DP Mathematics HL Questionbank

• Syllabus

2.7

Sub sections and their related questions

Solutions of \(g\left( x \right) \geqslant f\left( x \right)\) .

• 12M.2.hl.TZ2.1b: Find the smallest value of n such that the sum of the first n terms is greater than 600.
• 12N.3srg.hl.TZ0.4f: (i)     If \(x,{\text{ }}y \in G\) explain why \((c - x)(c - y) > 0\) . (ii)     Hence show...
• 08M.2.hl.TZ2.10: Find the set of values of x for which \(\left| {0.1{x^2} - 2x + 3} \right| < {\log _{10}}x\) .
• 08N.2.hl.TZ0.6: (a)     Sketch the curve \(y = \left| {\ln x} \right| - \left| {\cos x} \right| - 0.1\) ,...
• 10M.2.hl.TZ1.9: Let \(f(x) = \frac{{4 - {x^2}}}{{4 - \sqrt x }}\). (a)     State the largest possible domain for...
• 10M.2.hl.TZ2.8: (a)     Simplify the difference of binomial...
• 10N.1.hl.TZ0.1: Find the set of values of x for which \(\left| {x - 1} \right| > \left| {2x - 1} \right|\).
• 13M.1.hl.TZ2.9a: Show that \(f(x) > 1\) for all x > 0.
• 13M.1.hl.TZ2.9b: Solve the equation \(f(x) = 4\).
• 11M.1.hl.TZ1.12d: Now consider the functions \(g(x) = \frac{{\ln \left| x \right|}}{x}\) and...
• 09M.2.hl.TZ1.3: Let \(f(x) = \frac{{1 - x}}{{1 + x}}\) and \(g(x) = \sqrt {x + 1} \), \(x > - 1\). Find the...
• 09M.2.hl.TZ2.4b: Solve \(\ln \left( {2x + 1} \right) > 3\cos (x)\), \(x \in [0,10]\).
• 14M.2.hl.TZ1.6a: Solve the inequality \(f(x) > x\).
• 13N.2.hl.TZ0.3b: Solve the inequality \(\ln x \leqslant {{\text{e}}^{\cos x}},{\text{ }}0 < x \leqslant 10\).
• 15M.1.hl.TZ2.10d: Solve the inequality \(\left| {f(x)} \right| < \frac{3}{2}\).
• 15M.1.hl.TZ2.10e: Solve the inequality \(f\left( {\left| x \right|} \right) < \frac{3}{2}\).
• 15M.2.hl.TZ1.10a: A function \(f\) is defined by \(f(x) = (x + 1)(x-1)(x-5),{\text{ }}x \in \mathbb{R}\). Find the...
• 15M.2.hl.TZ1.10b: A function \(g\) is defined by \(g(x) = {x^2} + x - 6,{\text{ }}x \in \mathbb{R}\). Find the...
• 17N.1.hl.TZ0.6b: Hence or otherwise, solve the inequality \(\left| {\frac{{1 - 3x}}{{x - 2}}} \right| < 2\).
• 18M.1.hl.TZ1.5: Solve ...

Graphical or algebraic methods, for simple polynomials up to degree 3.

• 12M.2.hl.TZ2.1b: Find the smallest value of n such that the sum of the first n terms is greater than 600.
• 15M.2.hl.TZ1.10a: A function \(f\) is defined by \(f(x) = (x + 1)(x-1)(x-5),{\text{ }}x \in \mathbb{R}\). Find the...

Use of technology for these and other functions.

• 12M.2.hl.TZ2.1b: Find the smallest value of n such that the sum of the first n terms is greater than 600.
• 08M.2.hl.TZ2.10: Find the set of values of x for which \(\left| {0.1{x^2} - 2x + 3} \right| < {\log _{10}}x\) .
• 13M.2.hl.TZ2.5b: Determine the set of values of n for which \({u_n} > {v_n}\).
• 13M.2.hl.TZ2.5c: Determine the greatest value of \({u_n} - {v_n}\). Give your answer correct to four significant...
• 09M.2.hl.TZ1.3: Let \(f(x) = \frac{{1 - x}}{{1 + x}}\) and \(g(x) = \sqrt {x + 1} \), \(x > - 1\). Find the...
• 14N.2.hl.TZ0.7b: The seventh term of the arithmetic sequence is \(3\). The sum of the first \(n\) terms in the...
• 14N.2.hl.TZ0.9b: If \(n > 1\) and odd, it can be shown that...
• 15M.2.hl.TZ1.10b: A function \(g\) is defined by \(g(x) = {x^2} + x - 6,{\text{ }}x \in \mathbb{R}\). Find the...