Problem of the Week
skip to the Problem of the Week list below
To me, a 'problem' is a question where it is not immediately clear how to begin writing a solution. The vast majority of questions that students are asked to answer during a maths course are exercises where they are simply practicing (exercising) a certain skill and/or some type of mathematical knowledge - and it is clear from the start how to set up a successful solution. Although most of the 'problems' that appear in this Problem of the Week set will not fully meet my idea of a true problem; each is closer to a 'problem' than to an 'exercise'.
The level of problem solving will vary between questions but when writing these original questions, I am focusing on making some degree of resourceful thinking / problem solving necessary to successfully solve the 'problem'. Some problems - or part(s) of some problems - are more suitable for HL students than SL students. This will be clearly indicated in the problem. For example, problem of the week #1 asks for the volume of a solid of revolution in part (c). Solids of revolution are not in the SL syllabus for Analysis & Approaches - so, part (c) of Problem #1 has been marked as HL only.
I strive to write problems that involve the application of mathematics contained within the Analysis & Approaches syllabus - so, most of these problems can assist students in preparing for external exams - Paper 1 (no GDC), Paper 2 (GDC allowed) and HL Paper 3 (GDC allowed). Whether a GDC is allowed or not is indicated for each problem.
Problems of the Week on the Math HL/SL site
The 'old' collection (over 400 total) of Problems of the Day can still be found on the 'old' Math HL/SL site (click on large blue button on left of homepage). You may need to re-enter your password to gain entry to the Math HL/SL site. The large collection of Problems of the Day are in the Assessment section. I will soon be moving these to an appropriate location here on the Analysis & Approaches site.
Clicking on a problem in the list below will open a new P.o.t.W. page with the problem displayed. All of the P.o.t.W. pages are student accessible so they can be shared with (or assigned to) your students. Each P.o.t.W. page will have a link to a downloable PDF file containing the problem. The worked solution / notes for each problem is accessed by clicking on the 'solution' link. Solutions are not student accessible.
Green indicates that a GDC is allowed; red indicates no GDC.
|Problem of the Week||Solution||Brief description of P.o.t.W.|
|PotW_1_16-11-19||solution_1||integral calculus; areas (SL) and volume (HL); GDC allowed|
|PotW_2_26-11-19||solution_2||expected value for lottery and 'fair' game; GDC allowed|
|PotW_3_02-12-19||solution_3||domain, range and equation of tangent in terms of a constant; No GDC|
|PotW_4_13-12-19||solution_4||challenging problem requiring geometry & trigonometry; No GDC|
|PotW_5_02-01-20||solution_5||integral calculus; bisecting shape modelling a piece of toast. GDC allowed|
|PotW_6_22-01-20||solution_6||area of overlap of 2 circles; sectors & segments; calculus. GDC allowed|
|PotW_7_10-02-20||solution_7||rigorous application of cosine rule; using GDC to find max of a function|
|PotW_8_21-05-20||solution_8||geometry & trig; area bounded by circle & absolute value graph; No GDC|
|PotW_9_31-05-20||solution_9||integral calculus; area bounded by parabola & line (parabolic segment); No GDC|
|PotW_10_17-07-20||solution_10||trigonometry; find 2 different methods for proving result for an isosceles triangle|
|PotW_11_02-08-20||solution_11||sequences; 3 terms belong to both an arithmetic and a geometric sequence|
|PotW_12_29-08-20||solution_12||2 probability problems involving geometry & trigonometry; no GDC|
|PotW_13_5-12-20||solution_13||angles of a triangle consecutive terms of an arithmetic sequence; GDC allowed|