Resources tagged with Algebra - generally similar to Power Quady:
Other tags that relate to Power Quady
Inequality/inequalities. Manipulating algebraic expressions/formulae. Making and proving conjectures. Number theory. Mathematical reasoning & proof. Algebra - generally. Generalising. Patterned numbers. Index notation/Indices. Quadratic equations.There are 23 results
Broad Topics > Algebra > Algebra - generally
Power Quady
Stage: 5 Challenge Level: 
Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
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?
Euler's Squares
Stage: 4 Challenge Level:
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Converse
Stage: 4 Challenge Level:
Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?
Diophantine N-tuples
Stage: 4 Challenge Level:
Can you explain why a sequence of operations always gives you perfect squares?
DOTS Division
Stage: 4 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Our Ages
Stage: 4 Challenge Level:
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
For What?
Stage: 4 Challenge Level:
Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.
Unit Interval
Stage: 5 Short Challenge Level:
Can you prove our inequality holds for all values of x and y between 0 and 1?
Loopy
Stage: 4 Challenge Level:
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
Harmonic Triangle
Stage: 4 Challenge Level:
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Rudolff's Problem
Stage: 4 Challenge Level:
A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
Novemberish
Stage: 4 Challenge Level:
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
Coffee
Stage: 4 Challenge Level:
To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?
Interactive Workout - Further
Stage: 5 Challenge Level:
Give your further pure mathematics skills a workout with this interactive and reusable set of activities.
Building Tetrahedra
Stage: 4 Challenge Level:
Can you make a tetrahedron whose faces all have the same perimeter?
Interactive Workout - Mathmo
Stage: 5 Short Challenge Level:
Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!
Bird-brained
Stage: 5 Challenge Level:
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
The Development of Algebra - 1
Stage: 3, 4 and 5
This is the first of a two part series of articles on the history of Algebra from about 2000 BCE to about 1000 CE.
Reaction Rates!
Stage: 5
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
Medallions
Stage: 4 Challenge Level:
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
Diamonds Aren't Forever
Stage: 5 Challenge Level:
Ever wondered what it would be like to vaporise a diamond? Find out inside...
Gassy Information
Stage: 5 Challenge Level:
Do each of these scenarios allow you fully to deduce the required facts about the reactants?
NRICH is part of the family of activities in the Millennium Mathematics Project.