For secondary school age. Mathematics Textbooks. Williams, Robyn Robyn Ellen Reproduction and communication for other purposes Except as permitted under the Act for example, a fair dealing for the purposes of study, research, criticism or review , no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher. Cumulative exam practice Functions and graphs Algebra Rates of change and calculus Probability

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For secondary school age. Mathematics Textbooks. Williams, Robyn Robyn Ellen Reproduction and communication for other purposes Except as permitted under the Act for example, a fair dealing for the purposes of study, research, criticism or review , no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher. Cumulative exam practice Functions and graphs Algebra Rates of change and calculus Probability Student textbook Full colour is used throughout to produce clearer graphs and headings, to provide bright, stimulating photos and to make navigation through the text easier.

Cumulative exam practice questions assist students with exam preparation. Clear, concise theory sections contain worked examples and highlighted important text and remember boxes.

Icons appear for the eBookPLUS to indicate that interactivities and eLessons are available online to help with the teaching and learning of particular concepts. Many worked examples have eBookPLUS icons to indicate that a Tutorial is available to elucidate the concepts being explained. Worked examples also have calculator icons that indicate support in the Calculator Companion books, which contain comprehensive step-by-step CAS calculator instructions, fully integrated into the examples, for the TI-Nspire CAS and Casio ClassPad calculators.

Exercises contain many carefully graded skills and application problems, including multiple choice questions. Cross-references to relevant worked examples appear with the first matching question throughout the exercises.

A selection of questions are tagged as technology-free to indicate to students that they should avoid using their calculators or other technologies to assist them in finding a solution.

Exam practice sections contain exam style questions, including time and mark allocations for each question. Each chapter concludes with a summary and chapter review exercise containing examination-style questions multiple choice, short answer and extended response , which help consolidate students learning of new concepts. Also included are questions from past VCE exams along with relevant Exam tips.

Students may use the eBookPLUS on laptops, tablets and school or home computers, and cut and paste material for revision, assignments or the creation of notes for exams. Career profiles and History of mathematics place mathematical concepts in context. Investigations, often suggesting the use of technology, provide further discovery learning opportunities.

SkillSHEET icons link to printable pages designed to help students revise required concepts, and contain additional examples and problems. Interactivity icons link to dynamic animations, which help students to understand difficult concepts. Tutorial icons link to one-way engagement activities, which explain the worked examples in detail for students to view at home or in the classroom. Test yourself tests are also available and answers are provided for students to receive instant feedback.

Two tests per chapter, fully worked solutions to WorkSHEETs, the work program and other curriculum advice in editable Word format are provided. Maths Quest is a rich collection of teaching and learning resources within one package. The eGuidePLUS provides NEW material from which teachers may set school-assessed coursework SAC , such as application tasks, analysis tasks and semester exams, as well as additional investigations, worksheets and technology files.

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Acknowledgements The authors and publisher would like to thank the following copyright holders, organisations and individuals for their assistance and for permission to reproduce copyright material in this book.

Images iStockphoto: pp. Shutterstock: pp. Information that will enable the publisher to rectify any error or omission in subsequent editions will be welcome. Solving linear equations and inequations Rearrangement and substitution Gradient of a straight line Sketching linear functions Simultaneous equations Finding the equation of a straight line Distance between two points and midpoint of a segment Linear modelling.

A linear equation is one that involves a variable raised to the power of 1 only. Recall that x1 is the same as x, so a linear equation involving x would contain only xs, and not x , x2, x3, x 1, x 2 and so on.

Remember to do the same operation to both sides of an equation, in the reverse order to that originally used to make up the equation.

Though the focus of this chapter is linear equations, some other types of equations will be included for skills practice. When there is only one variable involved in an equation, we may attempt to solve and find a numerical value by rearranging to make the variable the subject. Solve the following linear equations. When an equation has variables on both sides, at some stage they must be gathered together on the same side of the equation. Worked example 2. Collect xs on one side, for example, the side that results in a positive x term, in this case, the left-hand side LHS.

That is, add 3x to both sides. Write all terms with the common denominator, adjusting numerators accordingly so that numerator and denominator have been multiplied by the same amount. Now that all terms have the same denominator, the numerators must be equal. Multiply each side by 6. Multiply each term by There is only one solution to a linear equation. The solution to a linear equation can be represented as a single point on a number line.

If the equals sign is replaced with an inequality sign, the solution is a portion of a number line. These expressions are referred to as linear inequations sometimes called inequalities. Worked example 3. Solve the following linear inequations.

Divide both sides by 3. Reverse the inequality sign, as you are dividing by a negative number. When there is more than one variable involved in an equation, we may rearrange the equation to make a particular variable the subject using the same rules of equation solving described in the previous section. Worked example 4. Rearrange each of the following to make the variable in parentheses the subject. Once a variable is isolated, we may substitute values of other variables to calculate various values of the isolated variable.

The following worked example illustrates some practical applications. Worked example 5. Write the equation with F first. Sometimes it may be appropriate to use a common denominator. Take the square root of both sides, and write r first. As r is the radius, we take the positive root only. Write the formula that has s as the subject see part b above. Substitute the values given in step 1. Each of the following is a real equation used in business, mathematics, physics or another area of science.

Make the variable shown in parentheses the subject in each case. Make the variable in parentheses the subject and find its value using the given information. Find the value of b in the triangle above. Given that the volume of a cone is cm3 and its radius at the widest point is 12 cm, find the height of the h cone, expressing your answer in terms of. Here are two examples of where gradient can affect our everyday lives.

Can you think of others? A cliff face with a steeper gradient provides a greater challenge for climbers. Scientists calculate the required gradient of solar panels so that the maximum amount of energy is absorbed.

Match up the terms in the formula with the values given. If the angle a line makes with the positive direction of the x-axis is known, the gradient may be found using trigonometry applied to the triangle shown below. The angle given is not the one between the graph and the positive direction of the x-axis. Calculate the required angle. Without drawing a graph, calculate the gradient of the line passing through: a 2, 4 and 10, 20 b 4, 4 and 6, 14 c 10, 4 and 3, 32 d 5, 31 and 7, What is the.

What is the gradient of the sloping section? Give your answer as a. One regulation requires that the maximum gradient of a ramp exceeding mm in length is 1. Find the horizontal length of the ramp required to meet the specifications.

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## Essential Mathematical Methods CAS 1 and 2 Solutions Supplement

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