DP Mathematics SL Questionbank

• Syllabus

1.1

Sub sections and their related questions

Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.

• 12N.2.sl.TZ0.1a: The first three terms of an arithmetic sequence are 5 , 6.7 , 8.4 . Find the common difference.
• 12N.2.sl.TZ0.1b: The first three terms of an arithmetic sequence are 5 , 6.7 , 8.4 . Find the 28th term of the...
• 12N.2.sl.TZ0.1c: The first three terms of an arithmetic sequence are \(5\) , \(6.7\) , \(8.4\) . Find the sum of...
• 12M.2.sl.TZ2.3a: The first term of a geometric sequence is 200 and the sum of the first four terms is 324.8. Find...
• 12M.2.sl.TZ2.3b: The first term of a geometric sequence is 200 and the sum of the first four terms is 324.8. Find...
• 08N.1.sl.TZ0.1a: Consider the infinite geometric sequence...
• 08N.1.sl.TZ0.1b: Consider the infinite geometric sequence...
• 08M.1.sl.TZ1.3a: Consider the arithmetic sequence \(2{\text{, }}5{\text{, }}8{\text{, }}11{\text{,}} \ldots \) ....
• 08M.1.sl.TZ1.3b: Consider the arithmetic sequence \(2{\text{, }}5{\text{, }}8{\text{, }}11{\text{,}} \ldots \) ....
• 08M.2.sl.TZ2.1a: Find the common ratio.
• 08M.2.sl.TZ2.1b: Find the 10th term.
• 08M.2.sl.TZ2.1c: Find the exact sum of the infinite sequence.
• 08M.2.sl.TZ2.10a(i) and (ii): (i)     Find the number of taxis in the city at the end of 2005. (ii)    Find the year in...
• 12M.2.sl.TZ1.1a(i) and (ii): (i)     Write down the value of d . (ii)    Find \({u_8}\) .
• 12M.2.sl.TZ1.1b(i) and (ii): (i)     Show that \({S_n} = 2{n^2} + 34n\) . (ii)    Hence, write down the value of \({S_{14}}\) .
• 10N.1.sl.TZ0.1a: Write down the value of r .
• 10N.1.sl.TZ0.1b: Find \({u_6}\) .
• 10N.1.sl.TZ0.1c: Find the sum to infinity of this sequence.
• 09N.2.sl.TZ0.1: In an arithmetic sequence, \({S_{40}} = 1900\) and \({u_{40}} = 106\) . Find the value of...
• 09M.2.sl.TZ1.1a: Find the common difference.
• 09M.2.sl.TZ1.1b: Find the value of the 78th term.
• 09M.2.sl.TZ1.6a: Find the value of \(r\) .
• 09M.2.sl.TZ1.6b: Find the smallest value of n for which \({S_n} > 40\) .
• 09M.2.sl.TZ2.5b: (i)     Find the value of \(\sum\limits_{r = 4}^{30} {{2^r}} \) . (ii)    Explain why...
• 10N.2.sl.TZ0.3a: Write down the common difference.
• 10N.2.sl.TZ0.3b(i) and (ii): (i)     Given that the nth term of this sequence is 115, find the value of n . (ii)    For this...
• 10M.2.sl.TZ1.2a: Write down the common difference.
• 10M.2.sl.TZ1.2b: Find the number of terms in the sequence.
• 10M.2.sl.TZ1.2c: Find the sum of the sequence.
• 10M.2.sl.TZ2.2a: Find \({u_1}\).
• 10M.2.sl.TZ2.2b(i) and (ii): (i)     Given that \({u_n} = 516\) , find the value of n . (ii)    For this value of n , find...
• SPNone.2.sl.TZ0.1a: Find the common difference.
• SPNone.2.sl.TZ0.1b: Find the value of the 78th term.
• 11N.2.sl.TZ0.8a(i) and (ii): Consider an infinite geometric sequence with \({u_1} = 40\) and \(r = \frac{1}{2}\) . (i)    ...
• 11N.2.sl.TZ0.8b(i) and (ii): Consider an arithmetic sequence with n terms, with first term (\( - 36\)) and eighth term...
• 11N.2.sl.TZ0.8c: The sum of the infinite geometric sequence is equal to twice the sum of the arithmetic sequence....
• 11M.2.sl.TZ1.3a: Find the value of the common difference.
• 11M.2.sl.TZ1.3b: Find the value of n .
• 11M.1.sl.TZ2.1a: Find d .
• 11M.1.sl.TZ2.1b: Find \({u_{20}}\) .
• 11M.1.sl.TZ2.1c: Find \({S_{20}}\) .
• 13M.2.sl.TZ2.5: The sum of the first three terms of a geometric sequence is \(62.755\), and the sum of the...
• 14M.1.sl.TZ1.2a: Find the common difference.
• 14M.1.sl.TZ1.2b: Find the first term.
• 14M.1.sl.TZ1.2c: Find the sum of the first 20 terms of the sequence.
• 14M.1.sl.TZ1.10a: The following table gives the values of \({x_n}\) and \({A_n}\), for...
• 14M.1.sl.TZ1.10b: The process described above is repeated. Find \({A_6}\).
• 14M.1.sl.TZ1.10c: Consider an initial square of side length \(k {\text{ cm}}\). The process described above is...
• 14M.1.sl.TZ2.7a: Given that \({u_1} = 1 + k\), find \({u_2},{\text{ }}{u_3}\) and \({u_4}\).
