y. The following model is proposed for predicting the change in the sizes of the two populations:

x = 0.3x - 0.1y

y = -0.2x + 0.4y

for x,y > 0

(a) For this system of coupled differential equations find

      (i) the eigenvalues

      (ii) the eigenvectors [6]

(b) Hence write down the general solution of the system of equations. [1]

(c) Sketch the phase portrait for this system, for x, y > 0. [3]

On your sketch show

• the equation of the line defined by the eigenvector in the first quadrant
• at least two trajectories either side of this line using arrows on those trajectories to represent the change in population as t increases.

When t = 0 X has population of 2000.

(d) Write down a condition on the size of the initial population of Y if it is to avoid its population reducing to zero. [1]

(e) It is known that Y has an initial population of 2900. 

      (i) Find the value of t at which x = 0

      (ii) Find the population of Y at this value of t. [8]

How to succeed in Math AI Paper 2?

Solving numerous past papers is one of the best ways to prepare for IB Math AI Paper 2, as it helps you get used to the style of questions and improves your ability to apply mathematical techniques effectively. It is important to do this under exam conditions to master your time management skills and get used to the exam format. It is also crucial you master the GDC. It is a truly powerful tool that can save you time on complex calculations, graphing, and statistical analysis while reducing the risk of human error. However, mastering its use is critical because it isn’t always intuitive to operate. We highly recommend you spend a considerable amount of time learning and practicing with your GDC as this will ensure that you can use its functions confidently during the exam. 

We hope you found this post helpful. For more useful materials associated with the IB check out the wide variety of IA, EE and TOK exemplars available at Clastify.