Search by Topic

Resources tagged with Inequality/inequalities similar to AMGM:

Filter by: Content type:
Stage:
Challenge level:

There are 19 results

Broad Topics > Algebra > Inequality/inequalities

Proofs with Pictures

Stage: 4 and 5

Some diagrammatic 'proofs' of algebraic identities and inequalities.

Unit Interval

Stage: 4 and 5 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?

Mediant

Stage: 4 Challenge Level:

If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.

Square Mean

Stage: 4 Challenge Level:

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

' Tis Whole

Stage: 4 and 5 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?

Rationals Between...

Stage: 4 Challenge Level:

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

Balance Point

Stage: 4 Challenge Level:

Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?

All-variables Sudoku

Stage: 3, 4 and 5 Challenge Level:

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

Tet-trouble

Stage: 4 Challenge Level:

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

Inside Outside

Stage: 4 Challenge Level:

Balance the bar with the three weight on the inside.

Fracmax

Stage: 4 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.

Two Cubes

Stage: 4 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. . . .

Christmas Trees

Stage: 3 Challenge Level:

Christmas trees are planted in a rectangular array. Which is the taller tree, A or B?

Inequalities

Stage: 3 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. . . .

Max Box

Stage: 4 Challenge Level:

Three rods of different lengths form three sides of an enclosure with right angles between them. What arrangement maximises the area

Not Continued Fractions

Stage: 4 and 5 Challenge Level:

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

Approximating Pi

Stage: 4 and 5 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?

Plutarch's Boxes

Stage: 3 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. . . .