Real memory problems are uncommon. But forgetting or not remembering to remember is very common. If it only happens once in a while and seldom involves important things, it is no big deal. It is a problem if forgetting is a regular reason for not doing things. It does get to a point when "I forgot," is not just one of those things.
It is tempting to accuse your child of lying or not paying attention. Either may be true. If so, they are themselves problems needing your attention. More likely are several other explanations.
First, your child did not see the assignment or expectation as important enough to remember. He thought it did not matter that much. Dealing with this is not complicated. It also is a good place to start when you first notice the sign. Talk with your child about how important you think the assignment or expectation is. Stress with him how important you think it is for him to treat it as important. This often helps a lot all by itself.
Also be sure you are not using "I forgot," with him or others in the family over things they thought you were going to do. Remembering is a part of caring, respecting each other, and living in a family.
The next step is to be sure your child understands what you expect. When you ask her to do something, have her repeat your request and briefly tell you how she will go about doing whatever it was. Take five minutes for her to explain her homework assignments and describe how she will do them. She might tell you, "I will start on page 144 and read to the end of page 147. Also I will work the nine problems on page 201." Be sure she knows what to do before you expect her to remember to do it.
The next step if the first ones do not work is to set some clear consequences for not remembering. You might say, "You forget to do your home work a lot. I also know you often forget to clean your room. You say they are important but you do not act like they are. I want to make them a little more important. Here is how I am going to do it. You will work on organizing and scheduling things. You and I are then going to figure out what will happen each time you forget to do your homework or clean your room. There need to be consequences. What should they be? If you cannot decide together, I will decide for you. What do you think?"
Positive consequences for remembering are a good idea if you can come up with them. If you use a negative consequence, be careful. It needs to be mild. Help your child remember and not to punish her for forgetting. It also needs to be something you can do daily if necessary and something you will remember. Your forgetting would itself be a problem.