Resources tagged with: Inequalities

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There are 16 results

Broad Topics > Algebraic expressions, equations and formulae > Inequalities

Plutarch's Boxes

Age 11 to 14
Challenge Level

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .

Rationals Between...

Age 14 to 16
Challenge Level

What fractions can you find between the square roots of 65 and 67?

Fracmax

Age 14 to 16
Challenge Level

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.

All-variables Sudoku

Age 11 to 18
Challenge Level

The challenge is to find the values of the variables if you are to solve this Sudoku.

Tet-trouble

Age 14 to 16
Challenge Level

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

Square Mean

Age 14 to 16
Challenge Level

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Inequalities

Age 11 to 14
Challenge Level

A bag contains 12 marbles. There are more red than green but green and blue together exceed the reds. The total of yellow and green marbles is more than the total of red and blue. How many of. . . .

Mediant Madness

Age 14 to 16
Challenge Level

Kyle and his teacher disagree about his test score - who is right?

Biggest Enclosure

Age 14 to 16
Challenge Level

Three fences of different lengths form three sides of an enclosure. What arrangement maximises the area?

Not Continued Fractions

Age 14 to 18
Challenge Level

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Proofs with Pictures

Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities.

Almost Total Inequality

Age 14 to 16
Challenge Level

' Tis Whole

Age 14 to 18
Challenge Level

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

Two Cubes

Age 14 to 16
Challenge Level

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to. . . .

Unit Interval

Age 14 to 18
Challenge Level

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

Approximating Pi

Age 14 to 18
Challenge Level

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?