Formulating Subnet Information Quicker

Hello,

      I am going for my Network+ N10-006 test this next week and I am having some issues with some subnetting. I need to find faster ways to obtain the following details with IP addresses. I can work them out in the long run, taking a lot of time with converting dotted decimal to binary then comparing the subnet mask to the IP address to find network etc. etc. But the real problem is in my test I will be under the time clock with NO calculator. I have done quite a bit of these and not seeming to get faster at them so I am hoping some of you have some good tricks to help speed it up. I have searched the web too but most of them require excel and calculators which I wont be able to use. Info I need to determine quickly is below.

A random IP, 10.150.174.20/17 (If you know a quicker way to convert to binary instead of lining up the formula and plugging in 1/0 in the following: 128 64 32 16 8 4 2 1, that would also be super helpful!)

Network ID
Broadcast
First Valid IP
Last Valid IP

      One other thing that is kind of escaping me that I cannot fully grasp yet. If my number of subnets are quite high, like in a /27 that allows me 32 diferent subnet ranges, with 30 valid addresses in each one minus my ID and Broadcast. When you add those up, it goes above the .254 range for the octet and has to increase the octet prior, correct? If so, is there an easier way to calculate these ranges from ID to Broadcast easier then setting down and writing each range out individually? I also experienced that at some point I will hit mid range at .254 and cannot go higher so does that range just lose the rest of the valid IP's or does it carry over with the octet increase?

I know this is a lot of beginner questions to you guys probably but at 300.00 for my cert test I cannot afford to not know why I am answering something haha. Thanks so much in advance!