Includes index.

Part 1 Elementary algebra: algebraic expressions and equations; the addition and subtraction of algebraic forms; products of positive and negative real numbers; expansion of bracketed terms; fractions; exponents; negative exponents; cancelling out terms; order in multiplication and the hierarchy of operations; factorization; degree of an expression; perfect squares; applications. Part 2 Solving equations: drawing graphs; straight-line or linear functions; quadratic functions; cubic functions; algebraic solution of equations; equations involving fractions; quadratic equations; solution of cubic equations; applications. Part 3 Simultaneous equations and inequalities: simple equations with one variable; pairs of equations; using a set of equations as a model; sets of three or more equations; independent and dependent equations; linear and non-linear equations; inequalities; simultaneous inequalities; applications of inequalities. Part 4 Series: arithmetic progression (AP); sigma notation for summation; sum of terms of an AP; geometric progression (GP) sum of terms of a GP; notation for interest calculations; compound interest. Part 5 Logarithms and exponentials: logarithms and exponents; how logarithms work; rules for combining logarithms; the exponential function and continuous compounding; nominal interest rates and effective interest rates; negative growth; applications. Part 6 Matrices: matrix notation; equality, addition and subtraction of matrices; multiplication of matrices; transposing matrices; matrix formulation of simultaneous equations; the identity matrix and the inverse; determinants; the inverse of a 2 x 2 matrix; summary. Part 7 Differentiation: the slope of a straight line; a numerical method for finding the slope of a curve; the general method of differentiation; rules for derivatives; the derivative of the reciprocal of a function. Part 8 More about differentiation: the second and higher derivatives; alternative notation for the derivative; maxima and minima; points of inflexion; the function of a function rule; the product rule; mixing the function of function and product rules; differentiating expressions containing fractions; continuous functions; partial derivatives. Part 9 Integration: integration as the reverse of differentiation; rules for integration; the definite integral; the integral as the area between the curve and the x-axis; a general remark on integration and differentiation. Part 10 The application of mathematics: mathematical style; tackling mathematical examination questions; formulating real-life problems; solving real-life problems.