Post 16 Live Problems and Recent Solutions
Post 16 Live Problems
Flipping Twisty MatricesLive
Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
A Powerful MatrixLive
What happens when you find the powers of this matrix?
Square PairLive
Explore the shape of a square after it is transformed by the action of a matrix.
Two and Four Dimensional NumbersLive
Matrices and Complex Numbers combine to enable us to create four dimensional numbers.
Matrix MeaningLive
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Fix Me or Crush MeLive
Can you make matrices which will fix one lucky vector and crush another to zero?
Transformations for 10Live
Explore the properties of matrix transformations with these 10 questions.
Post 16 Students' Solutions
Square Remainders
What is the remainder if you divide a square number by $8$?
Divisible Factorisations
Can you show that $n^5-n^3$ is always divisible by $24$?
Proper Factors
Can you find the smallest integer which has exactly 426 proper factors?
Square Difference
Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?
Making Waves
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
Loch Ness
Draw graphs of the sine and modulus functions and explain the humps.
T for Tan
Can you find a way to prove the trig identities using a diagram?
Trig Identity
In this short challenge, can you use angle properties in a circle to figure out some trig identities?
Calculating with Cosines
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
