DP Mathematical Studies Questionbank

• Syllabus

1.7

Sub sections and their related questions

Arithmetic sequences and series, and their applications.

• 10M.1.sl.TZ2.7a: Find the common difference of this arithmetic sequence.
• 10M.2.sl.TZ1.5B.a: Calculate u1, the first term in the sequence.
• 10M.2.sl.TZ1.5B.b: Show that the common difference is 7.
• 11N.1.sl.TZ0.6a: Find the value of the common difference of this sequence.
• 10N.1.sl.TZ0.8a: Write down the second term of this sequence.
• 10N.1.sl.TZ0.8b: Write down the common difference of this sequence.
• 10N.1.sl.TZ0.8c: Write down the fourth term of this sequence.
• 10N.1.sl.TZ0.8d: The nth term is the first term in this sequence which is greater than 1000. Find the value of n.
• 12N.1.sl.TZ0.2a: Calculate the common difference;
• 12N.2.sl.TZ0.2f: The students are asked to collect money for charity. In the first month, the students collect x...
• 10M.2.sl.TZ2.3a: Find the amount of money that Ruby will have in the bank after 3 years.
• 12M.2.sl.TZ1.4A.a: (i) Write an equation for u6 in terms of d and u1. (ii) Write an equation for u10 in terms of d...
• 12M.1.sl.TZ2.5a: Find the first term of the sequence.
• 12M.1.sl.TZ2.5b: Find the 21st term of the sequence.
• 12M.1.sl.TZ2.5c: Find the sum of the first 30 terms of the sequence.
• 12M.2.sl.TZ2.2c: Cedric’s mother decides to help him by giving him an interest free loan of €8000 to buy the car....
• 09N.1.sl.TZ0.4a: Find the common difference.
• 09N.1.sl.TZ0.4b: Find the twelfth term.
• 09N.1.sl.TZ0.4c: Find the sum of the first 100 terms.
• 09M.1.sl.TZ1.3a: Calculate the number of leaves that the tree loses on the 21st October.
• 09M.1.sl.TZ1.3b: Find the total number of leaves that the tree loses in the 31 days of the month of October.
• 11M.1.sl.TZ1.8a: Calculate the annual salary for the fifth year of her employment.
• 11M.1.sl.TZ1.8b: She remains in this employment for 10 years. Calculate the total salary she earns in this...
• 09M.1.sl.TZ2.4a: Find the number of terms of the sequence.
• 09M.1.sl.TZ2.4b: Find the sum of the sequence.
• 13M.1.sl.TZ1.12a: Find the common difference, d.
• 13M.1.sl.TZ1.12b: The tenth term of the sequence is double the seventh term. (i) Write down an equation in u1 and...
• 11M.2.sl.TZ2.3B.b: The sum of the first \(n\) terms of this sequence is \(\frac{n}{2}(3n - 1)\). (i)     Find the...
• 11M.2.sl.TZ2.3B.a: Find the value of the eleventh term.
• 13M.2.sl.TZ2.4a: Find the time, in seconds, Paco takes to run his fifth lap.
• 13M.2.sl.TZ2.4b: Paco runs his last lap in 260 seconds. Find how many laps he has run on Monday.
• 13M.2.sl.TZ2.4c: Find the total time, in minutes, run by Paco on Monday.
• 07M.2.sl.TZ0.4i.a: State the values of u1 and d for this sequence.
• 07M.2.sl.TZ0.4i.b: Use an appropriate formula to show that the sum of the natural numbers from 1 to n is given by...
• 07M.2.sl.TZ0.4i.c: Calculate the sum of the natural numbers from 1 to 200.
• 07N.1.sl.TZ0.3a: (i) Find the common difference. (ii) Find the first term of the sequence.
• 07N.1.sl.TZ0.3b: Calculate the eighty-fourth term.
• 07N.1.sl.TZ0.3c: Calculate the sum of the first 200 terms.
• 08N.1.sl.TZ0.8a: Write down the common difference of the sequence.
• 08N.1.sl.TZ0.8b: Calculate the sum of the first \(50\) terms of the sequence.
• 08N.1.sl.TZ0.8c: \({u_k}\) is the first term in the sequence which is negative. Find the value of \(k\).
• 08N.2.sl.TZ0.1c: Grove School had \(110\) students in January 2000. Every full year, the number of students is...
• 08N.2.sl.TZ0.1d: Grove School had \(110\) students in January 2000. Every full year, the number of students is...
• 08N.2.sl.TZ0.1e: Each January, one of these two schools, the one that has more students, is given extra money to...
