# Maths in Focus 12 Advanced, 3rd Edition PDF by Margaret Grove

## Maths in Focus 12 Advanced, 3rd Edition

By Margaret Grove

Contents:

Preface……………………………………………….Iii

Syllabus Reference Grid………………………. Vii

Study Skills……………………………………….. Xiii

Mathematical Verbs…………………………… Xvi

1

Sequences And Series 2

M1.2 1.01 General sequences and series ….. 4

M1.2 1.02 Arithmetic sequences ….. 8

M1.2 1.03 Arithmetic series …….. 13

M1.3 1.04 Geometric sequences …….16

M1.3 1.05 Geometric series …….. 21

M1.3 1.06 Limiting sum of an infinite geometric series …… 25

Test yourself 1 ……..30

Challenge exercise 1 ……. 32

2

TRANSFORMATIONS OF FUNCTIONS 34

F2 2.01 Vertical translations of functions …….. 36

F2 2.02 Horizontal translations of functions ……. 40

F2 2.03 Vertical dilations of functions ……. 45

F2 2.04 Horizontal dilations of functions …….. 51

F2 2.05 Combinations of transformations ……. 58

F2 2.06 Graphs of functions with combined transformations ……. 66

F2 2.07 Equations and inequalities ……. 74

Test yourself 2 ………82

Challenge exercise 2 ……. 86

3

TRIGONOMETRIC FUNCTIONS 88

T3 3.01 Transformations of trigonometric functions ……. 90

T3 3.02 Combined transformations of trigonometric functions …… 100

T3 3.03 Trigonometric equations …… 104

Test yourself 3 …….. 110

Challenge exercise 3 ……… 113

PRACTICE SET 1 …………. 114

4

FURTHER DIFFERENTIATION 118

Revision 4.01 Differentiation review ……… 120

C2.1, 2.2 4.02 Derivative of exponential functions …….. 123

C2.1, 2.2 4.03 Derivative of logarithmic functions ……. 126

C2.1, 2.2 4.04 Derivative of trigonometric functions …….. 132

C3.1 4.05 Second derivatives …… 140

C4.1 4.06 Anti-derivative graphs ……. 143

C4.1 4.07 Anti-derivatives …………….. 147

C4.1 4.08 Further anti-derivatives ……. 153

Test yourself 4 ………. 159

Challenge exercise 4 ……. 162

5

GEOMETRICAL APPLICATIONS OF DIFFERENTIATION 164

C3.1 5.01 Increasing and decreasing curves …….166

C3.2 5.02 Stationary points …….. 169

C3.1 5.03 Concavity and points of inflection …….172

C3.2 5.04 Interpreting rates of change graphically ……. 176

C3.2 5.05 Stationary points and the second derivative ……. 179

C3.2 5.06 Curve sketching …… 183

C3.2 5.07 Global maxima and minima ……191

C3.2 5.08 Finding formulas for optimization problems …… 194

C3.2 5.09 Optimisation problems …… 198

Test yourself 5 …….. 207

Challenge exercise 5 ……. 209

6

INTEGRATION 210

C4.2 6.01 Approximating areas under a curve …… 212

C4.2 6.02 Trapezoidal rule …. 219

C4.2 6.03 Definite integrals ….. 225

C4.2 6.04 Indefinite integrals …….231

C4.1 6.05 Chain rule …… 233

C4.1 6.06 Integration involving exponential functions …… 237

C4.1 6.07 Integration involving logarithmic functions ….. 239

C4.1 6.08 Integration involving trigonometric functions …… 241

C4.2 6.09 Areas enclosed by the x-axis …… 244

C4.2 6.10 Areas enclosed by the y-axis ……. 251

C4.2 6.11 Sums and differences of areas ….. 254

Test yourself 6 …… 258

Challenge exercise 6 ….. 261

PRACTICE SET 2 ….. 262

7

STATISTICS 268

S2.1 7.01 Types of data …… 270

S2.1 7.02 Displaying numerical and categorical data ….. 273

S2.1 7.03 Measures of central tendency ….. 285

S2.1 7.04 Quartiles, deciles and percentiles ……. 298

S2.1 7.05 Range and interquartile range …… 306

S2.1 7.06 Variance and standard deviation …..311

S2.1 7.07 Shape and modality of data sets ….. 315

S2.1 7.08 Analysing data sets ….. 320

Test yourself 7 ….. 326

Challenge exercise 7 ….. 330

8

CORRELATION AND REGRESSION 332

S2.2 8.01 Bivariate data ….. 334

S2.2 8.02 Correlation ………. 340

S2.2 8.03 Line of best fit …… 349

S2.2 8.04 Least-squares regression line …… 353

Test yourself 8 …… 357

Challenge exercise 8 ….. 360

PRACTICE SET 3 ……. 361

9

INVESTMENTS, ANNUITIES AND LOANS 366

M1.2 9.01 Arithmetic growth and decay …… 368

M1.3 9.02 Geometric growth and decay …. 371

M1.1 9.03 Compound interest …… 378

M1.4 9.04 Compound interest formula …… 383

M1.1 9.05 Annuities ……….. 389

M1.4 9.06 Annuities and geometric series ….. 397

M1.1 9.07 Reducing balance loans ………. 400

M1.4 9.08 Loans and geometric series ….. 405

Test yourself 9 …………… 410

Challenge exercise 9 …… 413

10

CONTINUOUS PROBABILITY DISTRIBUTIONS 414

S3.1 10.01 Probability density functions ……. 416

S3.1 10.02 Calculating probabilities …….. 421

S3.1 10.03 Cumulative distribution function ………… 426

S3.1 10.04 Quantiles …………………. 433

S3.2 10.05 Normal distribution …….. 437

S3.2 10.06 Empirical rule …….. 449

S3.2 10.07 z-scores …….. 452

S3.2 10.08 Applications of the normal distribution ……….457

Test yourself 10 …………… 463

Challenge exercise 10 ….. 467

PRACTICE SET 4 ….. 468