Page 4 - ADVANCED MATH F.5

Form Five Form Five

Summation of series using partial Derivatives of trigonometric
functions ..............................................106 functions ............................................ 156
Derivatives of inverse trigonometric
Trigonometry ..................................... 110 functions ............................................ 157
Trigonometric ratios ............................ 111 Computer packages in differentiating
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Trigonometric identities ......................112 polynomial and trigonometric
Compound angle formulae ..................113 functions ............................................ 158
Double and half angle formulae ..........114 Derivatives of logarithmic
Trigonometric equations of the form functions ............................................ 159
a cos θ + b sin θ = c .............................116 Derivatives of exponential
General solutions ...............................118 functions ............................................ 161
Factor formulae ...................................119 The second derivative of a
Radians ................................................121 function ............................................ 162
Approximating small angles ..............122 Applications of differentiation .......... 163
Trigonometric functions ......................123 Problems on rates of change ............. 164
Graphs of sine and cosine functions ...125 Turning points and points of
Inverse trigonometric functions ..........125 inflexion of a curve .......................... 165
Graphs of inverse trigonometric Real life problems on maximum and
functions ..............................................127 minimum values ................................ 166
Taylor’s and Maclaurin’s series ........ 167
Linear programming ........................134 Introduction to partial derivatives ..... 169
Formulation of linear programming
problems .............................................135 Integration ........................................175
Transportation problems .....................136 The inverse process of
Formulation of transportation differentiation ................................... 176
problems ..............................................136 Integration of simple expressions ..... 177
Graphical solutions of transportation Integration by substitution method ... 179
problems ..............................................138 Integration by inspection method ..... 180
Integration by parts ........................... 182
Differentiation ....................................144 Integration using partial fractions ..... 184
Derivatives ..........................................145 Integration of trigonometric
Differentiation of a function from functions ........................................... 187
first principles .....................................145 Integration by trigonometric
Differentiation of a function ................147 substitutions ..................................... 189
Derivatives of polynomial Integration by splitting the
functions .............................................147 numerator ......................................... 193
Derivative of product of Integrals of exponential functions ..... 195
polynomials .........................................149 Integrals of logarithmic functions ..... 196
The derivative of the quotient of two Definite integrals .............................. 197
functions .............................................150 Applications of integration .............. 199
The chain rule ....................................152 The area under a curve and area
Differentiation of implicit functions ...153 enclosed between two curves ............ 199
Further implicit differentiation Volumes of solid revolution .............. 202
of functions ........................................154

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Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 4 30/06/2024 18:01:38
ADVANCED MATH F.5 TG CHAPTERS.indd 4