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Questions and Answers
The second term of an arithmetic sequence is 10 and the fourth term is 22. What is the common difference of this arithmetic sequence?
The second term of an arithmetic sequence is 10 and the fourth term is 22. What is the common difference of this arithmetic sequence?
6
The binomial expansion of $(1 + kx)^n$ is given by $1 + 12x + 28k^2x^2 + ... + k^nx^n$ where $n \in \mathbb{Z}^+$ and $k \in \mathbb{Q}$. The value of n is ______.
The binomial expansion of $(1 + kx)^n$ is given by $1 + 12x + 28k^2x^2 + ... + k^nx^n$ where $n \in \mathbb{Z}^+$ and $k \in \mathbb{Q}$. The value of n is ______.
8
In a geometric sequence with a first term of 3 and a fourth term of 81, the common ratio is 4.
In a geometric sequence with a first term of 3 and a fourth term of 81, the common ratio is 4.
False (B)
Daniela is considering Option B for receiving her winnings. The first payment is $2000, and each subsequent month, the payment increases by 6% from the previous month. What type of sequence does Option B represent?
Daniela is considering Option B for receiving her winnings. The first payment is $2000, and each subsequent month, the payment increases by 6% from the previous month. What type of sequence does Option B represent?
Sorin invested $120,000 at a nominal annual interest rate of 4% per annum, compounded monthly. Write an expression for the value of Sorin’s investment after n years.
Sorin invested $120,000 at a nominal annual interest rate of 4% per annum, compounded monthly. Write an expression for the value of Sorin’s investment after n years.
Daniela chose Option B and received her first payment on 1st January 2023. Sorin invested his inheritance on the same day. Which financial action yields more value after six months based on descriptions?
Daniela chose Option B and received her first payment on 1st January 2023. Sorin invested his inheritance on the same day. Which financial action yields more value after six months based on descriptions?
Given (n+1)^2 - n^2 = 2n + 1, this equation demonstrates that the difference between consecutive perfect squares is always an odd number.
Given (n+1)^2 - n^2 = 2n + 1, this equation demonstrates that the difference between consecutive perfect squares is always an odd number.
Match the sequence type with the method to find the next term:
Match the sequence type with the method to find the next term:
Flashcards
Arithmetic Sequence
Arithmetic Sequence
A sequence where the difference between consecutive terms is constant.
Common Difference (d)
Common Difference (d)
The constant difference added (or subtracted) in an arithmetic sequence.
nth term of Arithmetic Sequence
nth term of Arithmetic Sequence
𝑢_n = 𝑢_1 + (𝑛 − 1)𝑑, where u_1 is the first term, n is the term number, and d is the common difference.
Geometric Sequence
Geometric Sequence
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Binomial Expansion
Binomial Expansion
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Nominal Annual Interest Rate
Nominal Annual Interest Rate
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Compound Interest
Compound Interest
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Compounding Period
Compounding Period
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Study Notes
- These notes are based on the Year 1 IB Math Analysis and Approaches Chapter 1 Practice test
Arithmetic Sequence Problem
- The second term of an arithmetic sequence is 10, and the fourth term is 22
- Task: Find the common difference
- Task: Find an expression for the nth term (u_n)
- Task: Find the sum of the first 20 terms (S_20)
Geometric Sequence Problem
- The second term of a geometric sequence is 6, and the fourth term is 54
- Task: Find the 5th term
Binomial Expansion Problem
- The binomial expansion of (1 + kx)^n is given by 1 + 12x + 28k^2x^2 + ... + k^nx^n, where n ∈ Z+ and k ∈ Q
- Task: Find the value of n and the value of k
Proof Problem
- Task: Show that (n + 1)² – n² = 2n + 1
Geometric Sequence with Calculator Problem
- A geometric sequence has a first term of 3 and a fourth term of 81
- The sum of the first n terms of the sequence is S_n
- Task: Find the smallest value of n such that S_n > 10000
Daniela and Sorin's Investment Problem
- Daniela and Sorin receive money, Daniela from a cash prize and Sorin from an inheritance
- Daniela has two options for receiving her winnings, with payments on the first day of each month for three years
- Option A: Each payment is $5500
- Task: Find the total amount Daniela would receive choosing option A
- Option B: The first payment is $2000, with each subsequent month's payment being 6% more than the previous month
- Task: Find the total amount Daniela would receive choosing option B
- Sorin receives an inheritance of $120,000 and invests it in an account with a nominal annual interest rate of 4%, compounded monthly, with interest added on the last day of each month
- Task: Write an expression for the value of Sorin's investment after n years
- Daniela chooses Option B and receives her first payment on January 1, 2023; Sorin invests his inheritance on the same day
- Task: Find the total value of Daniela's winnings and Sorin's investment on the last day of the sixth month
- Task: Find the minimum number of complete months before the total value of Daniela's winnings and Sorin's investment is at least $250,000
- At the end of the three years, Daniela invests $40,000 for a further six years in a second account paying a nominal interest rate of r% per annum, compounded quarterly
- Task: Find the value of r if this investment grows to $53,000 after six years
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Description
Practice test problems for the first chapter of Year 1 IB Math Analysis and Approaches. Topics include arithmetic sequences, geometric sequences, binomial expansion, proof, and financial applications. Practice problems for Daniela and Sorin's investment.
