# Resources tagged with: Inequalities

### There are 16 results

Broad Topics >

Algebraic expressions, equations and formulae > Inequalities

##### 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. . . .

##### Age 14 to 16

Challenge Level

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

##### 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.

##### Age 11 to 18

Challenge Level

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

##### 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?

##### 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?

##### 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. . . .

##### Age 14 to 16

Challenge Level

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

##### Age 14 to 16

Challenge Level

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

##### 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?

##### Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities.

##### Age 14 to 16

Challenge Level

##### 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?

##### 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. . . .

##### 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?

##### 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?