[manage to]
1. A: Have you ever missed a flight?
B: I’ve never missed a flight, but I’ve almost missed it once.
I managed to arrive at the gate just as they were about to close it.
2. He managed to pass the test. If I were him, I would give up.
[no matter]
1. A: Did you look for any places to go?
B: Sorry, I’ve been so busy, I couldn’t.
No matter where you want to go, I’ll go without complaining.
2. A: I heard no matter how busy he is, he exercise every day.
B: Wow, If I were him, I couldn't exercise. It would be so hard. I'd probably just sleep.
[happen to]
1. Do you happen to have a pen? Could I borrow it?
2. A: It's raining.
B: Don't worry. I happened to bring an umbrella.