• 08M.1.sl.TZ1.8a: Find the value of the \({96^{{\text{th}}}}\) term of the sequence.
• 08M.1.sl.TZ1.8b: The first term of a geometric sequence is \(6\). The \({6^{{\text{th}}}}\) term of the geometric...
• 08M.2.sl.TZ2.1a: If Clara chooses option 1, (i) write down the values of the second and third installments; (ii)...
• 08M.2.sl.TZ2.1d: Clara knows that the total amount she would pay for the land is not the same for both options....
• 14M.2.sl.TZ2.4b: If Hugh chooses Option B, calculate (i)     the amount of money he will receive in the 17th...
• 13N.1.sl.TZ0.6a: Find the common difference of the sequence.
• 13N.1.sl.TZ0.6b: The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\). Find the value of \(n\).
• 13N.1.sl.TZ0.6c: The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\). Find \({S_{20}}\), the sum...
• 14M.2.sl.TZ1.3a: Find the value of \({u_{20}}\).
• 14M.2.sl.TZ1.3b: Find the sum of the first 10 terms of the sequence.
• 14M.2.sl.TZ1.3e: \(k\) is the smallest value of \(n\) for which \({v_n}\) is greater than \({u_n}\). Calculate...
• 14N.1.sl.TZ0.7a: Find the value of \(m\).
• 14N.1.sl.TZ0.7b: State what \(m\) represents in this context.
• 14N.1.sl.TZ0.7d: State what \(n\) represents in this context.
• 14N.2.sl.TZ0.5b: The distances she runs to collect each pumpkin form a sequence...
• 14N.2.sl.TZ0.5c: Write down the common difference, \(d\), of the sequence.
• 14N.2.sl.TZ0.5d: The final pumpkin Sirma collected was 24 metres from the start. (i)     Find the total number of...
• 14N.2.sl.TZ0.5e: Peter also plays the game. When the signal is given for the end of the game he has run 940...
• 14N.2.sl.TZ0.5f: Peter also plays the game. When the signal is given for the end of the game he has run 940...
• 15M.1.sl.TZ1.7a: Calculate (i)     the common difference of the sequence; (ii)     the first term of the sequence.
• 15M.1.sl.TZ1.7b: The first, second and fifth terms of this arithmetic sequence are the first three terms of a...
• 15M.1.sl.TZ2.9a: Only one of the following four sequences is arithmetic and only one of them is geometric.     ...
• 15M.2.sl.TZ2.3a: Write down the value of (i)     \({S_1}\); (ii)     \({S_2}\).
• 15M.2.sl.TZ2.3b: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Show that...
• 15M.2.sl.TZ2.3c: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the common...
• 15M.2.sl.TZ2.3d: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find \({u_{10}}\).
• 15M.2.sl.TZ2.3e: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the lowest...
• 15M.2.sl.TZ2.3f: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). There is a...
• 16N.1.sl.TZ0.13a: Find the year in which the comet was seen from Earth for the fifth time.
• 16N.1.sl.TZ0.13b: Determine how many times the comet has been seen from Earth up to the year 2014.
• 17N.2.sl.TZ0.2a.i: Write down the distance Rosa runs in the third training session;
• 17N.2.sl.TZ0.2a.ii: Write down the distance Rosa runs in the \(n\)th training session.
• 17N.2.sl.TZ0.2b: Find the value of \(k\).
• 17N.2.sl.TZ0.2c: Calculate the total distance, in kilometres, Rosa runs in the first 50 training sessions.
• 17N.2.sl.TZ0.2d: Find the distance Carlos runs in the fifth month of training.
• 17N.2.sl.TZ0.2e: Calculate the total distance Carlos runs in the first year.
• 18M.2.sl.TZ2.4a: Find the café’s profit during the 11th week.
• 18M.2.sl.TZ2.4b: Calculate the café’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4c: Find the tea-shop’s profit during the 11th week.
• 18M.2.sl.TZ2.4d: Calculate the tea-shop’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4e: In the mth week the tea-shop’s total profit exceeds the café’s total profit, for the first time...

