Mathematics: Applications and Interpretation SL-Textbook (Paperback)

Mathematics: Analysis and Approaches SL

1 THE BINOMIAL THEOREM 15
A Factorial notation 16
B Binomial expansions 17
C The binomial theorem 21
Review set 1A 26
Review set 1B 27

2 QUADRATIC FUNCTIONS 29
A Quadratic functions 31
B Graphs of quadratic functions 33
C Using the discriminant 40
D Finding a quadratic from its graph 43
E The intersection of graphs 47
F Problem solving with quadratics 50
G Optimisation with quadratics 53
H Quadratic inequalities 57
Review set 2A 61
Review set 2B 62

3 FUNCTIONS 65
A Relations and functions 66
B Function notation 69
C Domain and range 72
D Rational functions 78
E Composite functions 83
F Inverse functions 86
G Absolute value functions 91
Review set 3A 93
Review set 3B 96

4 TRANSFORMATIONS OF FUNCTIONS 99
A Translations 100
B Stretches 103
C Reflections 109
D Miscellaneous transformations 112
Review set 4A 115
Review set 4B 116

5 EXPONENTIAL FUNCTIONS 119
A Rational exponents 120
B Algebraic expansion and factorisation 122
C Exponential equations 125
D Exponential functions 127
E Growth and decay 132
F The natural exponential 138
Review set 5A 141
Review set 5B 143

6 LOGARITHMS 145
A Logarithms in base 1010 146
B Logarithms in base aa 149
C Laws of logarithms 151
D Natural logarithms 154
E Logarithmic equations 157
F The change of base rule 159
G Solving exponential equations using logarithms 160
H Logarithmic functions 164
Review set 6A 168
Review set 6B 170

7 THE UNIT CIRCLE AND RADIAN MEASURE 173
A Radian measure 174
B Arc length and sector area 177
C The unit circle 181
D Multiples of frac pi 6?6???? and frac pi 4?4???? 187
E The Pythagorean identity 190
F Finding angles 192
G The equation of a straight line 194
Review set 7A 195
Review set 7B 197

8 TRIGONOMETRIC FUNCTIONS 199
A Periodic behaviour 200
B The sine and cosine functions 204
C General sine and cosine functions 206
D Modelling periodic behaviour 211
E The tangent function 216
Review set 8A 219
Review set 8B 221

9 TRIGONOMETRIC EQUATIONS AND IDENTITIES 223
A Trigonometric equations 224
B Using trigonometric models 232
C Trigonometric identities 234
D Double angle identities 237
Review set 9A 241
Review set 9B 243

10 REASONING AND PROOF 245
A Logical connectives 248
B Proof by deduction 249
C Proof by equivalence 253
D Definitions 256
Review set 10A 259
Review set 10B 259

11 INTRODUCTION TO DIFFERENTIAL CALCULUS 261
A Rates of change 263
B Instantaneous rates of change 266
C Limits 269
D The gradient of a tangent 274
E The derivative function 276
F Differentiation from first principles 278
Review set 11A 281
Review set 11B 283

12 RULES OF DIFFERENTIATION 285
A Simple rules of differentiation 286
B The chain rule 291
C The product rule 294
D The quotient rule 297
E Derivatives of exponential functions 299
F Derivatives of logarithmic functions 303
G Derivatives of trigonometric functions 306
H Second derivatives 308
Review set 12A 310
Review set 12B 311

13 PROPERTIES OF CURVES 313
A Tangents 314
B Normals 319
C Increasing and decreasing 321
D Stationary points 326
E Shape 331
F Inflection points 333
G Understanding functions and their derivatives 338
Review set 13A 340
Review set 13B 342

14 APPLICATIONS OF DIFFERENTIATION 345
A Rates of change 346
B Optimisation 352
Review set 14A 362
Review set 14B 363

15 INTRODUCTION TO INTEGRATION 365
A Approximating the area under a curve 366
B The Riemann integral 369
C Antidifferentiation 372
D The Fundamental Theorem of Calculus 374
Review set 15A 379
Review set 15B 380

16 TECHNIQUES FOR INTEGRATION 381
A Discovering integrals 382
B Rules for integration 384
C Particular values 388
D Integrating f(ax + b)f(ax+b) 390
E Integration by substitution 393
Review set 16A 396
Review set 16B 397

17 DEFINITE INTEGRALS 399
A Definite integrals 400
B The area under a curve 404
C The area above a curve 409
D The area between two functions 411
E Problem solving by integration 416
Review set 17A 419
Review set 17B 422

18 KINEMATICS 425
A Displacement 427
B Velocity 429
C Acceleration 436
D Speed 439
Review set 18A 444
Review set 18B 446

19 BIVARIATE STATISTICS 449
A Association between numerical variables 450
B Pearson’s product-moment correlation coefficient 455
C Line of best fit by eye 460
D The least squares regression line 464
E The regression line of xx against yy 471
Review set 19A 474
Review set 19B 476

20 DISCRETE RANDOM VARIABLES 479
A Random variables 480
B Discrete probability distributions 482
C Expectation 486
D The binomial distribution 492
E Using technology to find binomial probabilities 496
F The mean and standard deviation of a binomial distribution 498
Review set 20A 500
Review set 20B 502

21 THE NORMAL DISTRIBUTION 505
A Introduction to the normal distribution 507
B Calculating probabilities 510
C The standard normal distribution 518
D Quantiles 522
Review set 21A 528
Review set 21B 529

ANSWERS 531

INDEX 611