Parsonson S.L. Pure Mathematics (Volumes 1 & 2)

Cambridge University Press, 1970. — 716 p.— Vol.1: 0521076838, 9780521076838; Vol.2: 0521080320, 9780521080323This is an English text from the Cambridge University Press which, according to the preface, covers "those parts of modern `A' level pure mathematics syllabuses not normally included in standard calculus texts." From the short time I've owned this book, I found it excellent, as it contains much more interesting and challenging problems than a regular pre-calc text. I found out about it because in his book, The Mathematical Olympiad Handbook: An Introduction to Problem Solving Based on the First 32 British Mathematical Olympiads 1965-1996 (Oxford Science Publications), A. Gardiner recommended it. I'm glad he did! If you want to read Hardy's classic book by the same title, this could be an excellent companion/prerequisite material.Volume 1:
Numbers and inequalities
Vectors and vector geometry
Polynomials
Functions and inequalities
The trigonometric functions
Probability in finite outcome spaces
Finite series and the binomial theorem
Revision exercise A
Mathematical induction
Expectation
Further trigonometry
Matrices 1
Matrices 2
Linear Equations
Discrete probability distributions
Revision exercise BAnswersVolume 2:
Complex numbers (1)
Polynomials and partial fractions
Complex numbers (2)
Mappings in the Argand diagram
Quadratic equations and quadratic functions
The parabola and rectangular hyperbola
Polynomial equations
Vector products and their applications
Continuous probability distributions
Numerical solution of equations
The ellipse and hyperbola
Further matrices
Further coordinate geometry
Revision exercise CAnswers