All Subjects/General/Productivity:

• Keynote  - A slideshow presentation program (Created by Apple).
• Pages - A word processing program (Created by Apple).
• Numbers - A spreadsheet application (Created by Apple).
• Whiteboard - Collaborate with friends and family with Whiteboard, the easy-to-use collaborative drawing app for iPhone, iPod touch, and iPad.
• TypeDrawing - TypeDrawing is a really easy app to use, but it's perfect for creating TYPOGRAPHY ART and UNIQUE WATERMARK over your photos.
• Ibooks - an ereader (Created by Apple, has books and textbooks).
• Inspiration Maps - This App is ideal for brainstorming, analyzing, and organizing information. If you are familiar with the desktop version of Inspiration, this is a great port to the iPad.
• Notability - text to speech or just a note taking app.
• Mobile Mouse - Mobile Mouse instantly transforms your iPad into a wireless mouse and trackpad for your computer.
• GoodReader - Within moments of downloading GoodReader, you'll be transferring files from the computer to the iPad. Supports a wide range of files.
• Note Taker HD - An app for writing handwritten notes, diagrams, etc.
• MindNode - Mind mapping, brainstorming, organization.
• iThoughtsHD - A mind map tool for the iPad.
• Evernote - Evernote turns the iPad into an extension of your brain, helping you remember anything and everything that happens in your life.
• Stick It - Sticky Notes with Bump™ - Sticky notes you can share with other iPad Users
• Cramberry - Create flash cards.
• PDF Reader Pro Edition - PDF reader.
• WolframAlpha - A powerful computational search engine.

Reading/Language Arts:

• Read Quick  - Improve yoru reading speed, this app shows one word at a time and is distraction free.
• Book Creator - Create your own iBooks right on the iPad. (Allows everything except video)/
• Popplet - Popplet is a platform for your ideas. Popplet's super simple interface allows you to move at the speed of your thoughts.
• Reading Trainer - This app teaches you how to train your eyes and brain to read and comprehend text faster. Think of it as exercise for your reading skills.
• TetterReflex- This app provides a fun way to overcome common letter reversals such as b’s and d’s. The app’s activities teach left from right and allows users to practice what they learned by practicing their letter discrimination skills.
• Dictionary.com - Dictionary & Thesaurus - A dictionary and a Thesaurus. 
• Literary Analysis Guide - Elements of literature are arranged graphically around three wheels (poetry, prose, and rhetoric). 
• Jules Verne Collection - Sixteen of Jules Verne's books.
• MaxJournal - A simple and elegant journal. 
• LitCharts - Link to LitCharts website. Each of the LitCharts are available on the iPad

Math:

• iFactor Quadratics - This is a simple application that will factor quadratic equations, if possible.
• eSolver HD - eSolver HD enables you to solve quadratic equations in a very simple way.
• Math Flash Cards - Math Flash Cards is a fun to use math drill application that looks and works just like the old paper flash cards. 
• Numerate: Count, Add and Subtract - Learn how to recognize numbers (1-20) and explore simple addition and subtraction with interactive calculations. 
• MakeChange - Practice counting change and doing addition problems.
• Hands-On Equations - This app makes learning algebra fun and easy for children as young as age 8! Equations such as 4x+3=3x+9 become child's play!
• Solids Elementary HD - Solids Elementary is complete elaborations of all main geometric solid - prisms, solids of revolution and pyramids, that allows to unfold and exam solids nets in 3D.
• Equation - EQUATION is a very fast and easy tool to solve Quadratic Equations. 
• Algebra Touch - An amazingly easy App that allows you to refresh your knowledge of Algebra with an interface designed for iOS devices.
• Alge-Bingo - Develop your algebraic equation solving skills through playing a Bingo game. This game takes you step by step through the process of learning how to solve the most basic equation up through multiple-step equations. 
• KineMath - Students can manipulate twelve different functions, interact with graphs and plots, copy and export their work, and view examples for deeper understanding.
• Math Formulas - Reference Guide - This app contains over 100 math formulas at a high school level. Most formulas have examples for ease of understanding. A great app for higher level math.
• The Ruler - measure things in inches or centimeters
• Quick Graph - 2D and 3D graphing calculator.

Productivity apps:

• Note-Taking
• istudiez Pro - Keep track of homework,schedules, and grades.
• Inspiration Maps
• Notability - text to speech or just a note taking app
• Penultimate - note taking app.

Other:

• iSign3D - Introducing an innovative application for learning the American Sign Language alphabet for the iPad!
• Chore Pad HD - Help your child with daily chores and routines.