Year 11 Being curious

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?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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?

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

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?

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?

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?

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

Your school has been left a million pounds in the will of an ex-pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

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?

There are unexpected discoveries to be made about square numbers...

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

If a sum invested gains 10% each year how long before it has doubled its value?

Explore the relationships between different paper sizes.

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

Do you have enough information to work out the area of the shaded quadrilateral?