Book Chapters
Central to mathematics is the practice of counting and processing numbers, which is indispensable in the current digital age. Arithmetic, derived from the Greek word ‘arithmos’, meaning ‘number’, is a branch of mathematics that deals with numbers and the relationships that exist between them. This chapter focuses on this important branch and covers a range of topics relating to this. Some of the concepts introduced here will be explained in greater details at a later stage in this book and others will simply be encountered and applied.
In the preceding chapter, we looked at numbers and their various types and applied basic operations on them. It is now time to deal with the second part of rational numbers, i.e., fractions, the first part being the integers. This chapter covers the principles of fractions, decimals, and percentages, and the relationships between them. The skills here will be the backbone for working with algebraic fractions that will be covered in Chapter 3.
​We earlier discussed numbers and carried out basic arithmetic operations involving them. We will now extend our application of this concept to the domain of algebra - – a branch of mathematics that deals with arithmetical operations of variables or changing numbers, which are represented by letters or symbols. This chapter covers the fundamentals of algebraic expressions, including opening brackets, factorisation, algebraic simplification, and transposition.
A coordinate system is a way of specifying the position of an object on a line (or a one-dimension), on a surface (or a two-dimension), and in a space (or a three-dimension). Coordinate systems are all around us, we use it, and we even live it. For example, you may want to describe the position of a passenger or customer in a straight-line queue or that of a student in a lecture theatre with chairs arranged in rows and columns or that of a book in a library shelf or a product in a big supermarket. All these are coordinate systems. We need to be able to specify a position precisely, especially in computing where the memory address should be accurately referenced. The way to do this is what we are about to learn in this and the succeeding chapters.
This chapter will, in continuation of our discussion on geometry, look at methods of determining the equation of a straight line, parallel and perpendicular lines, and the intersection of straight lines.
Earlier, we introduced the use of letters and symbols to represent unknown values, and this forms the basis of algebraic expressions. When these expressions are equated with another expression or a number, it becomes an algebraic equation. Consequently, the unknown letter or variable can only assume specific value(s) if the statement (of the equality) is to be true. We are often interested in determining these values, which is the focus of this chapter. We will cover, among other things, the difference between an expression and an equation, the method of solving linear equations, and solving quadratic equations by factorisation.
In this chapter, we will continue our discussion on solving equations, covering three other methods of solving quadratic equations. We will also discuss simultaneous equations.
Presenting numbers in surd forms is common and highly essential in science and engineering, including when solving a quadratic equation using the formula method or when working with trigonometric angles. In this chapter, we will explain this concept, covering its meaning, types, rules, and applications.
It may be interesting to learn that the algebraic equations that we covered in Chapters 6 and 7 belong to the family of polynomials, though they have only one or two valid values for their unknown variables. You can imagine what it will be if there are three or even more valid values for a variable and what the equations (henceforth called polynomials) will look like. This chapter will cover, among others, principles relevant to evaluating polynomials, determining zeros of polynomials, factor theorem, and remainder theorem.
An inequality (plural inequalities) is evident in our day-to-day affairs now than ever before. Like its sister (i.e., equality), inequalities are a key part of mathematics and will be discussed here in this chapter, covering linear, quadratic, and simultaneous inequalities.
Indices (sing. index) together with logarithms are central to many scientific and engineering processes and are regularly used in simplifying expressions and solving equations. They are used in our daily activities including finance, economics, and natural phenomena, and will be the focus of this chapter.
An inequality (plural inequalities) is evident in our day-to-day affairs now than ever before. Like its sister (i.e., equality), inequalities are a key part of mathematics and will be discussed here in this chapter, covering linear, quadratic, and simultaneous inequalities.
Logarithm is a derived term from two Greek words, namely, logos (expression) and arithmos (number); in other words, it is a technique of expressing numbers. In fact, it is a system of evaluating multiplication, division, powers, and roots by appropriately converting them to addition and subtraction. In continuation of our discussion in the preceding chapter on indices, this chapter will focus on logarithm, covering its meaning, types, and laws.
Indicial equations are equations involving powers, where either the base or the exponent is the unknown variable to be determined. For this case, we will need concepts covered in the previous two chapters and Chapters 6 and 7.
In this chapter, we will look at the common units of angle measurement and discuss triangles, covering their types, naming convention, and how to determine their area. We will also cover Pythagoras’ theorem, sine rule, and cosine rule.
As part of our discussion on plane geometry (a branch of mathematics that deals with two-dimensional shapes), this chapter will focus on circles, covering their perimeter, length of an arc and chord, and area of a circle, a sector, and a segment.
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