Is it normal to be nervous on takeoff and landing? Yes... takeoff leaves you very vulnerable (high A of A and low airspeed, moving away from a perfectly good runway), and landing is just... hard. Almost as hard as taxiing.

But landing is probably safer than any other phase of flight, statistically speaking.
If I had to have an electrical failure, an engine failure, a fire, a birdstrike, and control-lock all at the same time, but could choose when and where it happened, I'd want it on final, with a nice runway in front of me.

In such a situation, having the runway before me would actually give me something to smile about...
It's normal-and smart- to be a little nervous throughout the entire flight!! Reminds me of a quote from legendary flyer and writer Ernest Gann: when asked (often) as an airline captain if he was ever scared in the air, he said:
"Always."
He wasn't kidding, either.
But he did pretty well as a heavy-prop captain, even flying the North Atlantic military supply routes, the extremely dangerous Hump routes, and the Berlin Airlift- often in ridiculously overloaded planes and in the most godawful weather. He saw it all, and lasted much longer than many of his cockier comrades. He would say he was just lucky, but I think luck was only part of it. Can't take anything for granted up there; gotta be wary.
But don't dwell on it. If you pass your stage check and are signed off to solo, that means you've already done it, with the instructor aboard as an observer only. Don't sneak glances at him, trust me. There will soon be a flight where he doesn't even keep his hands 2 inches from the yoke, if that hasn't occurred already. He may even put them in his lap.
And don't sweat the "I'm gonna undershoot" feeling: as long as the numbers are getting bigger and not moving up or down (or sideways), you're golden. And if the engine is running, you'll be fine if you do get low... just add a shot of power to get back on-track, or go around. But you already know that.... right?

You may very likely have a "what the hell am I doing?" moment at some point in your first solo, but just remember you've already done it, and you know how. that was my mantra for a long time, and I still think of that when I'm faced with a new challenge in the air.