The Free High School Science Texts: Textbooks for …

1 FHSST AuthorsThe Free high School Science texts : Textbooks for high School StudentsStudying the SciencesMathematicsGrades 10 - 12 Version 0 September 17, 2008iiiiiCopyright 2007 Free high School Science texts Permissionisgranted to copy, distribute and/or modify this document under theterms of the GNU Free Documentation License, Version or any later versionpublished by the Free Software Foundation; with no Invariant Sections, no Front-Cover texts , and no Back-Cover texts . A copy of the license isincluded in thesection entitled GNU Free Documentation License .STOP!!!!Did you notice the FREEDOMS we ve granted you?Our copyright license isdifferent!It grants freedomsrather than just imposing restrictions like all those othertextbooks you probably own or use. We know people copy Textbooks illegally but we would LOVE it if you copiedour s - go ahead copy to your hearts content,legally! Publishers revenue is generated by controlling the market,we don t want anymoney, go ahead, distribute our books far and wide - we DARE you!

2 Ever wanted to change your textbook ? Of course you have! Go ahead changeours, make your own version, get your friends together, rip it apart and putit back together the way you like it. That s what we really want! Copy, modify, adapt, enhance, share, critique, adore, and contextualise. Do itall, do it with your colleagues, your friends or alone but getinvolved! Togetherwe can overcome the challenges our complex and diverse country presents. So what is the catch? The only thing you can t do is take this book, makea few changes and then tell others that they can t do the same with yourchanges. It s share and share-alike and we know you ll agreethat is only fair. These books were written by volunteers who want to help support education,who want the facts to be freely available for teachers to copy, adapt andre-use. Thousands of hours went into making them and they area gift toeveryone in the education Core TeamMark Horner ; Samuel Halliday ; Sarah Blyth ; Rory Adams ; Spencer WheatonFHSST EditorsJaynie Padayachee ; Joanne Boulle ; Diana Mulcahy ; Annette Nell ; Ren e Toerien ; DonovanWhitfieldFHSST ContributorsRory Adams ; Prashant Arora ; Richard Baxter ; Dr.

3 Sarah Blyth; Sebastian Bodenstein ;Graeme Broster ; Richard Case ; Brett Cocks ; Tim Crombie ; Dabrowski ; LauraDaniels ; Sean Dobbs ; Fernando Durrell ; Dr. Dan Dwyer ; Fransvan Eeden ; GiovanniFranzoni ; Ingrid von Glehn ; Tamara von Glehn ; Lindsay Glesener ; Dr. Vanessa Godfrey ; Gonzalez ; Hemant Gopal ; Umeshree Govender ; Heather Gray ; Lynn Greeff ; Dr. TomGutierrez ; Brooke Haag ; Kate Hadley ; Dr. Sam Halliday ; Asheena Hanuman ; Neil Hart ;Nicholas Hatcher ; Dr. Mark Horner ; Mfandaidza Hove ; RobertHovden ; Jennifer Hsieh ;Clare Johnson ; Luke Jordan ; Tana Joseph ; Dr. Jennifer Klay ;Lara Kruger ; Sihle Kubheka ;Andrew Kubik ; Dr. Marco van Leeuwen ; Dr. Anton Machacek ; Maheshwari ;Kosma von Maltitz ; Nicole Masureik ; John Mathew ; JoEllen McBride ; Nikolai Meures ;Riana Meyer ; Jenny Miller ; Abdul Mirza ; Asogan Moodaly ; Jothi Moodley ; Nolene Naidu ;Tyrone Negus ; Thomas O Donnell ; Dr. Markus Oldenburg ; Dr. Jaynie Padayachee ;Nicolette Pekeur ; Sirika Pillay ; Jacques Plaut ; Andrea Prinsloo ; Joseph Raimondo ; SanyaRajani ; Prof.

4 Sergey Rakityansky ; Alastair Ramlakan ; Razvan Remsing ; Max Richter ; SeanRiddle ; Evan Robinson ; Dr. Andrew Rose ; Bianca Ruddy ; KatieRussell ; Duncan Scott ;Helen Seals ; Ian Sherratt ; Roger Sieloff ; Bradley Smith ; Greg Solomon ; Mike Stringer ;Shen Tian ; Robert Torregrosa ; Jimmy Tseng ; Helen Waugh ; Webber ; MichelleWen ; Dr. Alexander Wetzler ; Dr. Spencer Wheaton ; Vivian White ; Dr. Gerald Wigger ;Harry Wiggins ; Wendy Williams ; Julie Wilson ; Andrew Wood ; Emma Wormauld ; SahalYacoob ; Jean YoussefContributors and editors have made a sincere effort to produce an accurate and useful you have suggestions, find mistakes or be prepared to donate material for inclusion,please don t hesitate to contact us. We intend to work with all who are willing to help makethis a continuously evolving resource! Basics11 Introduction to The Language of mathematics .. 3II grade 1052 Review of Past Introduction .. What is a number? .. Sets .. Letters and Arithmetic.

