Title Maths in Focus, Margaret Grove - Prelims Derivative Algebra Tangent Quadratic Equation 267.4 KB 13
```                            Maths in Focus
Maths in Focus: Mathematics Preliminary Course
Contents
Preface
Acknowledgements
Credits
Features of this Book
Syllabus Matrix
Study Skills
```
Document Text Contents
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Mathematics
Preliminary Course

maths

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Chapter 4: Geometry 1 136

INTRODUCTION 137
NOTATION 137
TYPES OF ANGLES 138
PARALLEL LINES 145
TYPES OF TRIANGLES 149
CONGRUENT TRIANGLES 155
SIMILAR TRIANGLES 159
PYTHAGORAS’ THEOREM 167
POLYGONS 180
AREAS 184
TEST YOURSELF 4 191
CHALLENGE EXERCISE 4 193

Practice Assessment Task Set 1 195

Chapter 5: Functions and Graphs 200

INTRODUCTION 201
FUNCTIONS 201
GRAPHING TECHNIQUES 212
LINEAR FUNCTION 220
ABSOLUTE VALUE FUNCTION 230
THE HYPERBOLA 238
CIRCLES AND SEMI-CIRCLES 242
OTHER GRAPHS 250
LIMITS AND CONTINUITY 256
REGIONS 260
TEST YOURSELF 5 270
CHALLENGE EXERCISE 5 271

Chapter 6: Trigonometry 274

INTRODUCTION 275
TRIGONOMETRIC RATIOS 275
RIGHT-ANGLED TRIANGLE PROBLEMS 283
APPLICATIONS 292
EXACT RATIOS 302
ANGLES OF ANY MAGNITUDE 306
TRIGONOMETRIC EQUATIONS 320
TRIGONOMETRIC IDENTITIES 326
NON-RIGHT-ANGLED TRIANGLE RESULTS 331
APPLICATIONS 342
AREA 346
TEST YOURSELF 6 349
CHALLENGE EXERCISE 6 350

Chapter 7: Linear Functions 352

INTRODUCTION 353
DISTANCE 353
MIDPOINT 358

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EQUATION OF A STRAIGHT LINE 370
PARALLEL AND PERPENDICULAR LINES 374
INTERSECTION OF LINES 379
PERPENDICULAR DISTANCE 384
TEST YOURSELF 7 389
CHALLENGE EXERCISE 7 390

Chapter 8: Introduction to Calculus 392

INTRODUCTION 393
DIFFERENTIATION FROM FIRST PRINCIPLES 403
SHORT METHODS OF DIFFERENTIATION 419
TANGENTS AND NORMALS 425
FURTHER DIFFERENTIATION AND INDICES 430
COMPOSITE FUNCTION RULE 432
PRODUCT RULE 436
QUOTIENT RULE 439
TEST YOURSELF 8 442
CHALLENGE EXERCISE 8 443

Practice Assessment Task Set 2 446

Chapter 9: The Quadratic Function 450

INTRODUCTION 451
GRAPH OF A QUADRATIC FUNCTION 451
THE DISCRIMINANT 461
SUM AND PRODUCT OF ROOTS 472
TEST YOURSELF 9 481
CHALLENGE EXERCISE 9 482

Chapter 10: Locus and the Parabola 484

INTRODUCTION 485
LOCUS 485
CIRCLE AS A LOCUS 493
PARABOLA AS A LOCUS 497
GENERAL PARABOLA 516
TANGENTS AND NORMALS 531
TEST YOURSELF 10 534
CHALLENGE EXERCISE 10 535

Practice Assessment Task Set 3 536

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Many of the assessment tasks for maths are closed book examinations.
You will cope better in exams if you have practised doing sample exams under exam conditions.

Regular revision will give you confi dence and if you feel well prepared, this will help get rid of nerves
in the exam. You will also cope better if you have had a reasonable night’s sleep before the exam.

One of the biggest problems students have with exams is in timing. Make sure you don’t spend too
much time on questions you’re unsure about, but work through and fi nd questions you can do fi rst.

Divide the time up into smaller chunks for each question and allow some extra time to go back
to questions you couldn’t do or fi nish. For example, in a 2 hour exam with 6 questions, allow around
15 minutes for each question. This will give an extra half hour at the end to tidy up and fi nish off
questions.

Here are some general guidelines for doing exams:

Read through and ensure you know how many questions there are ■

Divide your time between questions with extra time at the end ■

Don’t spend too much time on one question ■

Read each question carefully, underlining key words ■

Show all working out, including diagrams and formulae ■

Cross out mistakes with a single line so it can still be read ■

Write legibly ■

And fi nally…

Study involves knowing what you don’t know, and putting in a lot of time into concentrating on
these areas. This is a positive way to learn. Rather than just saying, ‘I can’t do this’, say instead, ‘I can’t
do this yet’, and use your teachers, friends, textbooks and other ways of fi nding out.

With the parts of the course that you do know, make sure you can remember these easily under
exam pressure by putting in lots of practice.

Remember to look at new work

today ■

tomorrow ■

in a week ■

in a month ■

Some people hardly ever fi nd time to study while others give up their outside lives to devote their
time to study. The ideal situation is to balance study with other aspects of your life, including going
out with friends, working and keeping up with sport and other activities that you enjoy.