Problem Solving

Practicing question sets on a specific topic is a great way to build mathematics skills and make them automatic. Compared with physical exercise it’s a bit like working out in the gym. Another useful way to develop is to practice questions that cover a range of topics at the same time, and nurture our problem solving skills to tackle them. Continuing the comparison with physical exercise, this would be more like going mountaineering. Below we have a selection of questions organised to develop specific problem solving approaches. Each of the questions are followed by worked solutions (but always attempt the question on your own first:

A. Draw a diagram	G. Logically reason
B. Work backwards	H. Use algebra
C. Change perspective	I. Be systematic
D. Simplify problem	J. Guess, iterate
E. Consider special cases	K. Use everything
F. Make connections