Using Captcha with custom forms

We have custom forms as pages on our site. We’d like to use a Captcha on these forms to prevent spam. But I’ve tried three different plug-ins and none of them work. They all seem to need me to use Contact form 7 or they want to put the captcha on a comments page which we don’t have. I tried to use a PHP based captcha but since these are WordPress pages, there was no header for me to put that info into. How do I make this work?