Of course, the reals aren't quite closed
under algebraic functions, since negative numbers have no real square roots (a negative times a negative is positive).
Written in the style of the new GCSE Mathematics Papers here are 41 questions and Answers helping students revise
Algebraic Fractions Arc length and Area of a sector Area
under the graph Calculating the mean Completing the square Composite and Inverse
functions Compound Percentage questions.