vi Contents
13.4 Solving more difficult simultaneous
equations
94
13.5 Practical problems involving simultaneous
equations
96
13.6 Solving simultaneous equations in three
unknowns
99
Revision Test 5
101
14 Solving quadratic equations
102
14.1 Introduction
102
14.2 Solution of quadratic equations by
factorization
102
14.3 Solution of quadratic equations by
‘completing the square’
105
14.4 Solution of quadratic equations by
formula
106
14.5 Practical problems involving quadratic
equations
108
14.6 Solution of linear and quadratic equations
simultaneously
110
15 Logarithms
111
15.1 Introduction to logarithms
111
15.2 Laws of logarithms
113
15.3 Indicial equations
115
15.4 Graphs of logarithmic functions
116
16 Exponential functions
118
16.1 Introduction to exponential functions
118
16.2 The power series for e x
119
16.3 Graphs of exponential functions
120
16.4 Napierian logarithms
122
16.5 Laws of growth and decay
125
Revision Test 6
129
17 Straight line graphs
130
17.1 Introduction to graphs
130
17.2 Axes, scales and co-ordinates
130
17.3 Straight line graphs
132
17.4 Gradients, intercepts and equations
of graphs
134
17.5 Practical problems involving straight line
graphs
141
18 Graphs reducing non-linear laws to linear form 147
18.1 Introduction
147
18.2 Determination of law
147
18.3 Revision of laws of logarithms
150
18.4 Determination of law involving logarithms 150
19 Graphical solution of equations
155
19.1 Graphical solution of simultaneous
equations
155
19.2 Graphical solution of quadratic equations 156
19.3 Graphical solution of linear and quadratic
equations simultaneously
160
19.4 Graphical solution of cubic equations
161
Revision Test 7
163
20 Angles and triangles
165
20.1 Introduction
165
20.2 Angular measurement
165
20.3 Triangles
171
20.4 Congruent triangles
175
20.5 Similar triangles
176
20.6 Construction of triangles
179
21 Introduction to trigonometry
181
21.1 Introduction
181
21.2 The theorem of Pythagoras
181
21.3 Sines, cosines and tangents
183
21.4 Evaluating trigonometric ratios of acute
angles
185
21.5 Solving right-angled triangles
188
21.6 Angles of elevation and depression
191
Revision Test 8
193
22 Trigonometric waveforms
195
22.1 Graphs of trigonometric functions
195
22.2 Angles of any magnitude
196
22.3 The production of sine and cosine waves
198
22.4 Terminology involved with sine and
cosine waves
199
22.5 Sinusoidal form: A sin(ωt ± α)
202
23 Non-right-angled triangles and some practical
applications
205
23.1 The sine and cosine rules
205
23.2 Area of any triangle
205
23.3 Worked problems on the solution of
triangles and their areas
206
23.4 Further worked problems on the solution
of triangles and their areas
207
23.5 Practical situations involving trigonometry 209
23.6 Further practical situations involving
trigonometry
211
24 Cartesian and polar co-ordinates
214
24.1 Introduction
214
24.2 Changing from Cartesian to polar
co-ordinates
214
24.3 Changing from polar to Cartesian
co-ordinates
216
24.4 Use of Pol/Rec functions on calculators
217
13.4 Solving more difficult simultaneous
equations
94
13.5 Practical problems involving simultaneous
equations
96
13.6 Solving simultaneous equations in three
unknowns
99
Revision Test 5
101
14 Solving quadratic equations
102
14.1 Introduction
102
14.2 Solution of quadratic equations by
factorization
102
14.3 Solution of quadratic equations by
‘completing the square’
105
14.4 Solution of quadratic equations by
formula
106
14.5 Practical problems involving quadratic
equations
108
14.6 Solution of linear and quadratic equations
simultaneously
110
15 Logarithms
111
15.1 Introduction to logarithms
111
15.2 Laws of logarithms
113
15.3 Indicial equations
115
15.4 Graphs of logarithmic functions
116
16 Exponential functions
118
16.1 Introduction to exponential functions
118
16.2 The power series for e x
119
16.3 Graphs of exponential functions
120
16.4 Napierian logarithms
122
16.5 Laws of growth and decay
125
Revision Test 6
129
17 Straight line graphs
130
17.1 Introduction to graphs
130
17.2 Axes, scales and co-ordinates
130
17.3 Straight line graphs
132
17.4 Gradients, intercepts and equations
of graphs
134
17.5 Practical problems involving straight line
graphs
141
18 Graphs reducing non-linear laws to linear form 147
18.1 Introduction
147
18.2 Determination of law
147
18.3 Revision of laws of logarithms
150
18.4 Determination of law involving logarithms 150
19 Graphical solution of equations
155
19.1 Graphical solution of simultaneous
equations
155
19.2 Graphical solution of quadratic equations 156
19.3 Graphical solution of linear and quadratic
equations simultaneously
160
19.4 Graphical solution of cubic equations
161
Revision Test 7
163
20 Angles and triangles
165
20.1 Introduction
165
20.2 Angular measurement
165
20.3 Triangles
171
20.4 Congruent triangles
175
20.5 Similar triangles
176
20.6 Construction of triangles
179
21 Introduction to trigonometry
181
21.1 Introduction
181
21.2 The theorem of Pythagoras
181
21.3 Sines, cosines and tangents
183
21.4 Evaluating trigonometric ratios of acute
angles
185
21.5 Solving right-angled triangles
188
21.6 Angles of elevation and depression
191
Revision Test 8
193
22 Trigonometric waveforms
195
22.1 Graphs of trigonometric functions
195
22.2 Angles of any magnitude
196
22.3 The production of sine and cosine waves
198
22.4 Terminology involved with sine and
cosine waves
199
22.5 Sinusoidal form: A sin(ωt ± α)
202
23 Non-right-angled triangles and some practical
applications
205
23.1 The sine and cosine rules
205
23.2 Area of any triangle
205
23.3 Worked problems on the solution of
triangles and their areas
206
23.4 Further worked problems on the solution
of triangles and their areas
207
23.5 Practical situations involving trigonometry 209
23.6 Further practical situations involving
trigonometry
211
24 Cartesian and polar co-ordinates
214
24.1 Introduction
214
24.2 Changing from Cartesian to polar
co-ordinates
214
24.3 Changing from polar to Cartesian
co-ordinates
216
24.4 Use of Pol/Rec functions on calculators
217