Problem of the Week

skip to the Problem of the Week list below

To me, a 'problem' is a question for which it is not clear how to begin 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 a piece of mathematical knowledge - and it is clear how to set up or start a successful solution. Although most of the 'problems' that will 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.

 Problem of the Week (P.o.t.W.)

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 SolutionBrief description of P.o.t.W.
PotW_1_16-11-19  solution_1integral calculus; areas (SL) and volume (HL); GDC allowed
PotW_2_26-11-19  solution_2expected value for lottery and 'fair' game; GDC allowed
PotW_3_02-12-19  solution_3domain, range and equation of tangent in terms of a constant; No GDC
PotW_4_13-12-19  solution_4challenging problem requiring geometry & trigonometry; No GDC
PotW_5_02-01-20   solution_5integral calculus; bisecting shape modelling a piece of toast. GDC allowed
PotW_6_22-01-20 solution_6area of overlap of 2 circles; sectors & segments; calculus. GDC allowed
PotW_7_10-02-20 solution_7rigorous application of cosine rule; using GDC to find max of a function
PotW_8_21-05-20 solution_8geometry & trig; area bounded by circle & absolute value graph; No GDC
PotW_9_31-05-20 solution_9integral calculus; area bounded by parabola & line (parabolic segment); No GDC
PotW_10_17-07-20 solution_10trigonometry; find 2 different methods for proving result for an isosceles triangle
PotW_11_02-08-20 solution_11sequences; 3 terms belong to both an arithmetic and a geometric sequence
PotW_12_29-08-20 solution_122 probability problems involving geometry & trigonometry; no GDC
PotW_13_5-12-20 solution_13angles of a triangle consecutive terms of an arithmetic sequence; GDC allowed
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