IB Mathematics AA HL - Questionbank
Sequences & Series
Arithmetic/Geometric, Sigma Notation, Applications, Compound Interest…
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Question 1
[Maximum mark: 6]
An arithmetic sequence has , , .
-
Find the common difference, . [2]
-
Find . [2]
-
Find . [2]
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Question 2
[Maximum mark: 6]
Jeremy invests into a savings account that pays an annual interest rate of %, compounded annually.
-
Write down a formula which calculates that total value of the investment after years. [2]
-
Calculate the amount of money in the savings account after:
-
year;
-
years. [2]
-
-
Jeremy wants to use the money to put down a deposit on an apartment. Determine if Jeremy will be able to do this within a -year timeframe.[2]
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Question 3
[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]
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Question 4
[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]
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Question 5
[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]
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Question 6
[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]
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Question 7
[Maximum mark: 6]
Hannah buys a car for . The value of the car depreciates by % each year.
-
Find the value of the car after years. [3]
Patrick buys a car for . The car depreciates by a fixed percentage each year, and after years it is worth .
- Find the annual rate of depreciation of the car.
[3]
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Question 8
[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]
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Question 9
[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]
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Question 10
[Maximum mark: 6]
A D printer builds a set of Eifel Tower Replicas in different sizes. The height of the largest tower in this set is cm. The heights of successive smaller towers are % of the preceding larger tower, as shown in the diagram below.
-
Find the height of the smallest tower in this set. [3]
-
Find the total height if all towers were placed one on top of another. [3]
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Question 11
[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]
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Question 12
[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]
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Question 13
[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]
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Question 14
[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]
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Question 15
[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]
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Question 16
[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]
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Question 17
[Maximum mark: 6]
Julia wants to buy a house that requires a deposit of Australian dollars (AUD).
Julia is going to invest an amount of AUD in an account that pays a nominal annual interest rate of %, compounded monthly.
-
Find the amount of AUD Julia needs to invest to reach AUD after years. Give your answer correct to the nearest dollar. [3]
Julia's parents offer to add AUD to her initial investment from part (a), however, only if she invests her money in a more reliable bank that pays a nominal annual interest rate only of %, compounded quarterly.
- Find the number of years it would take Julia to save the
AUD if she accepts her parents money and
follows their advice. Give your answer correct to the nearest
year. [3]
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Question 18
[Maximum mark: 7]
The first three terms of a geometric sequence are , , .
-
Find the value of the common ratio, . [2]
-
Find the sum of the first ten terms in the sequence. [2]
-
Find the greatest value of such that . [3]
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Question 19
[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]
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Question 20
[Maximum mark: 6]
On st of January , Fiona decides to take out a bank loan to purchase a new Tesla electric car. Fiona takes out a loan of with a bank that offers a nominal annual interest rate of , compounded monthly.
The size of Fiona's loan at the end of each year follows a geometric sequence with common ratio, .
-
Find the value of , giving your answer to five significant figures. [3]
The bank lets the size of Fiona's loan increase until it becomes triple the size of the original loan. Once this happens, the bank demands that Fiona pays the entire amount back to close the loan.
- Find the year during which Fiona will need to pay back the
loan. [3]
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Question 21
[Maximum mark: 6]
In this question give all answers correct to the nearest whole number.
A population of goats on an island starts at . The population is expected to increase by % each year.
-
Find the expected population size after:
-
years;
-
years. [4]
-
-
Find the number of years it will take for the population to reach . [2]
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Question 22
[Maximum mark: 6]
The first term of an arithmetic sequence is and the common difference is .
-
Find the value of the nd term of the sequence. [2]
The first term of a geometric sequence is . The th term of the geometric sequence is equal to the th term of the arithmetic sequence given above.
-
Write down an equation using this information. [2]
-
Calculate the common ratio of the geometric sequence. [2]
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Question 23
[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]
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Question 24
[Maximum mark: 6]
In this question give all answers correct to two decimal places.
Mia deposits Australian dollars (AUD) into a bank account. The bank pays a nominal annual interest rate of %, compounded semi-annually.
-
Find the amount of interest that Mia will earn over the next years. [3]
Ella also deposits AUD into a bank account. Her bank pays a nominal annual rate of %, compounded monthly. In years, the total amount in Ella's account will be AUD.
- Find the amount that Ella deposits in the bank account.
[3]
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Question 25
[Maximum mark: 5]
Maria invests into a savings account that pays a nominal annual interest rate of %, compounded monthly.
-
Calculate the amount of money in the savings account after years. [2]
-
Calculate the number of years it takes for the account to reach . [3]
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Question 26
[Maximum mark: 6]
On Gary's th birthday, he invests in an account that pays a nominal annual interest rate of %, compounded monthly.
