Here is the problem: Teacher notes: Level of difficulty: The first parts of this are accessible for all. The last part would be accessible for strong HL students. Syllabus knowledge required: None. This is a good introduction to the need to check that all solutions are found! It is likely that students will miss lotsContinue reading “Week 8: Hunting Integers”
Author Archives: Andrew Chambers
Week 7: A Reciprocal Sum
Week 7: A Reciprocal Sum This is a bit of a longer problem – and could be expanded to start a nice investigation. The problem is given below: Teacher notes: Level of difficulty: Only HL Syllabus knowledge required: This mixes a knowledge of graphs, ideas in formal proof and differentiation. This is a good introductionContinue reading “Week 7: A Reciprocal Sum”
Week 6: Sum of 3 Cubes
Week 6: Sum of 3 Cubes (a) How many of the following numbers in the table can you form as the sum of 3 cubes of integers? (You can use negative integers if you wish). (b) Research what the solution is for 30 and 33! (c) Can you find a pattern that describes the numbersContinue reading “Week 6: Sum of 3 Cubes”
Week 5: Circular Logic
A shape is formed as follows: A circle is drawn such that the points A, B, C, D are equally spaced around the circumference. The arcs AB and CD are reflected in the lines AB and CD respectively. This makes the following shape: (a) Find the area of the shaded shape when the radius, r,Continue reading “Week 5: Circular Logic”
Week 4: Decidedly Average
In the following grids, each blank square should be filled with the mean of the two numbers in adjacent squares. (a) Fill in the grid below. (b) Find x in the following grid, leaving your answer in terms of a,c: (c) Find x in the following grid, leaving your answer in terms of a,c: (d) Continue reading “Week 4: Decidedly Average”
Week 3: Make 2023
Using the numbers 10,9,8,7,6,5,4,3,2,1 in order, the standard arithmetic operations and brackets, can you make the number 2023? For example of the idea: This clearly doesn’t make the correct answer – but can you find a combination that does? Teacher notes: Level of difficulty: Accessible for all students Syllabus knowledge required: none. This would beContinue reading “Week 3: Make 2023”
Week 2: Message in the logs
Can you find the hidden message? Teacher notes: Level of difficulty: Accessible for SL Analysis and all HL students Syllabus knowledge required: Laws of logs This would be a good starter in December! Solutions: Using the laws of logs we get: Happy Christmas! You can download a pdf of this problem here.
Week 1: Square Dance
Week 1: Square Dance This puzzle is as follows: For the unit square shown above with vertices at (0,0), (1,0), (0,1) and (1,1), how many different types of functions can you find that go through at least 2 points? Teacher notes: Level of difficulty: Accessible for strong SL and all HL students. Syllabus knowledge required: Continue reading “Week 1: Square Dance”