Just a couple of things to mention; the hardest maths exam might not reflect the school that’s hardest to get into. People forget that there isn’t a set pass mark, but the pass mark is essentially set at whatever number of places the schools can offer. Independents will over-offer as not everyone will accept and they want to fill all or most places from those offered, as they know that once they go to waiting list, they often have to go quite a way down to get an acceptance, especially in areas where people apply to many schools.
Harder papers get lower scores generally. It will be harder for the majority, but the school will take the same number of students.
Some schools have easier questions, but it’s the quantity they have to get through which makes the exam difficult. Students who do well might not be the best mathematicians, but they are often trained in speed and accuracy….so such an exam is assessing these things, and certainly regardless if if you’ve covered the full range of topics or not, speed and accuracy will be absolutely key in who scores high enough to get a place. And these things certainly can be prepped for and those who haven’t seen a paper before might be brilliant mathematicians, but simply not finish the paper.
And this thing about tutoring. Of course they all say that tutoring isn’t needed…especially the state selectives. They absolutely must be seen to broaden access and not have an exam which favours those with money. But unfortunately all of these exams do, because those who have been prepared (by paid for tutors or by parents putting time and usually money into resources) are hugely advantaged.
I think it’s technically true to say that a child who has only covered the Yr5 NC COULD get a place. As others have mentioned, an exceptional child will be able to see Qs and apply knowledge they have of topics they have already covered to reach answers to get close to answers. They will also gain all of the marks for the easier questions and might score high enough that way, to get a place. 100% isn’t required. However, children who have learned more will be advantaged, as questions are likely to come up which don’t look familiar to Yr5 Maths, even if the answer might be found using that already known Maths. Those who’ve practised past papers will have been exposed to this higher level stuff and perhaps know more sophisticated techniques to find answers, or find them more quickly.
Schools know tutoring and home preparation is rife. They would prefer it wasn’t…but it is. The genie is out of the bottle and isn’t going back in. No test is untutorable, whatever schools say. It might not be the case that it’s impossible to get in without any prep, but for the most selective schools, the chances of getting in without any prep are very very slim. As number applying particularly for state super selectives continue to rocket, schools have to distinguish between candidates. One mark will separate those who either get an offer or get through to the next round. Often the difference between those 2 candidates isn’t who is best, but quite simply who was best prepared to avoid a simple error or to work a bit faster.
And I agree, that based on ratios of applicants per place, the top super selective state grammars are those that are hardest to get places at. Loads of those applicants don’t take the private school exams, as paying anything towards fees just isn’t an option. If money was no object though, many who get the state super selective places, would also get the top 10 indeoendnet places too. Often those who have applied to both state super selective and independent top 20 and got offers from both, have scholarship offers from the independent….because these kids are amongst the top performers in the indeoendnet entrance exams. The tests aren’t entirely comparable, and given that the numbers sitting and sifting that is required, and funding available for marking being different, the exact purpose and difficulty level of the tests differ. Independent school exams might have more scope for complex, more labour intensive to mark exams, which test complex understanding. More difficult and lengthy questions might appear. State schools have to rely more on multiple choice and often there will be far more questions, with few being long and really complex multi stage type questions, but the level of speed and accuracy that’s required is likely to be greater.
The vast majority of kids who get places at these schools are very able. Yes they might have been prepped hard, but they are also bright enough to have beat many others to their places. And it’s worth remembering again, that in some areas, more than 9/10 applicants won’t pass, even with prep of some type. The numbers applying are just too high. Much easier in some places, where perhaps 1/3 get in, or for some independents, pretty much everyone who applies gets an offer.