The amount of money in Gary's account at the end of each year follows a geometric sequence with common ratio, .
-
Find the value of , giving your answer to four significant figures. [3]
Gary makes no further deposits or withdrawals from the account.
- Find the age Gary will be when the amount of money in his
account will be double the amount he invested. [3]
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Question 27
[Maximum mark: 7]
In an arithmetic sequence, the third term is and the ninth term is .
-
Find the common difference. [2]
-
Find the first term. [2]
-
Find the smallest value of such that . [3]
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Question 28
[Maximum mark: 6]
The first three terms of a geometric sequence are , , .
-
Find the value of the common ratio, . [2]
-
Find . [2]
-
Find . [2]
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Question 29
[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]
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Question 30
[Maximum mark: 6]
Emily deposits Australian dollars (AUD) into a bank account. The bank pays a nominal annual interest rate of %, compounded monthly.
-
Find the amount of money that Emily will have in her bank account after years. Give your answer correct to two decimal places. [3]
Emily will withdraw the money back from her bank account when the amount reaches AUD.
- Find the time, in months, until Emily withdraws the
money from her bank account. [3]
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Question 31
[Maximum mark: 6]
The Australian Koala Foundation estimates that there are about koalas left in the wild in . A year before, in , the population of koalas was estimated as . Assuming the population of koalas continues to decrease by the same percentage each year, find:
-
the exact population of koalas in ; [3]
-
the number of years it will take for the koala population to reduce to half of its number in . [3]
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Question 32
[Maximum mark: 7]
The first three terms of a geometric sequence are , , .
-
Find the value of the common ratio, . [2]
-
Find the value of . [2]
-
Find the least value of such that . [3]
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Question 33
[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.
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Question 34
[Maximum mark: 6]
Ali bought a car for . The value of the car depreciates by % each year.
-
Find the value of the car at the end of the first year. [2]
-
Find the value of the car after years. [2]
-
Calculate the number of years it will take for the car to be worth exactly half its original value. [2]
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Question 35
[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]
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Question 36
[Maximum mark: 6]
Landmarks are placed along the road from London to Edinburgh and the distance between each landmark is km. The first landmark placed on the road is km from London, and the last landmark is near Edinburgh. The length of the road from London to Edinburgh is km.
-
Find the distance between the fifth landmark and London. [3]
-
Determine how many landmarks there are along the road. [3]
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Question 37
[Maximum mark: 7]
In a geometric sequence, , .
-
Find the common ratio, . [2]
-
Find . [2]
-
Find the greatest value of such that . [3]
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Question 38
[Maximum mark: 6]
Greg has saved British pounds (GBP) over the last six months. He decided to deposit his savings in a bank which offers a nominal annual interest rate of , compounded monthly, for two years.
-
Calculate the total amount of interest Greg would earn over the two years. Give your answer correct to two decimal places. [3]
Greg would earn the same amount of interest, compounded semi-annually, for two years if he deposits his savings in a second bank.
- Calculate the nominal annual interest rate the second bank
offers. [3]
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Question 39
[Maximum mark: 6]
Peter is playing on a swing during a school lunch break. The height of the first swing was m and every subsequent swing was % of the previous one. Peter's friend, Ronald, gives him a push whenever the height falls below m.
-
Find the height of the third swing. [2]
-
Find the number of swings before Ronald gives Peter a push. [2]
-
Calculate the total height of swings if Peter is left to swing until coming
to rest. [2]
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Question 40
[Maximum mark: 6]
On st of January , Grace invests in an account that pays a nominal annual interest rate of %, compounded quarterly.
The amount of money in Grace's account at the end of each year follows a geometric sequence with common ratio, .
-
Find the value of , giving your answer to four significant figures. [3]
Grace makes no further deposits or withdrawals from the account.
- Find the year in which the amount of money in Grace's
account will become triple the amount she invested. [3]
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Question 41
[Maximum mark: 6]
Let , for .
-
-
Using sigma notation, write down an expression for .
-
Find the value of the sum from part (a) (i). [4]
-
A geometric sequence is defined by , for .
- Find the value of the sum of the geometric series .[2]
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Question 42
[Maximum mark: 6]
Consider the sum , where is a positive integer greater than .
-
Write down the first three terms of the series. [2]
-
Write down the number of terms in the series. [1]
-
Given that , find the value of . [3]
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Question 43
[Maximum mark: 6]
Jack rides his bike to work each morning. During the first minute, he travels metres. In each subsequent minute, he travels % of the distance travelled during the previous minute.
The distance from his home to work is metres. Jack leaves his house at : am and must be at work at : am.
Will Jack arrive to work on time? Justify your answer.
