Speculatively means to "size up a situation." If a bully is eying you, he is usually calculating the odds of making you do what he wants you to do.
"Sam watched Oscar speculatively, trying to figure out what he was doing."
"Joe eyed Susan's approach speculatively, since she had never talked to him before."
You shouldn't speculate why you haven't heard from them, call them and ask them.
I speculate that you are trying to get someone to do your homework.
The base word of speculate is "specul."
I hesitate to speculate on that unique piece of jewelry.
"My colleagues speculate about my private life."
Yes. Speculate is a valid Scrabble word.
Charles Goodnight was a great speculator who created a huge cattle ranching business.
Why do you speculate the obvious
you can't
"People often speculate the creation of the world as the answer is not fully known."
The word speculate is a verb. The past tense form is speculated.
I hesitate to speculate on that unique piece of jewelry.