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# Download Maths Handbook and Study Guide by Kevin Smith: A Complete Guide to Grade 12 Mathematics

## Maths Handbook and Study Guide Grade 12 by Kevin Smith: A Review

If you are a grade 12 mathematics student looking for a comprehensive text book and reference book that covers everything in one book, you might want to check out Maths Handbook and Study Guide Grade 12 by Kevin Smith. This book is a best-selling guide that has been helping students ace their maths exams since 2009. It is suitable for both IEB and national curriculum maths students, as well as teachers, parents, tutors, homeschoolers, or anyone who wants to improve their maths skills.

In this review, we will take a closer look at what this book offers, what makes it different from other maths books, how it can help you achieve your maths goals, where you can get it, how much it costs, and more. By the end of this review, you will have a clear idea of whether this book is right for you or not.

## Content and Features

The Maths Handbook and Study Guide Grade 12 covers all the topics that you need to know for your grade 12 mathematics curriculum. It follows the CAPS guidelines for 2014 onwards. It has 386 pages of notes, explanations, examples, exercises, solutions, glossary, tips, tricks, tables, graphs, diagrams, formulas, symbols, units, conversions, rules, proofs, identities, laws, etc. It also includes exemplar June exams and preliminary examinations to help you prepare for your final exams.

The book is divided into 11 chapters, each covering a major topic in grade 12 mathematics. Each chapter has the following sections:

• A summary of the main concepts and skills that you need to master for that topic.

• A detailed explanation of each concept and skill, with examples and worked solutions to help you understand and apply them.

• A revision section at the end of each chapter, with a summary of the key points, a checklist of the outcomes, and a test yourself section with more exercises and solutions.

Here is a brief overview of each chapter and what it covers:

### Number Patterns, Sequences and Series

This chapter covers the following topics:

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• How to identify, describe, generate, and analyse number patterns, arithmetic sequences, geometric sequences, quadratic sequences, and Fibonacci sequences.

• How to use sigma notation to write and evaluate series.

• How to find the general term, the nth term, the sum of n terms, the sum to infinity, and the convergence or divergence of arithmetic series, geometric series, and p-series.

• How to use the binomial theorem to expand binomial expressions.

### Functions, Inverses and Logarithms

This chapter covers the following topics:

• How to define, identify, represent, interpret, and analyse functions and their graphs.

• How to determine the domain, range, intercepts, asymptotes, zeros, turning points, intervals of increase or decrease, and end behaviour of functions.

• How to perform operations on functions such as addition, subtraction, multiplication, division, composition, and inverse.

• How to identify and graph different types of functions such as linear functions, quadratic functions, cubic functions, exponential functions, logarithmic functions, rational functions, hyperbolic functions, absolute value functions, etc.

• How to use logarithms to solve exponential equations and simplify expressions.

• How to apply the laws of logarithms and the change of base formula.

### Financial Mathematics

This chapter covers the following topics:

• How to calculate simple interest, compound interest, nominal interest rate, effective interest rate, present value, future value, annuities, sinking funds, amortisation tables, etc.

• How to use financial formulas and calculators to solve problems involving loans, investments, savings plans, etc.

• How to compare different financial options using graphs and tables.

### Trigonometry

This chapter covers the following topics:

• How to define and use trigonometric ratios (sine, cosine, tangent) in right-angled triangles.

• How to use Pythagoras' theorem and trigonometric identities (reciprocal ratios, - How to use the product-to-sum and sum-to-product identities to rewrite trigonometric expressions.

• How to use the sine rule, the cosine rule, and the area rule to solve problems involving non-right-angled triangles.

### Two and Three Dimensional Trigonometry

This chapter covers the following topics:

• How to define and use angles of elevation and depression, bearings, and direction cosines.

• How to solve problems involving two and three dimensional figures such as triangles, quadrilaterals, polygons, prisms, pyramids, cones, cylinders, spheres, etc.

• How to calculate the distance, midpoint, gradient, and angle between two points in two and three dimensions.

• How to use the scalar product (dot product) and the vector product (cross product) to find the angle, length, area, and volume of two and three dimensional figures.

### Algebra and Differential Calculus

This chapter covers the following topics:

• How to simplify algebraic expressions involving fractions, radicals, exponents, logarithms, etc.

• How to factorise algebraic expressions using common factors, difference of two squares, perfect squares, trinomials, grouping, etc.

• How to solve linear equations, quadratic equations, simultaneous equations, exponential equations, logarithmic equations, rational equations, etc.

• How to define and use limits, continuity, derivatives, differentiation rules (power rule, product rule, quotient rule, chain rule), etc.

• How to apply differential calculus to find the gradient of a curve at a point, the equation of a tangent or normal to a curve at a point, the rate of change of a function with respect to another variable, etc.

### Curve Sketching and Graph Interpretation

This chapter covers the following topics:

• How to sketch graphs of functions using their domain, range, intercepts, asymptotes, zeros, turning points, intervals of increase or decrease, and end behaviour.

• How to interpret graphs of functions using their features, properties, and relationships.

• How to analyse graphs of functions using calculus techniques such as finding the first and second derivatives, the stationary points, the points of inflection, the concavity, the maximum and minimum values, etc.

• How to compare and contrast graphs of different functions using tables and diagrams.

### Optimisation of Functions and Rate of Change

This chapter covers the following topics:

• How to use differential calculus to find the optimal values of a function subject to certain constraints or conditions.

• How to solve problems involving optimisation of functions such as finding the maximum area, minimum cost, maximum profit, minimum time, etc.

• How to use differential calculus to find the rate of change of a function with respect to another variable.

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