Hmmmm! Looks like someone just wanted to get their agenda in the news and some journo was more than willing to entertain them on a slow news day!

The clue is in the titles really, problem 1 is an entrance test, the mathematics required to solve it are no more difficult than those required to solve the second problem. It does take considerably longer and requires a higher level of understanding, an ability to "read Maths" as the clues are in the question and the confidence in mathematics to be able to define exactly what you intend to do and why as the last part leaves one with several options.

Problem 2 is a diagnostic test, it's purpose is merely to establish a fundamental understanding of trig and as most people have noted it should be easily within the ability of any GCSE student to write down the answers with no working.

There is an issue in Mathematics in this country, but it is not the ability of mathematicians it is a general apathy with regard to the subject. Probably lots of reasons for this, a lack of qualified Maths teachers in schools, leaving teachers of other subjects to deal with the problem, in my opinion they tend to be less inspiring because they themselves aren't inspired by the subject. A perception that the subject is difficult, obviously it is not if you find it interesting and a brain drain of good mathematicians into the economics world. The move away from the more abstract and philosophical aspects of mathematics has led to a more practical approch "engineering mathematics" whilst this is appropriate for some careers it denies students the beauty and history of the subject which ultimately serve to inspire. How many people have you heard refer to their "Maths" degree as a BSc, traditionally mathematicians were awarded a BA for good reason, it is an art, most now get the choice and as employers outside of academia assume a BA is just pink and fluffy stuff they opt for the science.