Secondary Live Problems and Recent Solutions
Secondary 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.
Secondary Students' Solutions
Subtraction Surprise
Try out some calculations. Are you surprised by the results?
Non-transitive Dice
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Pair Products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Pick's Theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
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?
Sissa's Reward
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Square It
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Parallelogram It
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
Rhombus It
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.
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?
Trig Identity
In this short challenge, can you use angle properties in a circle to figure out some trig identities?
T for Tan
Can you find a way to prove the trig identities using a diagram?
Loch Ness
Draw graphs of the sine and modulus functions and explain the humps.
Making Waves
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
