Cool. So you can get the YouTube app up on TV, either on your Smart TV or using your set top box.
You just need to follow a couple of steps, and then you'll be able to get the quiz sent onto the TV screen.
Before you start.... make sure that you log into YouTube on your TV and on your phone with the same account. If you're not signed in, you won't see the 'cast' or 'add to watchlist' options which are essential.
Step 1 - open YouTube on your TV/Set Top Box
Step 2 - open the quiz link on your phone or tablet
(remember you need to be signed in on both)
Step 3 - Top right you should see the 'cast icon' press, this and then select your TV/Set Top box from the devices show (see below)
Step 4 - You can then press play on the Quiz, and boom - it's on the big screen :)
If you don't see the cast options, or the YouTube link won't open in the App on your phone. You can also choose 'Add to watch list' (see below) and then it should appear in the watch list section on your TV. Again, you need to make sure you are signed into the same account on both devices.