Year 11 Reasoning, convincing and proving

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

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?

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?

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

Can you make sense of the three methods to work out what fraction of the total area is shaded?

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

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?

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

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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

Explore the relationships between different paper sizes.

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.