IB Math AA HL - Questionbank
Topic 1 All - Number & Algebra
All Questions for Topic 1 (Number & Algebra). Sequences & Series, Exponents & Logs, Binomial Theorem, Counting Principles, Complex Numbers, Proofs, Systems of Equations
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Question 1
no calculator
easy
[Maximum mark: 6]
Consider an arithmetic sequence
-
Find the common difference, . [2]
-
Find the th term in the sequence. [2]
-
Find the sum of the first terms in the sequence. [2]
easy
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Question 2
calculator
easy
[Maximum mark: 6]
An arithmetic sequence has , , .
-
Find the common difference, . [2]
-
Find . [2]
-
Find . [2]
easy
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Question 3
calculator
easy
[Maximum mark: 6]
Only one of the following four sequences is arithmetic and only one of them is geometric.
-
State which sequence is arithmetic and find the common difference of the sequence. [2]
-
State which sequence is geometric and find the common ratio of the sequence.[2]
-
For the geometric sequence find the exact value of the eighth term. Give your answer as a fraction. [2]
easy
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Question 4
calculator
easy
[Maximum mark: 6]
Only one of the following four sequences is arithmetic and only one of them is geometric.
-
State which sequence is arithmetic and find the common difference of the sequence. [2]
-
State which sequence is geometric and find the common ratio of the sequence.[2]
-
For the geometric sequence find the exact value of the sixth term. Give your answer as a fraction. [2]
easy
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Question 5
no calculator
easy
[Maximum mark: 6]
Find the value of each of the following, giving your answer as an integer.
-
. [2]
-
. [2]
-
. [2]
easy
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Question 6
no calculator
easy
[Maximum mark: 7]
Find the value of each of the following, giving your answer as an integer.
-
. [2]
-
. [2]
-
. [3]
easy
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Question 7
no calculator
easy
[Maximum mark: 4]
Expand in descending powers of and simplify your answer.
easy
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Question 8
no calculator
easy
[Maximum mark: 4]
Consider two consecutive positive integers, and .
Show that the difference of their squares is equal to the sum of the two integers.
easy
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Question 9
no calculator
easy
[Maximum mark: 4]
Prove that the sum of three consecutive positive integers is divisible by .
easy
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Question 10
calculator
easy
[Maximum mark: 6]
Consider the infinite geometric sequence , , ,
-
Find the common ratio, . [2]
-
Find the th term. [2]
-
Find the exact sum of the infinite sequence. [2]
easy
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Question 11
calculator
easy
[Maximum mark: 6]
The table shows the first four terms of three sequences: , , and .
-
State which sequence is
-
arithmetic;
-
geometric. [2]
-
-
Find the sum of the first terms of the arithmetic sequence. [2]
-
Find the exact value of the th term of the geometric sequence. [2]
easy
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Question 12
no calculator
easy
[Maximum mark: 7]
An arithmetic sequence is given by , ,
-
Write down the value of the common difference, . [1]
-
Find
-
;
-
. [4]
-
-
Given that , find the value of . [2]
easy
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Question 13
calculator
easy
[Maximum mark: 6]
Consider the infinite geometric sequence , , , , ...
-
Find the common ratio. [2]
-
Find the th term. [2]
-
Find the exact sum of the infinite sequence. [2]
easy
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Question 14
calculator
easy
[Maximum mark: 6]
A tennis ball bounces on the ground times. The heights of the bounces, form a geometric sequence. The height that the ball bounces the first time, , is cm, and the second time, , is cm.
-
Find the value of the common ratio for the sequence. [2]
-
Find the height that the ball bounces the tenth time, . [2]
-
Find the total distance travelled by the ball during the first six bounces (up and down). Give your answer correct to decimal places. [2]
easy
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Question 15
calculator
easy
[Maximum mark: 6]
The third term, , of an arithmetic sequence is . The common
difference of
the sequence, , is .
-
Find , the first term of the sequence. [2]
-
Find , the th term of sequence. [2]
The first and fourth terms of this arithmetic sequence are the first two
terms
of a geometric sequence.
