Year 11 Being resourceful

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?

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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?

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?

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?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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

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?

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

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

Explore the relationships between different paper sizes.

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?