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Mathematics for Year 10

Mathematics for Year 10

          
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About the Book

The book caters for a range of student abilities. It contains many problems, graded from basic to advanced. Some exercises are designed to build skills, others contextualise the problem so that students can see the practical, everyday applications of the mathematics they are studying. Most chapters begin with an Opening Problem to show the application of the mathematics that will be studied in the chapter. Definitions and rules are highlighted and worked examples (with ) give step-by-step, easy-to-follow instructions. Investigations are included to help students develop problem-solving skills and discover mathematical concepts for themselves. This 6 edition is a thorough revision of our established course in mathematics for Year 10 students. The content of this new edition is presented in 29 short chapters: chapters 1-24 are printed in the book in full colour and chapters 25-29 are presented on theCDas printable pages. A feature of the 6th edition is our new software on the accompanying CD: click anywhere in any worked example to activate a teacher's voice which will explain each step in the worked example. The SELF TUTOR is intended as a help for students who have been absent from classes or for those who need extra revision and practice. The CD offers exciting possibilities for students and teachers. It contains links to spreadsheets, graphing and geometry software, calculator instructions, computer demonstrations and simulations. Teachers will be able to demonstrate concepts quickly, clearly and simply, and students have the opportunity to revisit the demonstrations and experiment for themselves. (See the note 'Using the interactive CD' on the page immediately after this Foreword.) An Opening Problem appears at the start of most chapters to offer an insight into the application of the mathematics that will be studied in the chapter. Definitions and rules are highlighted and worked examples provide step-by-step, easy-to-follow instructions. Exercises within each chapter are carefully graded and Investigations are included to assist students to develop their problem solving skills, discover mathematical concepts for themselves and appreciate the applications of mathematics. We hope the combination of textbook and interactive CD will foster the mathematical education of students in a stimulating way. In this changing world of mathematics education, we believe that the contextual approach adopted in this book, with the associated use of technology, will enhance students' understanding, knowledge and appreciation of mathematics, and its universal application. The interactive CD is ideal for independent study. Students can revisit concepts taught in class and undertake their own revision and practice. The CD also has the text of the book, allowing students to leave the textbook at school and keep the CD at home. Graphics calculators: instructions for using Texas Instruments and Casio calculators graphics calculators are also given on the CD and can be printed.

