DP Mathematical Studies Questionbank

• Syllabus

1.8

Sub sections and their related questions

Geometric sequences and series.

• 10M.2.sl.TZ1.5B.d: The first term, v1, of a geometric sequence is 20 and its fourth term v4 is 67.5. Show that the...
• 11N.1.sl.TZ0.12a: Calculate the exact value of the ninth term of the sequence.
• 11N.1.sl.TZ0.12b: Calculate the least number of terms required for the sum of the sequence to be greater than 682.6
• 10N.1.sl.TZ0.11a: Write down the common ratio.
• 10N.1.sl.TZ0.11b.i: Write down the value of a.
• 10N.1.sl.TZ0.11c: The sum of the first n terms is 31.9375. Find the value of n.
• 12N.1.sl.TZ0.6a: Calculate the common ratio of the sequence;
• 12N.1.sl.TZ0.6b: Calculate the eleventh term of the sequence;
• 12N.1.sl.TZ0.6c: Calculate the sum of the first 23 terms of the sequence.
• 12M.2.sl.TZ1.4B.a: Write down the next two terms of this geometric sequence.
• 12M.2.sl.TZ1.4B.b: Write down the common ratio of this geometric sequence.
• 12M.2.sl.TZ1.4B.c: Calculate the number of people who will receive the text message at 12:30.
• 12M.2.sl.TZ1.4B.d: Calculate the total number of people who will have received the text message by 12:30.
• 12M.2.sl.TZ1.4B.e: Calculate the exact time at which a total of 29 524 people will have received the text message.
• 12M.1.sl.TZ2.15a: Write down the distance he runs on the second day of training.
• 12M.1.sl.TZ2.15b: Calculate the total distance Javier runs in the first seven days of training.
• 12M.1.sl.TZ2.15c: Javier stops training on the day his total distance exceeds 100 km. Calculate the number of days...
• 09N.1.sl.TZ0.12a: Write down the population of big cats at the beginning of 2005.
• 09N.1.sl.TZ0.12b: Find the population of big cats at the beginning of 2010.
• 09N.1.sl.TZ0.12c: Find the number of years, from the beginning of 2004, it will take the population of big cats to...
• 09M.1.sl.TZ1.8a: Calculate the common ratio for the increasing sequence of fees.
• 09M.1.sl.TZ1.8b: Give your answer correct to 2 decimal places. The fees continue to increase in the same...
• 09M.1.sl.TZ1.8c: Give your answer correct to 2 decimal places. The fees continue to increase in the same...
• 11M.1.sl.TZ1.11a: Write down the common ratio of the sequence.
• 09M.2.sl.TZ2.4i, a: Calculate the value of the common ratio.
• 09M.2.sl.TZ2.4i, b: Calculate the 10th term of this sequence.
• 09M.2.sl.TZ2.4i, c: The kth term is the first term which is greater than 2000. Find the value of k.
• 13M.1.sl.TZ1.7a: Find the common ratio of the sequence.
• 13M.1.sl.TZ1.7b: Find u1, the first term of the sequence.
• 13M.1.sl.TZ1.7c: Calculate the sum of the first 10 terms of the sequence.
• 11M.2.sl.TZ2.3A.a: Show that the common ratio is $\frac{1}{2}$ .
• 13M.2.sl.TZ2.4d: On Wednesday Paco takes Lola to train. They both run the first lap of the track in 120 seconds....
• 13M.2.sl.TZ2.4e: Find the total time, in seconds, Lola takes to run her first four laps.
• 07M.2.sl.TZ0.4ii.a: The sum of the first n terms of G1 is 29 524. Find n.
• 07M.2.sl.TZ0.4ii.b: A second geometric progression G2 has the form $1,\frac{1}{3},\frac{1}{9},\frac{1}{{27}}...$
• 07M.2.sl.TZ0.4ii.c: Calculate the sum of the first 10 terms of G2.
• 07M.2.sl.TZ0.4ii.d: Explain why the sum of the first 1000 terms of G2 will give the same answer as the sum of the...
• 07M.2.sl.TZ0.4ii.e: Using your results from parts (a) to (c), or otherwise, calculate the sum of the first 10 terms...
• 08N.2.sl.TZ0.1a: Park School started in January 2000 with $100$ students. Every full year, there is an increase...
• 08N.2.sl.TZ0.1b: Park School started in January 2000 with $100$ students. Every full year, there is an increase...
• 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.TZ1.8b: The first term of a geometric sequence is $6$. The ${6^{{\text{th}}}}$ term of the geometric...
• 08M.1.sl.TZ1.8c: The first term of a geometric sequence is $6$. The \${6^{{\text{th}}}}$ term of the geometric...
• 08M.2.sl.TZ2.1b: If Clara chooses option 2, (i) find the value of the second installment; (ii) show that the...
• 08M.2.sl.TZ2.1d: Clara knows that the total amount she would pay for the land is not the same for both options....
• 10N.1.sl.TZ0.11b.ii: Write down the value of b.
• 14M.2.sl.TZ2.4c: If Hugh chooses Option C, calculate (i)     the amount of money Hugh would receive in the 13th...
• 13N.1.sl.TZ0.11a: Find the number of competitors who play in round 6 of the tournament.
• 13N.1.sl.TZ0.11b: Find the total number of matches played in the tournament.
• 14M.2.sl.TZ1.3c: Now consider the sequence...
