IB Mathematics AA SL  Questionbank
Proofs
Simple Deductive Proofs, LHS to RHS Proofs...
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Question 1
[Maximum mark: 4]
Prove that the sum of three consecutive positive integers is divisible by $3$.
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Question 2
[Maximum mark: 4]
Consider two consecutive positive integers, $k$ and $k+1$.
Show that the difference of their squares is equal to the sum of the two integers.
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Question 3
[Maximum mark: 4]
The product of three consecutive integers is increased by the middle integer.
Prove that the result is a perfect cube.
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Question 4
[Maximum mark: 6]

Show that $(2n1)^3 + (2n+1)^3 = 16n^3+12n$ for $n \in \mathbb{Z}$. [3]

Hence, or otherwise, prove that the sum of the cubes of any two consecutive odd integers is divisible by four. [3]
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Question 5
[Maximum mark: 5]

Prove that $\dfrac{5}{x^2} = \dfrac{5}{x(x2)}\dfrac{10}{x^2(x2)}$. [3]

Determine the set of numbers $x$ for which the proof in part (a) is valid. [2]
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Frequently Asked Questions
What is the IB Math AA SL Questionbank?
The IB Math Analysis and Approaches (AA) SL Questionbank is a comprehensive set of IB Mathematics exam style questions, categorised into syllabus topic and concept, and sorted by difficulty of question. The bank of exam style questions are accompanied by high quality stepbystep markschemes and video tutorials, taught by experienced IB Mathematics teachers. The IB Mathematics AA SL Question bank is the perfect exam revision resource for IB students looking to practice IB Math exam style questions in a particular topic or concept in their AA Standard Level course.
Where should I start in the AA SL Questionbank?
The AA SL Questionbank is designed to help IB students practice AA SL exam style questions in a specific topic or concept. Therefore, a good place to start is by identifying a concept that you would like to practice and improve in and go to that area of the AA SL Question bank. For example, if you want to practice AA SL exam style questions that have Exponents & Logarithms in them, you can go to AA SL Topic 1 (Number & Algebra) and go to the Exponents & Logarithms area of the question bank. On this page there is a carefully designed set of IB Math AA SL exam style questions, progressing in order of difficulty from easiest to hardest. If you’re just getting started with your revision, you could start at the top of the page with Question 1, or if you already have some confidence, you could start at the medium difficulty questions and progress down.
How should I use the AA SL Questionbank?
The AA SL Questionbank is perfect for revising a particular topic or concept, indepth. For example, if you wanted to improve your knowledge of The Binomial Theorem, there are over 20 full length IB Math AA SL exam style questions focused specifically on this concept. Alternatively, Revision Village also has an extensive library of AA SL Practice Exams, where students can simulate the length and difficulty of an IB exam with the Mock Exam sets, as well as AA SL Key Concepts, where students can learn and revise the underlying theory, if missed or misunderstood in class.
What if I finish the AA SL Questionbank?
With an extensive and growing library of full length IB Math Analysis and Approaches (AA) SL exam style questions in the AA SL Question bank, finishing all of the questions would be a fantastic effort, and you will be in a great position for your final exams. If you were able to complete all the questions in the AA SL Question bank, then a popular option would be to go to the AA SL Practice Exams section on Revision Village and test yourself with the Mock Exam Papers, to simulate the length and difficulty of an actual IB Mathematics AA SL exam.