DP Mathematics HL Questionbank

• Syllabus

1.2

Sub sections and their related questions

Exponents and logarithms.

• 12M.1.hl.TZ1.8: Solve the equation \(2 - {\log _3}(x + 7) = {\log _{\tfrac{1}{3}}}2x\) .
• 11M.2.hl.TZ1.9: Solve the following system of equations. \[{\log _{x + 1}}y = 2\]\[{\log _{y + 1}}x = \frac{1}{4}\]
• 14M.1.hl.TZ2.2: Solve the equation \({8^{x - 1}} = {6^{3x}}\). Express your answer in terms of \(\ln 2\) and...
• 15M.1.hl.TZ1.12a: (i)     Show that \(\frac{{{v_{n + 1}}}}{{{v_n}}}\) is a constant. (ii)     Write down the first...
• 15M.1.hl.TZ1.12b: Let \({S_n}\) be the sum of the first \(n\) terms of the sequence \(\{ {v_n}\} \). (i)     Find...
• 16M.2.hl.TZ1.7a: Use these results to find estimates for the value of \(a\) and the value of \(b\). Give your...
• 16M.2.hl.TZ1.7b: Use this model to estimate the mean time for the finalists in an Olympic race for boats with 8...
• 16M.2.hl.TZ1.7c: Calculate the error in your estimate as a percentage of the actual value.
• 16M.2.hl.TZ1.7d: Comment on the likely validity of the model as \(N\) increases beyond 8.
• 16M.1.hl.TZ1.6: Find integer values of \(m\) and \(n\) for which \[m - n{\log _3}2 = 10{\log _9}6\]
• 16M.2.hl.TZ2.3: Solve the simultaneous equations \[\ln \frac{y}{x} = 2\] \[\ln {x^2} + \ln {y^3} = 7.\]
• 16N.1.hl.TZ0.7: Solve the equation \({4^x} + {2^{x + 2}} = 3\).
• 17N.1.hl.TZ0.1: Solve the equation \({\log _2}(x + 3) + {\log _2}(x - 3) = 4\).
• 18M.1.hl.TZ1.5: Solve ...
• 18M.1.hl.TZ2.11a: Show that \({\text{lo}}{{\text{g}}_{{r^2}}}x =...
• 18M.1.hl.TZ2.11b: Express \(y\) in terms of \(x\). Give your answer in the form \(y = p{x^q}\), where p , q...

Laws of exponents; laws of logarithms.

• 12M.1.hl.TZ1.8: Solve the equation \(2 - {\log _3}(x + 7) = {\log _{\tfrac{1}{3}}}2x\) .
• 12M.2.hl.TZ1.6: Let \(f(x) = \ln x\) . The graph of f is transformed into the graph of the function g by a...
• 13M.1.hl.TZ1.8: The first terms of an arithmetic sequence are...
• 10M.1.hl.TZ1.4: Solve the equation \({4^{x - 1}} = {2^x} + 8\).
• 14M.1.hl.TZ1.3: Consider...
• 14M.1.hl.TZ2.2: Solve the equation \({8^{x - 1}} = {6^{3x}}\). Express your answer in terms of \(\ln 2\) and...
• 15M.1.hl.TZ1.12c: Let \(\{ {w_n}\} ,{\text{ }}n \in {\mathbb{Z}^ + }\), be a geometric sequence with first term...
• 16M.2.hl.TZ1.7a: Use these results to find estimates for the value of \(a\) and the value of \(b\). Give your...
• 16M.2.hl.TZ1.7b: Use this model to estimate the mean time for the finalists in an Olympic race for boats with 8...
• 16M.2.hl.TZ1.7c: Calculate the error in your estimate as a percentage of the actual value.
• 16M.2.hl.TZ1.7d: Comment on the likely validity of the model as \(N\) increases beyond 8.
• 16M.1.hl.TZ1.6: Find integer values of \(m\) and \(n\) for which \[m - n{\log _3}2 = 10{\log _9}6\]
• 16M.2.hl.TZ2.3: Solve the simultaneous equations \[\ln \frac{y}{x} = 2\] \[\ln {x^2} + \ln {y^3} = 7.\]
• 16N.1.hl.TZ0.7: Solve the equation \({4^x} + {2^{x + 2}} = 3\).
• 17N.1.hl.TZ0.1: Solve the equation \({\log _2}(x + 3) + {\log _2}(x - 3) = 4\).
• 18M.1.hl.TZ1.5: Solve ...
• 18M.1.hl.TZ2.11a: Show that \({\text{lo}}{{\text{g}}_{{r^2}}}x =...
• 18M.1.hl.TZ2.11b: Express \(y\) in terms of \(x\). Give your answer in the form \(y = p{x^q}\), where p , q...

Change of base.

• 12M.1.hl.TZ1.8: Solve the equation \(2 - {\log _3}(x + 7) = {\log _{\tfrac{1}{3}}}2x\) .
• 14M.1.hl.TZ1.3: Consider...