Contents vii
Revision Test 9
218
25 Areas of common shapes
219
25.1 Introduction
219
25.2 Common shapes
219
25.3 Areas of common shapes
221
25.4 Areas of similar shapes
229
26 The circle
230
26.1 Introduction
230
26.2 Properties of circles
230
26.3 Radians and degrees
232
26.4 Arc length and area of circles and sectors 233
26.5 The equation of a circle
236
Revision Test 10
238
27 Volumes of common solids
240
27.1 Introduction
240
27.2 Volumes and surface areas of common
shapes
240
27.3 Summary of volumes and surface areas of
common solids
247
27.4 More complex volumes and surface areas 247
27.5 Volumes and surface areas of frusta of
pyramids and cones
252
27.6 Volumes of similar shapes
256
28 Irregular areas and volumes, and mean values
257
28.1 Areas of irregular figures
257
28.2 Volumes of irregular solids
259
28.3 Mean or average values of waveforms
260
Revision Test 11
264
29 Vectors
266
29.1 Introduction
266
29.2 Scalars and vectors
266
29.3 Drawing a vector
266
29.4 Addition of vectors by drawing
267
29.5 Resolving vectors into horizontal and
vertical components
269
29.6 Addition of vectors by calculation
270
29.7 Vector subtraction
274
29.8 Relative velocity
276
29.9 i, j and k notation
277
30 Methods of adding alternating waveforms
278
30.1 Combining two periodic functions
278
30.2 Plotting periodic functions
278
30.3 Determining resultant phasors by drawing 280
30.4 Determining resultant phasors by the sine
and cosine rules
281
30.5 Determining resultant phasors by
horizontal and vertical components
283
Revision Test 12
286
31 Presentation of statistical data
288
31.1 Some statistical terminology
288
31.2 Presentation of ungrouped data
289
31.3 Presentation of grouped data
292
32 Mean, median, mode and standard deviation
299
32.1 Measures of central tendency
299
32.2 Mean, median and mode for discrete data 299
32.3 Mean, median and mode for grouped data 300
32.4 Standard deviation
302
32.5 Quartiles, deciles and percentiles
303
33 Probability
306
33.1 Introduction to probability
306
33.2 Laws of probability
307
Revision Test 13
312
34 Introduction to differentiation
313
34.1 Introduction to calculus
313
34.2 Functional notation
313
34.3 The gradient of a curve
314
34.4 Differentiation from first principles
315
34.5 Differentiation of y = ax n by the
general rule
315
34.6 Differentiation of sine and cosine functions 318
34.7 Differentiation of e ax and ln ax
320
34.8 Summary of standard derivatives
321
34.9 Successive differentiation
322
34.10 Rates of change
323
35 Introduction to integration
325
35.1 The process of integration
325
35.2 The general solution of integrals of the
form ax n
325
35.3 Standard integrals
326
35.4 Definite integrals
328
35.5 The area under a curve
330
Revision Test 14
335
List of formulae
336
Answers to practice exercises
340
Index
356
Revision Test 9
218
25 Areas of common shapes
219
25.1 Introduction
219
25.2 Common shapes
219
25.3 Areas of common shapes
221
25.4 Areas of similar shapes
229
26 The circle
230
26.1 Introduction
230
26.2 Properties of circles
230
26.3 Radians and degrees
232
26.4 Arc length and area of circles and sectors 233
26.5 The equation of a circle
236
Revision Test 10
238
27 Volumes of common solids
240
27.1 Introduction
240
27.2 Volumes and surface areas of common
shapes
240
27.3 Summary of volumes and surface areas of
common solids
247
27.4 More complex volumes and surface areas 247
27.5 Volumes and surface areas of frusta of
pyramids and cones
252
27.6 Volumes of similar shapes
256
28 Irregular areas and volumes, and mean values
257
28.1 Areas of irregular figures
257
28.2 Volumes of irregular solids
259
28.3 Mean or average values of waveforms
260
Revision Test 11
264
29 Vectors
266
29.1 Introduction
266
29.2 Scalars and vectors
266
29.3 Drawing a vector
266
29.4 Addition of vectors by drawing
267
29.5 Resolving vectors into horizontal and
vertical components
269
29.6 Addition of vectors by calculation
270
29.7 Vector subtraction
274
29.8 Relative velocity
276
29.9 i, j and k notation
277
30 Methods of adding alternating waveforms
278
30.1 Combining two periodic functions
278
30.2 Plotting periodic functions
278
30.3 Determining resultant phasors by drawing 280
30.4 Determining resultant phasors by the sine
and cosine rules
281
30.5 Determining resultant phasors by
horizontal and vertical components
283
Revision Test 12
286
31 Presentation of statistical data
288
31.1 Some statistical terminology
288
31.2 Presentation of ungrouped data
289
31.3 Presentation of grouped data
292
32 Mean, median, mode and standard deviation
299
32.1 Measures of central tendency
299
32.2 Mean, median and mode for discrete data 299
32.3 Mean, median and mode for grouped data 300
32.4 Standard deviation
302
32.5 Quartiles, deciles and percentiles
303
33 Probability
306
33.1 Introduction to probability
306
33.2 Laws of probability
307
Revision Test 13
312
34 Introduction to differentiation
313
34.1 Introduction to calculus
313
34.2 Functional notation
313
34.3 The gradient of a curve
314
34.4 Differentiation from first principles
315
34.5 Differentiation of y = ax n by the
general rule
315
34.6 Differentiation of sine and cosine functions 318
34.7 Differentiation of e ax and ln ax
320
34.8 Summary of standard derivatives
321
34.9 Successive differentiation
322
34.10 Rates of change
323
35 Introduction to integration
325
35.1 The process of integration
325
35.2 The general solution of integrals of the
form ax n
325
35.3 Standard integrals
326
35.4 Definite integrals
328
35.5 The area under a curve
330
Revision Test 14
335
List of formulae
336
Answers to practice exercises
340
Index
356