This book contains a selection of more than 500 mathematical problems and their solutions from the phd qualifying examination papers of more than ten famous american universities the problems cover six aspects of graduate school mathematics algebra topology differential geometry real analysis complex analysis and partial differential equations the depth of knowledge involved is not beyond the contents of the textbooks for graduate students while solution of the problems requires deep . Maths problems with solutions grade 11 maths problems with answers and solutions are presented problems an airplane flies against the wind from a to b in 8 hours the same airplane returns from b to a in the same direction as the wind in 7 hours find the ratio of the speed of the airplane in still air to the speed of the wind find the area between two concentric circles defined by x 2 . Although mathematical problems have traditionally been a part of the mathematics curriculum it has been only comparatively recently that problem solving has come to be regarded as an important medium for teaching and learning mathematics stanic and kilpatrick 1989 in the past problem solving had a place in the mathematics classroom but it was usually used in a token way as a starting . Solutions to advanced problems we find that for some polynomial hx independent of m with integer coefficients such that 1 wthw 2 but then x 1hx 2 is divisible by xt 1 and hence we can write x 1hx 2 xt 1ux for some polynomial ux with integer coefficients. Math word problems and solutions distance speed time problem 1 a salesman sold twice as much pears in the afternoon than in the morning if he sold 360 kilograms of pears that day how many kilograms did he sell in the morning and how many in the afternoon click to see solution problem 2 mary peter and lucy were picking chestnuts mary picked twice as much chestnuts than peter lucy