5 Addition and Subtraction .. Multiplication and Division .. Brackets .. Negative Numbers .. What is a negative number? .. Working with Negative Numbers .. Living Without the Number Line .. Rearranging Equations .. Fractions and Decimal Numbers .. Scientific Notation .. Real Numbers .. Natural Numbers .. Integers .. Rational Numbers .. Irrational Numbers .. Mathematical Symbols .. Infinity .. End of Chapter Exercises .. 213 Rational Numbers - grade Introduction .. The Big Picture of Numbers .. Definition .. Forms of Rational Numbers .. Converting Terminating Decimals into Rational Numbers.. Converting Repeating Decimals into Rational Numbers .. Summary .. End of Chapter Exercises .. 274 Exponentials - grade Introduction .. Definition .. Laws of Exponents .. Exponential Law 1:a0= 1.. Exponential Law 2:am an=am+n.. Exponential Law 3:a n=1an, a6= 0.. Exponential Law 4:am an=am n.

6 Exponential Law 5:(ab)n=anbn.. Exponential Law 6:(am)n=amn.. End of Chapter Exercises .. 345 Estimating Surds - grade Introduction .. Drawing Surds on the Number Line (Optional) .. End of Chapter Excercises .. 396 Irrational Numbers and Rounding Off - grade Introduction .. Irrational Numbers .. Rounding Off .. End of Chapter Exercises .. 437 Number Patterns - grade Common Number Patterns .. Special Sequences .. Make your own Number Patterns .. Notation .. Patterns and Conjecture .. Exercises ..508 Finance - grade Introduction .. Foreign Exchange Rates .. How much is R1 really worth? .. Cross Currency Exchange Rates .. Enrichment: Fluctuating exchange rates .. Being Interested in Interest .. Simple Interest .. Other Applications of the Simple Interest Formula .. Compound Interest .. Fractions add up to the Whole .. The Power of Compound Interest .. Other Applications of Compound Growth.

7 Summary .. Definitions .. Equations .. End of Chapter Exercises .. 699 Products and Factors - grade Introduction .. Recap of Earlier Work .. Parts of an Expression .. Product of Two Binomials .. Factorisation .. More Products .. Factorising a Quadratic .. Factorisation by Grouping .. Simplification of Fractions .. End of Chapter Exercises .. 8210 Equations and Inequalities - grade Strategy for Solving Equations .. Solving Linear Equations .. Solving Quadratic Equations .. Exponential Equations of the formka(x+p)=m.. Algebraic Solution .. Linear Inequalities .. Linear Simultaneous Equations .. Finding solutions .. Graphical Solution .. Solution by Substitution .. Mathematical Models .. Introduction .. Problem Solving Strategy .. Application of Mathematical Modelling .. End of Chapter Exercises .. Introduction to Functions and Graphs .. Functions and Graphs in the Real-World .. and Constants.

8 And Functions .. Cartesian Plane .. Graphs .. used for Functions .. of Functions - All Grades .. and Independent Variables .. and Range .. with the Axes .. Points .. of Symmetry .. on which the Function Increases/Decreases .. or Continuous Nature of the Graph .. of Functions .. of the formy=ax+q.. of the Formy=ax2+q.. of the Formy=ax+q.. of the Formy=ab(x)+q.. of Chapter Exercises .. 13311 Average Gradient - grade 10 Introduction .. Straight-Line Functions .. Parabolic Functions .. End of Chapter Exercises .. 13812 Geometry Introduction .. Points and Lines .. Angles .. Measuring angles .. Special Angles .. Special Angle Pairs .. Parallel Lines intersected by Transversal Lines .. Polygons .. Triangles .. Quadrilaterals .. Other polygons .. Extra .. Exercises .. Challenge Problem ..159xCONTENTSCONTENTS13 Geometry - grade Introduction .. Right Prisms and Cylinders .. Surface Area .. Volume .. Polygons.

9 Similarity of Polygons .. Co-ordinate Geometry .. Introduction .. Distance between Two Points .. Calculation of the Gradient of a Line .. Midpoint of a Line .. Transformations .. Translation of a Point .. Reflection of a Point .. End of Chapter Exercises .. 18514 Trigonometry - grade Introduction .. Where Trigonometry is Used .. Similarity of Triangles .. Definition of the Trigonometric Functions .. Simple Applications of Trigonometric Functions .. Height and Depth .. Maps and Plans .. Graphs of Trigonometric Functions .. Graph ofsin .. Functions of the formy=asin(x) +q.. Graph ofcos .. Functions of the formy=acos(x) +q.. Comparison of Graphs ofsin andcos .. Graph oftan .. Functions of the formy=atan(x) +q.. End of Chapter Exercises .. 20815 Statistics - grade Introduction .. Recap of Earlier Work .. Data and Data Collection .. Methods of Data Collection .. Samples and Populations .. Example Data Sets .. Data Set 1: Tossing a Coin.

10 Data Set 2: Casting a die .. Data Set 3: Mass of a Loaf of Bread .. Data Set 4: Global Temperature .. Data Set 5: Price of Petrol .. Grouping Data .. Exercises - Grouping Data .. Graphical Representation of Data .. Bar and Compound Bar Graphs .. Histograms and Frequency Polygons .. Pie Charts .. Line and Broken Line Graphs .. Exercises - Graphical Representation of Data .. Summarising Data .. Measures of Central Tendency .. Measures of Dispersion .. Exercises - Summarising Data .. Misuse of Statistics .. Exercises - Misuse of Statistics .. Summary of Definitions .. Exercises .. 23216 Probability - grade Introduction .. Random Experiments .. Sample Space of a Random Experiment .. Probability Models .. Classical Theory of Probability .. Relative .. Project Idea .. Probability Identities .. Mutually Exclusive Events .. Complementary Events .. End of Chapter Exercises .. 246 III grade 1124917 Exponents - grade Introduction.