• 14M.1.sl.TZ2.7b: Find a general expression for \({u_n}\).
• 13N.1.sl.TZ0.9a(i): Write down an expression for the common ratio, \(r\).
• 13N.1.sl.TZ0.9a(ii): Hence, show that \(m\) satisfies the equation \({m^2} + 3m - 40 = 0\).
• 13N.1.sl.TZ0.9b(i): Find the two possible values of \(m\).
• 13N.1.sl.TZ0.9b(ii): Find the possible values of \(r\).
• 13N.1.sl.TZ0.9c(i): The sequence has a finite sum. State which value of \(r\) leads to this sum and justify your...
• 13N.1.sl.TZ0.9c(ii): The sequence has a finite sum. Calculate the sum of the sequence.
• 13M.2.sl.TZ1.1a: Write down the value of \(d\) .
• 13M.2.sl.TZ1.1b: Find   (i)      \({u_{100}}\) ;   (ii)      \({S_{100}}\) .
• 13M.2.sl.TZ1.1c: Given that \({u_n} = 1502\) , find the value of \(n\) .
• 14N.1.sl.TZ0.2a: Find the common difference.
• 14N.1.sl.TZ0.2b: Find the eighth term.
• 14N.1.sl.TZ0.2c: Find the sum of the first eight terms of the sequence.
• 14N.2.sl.TZ0.9a: (i)     Find the common ratio. (ii)     Hence or otherwise, find \({u_5}\).
• 15M.1.sl.TZ1.10c: Find the probability that Ann wins the game.
• 15M.2.sl.TZ1.3a: Write down the value of the common difference.
• 15M.2.sl.TZ1.3b: Find the first term.
• 15M.2.sl.TZ1.3c: Find the sum of the first 50 terms of the sequence.
• 15M.2.sl.TZ2.6: Ramiro walks to work each morning. During the first minute he walks \(80\) metres. In each...
• 15N.1.sl.TZ0.7: An arithmetic sequence has the first term \(\ln a\) and a common difference \(\ln 3\). The 13th...
• 15N.2.sl.TZ0.4a: Find the value of \(r\).
• 15N.2.sl.TZ0.4b: Find the value of \({S_6}\).
• 16M.1.sl.TZ1.4a: Given that Figure \(n\) contains 801 line segments, show that \(n = 200\).
• 16M.1.sl.TZ1.4b: Find the total number of line segments in the first 200 figures.
• 16M.2.sl.TZ1.6: In a geometric sequence, the fourth term is 8 times the first term. The sum of the first 10 terms...
• 16M.1.sl.TZ2.4: Three consecutive terms of a geometric sequence are \(x - 3\), 6 and \(x + 2\). Find the...
• 16M.2.sl.TZ2.1a: Find the common difference.
• 16M.2.sl.TZ2.1b: Find the 30th term of the sequence.
• 16M.2.sl.TZ2.1c: Find the sum of the first 30 terms.
• 16N.1.sl.TZ0.9a: Find \(r\).
• 16N.1.sl.TZ0.9b: Show that the sum of the infinite sequence is \(4{\log _2}x\).
• 16N.1.sl.TZ0.9c: Find \(d\), giving your answer as an integer.
• 16N.1.sl.TZ0.9d: Show that \({S_{12}} = 12{\log _2}x - 66\).
• 17M.1.sl.TZ1.7a: Find the common ratio.
• 17M.1.sl.TZ1.7b: Solve \(\sum\limits_{k = 1}^\infty  {{2^{5 - k}}\ln x = 64} \).
• 17M.1.sl.TZ2.1a: Find the common difference.
• 17M.1.sl.TZ2.1b: Find the tenth term.
• 17M.1.sl.TZ2.1c: Find the sum of the first ten terms of the sequence.
• 17M.2.sl.TZ2.5: Consider a geometric sequence where the first term is 768 and the second term is 576. Find the...
• 17N.1.sl.TZ0.2a: Find the common difference.
• 17N.1.sl.TZ0.2b: Find the tenth term.
• 17N.1.sl.TZ0.2c: Find the sum of the first ten terms.
• 17N.1.sl.TZ0.10a: The following diagram shows [AB], with length 2 cm. The line is divided into an infinite number...
• 17N.1.sl.TZ0.10b: The following diagram shows [CD], with length \(b{\text{ cm}}\), where \(b > 1\). Squares with...
• 18M.1.sl.TZ1.10a.i: Find an expression for r in terms of θ.
• 18M.1.sl.TZ1.10a.ii: Find the possible values of r.
• 18M.1.sl.TZ1.10b: Show that the sum of the infinite sequence...
• 18M.1.sl.TZ1.10c: Find the values of θ which give the greatest value of the sum.
• 18M.2.sl.TZ1.7a: Given that xk + 1 = xk + a, find a.
• 18M.2.sl.TZ1.7b: Hence find the value of n such that \(\sum\limits_{k = 1}^n {{x_k} = 861} \).
• 18M.1.sl.TZ2.7a: Show that \(d = {\text{lo}}{{\text{g}}_c}\left( q \right)\).
• 18M.1.sl.TZ2.7b: Let \(p = {c^2}\) and \(q = {c^3}\). Find the value of \(\sum\limits_{n = 1}^{20} {{u_n}} \).
• 18M.2.sl.TZ2.4a: Find the common ratio.
• 18M.2.sl.TZ2.4b: Find the sum of the first 8 terms.
• 18M.2.sl.TZ2.4c: Find the least value of n for which Sn > 163.