- Calculate the sixth term of the geometric sequence.
[2]
easy
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Question 16
calculator
easy
[Maximum mark: 6]
The fifth term, , of a geometric sequence is . The sixth term, , is .
-
Find the common ratio of the sequence. [2]
-
Find , the first term of the sequence. [2]
-
Calculate the sum of the first terms of the sequence. [2]
easy
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Question 17
calculator
easy
[Maximum mark: 6]
The fourth term, , of a geometric sequence is . The fifth term, , is .
-
Find the common ratio of the sequence. [2]
-
Find , the first term of the sequence. [2]
-
Calculate the sum of the first terms of the sequence. [2]
easy
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Question 18
calculator
easy
[Maximum mark: 6]
The fifth term, , of an arithmetic sequence is . The eleventh term, , of the same sequence is .
-
Find , the common difference of the sequence. [2]
-
Find , the first term of the sequence. [2]
-
Find , the sum of the first terms of the sequence. [2]
easy
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Question 19
no calculator
easy
[Maximum mark: 7]
Let and . Write down the following expressions in terms of and .
-
[2]
-
[2]
-
[3]
easy
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Question 20
no calculator
easy
[Maximum mark: 7]
Let and . Write down the in terms of and .
-
[2]
-
[2]
-
[3]
easy
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Question 21
no calculator
easy
[Maximum mark: 6]
Let , , . Write down the following expressions in terms of , and .
-
[2]
-
[2]
-
[2]
easy
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Question 22
no calculator
easy
[Maximum mark: 5]
Solve the equation , giving your answer in the form where , .
easy
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Question 23
no calculator
easy
[Maximum mark: 5]
Consider . Given that , find the value of .
easy
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Question 24
no calculator
easy
[Maximum mark: 5]
Consider . Given that , find the value of .
easy
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Question 25
calculator
easy
[Maximum mark: 4]
Expand in descending powers of and simplify your answer.
easy
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Question 26
no calculator
easy
[Maximum mark: 5]
Consider the expansion of .
-
Write down the number of terms in this expansion. [1]
-
Find the term in . [4]
easy
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Question 27
calculator
easy
[Maximum mark: 6]
Consider the expansion of .
-
Write down the number of terms in this expansion. [1]
-
Find the coefficient of the term in . [5]
easy
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Question 28
no calculator
easy
[Maximum mark: 4]
The product of three consecutive integers is increased by the middle integer.
Prove that the result is a perfect cube.
easy
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Question 29
no calculator
easy
[Maximum mark: 6]
Consider the following sequence of figures.
Figure 1 contains line segments.
-
Given that Figure contains line segments, show that .[3]
-
Find the total number of line segments in the first figures. [3]
easy
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Question 30
no calculator
easy
[Maximum mark: 5]
Consider an arithmetic sequence where . Find the value of the first term, , and the value of the common difference, .
easy
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Question 31
calculator
easy
[Maximum mark: 6]
In an arithmetic sequence, , .
-
Find the common difference. [2]
-
Find the first term. [2]
-
Find the sum of the first terms in the sequence. [2]
easy
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Question 32
no calculator
easy
[Maximum mark: 6]
The first three terms of a geometric sequence are , , .
-
Find the value of the common ratio, . [2]
-
Find . [2]
-
Find . [2]
easy
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Question 33
no calculator
easy
[Maximum mark: 6]
In an arithmetic sequence, , .
-
Find the common difference. [2]
-
Find the first term. [2]
-
Find the sum of the first terms in the sequence. [2]
easy
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Question 34
calculator
easy
[Maximum mark: 5]
In an arithmetic sequence, the sum of the 2nd and 6th term is .
Given that the sum of the first six terms is , determine the first
term and common difference of the sequence.
easy
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Question 35
calculator
easy
[Maximum mark: 5]
An arithmetic sequence has first term and common difference .
-
Given that the th term of the sequence is zero, find the value of . [2]
Let denote the sum of the first terms of the sequence.
- Find the maximum value of . [3]
easy
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