Inequalities

There are 47 NRICH Mathematical resources connected to Inequalities
Approximating Pi
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Approximating pi

Age
14 to 18
Challenge level
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By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
Square Mean
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Square mean

Age
14 to 16
Challenge level
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Is the mean of the squares of two numbers greater than, or less than, the square of their means?
Eyes Down
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Eyes down

Age
16 to 18
Challenge level
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The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?
In Between
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In between

Age
16 to 18
Challenge level
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Can you find the solution to this algebraic inequality?
Which is cheaper?
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Which is cheaper?

Age
14 to 16
Challenge level
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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?
Quadratic Harmony
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Quadratic harmony

Age
16 to 18
Challenge level
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Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
Discrete Trends
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Discrete trends

Age
16 to 18
Challenge level
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Find the maximum value of n to the power 1/n and prove that it is a maximum.
Which is bigger?
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Which is bigger?

Age
14 to 16
Challenge level
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Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
Squareness
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Squareness

Age
16 to 18
Challenge level
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The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
Tet-Trouble
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Tet-trouble

Age
14 to 16
Challenge level
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Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?