# 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 | 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 |