Use of the formulae for the \(n\)th term and the sum of the first \(n\) terms of the sequence.

• 10M.1.sl.TZ2.7b: There are 10 rows in the choir and 11 singers in the first row. Find the total number of singers...
• 10M.2.sl.TZ1.5B.c: Sn is the sum of the first n terms of the sequence. Find an expression for Sn. Give your answer...
• 11N.1.sl.TZ0.6b: Calculate the sum of the first 10 terms of this sequence.
• 11N.1.sl.TZ0.6c: Find the number of terms in this sequence.
• 10N.1.sl.TZ0.8a: Write down the second term of this sequence.
• 10N.1.sl.TZ0.8b: Write down the common difference of this sequence.
• 10N.1.sl.TZ0.8c: Write down the fourth term of this sequence.
• 10N.1.sl.TZ0.8d: The nth term is the first term in this sequence which is greater than 1000. Find the value of n.
• 12N.1.sl.TZ0.2b: Calculate the 95th term of the sequence;
• 12N.1.sl.TZ0.2c: Calculate the sum of the first 250 terms.
• 12M.2.sl.TZ1.4A.c: Find the total number of seats in the amphitheatre.
• 12M.2.sl.TZ1.4A.d: A few years later, a second level was added to increase the amphitheatre’s capacity by another...
• 12M.1.sl.TZ2.5b: Find the 21st term of the sequence.
• 12M.1.sl.TZ2.5c: Find the sum of the first 30 terms of the sequence.
• 09N.1.sl.TZ0.4b: Find the twelfth term.
• 09N.1.sl.TZ0.4c: Find the sum of the first 100 terms.
• 11M.1.sl.TZ1.8a: Calculate the annual salary for the fifth year of her employment.
• 11M.1.sl.TZ1.8b: She remains in this employment for 10 years. Calculate the total salary she earns in this...
• 09M.1.sl.TZ2.4a: Find the number of terms of the sequence.
• 09M.1.sl.TZ2.4b: Find the sum of the sequence.
• 13M.1.sl.TZ1.12a: Find the common difference, d.
• 13M.1.sl.TZ1.12b: The tenth term of the sequence is double the seventh term. (i) Write down an equation in u1 and...
• 11M.2.sl.TZ2.3B.b: The sum of the first \(n\) terms of this sequence is \(\frac{n}{2}(3n - 1)\). (i)     Find the...
• 11M.2.sl.TZ2.3B.a: Find the value of the eleventh term.
• 13M.2.sl.TZ2.4a: Find the time, in seconds, Paco takes to run his fifth lap.
• 13M.2.sl.TZ2.4b: Paco runs his last lap in 260 seconds. Find how many laps he has run on Monday.
• 13M.2.sl.TZ2.4c: Find the total time, in minutes, run by Paco on Monday.
• 07M.2.sl.TZ0.4i.b: Use an appropriate formula to show that the sum of the natural numbers from 1 to n is given by...
• 07M.2.sl.TZ0.4i.c: Calculate the sum of the natural numbers from 1 to 200.
• 07N.1.sl.TZ0.3a: (i) Find the common difference. (ii) Find the first term of the sequence.
• 07N.1.sl.TZ0.3b: Calculate the eighty-fourth term.
• 07N.1.sl.TZ0.3c: Calculate the sum of the first 200 terms.
• 08N.1.sl.TZ0.8b: Calculate the sum of the first \(50\) terms of the sequence.
• 08N.1.sl.TZ0.8c: \({u_k}\) is the first term in the sequence which is negative. Find the value of \(k\).
• 08N.2.sl.TZ0.1d: Grove School had \(110\) students in January 2000. Every full year, the number of students is...
• 08M.1.sl.TZ1.8a: Find the value of the \({96^{{\text{th}}}}\) term of the sequence.
• 08M.1.sl.TZ1.8b: The first term of a geometric sequence is \(6\). The \({6^{{\text{th}}}}\) term of the geometric...
• 08M.2.sl.TZ2.1a: If Clara chooses option 1, (i) write down the values of the second and third installments; (ii)...
• 14M.2.sl.TZ2.4b: If Hugh chooses Option B, calculate (i)     the amount of money he will receive in the 17th...
• 13N.1.sl.TZ0.6b: The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\). Find the value of \(n\).
• 13N.1.sl.TZ0.6c: The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\). Find \({S_{20}}\), the sum...
• 14M.2.sl.TZ1.3a: Find the value of \({u_{20}}\).
• 14M.2.sl.TZ1.3b: Find the sum of the first 10 terms of the sequence.
• 14M.2.sl.TZ1.3e: \(k\) is the smallest value of \(n\) for which \({v_n}\) is greater than \({u_n}\). Calculate...
• 14N.1.sl.TZ0.7a: Find the value of \(m\).
• 14N.2.sl.TZ0.5d: The final pumpkin Sirma collected was 24 metres from the start. (i)     Find the total number of...
• 14N.2.sl.TZ0.5e: Peter also plays the game. When the signal is given for the end of the game he has run 940...
• 14N.2.sl.TZ0.5f: Peter also plays the game. When the signal is given for the end of the game he has run 940...
• 15M.1.sl.TZ1.7a: Calculate (i)     the common difference of the sequence; (ii)     the first term of the sequence.
• 15M.2.sl.TZ2.3a: Write down the value of (i)     \({S_1}\); (ii)     \({S_2}\).
• 15M.2.sl.TZ2.3b: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Show that...
• 15M.2.sl.TZ2.3c: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the common...
• 15M.2.sl.TZ2.3d: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find \({u_{10}}\).
• 15M.2.sl.TZ2.3e: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). Find the lowest...
• 15M.2.sl.TZ2.3f: The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\). There is a...
• 18M.2.sl.TZ2.4a: Find the café’s profit during the 11th week.
• 18M.2.sl.TZ2.4b: Calculate the café’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4c: Find the tea-shop’s profit during the 11th week.
• 18M.2.sl.TZ2.4d: Calculate the tea-shop’s total profit for the first 12 weeks.
• 18M.2.sl.TZ2.4e: In the mth week the tea-shop’s total profit exceeds the café’s total profit, for the first time...