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Teacher notes: Level of difficulty:  Accessible for all students Syllabus knowledge required:  none. This would be a good starter for the start of 2024! You can download a pdf of the problem and some possible solutions here.

Starter of the Week 17: WIFI password This is the clue to solve to gain a 9-digit WIFI password. What is the password? Teacher notes Level of difficulty: Accessible for HL students Syllabus knowledge required: A knowledge of odd and even functions and their link to integration. Students who are struggling can be shown theContinue reading “Starter of the Week 17: WIFI password”

Starter of the Week 16: Stairway to Heaven Starting with the numbers: 2,4,6,8 fill in the bottom grid in any order. Work out the box above by adding the two numbers below. Here are some possible questions to explore: What is the biggest possible total you can make in the top row? Create a hypothesisContinue reading “Starter of the Week 16: Stairway to Heaven”

Starter of the Week 15: Hollow Squares A hollow square was a battle formation used in the 1800s.  This consisted of a hollow square inside a larger square where the generals could safely command their troops. Here we can see that 12 men can be arranged in a hollow square formation (12 = 4 squaredContinue reading “Starter of the Week 15: Hollow Squares”

Starter of the Week 14: On reflection We start with the curve: What is the equation formed when  f(x) is subject to the following transformations: (a)       Reflection in the line y = 2 (b)       Reflection in the line y = x+2 (c)       Reflection in the line y = x+c Teacher notes: Level of difficulty:  AccessibleContinue reading “Starter of the Week 14: On reflection”

We make a model of a penny farthing bicycle shown above such that the small circle centred at A with radius, r  and the large circle centred as B with radius, R  both share a tangent with the  x axis and  y axis and also share a tangent at point C. Find the value ofContinue reading “Week 13 Penny for Thoughts”

This starter is as follows: One of the most incredible discoveries in human history has been that time is relative rather than absolute.  This means that all clocks – digital, mechanical and biological tick at a different speed for someone in motion relative to someone at rest. For someone travelling at v m/s, the timeContinue reading “Starter of the Week: 12 – Time Dilation”

This week’s problem gives you a chance to become famous (and potentially rich)!  German mathematician Christian Goldbach (above) in 1742 proposed the following conjecture: “Every even integer greater than 2 can be written as the sum of 2 prime numbers.” Over 250 years later no-one has been able to prove it.  Anyone who can proveContinue reading “Week 11: A $1 million maths problem (Goldbach)”

This week’s problem allows you to follow in the footsteps of Pythagoras!  Have a look at the diagram below.  Can you use this to discover Pythagoras’ theorem? You can download the pdf solution here. Teacher notes: Level of difficulty:  Accessible for all students (with some potential support). Syllabus knowledge required:  None. This would be aContinue reading “Week 10: As Smart as Pythagoras?”