IB Mathematics AI HL - Questionbank
Number Skills
Approximation, Rounding, Decimal Places, Significant Figures, Scientific Notation, Percentage Error...
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Question 1
[Maximum mark: 6]
After solving a problem, John has an exact answer of .
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Write down the exact value of in the form , where .[2]
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State the value of given correct to significant figures. [1]
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Calculate the percentage error if is given correct to significant figures. [3]
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Question 2
[Maximum mark: 6]
Given that , where , and .
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Find the exact value of . [2]
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Write your answer to part (a)
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correct to decimal places;
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correct to significant figures;
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in the form , where and .[4]
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Question 3
[Maximum mark: 6]
Let , where , , and .
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Find the value of . Write down your full calculator display. [2]
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Give your answer to part (a) correct to
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three significant figures;
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three decimal places. [2]
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Give the answer to part (b) (i) in the form , where , .[2]
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Question 4
[Maximum mark: 6]
Let , where , and .
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Find the exact value of . [2]
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Give your answer to part (a) correct to
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three decimal places;
-
three significant figures. [2]
-
-
Calculate the percentage error if is given to three decimal places. [2]
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Question 5
[Maximum mark: 6]
The volume of a hemisphere, , is given by the formula
where is the total surface area.
The total surface area of a given hemisphere is cm.
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Calculate the volume of this hemisphere in cm. Give your answer correct to one decimal place. [3]
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Write down your answer to part (a) correct to the nearest integer. [1]
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Write down your answer to part (b) in the form , where and .[2]
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Question 6
[Maximum mark: 6]
Four cement bags labelled, "5 kg", were delivered to a customer. The customer measured each bag to check their weights and recorded the following:
-
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Find the mean of the customer's measurements.
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Calculate the percentage error between the mean and the stated,
approximate weight of kg. [3]
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Calculate , giving your answer
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correct to the nearest integer;
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in the form , where and . [3]
-
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Question 7
[Maximum mark: 6]
The distance between two points with coordinates and is equal to .
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Calculate the distance between points A and B. Give your answer correct to three significant figures. [3]
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Give your answer from part (a) correct to one decimal place. [1]
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Write the answer to part (b) in the form , where , . [2]
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Question 8
[Maximum mark: 6]
The following diagram shows a rectangle with sides of length cm and cm.
- Write down the area of the rectangle in the form ,
where
and . [3]
Natalie estimates the area of the rectangle to be cm.
- Find the percentage error in Natalie's estimate.
[3]
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Question 9
[Maximum mark: 8]
A cuboid has the following dimensions: cm, cm, and cm, measured correct to the nearest millimetre.
- Using these measurements, calculate the volume of the cuboid, in cm. Give your answer to two decimal places. [2]
The lower and upper bounds for the length of the cuboid can be expressed as .
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Write similar expressions for
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the width;
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the height. [2]
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Hence, calculate the minimum volume of the cuboid. Give your answer to three significant figures. [2]
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Write your answer to part (c) in the form , where and . [2]
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Question 10
[Maximum mark: 6]
Let , where , and .
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Calculate the exact value of . [2]
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Give your answer to correct to
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two significant figures;
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two decimal places. [2]
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Sasha estimates the value of to be .
- Calculate the percentage error in Sasha's estimate.
[2]
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Question 11
[Maximum mark: 6]
Given , , and ,
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calculate the value of . [2]
Albert first writes , and correct to one significant figure and then uses these values to estimate the value of .
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Write down , and each correct to one significant figure.
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Find Albert's estimate of the value of . [2]
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Calculate the percentage error in Albert's estimate of the value of . [2]
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Frequently Asked Questions
What is the IB Math AI HL Questionbank?
The IB Math Applications and Interpretation (AI) 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 step-by-step markschemes and video tutorials, taught by experienced IB Mathematics teachers. The IB Mathematics AI 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 AI Higher Level course.
Where should I start in the AI HL Questionbank?
The AI HL Questionbank is designed to help IB students practice AI 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 AI HL Question bank. For example, if you want to practice AI HL exam style questions involving Matrices, you can go to AI HL Topic 1 (Number & Algebra) and go to the Matrices area of the question bank. On this page there is a carefully designed set of IB Math AI 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 AI HL Questionbank?
The AI HL Questionbank is perfect for revising a particular topic or concept, in-depth. For example, if you wanted to improve your knowledge of Complex Numbers, there is a designed set of full length IB Math AI HL exam style questions focused specifically on this concept. Alternatively, Revision Village also has an extensive library of AI HL Practice Exams, where students can simulate the length and difficulty of an IB exam with the Mock Exam sets, as well as AI HL Key Concepts, where students can learn and revise the underlying theory, if missed or misunderstood in class.
What if I finish the AI HL Questionbank?
With an extensive and growing library of full length IB Math Applications and Interpretation (AI) HL exam style questions in the AI 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 AI HL Question bank, then a popular option would be to go to the AI 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 AI HL exam.