It might be silly but Google does also optimize your pages if you want to.
With this tool you can see the adsense ads google would show on your site if you use adsense.
https://www.digitalpoint.com/tools/adsense-sandbox/
I also started with adsense on one of my sites...and come to the conclusion that for some pages immediately the RIGHT ads are shown and for others not.
This means also if google does recognise the page then it is sure well optimized for those words and the related ads !!!!
Get my point.....
So in other words you can verify with this tool how google sees your pages by looking at the ads placed on it...
How... simple
First try the URL....see the ads.
Then try your major keywords from that same page.
If you see the same ads...(most of them) then your page is good
If not...so complete others then there might be something wrong

My Slogan... Let google optimize your pages

regards,
OPtimizer
One condition... with the keywords, appropriate ads should be shown else i wont work.