• 14M.2.sl.TZ1.3d: Now consider the sequence...
• 14M.2.sl.TZ1.3e: $k$ is the smallest value of $n$ for which ${v_n}$ is greater than ${u_n}$. Calculate...
• 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.1.sl.TZ2.9b(i): For another geometric sequence...
• 15M.1.sl.TZ2.9b(ii): For another geometric sequence...
• 16M.2.sl.TZ1.5a: Antonio and Barbara start work at the same company on the same day. They each earn an annual...
• 17M.1.sl.TZ1.10a: Find the value of $r$, the common ratio of the sequence.
• 17M.1.sl.TZ1.10b: Find the value of $n$ for which ${u_n} = 2$.
• 17M.1.sl.TZ1.10c: Find the sum of the first 30 terms of the sequence.
• 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.2.sl.TZ1.5B.e: Tn is the sum of the first n terms of the geometric sequence. Calculate T7, the sum of the first...
• 11N.1.sl.TZ0.12a: Calculate the exact value of the ninth term of the sequence.
• 11N.1.sl.TZ0.12b: Calculate the least number of terms required for the sum of the sequence to be greater than 682.6
• 10N.1.sl.TZ0.11c: The sum of the first n terms is 31.9375. Find the value of n.
• 12N.1.sl.TZ0.6b: Calculate the eleventh term of the sequence;
• 12N.1.sl.TZ0.6c: Calculate the sum of the first 23 terms of the sequence.
• 12M.2.sl.TZ1.4B.c: Calculate the number of people who will receive the text message at 12:30.
• 12M.2.sl.TZ1.4B.d: Calculate the total number of people who will have received the text message by 12:30.
• 12M.2.sl.TZ1.4B.e: Calculate the exact time at which a total of 29 524 people will have received the text message.
• 12M.1.sl.TZ2.15b: Calculate the total distance Javier runs in the first seven days of training.
• 12M.1.sl.TZ2.15c: Javier stops training on the day his total distance exceeds 100 km. Calculate the number of days...
• 09N.1.sl.TZ0.12b: Find the population of big cats at the beginning of 2010.
• 09N.1.sl.TZ0.12c: Find the number of years, from the beginning of 2004, it will take the population of big cats to...
• 09M.1.sl.TZ1.8b: Give your answer correct to 2 decimal places. The fees continue to increase in the same...
• 09M.1.sl.TZ1.8c: Give your answer correct to 2 decimal places. The fees continue to increase in the same...
• 11M.1.sl.TZ1.11b: Find ${u_1}$ .
• 11M.1.sl.TZ1.11c: The sum of the first $k$ terms in the sequence is $118 096$ . Find the value of $k$ .
• 09M.2.sl.TZ2.4i, b: Calculate the 10th term of this sequence.
• 09M.2.sl.TZ2.4i, c: The kth term is the first term which is greater than 2000. Find the value of k.
• 13M.1.sl.TZ1.7b: Find u1, the first term of the sequence.
• 13M.1.sl.TZ1.7c: Calculate the sum of the first 10 terms of the sequence.
• 11M.2.sl.TZ2.3A.b: Find the value of the eleventh term.
• 11M.2.sl.TZ2.3A.c: Find the sum of the first eight terms.
• 11M.2.sl.TZ2.3A.d: Find the number of terms in the sequence for which the sum first exceeds $2047.968$.
• 13M.2.sl.TZ2.4d: On Wednesday Paco takes Lola to train. They both run the first lap of the track in 120 seconds....
• 13M.2.sl.TZ2.4e: Find the total time, in seconds, Lola takes to run her first four laps.
• 07M.2.sl.TZ0.4ii.a: The sum of the first n terms of G1 is 29 524. Find n.
• 07M.2.sl.TZ0.4ii.c: Calculate the sum of the first 10 terms of G2.
• 07M.2.sl.TZ0.4ii.d: Explain why the sum of the first 1000 terms of G2 will give the same answer as the sum of the...
• 07M.2.sl.TZ0.4ii.e: Using your results from parts (a) to (c), or otherwise, calculate the sum of the first 10 terms...
• 08N.2.sl.TZ0.1a: Park School started in January 2000 with $100$ students. Every full year, there is an increase...
• 08N.2.sl.TZ0.1b: Park School started in January 2000 with $100$ students. Every full year, there is an increase...
• 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.TZ2.1b: If Clara chooses option 2, (i) find the value of the second installment; (ii) show that the...
• 14M.2.sl.TZ2.4c: If Hugh chooses Option C, calculate (i)     the amount of money Hugh would receive in the 13th...
• 13N.1.sl.TZ0.11a: Find the number of competitors who play in round 6 of the tournament.
• 13N.1.sl.TZ0.11b: Find the total number of matches played in the tournament.
• 14M.2.sl.TZ1.3c: Now consider the sequence...
• 14M.2.sl.TZ1.3d: Now consider the sequence...
• 14M.2.sl.TZ1.3e: $k$ is the smallest value of $n$ for which ${v_n}$ is greater than ${u_n}$. Calculate...
• 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.TZ2.9b(ii): For another geometric sequence...
• 16M.2.sl.TZ1.5a: Antonio and Barbara start work at the same company on the same day. They each earn an annual...
• 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...