Home Security System
Is this detector for a home security system? A detector for a home security system is just like a detector for the common halls of an apartment building; it's connected to a fire alarm system that can call the fire department. Make sure the system isn't going to call the fire department when you are testing the detector.
When you "Test" the smoke detector with a magnet or with smoke, keep in mind that you are sounding the alarm. Just before testing the detector, call your monitoring company (like ADT, Brinks, or other security monitoring company) and let them know that you are testing. Make sure they will take "No Action"; they won't call the fire department when they get the alarm.
You also need to be prepared to reset the security system if it's connected to the security system.
If you are in an apartment, and there's no test button on the smoke detector, there's at least a small chance that the smoke detector is tied into the common fire alarm system for the entire apartment building. If that's the case, talk to your apartment building manager before testing the detector. You don't want to sound off the alarms in the whole building.
The magnet-on-a-stick that you get from a hardware store should work just fine. The one thing you have to remember with any magnet you test with is that the magnet-test inside the smoke detector is somewhat directional; you might have to rotate your test magnet so is "parallel" with the edge of the smoke detector because most magnetic switches inside the detector are also in parallel with the edge of the detector. but then, you might have to "point" the test magnet directly at the edge of the detector. Try it several ways.
Also, the smoke detector should have raised letters that say "Magnet Test" or just "Magnet" to indicate where on the smoke detector to use the magnet. The letters may be very faint, so you might have to climb up and look closely on the case of the detector to know where to place the magnet for testing. Once you've seen the letters, then you can use the magnet-on-a-stick from then on.
Smoke versus Magnet
In all this, remember that the button or the magnet will only test the electronics inside the detector, the sounder, and the security system if it's attached to the security system. The button or magnet do not test the smoke detecting chamber. To test to see if the smoke detector detects smoke, smoke (or canned smoke) needs to be used for testing.