List

Year 11+ Working systematically

problem

Shopping basket

Age
11 to 16
Challenge level
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The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Parabolic Patterns
problem

Parabolic patterns

Age
14 to 18
Challenge level
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The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

Vector walk
problem

Vector walk

Age
14 to 18
Challenge level
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Starting with two basic vector steps, which destinations can you reach on a vector walk?

Expenses
problem

Expenses

Age
14 to 16
Challenge level
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What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

Mathsland National Lottery
problem

Mathsland national lottery

Age
14 to 16
Challenge level
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Can you work out the probability of winning the Mathsland National Lottery?

Bendy Quad
problem

Bendy quad

Age
14 to 16
Challenge level
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Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Squirty
problem

Squirty

Age
14 to 16
Challenge level
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Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

Difference Sudoku
problem

Difference Sudoku

Age
14 to 16
Challenge level
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Use the differences to find the solution to this Sudoku.

problem

Funnel

Age
14 to 16
Challenge level
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A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?