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...