INFINITY Test and Homework Generator

1. Whole Numbers

9. Equations

12. Measurement

16. Statistics

17. Transformations

Mathematics for Australia 7 has been designed and written for the Australian Curriculum. The textbook and interactive student CD provide an engaging and structured package, allowing students to explore and develop their confidence in Mathematics.

The book contains a variety of exercises ranging from basic to advanced, to cater for a range of student abilities and interests. The material is presented in a clear, easy-to-follow style, free from unnecessary distractions, while effort has been made to contextualise questions so that students can relate concepts to everyday use.

Each chapter begins with an Opening Problem, offering an insight into the application of the mathematics that will be studied in the chapter. Important information and key notes are highlighted while worked examples provide step-by-step instructions with concise and relevant explanations. Discussions, Activities, Investigations and Research exercises are used throughout the chapters to develop understanding, problem solving, and reasoning, within an interactive environment.

Extensive Review Sets are located at the end of each chapter, comprising a range of question types including short answer, extended response and multiple choice.

The accompanying CD contains specially designed SELF TUTOR software. Click on any worked example throughout the book to activate a teacher's voice which will explain each step in the worked example. SELF TUTOR is an excellent tool for students who have been absent from class or for those who need extra revision and practice.

In addition to SELF TUTOR the interactive CD contains links to geometry software, statistics packages, demonstrations, calculator instructions and a range of printable worksheets, tables, spreadsheets and diagrams, allowing teachers to demonstrate concepts and students to experiment for themselves.

We have endeavoured to provide a stimulating textbook and CD package aiming to develop and encourage student understanding. Through the use of contextual problems and the application of technology we hope to help students appreciate the application of mathematics in everyday use.

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.

By clicking on the relevant icon, a range of new interactive features can be accessed:

- Self Tutor
- Interactive Links – to spreadsheets, video clips, graphing and geometry software, computer demonstrations and simulations

Self Tutor is an exciting feature of this book.

The icon on each worked example denotes an active link on the CD.

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.

Simply click on the (or anywhere in the example box) to access the worked example, with a teacher’s voice explaining each step necessary to reach the answer.

Play any line as often as you like. See how the basic processes come alive using movement and colour on the screen. Ideal for students who have missed lessons or need extra help.