Table of Contents:
Table of contents 1 ALGEBRA (NOTATION AND EQUATIONS) 11 A Algebraic notation 12 B Algebraic substitution 14 C Linear equations 17 D Rational equations 20 E Linear inequations 23 F Problem solving 26 G Money and investment problems 28 H Motion problems (Extension) 30 Review set 1A 31 Review set 1B 32 2 PYTHAGORAS' THEOREM 33 A Pythagoras' theorem 35 B The converse of Pythagoras' theorem 39 C Problem solving using Pythagoras' theorem 42 D Three-dimensional problems 47 E More difficult problems (Extension) 49 Review set 2A 49 Review set 2B 50 3 ALGEBRAIC EXPANSION AND SIMPLIFICATION 51 A Products and expansions 52 B The product (a+b)(c+d) 54 C Difference of two squares 56 D Perfect squares expansion 58 E Further expansion (Extension) 60 F The binomial expansion (Extension) 62 Review set 3A 64 Review set 3B 64 4 SURDS 65 A Operations with surds 67 B Multiplication of surds 71 C Division by surds (Extension) 74 Review set 4A 76 Review set 4B 76 5 PROBABILITY 77 A Experimental probability (Review) 79 B Probabilities from data 80 C Life tables 82 D Sample spaces (Review) 84 E Calculating theoretical probabilities 85 F Using 2-dimensional grids 87 G Compound events 88 H Events and Venn diagrams 91 I Expectation 95 Review set 5A 97 Review set 5B 98 6 INDICES 99 A Index notation 100 B Index laws 103 C Exponential equations 108 D Standard form (scientific notation) 110 E Rational (fractional) indices 113 Review set 6A 116 Review set 6B 116 7 COORDINATE GEOMETRY 117 A Distance between two points 119 B Midpoints 122 C Gradient (or slope) 124 D Using gradients 130 E Using coordinate geometry 132 F Vertical and horizontal lines 134 G Equations of straight lines 135 H Graphing lines 141 I Points on lines 143 J Where lines meet 143 Review set 7A 146 Review set 7B 147 8 MENSURATION 149 A Length and perimeter 150 B Area 157 C Surface area 164 D Volume and capacity 169 Review set 8A 175 Review set 8B 176 9 QUADRATIC FACTORISATION AND EQUATIONS 177 A Factorisation of quadratic expressions 178 B Factorisation of ax2 + bx + c (a 1) 185 C Quadratic equations 189 D Completing the square 195 E Problem solving with quadratics 199 Review set 9A 202 Review set 9B 202 10 GEOMETRY OF POLYGONS 203 A Review of facts and theorems 205 B Congruence of triangles 209 C Similar triangles 212 D Problem solving with similar triangles 216 E The midpoint theorem 218 F Euler's rule 221 Review set 10A 222 Review set 10B 223 11 STATISTICS 225 A Discrete numerical data 227 B Continuous numerical data 231 C Measuring the middle of a data set 233 D Measuring the spread of data 239 E Box-and-whisker plots 242 F Statistics using technology 245 G Already grouped continuous data 246 H Cumulative data 249 Review set 11A 251 Review set 11B 252 12 TRIGONOMETRY 253 A The unit circle 255 B Labelling triangles 258 C The trigonometric ratios 259 D Trigonometric problem solving 265 E 3-dimensional problem solving 272 Review set 12A 276 Review set 12B 277 13 FORMULAE 279 A Formula substitution 280 B Formula rearrangement 283 C Substitution after rearrangement 285 D Formula construction 286 E Formula by induction (Extension) 287 F More difficult rearrangements (Extension) 289 Review set 13A 291 Review set 13B 292 14 COMPARING NUMERICAL DATA 293 A Graphical comparison 294 B Parallel boxplots 296 C A statistical project 301 Review set 14A 302 Review set 14B 303 15 THE GEOMETRY OF CIRCLES 305 A Some circle theorems (Review) 306 B Further circle theorems 312 C Geometric proof (Extension) 317 Review set 15A 320 Review set 15B 321 16 QUADRATIC FUNCTIONS 323 A Function notation 324 B Quadratic functions 326 C Graphs of quadratic functions 329 D Axis intercepts 337 E Graphs from axis intercepts 339 F Axis of symmetry and vertex 343 G Quadratic modelling 345 Review set 16A 347 Review set 16B 348 17 SIMULTANEOUS EQUATIONS 349 A Linear simultaneous equations 350 B Problem solving 355 C Where functions meet 358 Review set 17A 359 Review set 17B 360 18 FINANCIAL MATHEMATICS 361 A Business calculations 362 B Appreciation 368 C Compound interest 369 D Depreciation 374 E Borrowing 377 Review set 18A 383 Review set 18B 384 19 OTHER FUNCTIONS: THEIR GRAPHS AND USES 385 A Exponential functions 386 B Growth problems 392 C Decay problems 395 D Simple rational functions 397 E Problem solving (rational functions) 400 F Unfamiliar functions 402 Review set 19A 403 Review set 19B 404 20 TREE DIAGRAMS AND BINOMIAL PROBABILITIES 405 A Sample spaces using tree diagrams 406 B Probabilities from tree diagrams 407 C Binomial probabilities 414 Review set 20A 418 Review set 20B 418 21 ALGEBRAIC FRACTIONS 419 A Simplifying algebraic fractions 420 B Adding and subtracting algebraic fractions 423 C Multiplying and dividing algebraic fractions 426 D Further simplification (Extension) 428 E More complicated fractions (Extension) 431 F Handling exponentials (Extension) 434 Review set 21A 435 Review set 21B 436 22 BIVARIATE STATISTICS 437 A Correlation 439 B Pearson's correlation coefficient, r 444 C Line of best fit 448 D Time series data 454 Review set 22A 456 Review set 22B 457 23 NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY 459 A Obtuse angles 460 B Area of a triangle using sine 462 C The sine rule 464 D The cosine rule 467 E Problem solving with the sine and cosine rules 469 Review set 23A 470 Review set 23B 471 24 VECTORS 473 A Directed line segment representation 474 B Operations with vectors 477 C Vectors in component form 483 D Further problem solving (Extension) 487 Review set 24 488 25 VARIATION (on CD only) 1 A Direct variation 2 B Inverse variation 9 Review set 25A 13 Review set 25B 13 Answers 15 26 MATRICES (on CD only) 1 A Matrix structure 2 B Addition and subtraction of matrices 4 C Matrix multiplication 9 Review set 26 14 Answers 15 27 NETWORKS AND TREES (on CD only) 1 A Some network descriptions 3 B Eulerian circuits 7 C Hamiltonian paths and circuits 9 D Trees 11 E Topology and the Mobius strip 15 Review set 27A 16 Review set 27B 18 Answers 21 28 LINEAR PROGRAMMING (on CD only) 1 A Feasible regions 2 B Regions defined by ax + by c or ax + by c 5 C Constructing constraints 9 D Linear programming 10 Review set 28 16 29 CHALLENGE SETS (on CD only) 1


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Product Details
  • ISBN-13: 9781876543525
  • Publisher: Haese & Harris Publications
  • Publisher Imprint: Haese & Harris Publications
  • Height: 250 mm
  • ISBN-10: 1876543523
  • Publisher Date: 30 Apr 2007
  • Binding: Paperback
  • No of Pages: 544


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Mathematics for Year 10
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