DP Mathematics SL Questionbank

• Syllabus

1.2

Sub sections and their related questions

Elementary treatment of exponents and logarithms.

• 10M.1.sl.TZ2.6: Solve \({\log _2}x + {\log _2}(x - 2) = 3\) , for \(x > 2\) .
• 09M.1.sl.TZ2.4a: Find \({\log _2}32\) .
• 14M.1.sl.TZ1.4a(i): (i)     \({\log _3}27\);
• 14M.1.sl.TZ1.4a(ii): (ii)     \({\log _8}\frac{1}{8}\);
• 14M.1.sl.TZ1.4a(iii): (iii)     \({\log _{16}}4\).
• 14M.1.sl.TZ2.2a: \({\log _6}36\)
• 16M.1.sl.TZ2.3a: \(\ln \left( {\frac{5}{3}} \right)\).
• 16M.1.sl.TZ2.3b: \(\ln 45\).
• 18M.2.sl.TZ1.8a: Find the value of a and of b.
• 18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
• 18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
• 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 \(\sum\limits_{n = 1}^{20} {{u_n}} \).

Laws of exponents; laws of logarithms.

• 08N.2.sl.TZ0.2b: Find the term in \({x^3}\) in \((3x + 4){(x - 2)^4}\) .
• 10M.1.sl.TZ1.7a: Show that \({f^{ - 1}}(x) = {3^{2x}}\) .
• 10M.1.sl.TZ1.7b: Write down the range of \({f^{ - 1}}\) .
• 10M.1.sl.TZ1.7c: Let \(g(x) = {\log _3}x\) , for \(x > 0\) . Find the value of \(({f^{ - 1}} \circ g)(2)\) ,...
• 10M.1.sl.TZ2.6: Solve \({\log _2}x + {\log _2}(x - 2) = 3\) , for \(x > 2\) .
• 09N.1.sl.TZ0.7a: Given that \({f^{ - 1}}(1) = 8\) , find the value of \(k\) .
• 09N.1.sl.TZ0.7b: Find \({f^{ - 1}}\left( {\frac{2}{3}} \right)\) .
• 09M.1.sl.TZ1.6b: Solve the equation \({f^{ - 1}}(x) = \ln \frac{1}{x}\) .
• 09M.1.sl.TZ2.4b: Given that \({\log _2}\left( {\frac{{{{32}^x}}}{{{8^y}}}} \right)\) can be written as \(px + qy\)...
• 11N.1.sl.TZ0.10a: Find the equation of L .
• 11N.1.sl.TZ0.10b: Find the area of the region enclosed by the curve of g , the x-axis, and the lines \(x = 2\) and...
• 11N.1.sl.TZ0.10c: The graph of g is reflected in the x-axis to give the graph of h . The area of the region...
• 11M.2.sl.TZ1.10a: Show that \(f(x) = {\log _3}2x\) .
• 11M.2.sl.TZ1.10b: Find the value of \(f(0.5)\) and of \(f(4.5)\) .
• 11M.2.sl.TZ1.10c(i), (ii) and (iii): The function f can also be written in the form \(f(x) = \frac{{\ln ax}}{{\ln b}}\) . (i)    ...
• 11M.2.sl.TZ1.10d: Write down the value of \({f^{ - 1}}(0)\) .
• 11M.2.sl.TZ1.10e: The point A lies on the graph of f . At A, \(x = 4.5\) . On your diagram, sketch the graph of...
• 11M.1.sl.TZ2.5a: Express \(g(x)\) in the form \(f(x) + \ln a\) , where \(a \in {{\mathbb{Z}}^ + }\) .
• 11M.1.sl.TZ2.5b: The graph of g is a transformation of the graph of f . Give a full geometric description of this...
• 13M.1.sl.TZ1.7a: Find the value of \({\log _2}40 - {\log _2}5\) .
• 13M.1.sl.TZ1.7b: Find the value of \({8^{{{\log }_2}5}}\) .
• 14M.1.sl.TZ2.2b: \({\log _6}4 + {\log _6}9\)
• 14M.1.sl.TZ2.2c: \({\log _6}2 - {\log _6}12\)
• 13M.1.sl.TZ2.3a: Find \({\log _3}{p^2}\) .
• 13M.1.sl.TZ2.3b: Find \({\log _3}\left( {\frac{p}{q}} \right)\) .
• 13M.1.sl.TZ2.3c: Find \({\log _3}(9p)\) .
• 14N.1.sl.TZ0.4a: Write the expression \(3\ln 2 - \ln 4\) in the form \(\ln k\), where \(k \in \mathbb{Z}\).
• 14N.1.sl.TZ0.4b: Hence or otherwise, solve \(3\ln 2 - \ln 4 =  - \ln x\).
• 15M.1.sl.TZ1.3a: Given that \({2^m} = 8\) and \({2^n} = 16\), write down the value of \(m\) and of \(n\).
• 15N.1.sl.TZ0.7: An arithmetic sequence has the first term \(\ln a\) and a common difference \(\ln 3\). The 13th...
• 16M.1.sl.TZ1.9a: Find the \(x\)-coordinate of P.
• 16M.1.sl.TZ1.9b: Find \(f(x)\), expressing your answer as a single logarithm.
• 16M.1.sl.TZ1.9c: The graph of \(f\) is transformed by a vertical stretch with scale factor \(\frac{1}{{\ln 3}}\)....
• 16M.2.sl.TZ1.5a: State two words that describe the linear correlation between \(\ln M\) and \(t\).
• 16M.2.sl.TZ1.5b: The equation of the line of best fit is \(\ln M =  - 0.12t + 4.67\). Given that...
• 16M.1.sl.TZ2.3a: \(\ln \left( {\frac{5}{3}} \right)\).
• 16M.1.sl.TZ2.3b: \(\ln 45\).
• 16N.1.sl.TZ0.9a: Find \(r\).
• 16N.1.sl.TZ0.9c: Find \(d\), giving your answer as an integer.
• 16N.1.sl.TZ0.9e: Given that \({S_{12}}\) is equal to half the sum of the infinite geometric sequence, find \(x\),...
• 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.TZ1.8a: Find the value of a and of b.
• 18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
• 18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
• 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 \(\sum\limits_{n = 1}^{20} {{u_n}} \).

Change of base.

• 18M.2.sl.TZ1.8a: Find the value of a and of b.
• 18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
• 18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...