# Post 16 Students' Solutions

Take a look at these recently solved problems. ### Square Remainders

##### Age 16 to 18Challenge Level

What is the remainder if you divide a square number by $8$? ### Divisible Factorisations

##### Age 16 to 18Challenge Level

Can you show that $n^5-n^3$ is always divisible by $24$? ### Proper Factors

##### Age 16 to 18Challenge Level

Can you find the smallest integer which has exactly 426 proper factors? ### Square Difference

##### Age 16 to 18Challenge Level

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? ### Degree Ceremony

##### Age 16 to 18Challenge Level

Can you find the sum of the squared sine values? ### Making Waves

##### Age 16 to 18Challenge Level

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ? ### Loch Ness

##### Age 16 to 18Challenge Level

Draw graphs of the sine and modulus functions and explain the humps. ### T for Tan

##### Age 16 to 18Challenge Level

Can you find a way to prove the trig identities using a diagram? ### Trig Identity

##### Age 16 to 18Challenge Level

In this short challenge, can you use angle properties in a circle to figure out some trig identities? ### Calculating with Cosines

##### Age 14 to 18Challenge Level

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? ### Tri-angled Trig

##### Age 16 to 18Challenge Level

Can you justify this equation involving three angles?