Like you, first time round I left it to the tutor, but this time I supplemented what she did. Our tutor (small groups, a fiver an hour, excellent) did not like the children getting "mummy's help" at home with the work she set. Quite right, too, since it warped her idea of their progress. And she gave mainly comprehension homework (this for VR tests) because of the vocab and the patience and the understanding. Question types were worked on in the lessons and full papers introduced towards the end - summer holidays probably at the end of Y5.
So I introduced the odd other paper (the kind I knew she didn't use so as not to clash or give him a false leg up). I timed him in sections so I could break down his aptitude. This was valuable for him, too, he could be proud that he was doing so well in the vocab based ones and taking between 10 and 15 seconds per question and also found it salutory to see the Z type and the 3 codes/4 words taking so very much longer. True he'd bought time for them by whizzing through the vocab ones but laurels are not to be rested on!
I would talk through the corrections with him, rather than leave him to tackle them on his own; to be honest there weren't often many and this way suited us - by then he'd "done" it and was a bit bored and, like eating cold soup, the paper was never quite as appealing second time round. He'd argue, I mean "reason",
, but take eventual notice once confronted with the authority of the answer sheet. I was able to have control over his progress, work on the sections which were slow / accrued poorer marks and be absolutely focused.
For vocab try Stephen Curran (??) or Schonell - I don't know the latter but my son did a few crosswords in one of the former, the sort of thing he likes doing. You've got plenty of time, remember!