For test whether address is yours or not, when Bitcoin Core using your backup wallet, open the console and type validateaddress "bitcoinaddress"
One of the result is "ismine" : true|false, (boolean) If the address is yours or not.
Without running this command (or sending some coins to the address) it is hard to give you definitive answer whether your old backup contains private key for the new address you created later. The reason is your old backup contains also next 100 private keys that going to be needed later, this mean for new change address when you sending transaction or when you add new address to receive Bitcoins to. So you have to ask yourselves how many such operations requiring new address you made since you make your old backup. If its under 100, you should have the private key in your backup.