Year 10 Being resourceful

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Charlie has moved between countries and the average income of both has increased. How can this be so?

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Can you match up these equivalent algebraic expressions?

Which numbers can we write as a sum of square numbers?

If you know the perimeter of a right angled triangle, what can you say about the area?

Can you explain what is going on in these puzzling number tricks?

Can you create a Latin Square from multiples of a six digit number?

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Can you work out which spinners were used to generate the frequency charts?

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?