IB Questionbank

Updates to Questionbank

User interface language: English | Español

Date	May 2015	Marks available	2	Reference code	15M.2.hl.TZ2.3
Level	HL only	Paper	2	Time zone	TZ2
Command term	Hence or otherwise and Solve	Question number	3	Adapted from	N/A

Question

Sketch the graph of $y = {(x - 5)^2} - 2\left| {x - 5} \right| - 9,{\text{ for }}0 \le x \le 10$ .

[3]

a.

Hence, or otherwise, solve the equation ${(x - 5)^2} - 2\left| {x - 5} \right| - 9 = 0$ .

[2]

b.

Markscheme

general shape including \[(\) minimums, cusp A1A1

correct domain and symmetrical about the middle $(x = 5)$ A1

[3 marks]

a.

$x = 9.16\;\;\;{\text{or}}\;\;\;x = 0.838$ A1A1

[2 marks]

Total [5 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

Topic 2 - Core: Functions and equations » 2.6 » Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.

12M.2.hl.TZ1.11a: Write down the coordinates of the minimum point on the graph of f .
12M.2.hl.TZ1.11c: Find the coordinates of the point, on $y = f(x)$ , where the gradient of the graph is 3.
08N.2.hl.TZ0.6: (a) Sketch the curve $y = \left| {\ln x} \right| - \left| {\cos x} \right| - 0.1$ ,...
11M.2.hl.TZ2.7b: Calculate the size of the acute angle between the tangents to the two graphs at the point P.
11M.2.hl.TZ2.7a: Find the coordinates of P.
13M.2.hl.TZ2.4b: Determine the value of m if $\int_0^m {x{{\sec }^2}x{\text{d}}x = 0.5}$ , where m > 0.
13M.2.hl.TZ2.11b: A number of distinct points are marked on the circumference of a circle, forming a polygon....
11N.2.hl.TZ0.8b: find the value of x such that $f(x) = {f^{ - 1}}(x)$ .
14M.2.hl.TZ2.3a: Find the value of ${x_{\text{A}}}$ and the value of ${x_{\text{B}}}$ .
13N.2.hl.TZ0.8b: Find the value of $\theta$ for which the shaded area is equal to half that of the unshaded...
15M.2.hl.TZ2.8c: Find the value of $a$ .
14N.2.hl.TZ0.13c: Once empty, water is pumped back into the container at a rate of...