IB Mathematics AA SL - Questionbank
Exponents & Logs
Exponent & Log Laws, Solving Exponential & Logarithmic Equations…
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Question 1
[Maximum mark: 7]
Find the value of each of the following, giving your answer as an integer.
-
. [2]
-
. [2]
-
. [3]
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Question 2
[Maximum mark: 6]
Find the value of each of the following, giving your answer as an integer.
-
. [2]
-
. [2]
-
. [2]
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Question 3
[Maximum mark: 6]
Let , , . Write down the following expressions in terms of , and .
-
[2]
-
[2]
-
[2]
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Question 4
[Maximum mark: 7]
Let and . Write down the following expressions in terms of and .
-
[2]
-
[2]
-
[3]
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Question 5
[Maximum mark: 6]
Let , where . Write down each of the following
expressions
in terms of .
-
[2]
-
[2]
-
[2]
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Question 6
[Maximum mark: 5]
Consider . Given that , find the value of .
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Question 7
[Maximum mark: 6]
-
Write the expression in the form of , where . [3]
-
Hence, or otherwise, solve . [3]
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Question 8
[Maximum mark: 5]
Solve the equation for .
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Question 9
[Maximum mark: 6]
Given that .
-
Find the exact value of . [2]
-
Find the exact value of . [2]
-
Find the value of , giving your answer correct to significant figures. [2]
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Question 10
[Maximum mark: 5]
Find the values of when .
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Question 11
[Maximum mark: 5]
Solve the equation for .
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Question 12
[Maximum mark: 6]
-
Write down the value of
-
;
-
;
-
. [3]
-
-
Hence solve .[3]
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Question 13
[Maximum mark: 6]
-
Write down the value of
-
;
-
;
-
. [3]
-
-
Hence solve .[3]
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Question 14
[Maximum mark: 6]
Given that .
-
Find the exact value of . [2]
-
Find the exact value of . [2]
-
Find the value of , giving your answer correct to significant figures. [2]
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Question 15
[Maximum mark: 5]
Find the values of when .
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Question 16
[Maximum mark: 5]
Solve the equation .
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Question 17
[Maximum mark: 5]
Solve the equation .
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Question 18
[Maximum mark: 5]
Solve , for .
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Question 19
[Maximum mark: 6]
Find the value of
-
; [2]
-
. [4]
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Question 20
[Maximum mark: 6]
Find the value of
-
; [2]
-
. [4]
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Question 21
[Maximum mark: 15]
The equation has two solutions, and .
- Find the value of and the value of .[5]
A second equation, , also has two solutions, and .
-
-
Show that this second equation can be expressed as
-
Hence find the value of and the value of . [7]
-
-
Given that , find the value of . Give your answer in the form , where .[3]
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Question 22
[Maximum mark: 18]
The first three terms of an infinite sequence, in order, are
First consider the case in which the series is geometric.
-
-
Find the possible values of .
-
Hence or otherwise, show that the series is convergent. [3]
-
-
Given that and , find the value of . [3]
Now suppose that the series is arithmetic.
-
-
Show that .
-
Write down the common difference in the form , where . [4]
-
-
Given that the sum of the first terms of the sequence is , find the value of . [8]
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Question 23
[Maximum mark: 5]
Solve the equation .
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Question 24
[Maximum mark: 7]
Solve the simultaneous equations:
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Question 25
[Maximum mark: 14]
The first two terms of an infinite geometric sequence, in order, are
-
Find the common ratio, . [2]
-
Show that the sum of the infinite sequence is . [3]
The first three terms of an arithmetic sequence, in order, are
-
Find the common difference , giving your answer as an integer. [3]
Let be the sum of the first terms of the arithmetic sequence.
-
Show that . [3]
-
Given that is equal to one third of the sum of the infinite geometric
sequence, find , giving your answer in the form where . [3]
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Question 26
[Maximum mark: 7]
Consider , for , where .
The equation has exactly one solution. Find the value of .
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Question 27
[Maximum mark: 6]
Solve , for .
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Question 28
[Maximum mark: 5]
Solve the equation for . Express your answer in terms of and .
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Question 29
[Maximum mark: 5]
Find the integer values of and for which
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Question 30
[Maximum mark: 5]
Solve the equation for . Express your answer in terms of and .
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Question 31
[Maximum mark: 8]
The first three terms of a geometric sequence are , , , for .
-
Find the common ratio. [3]
-
Solve . [5]
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Question 32
[Maximum mark: 8]
-
Show that . [3]
-
Hence, or otherwise, solve , for .[5]
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Question 33
[Maximum mark: 8]
-
Show that . [3]
-
Hence, or otherwise, solve , for .[5]
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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 step-by-step 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.
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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.
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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.