Year 11 Explaining, convincing and proving

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Which of these games would you play to give yourself the best possible chance of winning a prize?

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

Here are two games you can play. Which offers the better chance of winning?

Can you find the hidden factors which multiply together to produce each quadratic expression?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Simple additions can lead to intriguing results...

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Can you work out the dimensions of the three cubes?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Two ladders are propped up against facing walls. At what height do the ladders cross?

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Can you express every recurring decimal as a fraction?

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

What is special about the difference between squares of numbers adjacent to multiples of three?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?