MyScript CalculatorMyScript is really easy to use – you just write the calculations with your finger.
Problem to try: What’s the maximum product of a set of positive numbers that sum to 19?
Desmos is a very user-friendly graphing calculator. In my experience most people find the interface intuitive and are able to work with it very quickly.
Problem to try: What’s the effect of varying a in the graph of y=x^3+ax+1 ?
GeoGebraGeoGebra is a very powerful mathematical package that I’ve discussed many times on here. Currently the app is available for Android but not iOS. You can see my thoughts on the app at http://digitalmathematics.blogspot.co.uk/2016/01/geogebra-app-for-android-phones.html
In addition to the app you can also open files from the extensive set of materials at http://www.geogebra.org/materials/ using a browser. At the time of writing there are over 360,000 materials on there.
iOS: not currently available for iOS phones
Problem to try: Add the points A and B on the x-axis and C on the y-axis. Find the equation of the quadratic that will always go through A, B and C wherever they are moved to.
Sumaze! is a mathematical puzzle app that requires you to move a block around a maze with various routes involving operations or restrictions on the value of your block. It’s a great puzzle and features lots of maths including arithmetic, inequalities, the modulus function, indices, logarithms and primes.