This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
problem
Favourite
Arithmagons
Age
11 to 16
Challenge level
Can you find the values at the vertices when you know the values on the edges?
problem
Favourite
Warmsnug Double Glazing
Age
14 to 16
Challenge level
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
problem
Favourite
Which is cheaper?
Age
14 to 16
Challenge level
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
problem
Mega Quadratic Equations
Age
14 to 18
Challenge level
What do you get when you raise a quadratic to the power of a quadratic?
problem
Favourite
How old am I?
Age
14 to 16
Challenge level
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?
problem
Symmetricality
Age
14 to 18
Challenge level
Five equations and five unknowns. Is there an easy way to find the unknown values?
problem
Favourite
Iff
Age
14 to 18
Challenge level
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
problem
Favourite
CD Heaven
Age
14 to 16
Challenge level
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?
problem
Favourite
Terminology
Age
14 to 16
Challenge level
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
problem
Favourite
Pick's Theorem
Age
14 to 16
Challenge level
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.
problem
Favourite
Matchless
Age
14 to 16
Challenge level
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
problem
Favourite
Which is bigger?
Age
14 to 16
Challenge level
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
problem
Favourite
Training schedule
Age
14 to 16
Challenge level
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
problem
Favourite
Multiplication arithmagons
Age
14 to 16
Challenge level
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
problem
Favourite
Fair Shares?
Age
14 to 16
Challenge level
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.