You might already know the word "rigid," which means "strong and hard." For example, a rigid tree trunk is strong and hard, and it can't bend; a rigid ruler is firm and stiff, and you can't bend it; and a rigid rule is a rule that you have to follow all the time—you can't bend that rule.
A closely related word is "rigor," which means "harshness, strictness, or cruelty." The rigors of a job or a task are the hard things that you have to do to get them done. For example, I'm totally not ready for the rigors of mountain climbing, like breathing the cold thin air, carrying your heavy backpack, balancing on the slippery ice and snow, and ignoring all the muscle aches and foot blisters that you get along the way.
As you can see, mountain climbing is a rigorous activity. Rigorous things make you do lots of hard work and make you follow strict rules.
When you take a rigorous class, it's full of very hard work—we're talking big projects and long papers. If you have a rigorous schedule, then your days are very full of difficult activities, and you have to follow your schedule exactly, not skipping any activities and not taking any rest.
A rigorous test is long and difficult. A rigorous workout is hard, sweaty, and intense. And a rigorous cleaning takes a long time and a lot of hard work.
Remember: something rigorous has lots of strict rules or makes you do lots of hard work.
Idea 1: "After many weeks of rigorous (training or practice), I could (do something difficult or advanced)."
Idea 2: "I really wanted to succeed (on some task, or in some competition), so I prepared rigorously by (studying, practicing, or researching in a certain way)."
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