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Question 44
[Maximum mark: 6]
Sarah walks to school each morning. During the first minute, she travels . In each subsequent minute, she travels metres less than the distance she travelled during the previous minute. The distance from her home to school is metres. Sarah leaves her house at : am and must be at school by : am.
Will Sarah arrive to school on time? Justify your answer.
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Question 45
[Maximum mark: 6]
The fourth term of an arithmetic sequence is equal to and the sum of the first terms is .
-
Find the common difference and the first term. [4]
-
Determine the greatest value of such that the th term is positive. [2]
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Question 46
[Maximum mark: 6]
The sum of an infinite geometric sequence is . The second term of the sequence is . Find the possible values of .
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Question 47
[Maximum mark: 6]
The first term and the common ratio of a geometric series are denoted, respectively, by and , where . Given that the fourth term is and the sum to infinity is , find the value of and the value of .
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Question 48
[Maximum mark: 6]
The sum of the first three terms of a geometric sequence is , and the sum of the infinite sequence is . Find the common ratio.
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Question 49
[Maximum mark: 6]
The seventh term of an arithmetic sequence is equal to and the sum of the first terms is .
Find the common difference and the first term.
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Question 50
[Maximum mark: 5]
The third term of an arithmetic sequence is equal to and the sum of the first terms is .
Find the common difference and the first term.
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Question 51
[Maximum mark: 6]
The st, th and th terms of an arithmetic sequence, with common difference , , are the first three terms of a geometric sequence, with common ratio , . Given that the st term of both sequences is , find the value of and the value of .
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Question 52
[Maximum mark: 7]
The sides of a square are cm long. A new square is formed by joining the midpoints of the adjacent sides and two of the resulting triangles are shaded as shown. This process is repeated more times to form the right hand diagram below.
-
Find the total area of the shaded region in the right hand diagram above. [4]
-
Find the total area of the shaded region if the process is repeated indefinitely.[3]
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Question 53
[Maximum mark: 15]
The first three terms of an infinite geometric sequence are , where .
-
-
Write down an expression for the common ratio, .
-
Hence show that satisfies the equation .[5]
-
-
-
Find the possible values for .
-
Find the possible values for . [5]
-
-
The geometric sequence has an infinite sum.
-
Which value of leads to this sum. Justify your answer.
-
Find the sum of the sequence. [5]
-
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Question 54
[Maximum mark: 14]
Alex and Julie each have a goal of saving to put towards a house deposit. They each have to invest.
-
Alex chooses his local bank and invests his in a savings account that offers an interest rate of per annum compounded annually.
-
Find the value of Alex's investment after years, to the nearest hundred dollars.
-
Alex reaches his goal after n years, where n is an integer. Determine the value of n. [4]
-
-
Julie chooses a different bank and invests her in a savings account that offers an interest rate of per annum compounded monthly, where is set to two decimal places.
Find the minimum value of needed for Julie to reach her goal after years. [3]
-
Xavier also wants to reach a savings goal of . He doesn't trust his local bank so he decides to put his money into a safety deposit box where it does not earn any interest. His system is to add more money into the safety deposit box each year. Each year he will add one third of the amount he added in the previous year.
-
Show that Xavier will never reach his goal if his initial deposit into the safety deposit box is .
-
Find the amount Xavier needs to initially deposit in order to reach his goal after years. Give your answer to the nearest dollar. [7]
-
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Question 55
[Maximum mark: 6]
A bouncy ball is dropped from a height of metres onto a concrete floor. After hitting the floor, the ball rebounds back up to % of it's previous height, and this pattern continues on repeatedly, until coming to rest.
-
Show that the total distance travelled by the ball until coming to rest can be expressed by
[2]
-
Find an expression for the total distance travelled by the ball, in terms of the number of bounces, . [2]
-
Find the total distance travelled by the ball. [2]
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Question 56
[Maximum mark: 6]
The sum of the first three terms of a geometric sequence is , and the sum of the infinite sequence is . Find the common ratio.
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Question 57
[Maximum mark: 5]
Consider a geometric sequence with common ratio such that .
- Show that .[2]
A geometric sequence has a first term of 150 and a second term of 120.
- Find the smallest value of such that .[3]
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Question 58
[Maximum mark: 13]
Grant wants to save over 5 years to help his son pay for his college tuition. He deposits into a savings account that has an interest rate of per annum compounded monthly for years.
-
Show that Grant will not be able to reach his target. [2]
-
Find the minimum amount, to the nearest dollar, that Grant would need to deposit initially for him to reach his target. [3]
Grant only has to invest, so he asks his sister, Caroline, to help him accelerate the saving process. Caroline is happy to help and offers to contribute part of her income each year. Her annual income is per year. She starts by contributing one fifth of her annual income, and then decreases her contributions by half each year until the target is reached. Caroline's contributions do not yield any interest.
