Is it your ds who wants him to go to the grammar, or you? If the former, reminding him that it is so he attains his goal, and gets to go to his preferred school, and that it is only for a short time more, should help. If the latter, you need to discuss your choice and the rationale behind it with your ds - if the motivation is not coming from him, then you will be really up against it.
Plus - bribery - I paid my dd cold hard cash when she got over certain marks, where I knew she could do it, but was being lazy and there were too many careless errors creeping in. Or bribing with treats, chocs, computer time, days out - whatever would work for your ds. Plus competing against you or a friend or their previous score or a sibling might work for a robust, competitive child - obviously a less robust one might feel downhearted if they 'lose' so it depends on the child.
Motivate by keeping a tab or even graph of results, so they can see how they have improved and that progress is being made!
Use progress made at school to motivate eg if they are getting higher levels at school or moving up a table etc - my dd was v pleased to get 5As after a few months with me.
Above all else - don't overdo it! If your ds is bored, maybe you need to back off - 1 paper a week in each subject they'll be doing in tests is more than ample. Maybe leaving test papers altogether and focusing on a few areas your ds finds hard? Or ASK your ds why he's bored and what he'd like to do - his answers may surprise you!
As a teacher, I'm a great believer in 'you can take a horse to water but you can't make it drink' - all the teaching in the world will be worthless if your son is resistent. So focus on following his interests and needs. And - as you are clearly motivated - explain the reasons for that to him, so you are working as a team, not you dragging him forward, kicking and screaming, by the metaphorical hair...