IB Math AA HL  Questionbank
Systems of Equations
Solving 3 x 3 Systems of Linear Equations, Row Operations, Unique/No/Infinite Solutions…
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Question 1
no calculator
easy
[Maximum mark: 6]
The system of equations given below represents three planes in space.

Show that this system of equations has an infinite number of solutions. [3]

Find the parametric equations of the line of intersection of the three planes. [3]
easy
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Question 2
no calculator
medium
[Maximum mark: 5]
The system of equations given below represents three planes in space.
Find the set of values of
$a$ and $b$ such that the three planes have no points of
intersection.
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Question 3
calculator
medium
[Maximum mark: 6]
The system of equations given below represents three planes in space.
Find the set of values of $a$ and $b$ such that the three planes have exactly one intersection point.
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Question 4
no calculator
medium
[Maximum mark: 9]
Consider the following system of equations:
where $a,b \in \mathbb{R}$.

Find conditions on $a$ and $b$ for which

the system has no solutions;

the system has only one solution;

the system has an infinite number of solutions. [6]


In the case where the number of solutions is infinite, find the general
solution of the system of equations in Cartesian form. [3]
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Question 5
no calculator
medium
[Maximum mark: 9]
Consider the following system of equations:
where $a,b \in \mathbb{R}$.

Find conditions on $a$ and $b$ for which

the system has no solutions;

the system has only one solution;

the system has an infinite number of solutions. [6]


In the case where the number of solutions is infinite, find the general
solution of the system of equations in Cartesian form. [3]
medium
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Question 6
no calculator
medium
[Maximum mark: 8]
Consider the following system of equations:
where $p \in \mathbb{R}$.

Show that this system does not have a unique solution for any value of $p$. [4]


Determine the value of $p$ for which the system is consistent.

For this value of $p$, find the general solution of the system. [4]

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Frequently Asked Questions
What is the IB Math AA HL Questionbank?
The IB Math Analysis and Approaches (AA) HL 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 HL 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 Higher Level course.
Where should I start in the AA HL Questionbank?
The AA HL Questionbank is designed to help IB students practice AA HL 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 HL Question bank. For example, if you want to practice AA HL exam style questions that involve Complex Numbers, you can go to AA SL Topic 1 (Number & Algebra) and go to the Complex Numbers area of the question bank. On this page there is a carefully designed set of IB Math AA HL 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 HL Questionbank?
The AA HL Questionbank is perfect for revising a particular topic or concept, indepth. For example, if you wanted to improve your knowledge of Counting Principles (Combinations & Permutations), there is a set of full length IB Math AA HL exam style questions focused specifically on this concept. Alternatively, Revision Village also has an extensive library of AA HL Practice Exams, where students can simulate the length and difficulty of an IB exam with the Mock Exam sets, as well as AA HL Key Concepts, where students can learn and revise the underlying theory, if missed or misunderstood in class.
What if I finish the AA HL Questionbank?
With an extensive and growing library of full length IB Math Analysis and Approaches (AA) HL exam style questions in the AA HL 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 HL Question bank, then a popular option would be to go to the AA HL 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 HL exam.
More IB Math AA HL Resources
Questionbank
All the questions you could need! Sorted by topic and arranged by difficulty, with mark schemes and video solutions for every question.
Practice Exams
Choose your revision tool! Contains topic quizzes for focused study, Revision Village mock exams covering the whole syllabus, and the revision ladder to precisely target your learning.
Key Concepts
Helpful refreshers summarizing exactly what you need to know about the most important concepts covered in the course.
Past Papers
Full worked solutions to all past paper questions, taught by experienced IB instructors.