See **Chapter 9, Equations**, p. 204

1 | WHOLE NUMBERS (click to download sample) | 9 | |

A | The number system | 11 | |

B | Number strategies | 13 | |

C | Rounding numbers | 16 | |

D | Estimation | 17 | |

E | Operating with numbers | 19 | |

F | Index notation | 24 | |

G | Square numbers | 26 | |

H | Order of operations | 27 | |

Review set 1 | 31 | ||

Practice test 1A: Multiple choice | 32 | ||

Practice test 1B: Short response | 33 | ||

Practice test 1C: Extended response | 33 | ||

2 | ANGLES, LINES, AND PARALLELISM | 35 | |

A | Points and lines | 36 | |

B | Measuring and classifying angles | 39 | |

C | Angle properties | 42 | |

D | Angle pairs | 46 | |

E | Parallel lines | 49 | |

F | Geometric construction | 54 | |

Review set 2 | 58 | ||

Practice test 2A: Multiple choice | CD | ||

Practice test 2B: Short response | 60 | ||

Practice test 2C: Extended response | 61 | ||

3 | PROPERTIES OF NUMBERS | 63 | |

A | Divisibility tests | 64 | |

B | Factors of natural numbers | 67 | |

C | Prime and composite numbers | 69 | |

D | Highest common factor | 72 | |

E | Multiples of natural numbers | 74 | |

F | Square roots of whole numbers | 76 | |

Review set 3 | 78 | ||

Practice test 3A: Multiple choice | CD | ||

Practice test 3B: Short response | 79 | ||

Practice test 3C: Extended response | 79 | ||

4 | POSITIVE AND NEGATIVE NUMBERS | 81 | |

A | Opposites | 82 | |

B | The number line | 85 | |

C | Adding and subtracting negatives | 89 | |

D | Multiplying negative numbers | 93 | |

E | Dividing negative numbers | 95 | |

F | Combined operations | 96 | |

G | Using your calculator | 97 | |

Review set 4 | 98 | ||

Review test 4A: Multiple choice | 99 | ||

Review test 4B: Short response | 100 | ||

Review test 4C: Extended response | 101 | ||

5 | FRACTIONS | 103 | |

A | Common fractions | 105 | |

B | Fractions as division | 106 | |

C | Proper and improper fractions | 109 | |

D | Placing fractions on a number line | 110 | |

E | Equal fractions and simplifying | 111 | |

F | Comparing fractions | 116 | |

G | Adding and subtracting fractions | 117 | |

H | Multiplying fractions | 119 | |

I | Reciprocals | 121 | |

J | Dividing fractions | 121 | |

K | Evaluating fractions using a calculator | 123 | |

L | Problem solving | 124 | |

Review set 5 | 126 | ||

Practice test 5A: Multiple choice | CD | ||

Practice test 5B: Short response | 127 | ||

Practice test 5C: Extended response | 127 | ||

6 | DECIMAL NUMBERS | 129 | |

A | Place value | 130 | |

B | Converting decimals to fractions | 132 | |

C | Rounding decimal numbers | 133 | |

D | Ordering decimal numbers | 134 | |

E | Adding and subtracting decimal numbers | 137 | |

F | Multiplying by powers of 10 | 140 | |

G | Dividing by powers of 10 | 141 | |

H | Multiplying decimal numbers | 142 | |

I | Dividing decimal numbers | 145 | |

Review set 6 | 147 | ||

Practice test 6A: Multiple choice | 148 | ||

Practice test 6B: Short response | 149 | ||

Practice test 6C: Extended response | 149 | ||

7 | ALGEBRA: EXPRESSIONS AND FORMULAE | 151 | |

A | Building expressions | 152 | |

B | Key words in algebra | 158 | |

C | Simplifying expressions | 159 | |

D | Algebraic products | 162 | |

E | Evaluating algebraic expressions | 164 | |

F | Formulae | 166 | |

G | Practical problems using formulae | 168 | |

Review set 7 | 171 | ||

Practice test 7A: Multiple choice | 172 | ||

Practice test 7B: Short response | 173 | ||

Practice test 7C: Extended response | 173 | ||

8 | PERCENTAGE | 175 | |

A | Understanding percentages | 176 | |

B | Interchanging number forms | 178 | |

C | One quantity as a percentage of another | 182 | |

D | Finding a percentage of a quantity | 185 | |

Review set 8 | 187 | ||

Practice test 8A: Multiple choice | 188 | ||

Practice test 8B: Short response | 189 | ||

Practice test 8C: Extended response | 190 | ||

9 | EQUATIONS (click to download sample) | 191 | |

A | Equations | 192 | |

B | Solving simple equations | 193 | |

C | Maintaining balance | 195 | |

D | Inverse operations | 199 | |

E | Algebraic flowcharts | 202 | |

F | Solving equations | 203 | |

G | Equations with a repeated variable | 206 | |

H | Writing equations | 207 | |

I | Problem solving | 207 | |

Review set 9 | 209 | ||

Practice test 9A: Multiple choice | CD | ||

Practice test 9B: Short response | 210 | ||

Practice test 9C: Extended response | 211 | ||

10 | POLYGONS | 213 | |

A | Polygons | 214 | |

B | Triangles | 218 | |

C | Angles of a triangle | 219 | |

D | Isosceles triangles | 223 | |

E | Quadrilaterals | 226 | |

F | Angles of a quadrilateral | 230 | |

Review set 10 | 231 | ||

Practice test 10A: Multiple choice | CD | ||

Practice test 10B: Short response | 233 | ||

Practice test 10C: Extended response | 235 | ||

11 | COORDINATES | 237 | |

A | Map references | 239 | |

B | Number grids | 241 | |

C | Positive and negative coordinates | 244 | |

D | Plotting points from a table of values | 247 | |

Review set 11 | 249 | ||

Practice test 11A: Multiple choice | CD | ||

Practice test 11B: Short response | 250 | ||

Practice test 11C: Extended response | 251 | ||

12 | MEASUREMENT (click to download sample) | 253 | |

A | Length | 254 | |

B | Perimeter | 256 | |

C | Area | 260 | |

D | The area of a rectangle | 263 | |

E | Other areas | 265 | |

F | Volume | 269 | |

Review set 12 | 272 | ||

Practice test 12A: Multiple choice | 273 | ||

Practice test 12B: Short response | 274 | ||

Practice test 12C: Extended response | 275 | ||

13 | RATIO AND RATES | 277 | |

A | Ratio | 278 | |

B | Writing ratios as fractions | 280 | |

C | Equal ratios | 281 | |

D | Problem solving using ratios | 284 | |

E | Rates | 289 | |

F | Comparing prices | 290 | |

Review set 13 | 292 | ||

Practice test 13A: Multiple choice | CD | ||

Practice test 13B: Short response | 293 | ||

Practice test 13C: Extended response | 294 | ||

14 | LINE GRAPHS | 295 | |

A | Properties of line graphs | 296 | |

B | Estimating from line graphs | 298 | |

C | Travel graphs | 304 | |

Review set 14 | 306 | ||

Practice test 14A: Multiple choice | CD | ||

Practice test 14B: Short response | 308 | ||

Practice test 14C: Extended response | 309 | ||

15 | PROBABILITY | 311 | |

A | Describing probability | 312 | |

B | Assigning numbers to probabilities | 314 | |

C | Sample space | 316 | |

D | Theoretical probability | 317 | |

Review set 15 | 323 | ||

Practice test 15A: Multiple choice | CD | ||

Practice test 15B: Short response | 324 | ||

Practice test 15C: Extended response | 325 | ||

16 | STATISTICS (click to download sample) | 327 | |

A | Data collection | 329 | |

B | Categorical data | 330 | |

C | Numerical data | 336 | |

D | Measuring the centre and spread | 341 | |

Review set 16 | 347 | ||

Practice test 16A: Multiple choice | CD | ||

Practice test 16B: Short response | 349 | ||

Practice test 16C: Extended response | 350 | ||

17 | TRANSFORMATIONS (click to download sample) | 351 | |

A | Translations | 352 | |

B | Reflections and line symmetry | 355 | |

C | Rotations and rotational symmetry | 359 | |

D | Combinations of transformations | 365 | |

Review set 17 | 368 | ||

Practice test 17A: Multiple choice | CD | ||

Practice test 17B: Short response | 369 | ||

Practice test 17C: Extended response | 371 | ||

18 | SOLIDS | 373 | |

A | Drawing rectangular solids | 374 | |

B | Views of solids | 378 | |

Review set 18 | 382 | ||

Practice test 18A: Multiple choice | CD | ||

Practice test 18B: Short response | 383 | ||

Practice test 18C: Extended response | 384 | ||

ANSWERS | 385 | ||

INDEX | 422 |