Destin explains the strength of a Prince Rupert’s drop by comparing it to…
A bicep
A spring
A catapult
An arch bridge
An elephant
This is a UKMT JMC (Junior Maths Challenge) question. I’ve been using it with my students, who applied to St Paul’s Girls’ School, in the recent 11+ entrance exams.
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What is the shape of the path that the snail traces out as the ladder falls?
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Every card in this deck has a number on one side and a letter on the other. The same number can appear on more than one card.
Euna places four of these cards in a row, then flips over some (maybe all) of the cards and mixes them up. The before and after state is pictured below. What number is on the other side of the A?
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Can you help solve how much money April, May and June began with, before sharing equally?
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10 silver beads and 10 gold beads are arranged randomly on a necklace.
Is it always possible to make one straight line cut that divides the necklace into two pieces that each have 5 silver and 5 gold beads?
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Could you solve this? My year 8 daughter’s homework from last weekend. I did point her in the right direction and then she finished it off. She was very happy as she worked out how to solve it.
Last night, she asked if she could work on really hard maths over half term, to help her find maths at school easy and also to have fun (apparently). I’ve pulled out UKMT’s Intermediate Problems by Andrew Jobbings (years 9-11 Intermediate Maths Challenge questions) and a pile of Art of Problem Solving books.
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A set of positive integers has sum 25. What is the biggest you can make the product of the numbers?
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Can you work out the area of the inner square?
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The pattern 123451234512345... is continued to form a 2000-digit number. What is the sum of all 2000 digits?
6000
7500
30,000
60,000
75,000
![UKMT (UK Mathematics Trust): [√ n]](https://images.squarespace-cdn.com/content/v1/580f3dddc534a5c144fe8a58/1600772690017-AF5AAN2C2RCFEV33MKQF/Screen+Shot+2020-09-22+at+11.24.25.png)
The notation [√ n] means the integer part of the square root of n. How quickly can you solve?
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Take away two matches to leave two squares.
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It is extraordinary that so much of the universe can be explained using mathematical equations. Indeed, it is often said that mathematics is the language of the universe. It is certainly the language of science.
In this clip, from a documentary in the American Nova series, the jazz musician Esperanza Spalding explains how maths is also at the heart of music. Pay attention to the way that numbers relate to musical intervals (an octave, a fifth and a fourth).
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Shawn has dealt four cards in front of you. He claims that if a card has an even number on one side of it, then the other side of the card is blue. Which cards do you need to turn over, in order to confirm if Shawn is telling you the truth?
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Shearing is a transformation of a shape in which a particular line (in this case the base of the triangle or parallelogram) remains fixed and all other points in the shape are translated parallel to that line by an amount proportional to the distance from that line.
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A cone shaped iceberg with tip pointing up is 80% submerged in water. Part I can see is 8m high & 6m across. What is height of full iceberg?
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2. Is there a link between the number of squares in a polynomial (a shape made out of squares joining on a complete edge) and the minimum perimeter that can be made for each number of squares?
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Who is the landlord? Can you solve it?
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