Needing to install things is kind of the point of needing the laptop, so it makes perfect sense that they want to install Office, AV, and certificates. There are no surprises there. To do that, they need admin access, but I would want to revoke that access once they were done.
I would want to know the list of everything they want to install, and if they have central control over the AV (and if they do, why they want that).
If your worry is that they might install malware, then download a Live CD of an anti-malware program and run it on the laptop after they are done.
If the laptop is only used for school work, then there is really no harm here. If your child will be using it for other things, then there might be some privacy conflicts.
The onslaught of comments and the split in votes highlights a difference in understanding of the operating model here. This is not a situation where the school wants sudden control of a personal device. This is a situation where the school is asking the parent to purchase a device for the school to control and this answer is meant to be applied in this model. The school needs to be able to control the device as a part of due care (and remember that the child in this case is a minor; 12 or 13). In terms of protecting the child's privacy, my advice to make sure that the device is only used for school work holds.
The fact that the parent can retain admin control is a great thing for the protection of the child, something that would not be possible if the school owned the device. The parent can inventory, patch, and uninstall.
This operating model means that the school can ensure consistency of software, which would be required for teaching consistency, it lowers the cost to the school (yes, it increases direct costs to the parents, but does offer cost efficient options) and it offers due care controls for the protection of the child. You just have to shift your mindset that just because you bought the device does not mean that you should have 100% control of the device.
And again, with the new onslaught of comments, I say: consider the idea of a "burner" device. You own it, but it is meant to be, at least in part, out of your control and properly classified for certain activities.
If the operating model was that the school wanted sudden control of a personal device, my answer would be very different (more like AviD's).