Below are the simple steps to create a WordPress Page with capability to execute php code without any wordpress plug-ins!
Step1 : Goto your theme directory and create a page template as follows in the screen shot!
Step 2: Save this file in your current theme directory.
Step 3: Go to WordPress Admin panel -> dashboard -> Pages -> Add New
Step 4: Choose the template that you have created and publish!
Step 5: You can see the published page in your site!