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 ,...