Page 3 - ADVANCED MATH F.5

Form Five Form Five

Table of contents

Acknowledgements ............................. v Orthogonal circles ............................... 46
Introduction ........................................ vi Length of a tangent from a point to
a circle ................................................ 47
FOR ONLINE READING ONLY
Sets ........................................................ 1 Functions ............................................ 50
Methods of representing sets ................ 2 Polynomial functions .......................... 51
Types of sets .......................................... 3
Basic set operations ............................... 4 Graphs of linear functions ................... 51
Graphs of quadratic functions ............. 54
Representation of sets on a number
line ......................................................... 7 Graphs of cubic functions ................... 56
Graphs of quartic equations ................ 59
Fundamental laws of algebra of sets ..... 9
Venn diagrams ..................................... 10 Graphs of rational functions ................ 60
Composite functions ........................... 64
Number of elements/cardinality of
sets....................................................... 12 Graphs of composite functions ........... 65
Graphs of exponential functions ......... 67
Logic ................................................... 17 Graphs of logarithmic functions ......... 68
Concept of logic .................................. 18 Algebra ............................................... 85
Logical connectives ............................ 19 Sequences and series .......................... 86
Converse, inverse, and
contrapositive ...................................... 24 Proofs by mathematical induction ...... 88
Roots of polynomial functions ............ 88
Logic symbols dominance .................. 26
Logical equivalences .......................... 26 Remainder theorem, factor theorem
and operations on polynomials ........... 90
Laws of algebra of propositions ......... 27
Arguments ........................................... 28 Inequalities .......................................... 92
Matrices ............................................... 94
Electrical networks .............................. 29
Construction of a compound Minors, cofactors, and determinant
of a 3×3 matrix .................................... 96
proposition from a truth table ............. 31
Solution of systems of linear
Coordinate geometry I ...................... 35 simultaneous equations by
The angle between two lines ............... 36 Cramer’s rule....................................... 97
Adjoint and Inverse of a 3×3 matrix ... 98
Perpendicular distance of a point
from a line ........................................... 37 Solution of systems of linear
equations using inverse matrix
Locus ................................................... 38
Ratio theorem ...................................... 39 method or determinant method ........... 98
Binomial theorem .............................. 100
A circle ................................................ 40
Equation of a circle given the Binomial expansion .......................... 100
Binomial expansion for fractional
endpoints of a diameter ....................... 42
Equation of a circle passing through and negative indices .......................... 101
The general term in the binomial
three given points ................................ 42
Equation of tangent and normal to expansion .......................................... 102
Middle terms in a binomial
a circle ................................................. 43
Point of intersection of circles ............ 45 expansion .......................................... 103
Partial functions ................................ 104
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Mathematics for Advanced Secondary Schools

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