# Delta Mathematics: NCEA Level 3 (3e)

##### Description

This brand-new and completely revised third edition of *Delta Mathematics* is closely aligned with recent developments in New Zealand mathematics education. The content has been carefully revised in line with best teaching practice, and expanded to respond to changes in the curriculum and assessment. *Delta Mathematics* covers all eight of the NCEA Level 3 Mathematics Achievement Standards.

*Delta Mathematics* includes groundbreaking and balanced coverage of critical-path analysis, a new area in secondary mathematics, and incorporates:

- critical-path method (earliest and latest start and finish times)
- the backflow algorithm
- scheduling, with both unlimited and limited processors
- allocation of tasks, with priority lists based on critical times and decreasing times.

All the topics in *Delta Mathematics* are accompanied by a large number of well-balanced questions, graded in difficulty, to reinforce students’ understanding and build solid foundations for future learning. Many investigations, applications, spreadsheet activities and puzzles help to make the underlying mathematics more interesting and relevant. Full answers are provided.

*Delta Mathematics* is part of a comprehensive package that comprises:

- textbook
- workbook
- online resources
- teaching resource (electronic)
- eText option.

##### Table of contents

The NCEA Level 3 Mathematics and Statistics Achievement Standards for Year 13

The Delta package

About the authors

Foreword to students and teachers

Investigations

Puzzles

**3.1 Geometry of conic sections
**1 Graphs and equations of conic sections

2 Lines and conics, parametric form

**3.2 Linear-programming methods**

3 Linear inequalities

4 Optimisation (two variable)

**3.3 Trigonometric methods**

5 Trig graphs and reciprocal trig functions

6 Trig identities and formulae

7 Trig equations

**3.4 Critical-path analysis**

8 Networks

9 Critical paths

10 Scheduling and processor allocation

**3.5 Complex numbers**

11 The algebra of complex numbers

12 Polynomials

13 De Moivre’s theorem and complex roots

**3.6 Differentiation methods**

14 Limits, continuity and differentiability

15 Derivatives and differentiation rules

16 Properties of curves

17 Optimisation (one variable)

18 Rates of change and parametric functions

**3.7 Integration methods**

19 Anti-differentiation

20 Integration techniques

21 Definite integration and area

22 Numerical integration

23 Differential equations

**3.15 Systems of simultaneous equations**

24 Systems of equations

25 Solving a set of equations in context

**Appendices**

Appendix 1: Functions

Appendix 2: Binomial expansions

Appendix 3: The exponential function and logarithms

Appendix 4: Proofs

Appendix 5: Useful formulae

Answers

Index

##### Features & benefits

**The NCEA Level 3 Mathematics and Statistics Achievement Standards for Year 13 **

There are 15 Achievement Standards for the realigned NCEA Level 3 assessment in 2013. These comprise eight Achievement Standards covering mathematics – including calculus, algebra, trigonometry and geometry, and seven Achievement Standards covering statistics. All 15 Achievement Standards relate to Level 8 of the New Zealand Mathematics and Statistics Curriculum.

*Delta Mathematics* provides full coverage of the eight NCEA Level 3 Mathematics Achievement Standards (AS 3.1 to AS 3.7 inclusive, and AS 3.15).

*Sigma Statistics* addresses all seven NCEA Level 3 Statistics Achievement Standards (AS 3.8 to AS 3.14 inclusive).

**Delta Mathematics **

The content of *Delta Mathematics* (third edition) is closely aligned with, and responds to, recent developments in New Zealand mathematics education.

The section on Achievement Standard 3.4 provides ground-breaking and balanced coverage of a new area in secondary mathematics – critical-path analysis. After an introduction (Chapter 8) that adds to the Year 12 treatment of networks (with Hamiltonian paths, maximum flow, and more on spanning trees, including Steiner points), there are two chapters (9 and 10) devoted to critical-path analysis:

- the concept of critical paths (earliest and latest start and finish times)
- the backflow algorithm for determining the critical path and earliest finish time for a project
- scheduling
- priority lists based on both decreasing times and critical times
- float time for tasks and idle time for processors
- allocating tasks to a limited number of processors
- scheduling independent tasks.

The parts of Year 13 Mathematics that have evolved from the current NCEA Level 3 Mathematics Achievement Standards have been extensively reviewed. The content has been carefully revised in line with best teaching practice, and expanded to respond to changes in then curriculum and assessment.

The textbook takes into account the difference between the curriculum and current assessment coverage. The appendices at the end of the textbook provide additional material that is in the curriculum.

There are several places where teachers may decide to introduce students to some prerequisite mathematics before concentrating on a strictly assessment-based programme, including the following:

- composite and inverse functions – useful for algebra, calculus (e.g. chain rule) and trigonometry
- exponential and log functions – help in understanding calculus

##### Author biography

**David Barton** needs no introduction to a generation of New Zealand mathematics students and teachers. He has written a full six-book, award-winning series for secondary-school mathematics, and his material has also been published in Australia, South Africa, Fiji and Abu Dhabi. David Barton was educated at Wellington College and has taught at Wellington College and Rangitoto College in Auckland.

**Anna Cox is** the Head of Mathematics at St Hilda’s College in Dunedin and, before that, was HOD of Mathematics and Physics at King’s High School. She is the co-author of *Beginning Physics* and *Continuing Physics*, both published by Pearson. An enthusiastic and expert teacher, Anna brings fresh new ideas to the writing team.

##### Target audience

Year 13 students

##### Supplement URL

Find out more about Barton Mathematics.

Visit David Barton's website for additional links for each text, spreadsheets, statistics resources and more.