Sigma notation.

• 09M.2.sl.TZ2.5a: Expand \(\sum\limits_{r = 4}^7 {{2^r}} \) as the sum of four terms.
• 09M.2.sl.TZ2.5b: (i)     Find the value of \(\sum\limits_{r = 4}^{30} {{2^r}} \) . (ii)    Explain why...
• 16N.2.sl.TZ0.8a: Find the mean number of hours spent browsing the Internet.
• 16N.2.sl.TZ0.8b: During week 2, the students worked on a major project and they each spent an additional five...
• 16N.2.sl.TZ0.8c: During week 3 each student spent 5% less time browsing the Internet than during week 1. For week...
• 16N.2.sl.TZ0.8d: (i)     Find the number of students who spent between 25 and 30 hours browsing the...
• 17M.1.sl.TZ1.7a: Find the common ratio.
• 17M.1.sl.TZ1.7b: Solve \(\sum\limits_{k = 1}^\infty  {{2^{5 - k}}\ln x = 64} \).
• 18M.2.sl.TZ1.7a: Given that xk + 1 = xk + a, find a.
• 18M.2.sl.TZ1.7b: Hence find the value of n such that \(\sum\limits_{k = 1}^n {{x_k} = 861} \).
• 18M.1.sl.TZ2.7a: Show that \(d = {\text{lo}}{{\text{g}}_c}\left( q \right)\).
• 18M.1.sl.TZ2.7b: Let \(p = {c^2}\) and \(q = {c^3}\). Find the value of \(\sum\limits_{n = 1}^{20} {{u_n}} \).

Applications.

• 15M.2.sl.TZ2.6: Ramiro walks to work each morning. During the first minute he walks \(80\) metres. In each...
• 16M.2.sl.TZ1.7a: (i)     Find the value of \(k\). (ii)     Interpret the meaning of the value of \(k\).
• 16M.2.sl.TZ1.7b: Find the least number of whole years for which \(\frac{{{P_t}}}{{{P_0}}} < 0.75\).
• 18M.1.sl.TZ2.7a: Show that \(d = {\text{lo}}{{\text{g}}_c}\left( q \right)\).
• 18M.1.sl.TZ2.7b: Let \(p = {c^2}\) and \(q = {c^3}\). Find the value of \(\sum\limits_{n = 1}^{20} {{u_n}} \).