-
Show that Grant and Caroline together can reach the target in 5 years. [4]
Grant and Caroline agree that Caroline should stop contributing once she contributes enough to complement the deficit of Grant's investment.
- Find the whole number of years after which Caroline
will will stop contributing. [4]
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Question 59
[Maximum mark: 8]
Let , for .
The th maximum point on the graph of has -coordinate , where .
-
Given that , find . [4]
-
Hence find the value of such that . [4]
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Question 60
[Maximum mark: 8]
It is known that the number of trees in a small forest will decrease by % each year unless some new trees are planted. At the end of each year, new trees are planted to the forest. At the start of , there are trees in the forest.
-
Show that there will be roughly trees in the forest at the start of . [4]
-
Find the approximate number of trees in the forest at the start of . [4]
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Question 61
[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 62
[Maximum mark: 13]
-
The following diagram shows [PQ], with length cm. The line is divided into an infinite number of line segments. The diagram shows the first four segments.
The length of the line segments are cm, cm, cm, , where .
Show that . [5]
-
The following diagram shows [RS], with length cm, where . Squares with side lengths cm, cm, cm, , where , are drawn along [RS]. This process is carried on indefinitely. The diagram shows the first four squares.
The total sum of the areas of all the squares is . Find the value of . [8]
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Question 63
[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 64
[Maximum mark: 6]
Given a sequence of integers, between and , which are divisible by .
-
Find their sum. [2]
-
Express this sum using sigma notation. [2]
An arithmetic sequence has first term and common difference of . The sum of the first terms of this sequence is negative.
- Find the greatest value of . [2]
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Question 65
[Maximum mark: 15]
The first two terms of an infinite geometric sequence are and , where , and .
-
-
Find an expression for in terms of .
-
Find the possible values of . [5]
-
-
Show that the sum of the infinite sequence is . [4]
-
Find the values of which give the greatest value of the sum. [6]
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Question 66
[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 67
[Maximum mark: 15]
Bill takes out a bank loan of to buy a premium electric car, at an annual interest rate of %. The interest is calculated at the end of each year and added to the amount outstanding.
-
Find the amount of money Bill would owe the bank after years. Give your answer to the nearest dollar. [3]
To pay off the loan, Bill makes quarterly deposits of at the end of every quarter in a savings account, paying a nominal annual interest rate of %. He makes his first deposit at the end of the first quarter after taking out the loan.
-
Show that the total value of Bill's savings after years is . [3]
-
Given that Bill's aim is to own the electric car after years, find the value for to the nearest dollar. [3]
Melinda visits a different bank and makes a single deposit of , the annual rate being %.
-
-
Melinda wishes to withdraw at the end of each year for a period of years. Show that an expression for the minimum value of is
-
Hence, or otherwise, find the minimum value of that would permit Melinda to withdraw annual amounts of indefinitely. Give your answer to the nearest dollar. [6]
-
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Question 68
[Maximum mark: 28]
This question asks you to explore the sequence defined by
where and are the roots of the quadratic equation and .
-
Find the value of and the value of . Give your answers in the form , where .[3]
-
Hence find the values of and . [4]
-
Show that and . [1]
-
Hence show that .[4]
-
Suppose that and are integers. Show that is also an integer.[2]
-
Hence show that is an integer for all .[2]
Now consider the sequence defined by
-
Find the exact values of and .[4]
-
Express in terms of and .[4]
-
Hence show that is a multiple of for all .[4]
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Question 69
[Maximum mark: 24]
This question asks you to investigate some properties of hexagonal numbers.
Hexagonal numbers can be represented by dots as shown below where denotes the th hexagonal number, .
Note that points are required to create the regular hexagon with side of length , while points are required to create the next hexagon with side of length , and so on.
-
Write down the value of .[1]
-
By examining the pattern, show that , . [3]
-
By expressing as a series, show that , .[3]
-
Hence, determine whether is a hexagonal number.[3]
-
Find the least hexagonal number which is greater than .[5]
-
Consider the statement:
is the only hexagonal number which is divisible by .
Show that this statement is false.[2]
Matt claims that given and , , then
- Show, by mathematical induction, that Matt's claim is true
for all .[7]
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Question 70
[Maximum mark: 14]
The cubic polynomial equation has three roots and . By expanding the product , show that
-
-
;
-
;
-
. [3]
-
It is given that and for parts (b) and (c) below.
-
-
In the case that the three roots and form an arithmetic
sequence, show that one of the roots is . -
Hence determine the value of . [5]
-
-
In another case the three roots form a geometric sequence. Determine
the value of . [6]
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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 step-by-step 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, in-depth. 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.