Mathematics I

Frontmatter

1. Integers

Abstract

A number system consists of a set of numbers, operations such as addition and multiplication for combining the numbers, and mathematical laws to govern the use of the operations.

Owen Perry, Joyce Perry

2. Common Fractions

Abstract

All numbers which are quotients of two integers are called rational numbers, and those quotients which are not integers are called fractions. Fractions occupy positions between integers on the number line. In a common fraction (sometimes called a vulgar fraction) the two integers are written one above the other with a line between them, such as

meaning .

Owen Perry, Joyce Perry

3. Decimal Fractions

Abstract

A fraction in the denary system of powers of ten is called a decimal fraction. It was shown earlier (page 3) that dividing a power of ten by ten decreases the index by one so that . This can be extended to negative powers, so that .

Owen Perry, Joyce Perry

4. Powers and Indices, Binary Arithmetic

Abstract

Powers of ten were introduced in chapter 3, and powers of any positive integer can be evaluated in the same way. For example, 2³,the third power of 2, = 2 × 2 × 2 = 8 and 3⁴, the fourth power of three = 3 × 3 × 3 × 3 = 81 In 3⁴ 3 is called the base and 4 is the index. Similarly 2⁷ has base 2 and index 7. The numbers 3⁴ and 2⁷ are said to be in index form.

Owen Perry, Joyce Perry

5. Limits of Accuracy. Standard Index Form. Four Figure Tables

Abstract

Exact values are possible in theory, for example in a geometry problem the side of a triangle could be exactly 70 mm. However, in practical work a line can never be drawn exactly to a given length, how near might depend on the accuracy of the ruler used and the fineness of the drawing point, as well as the skill of the person drawing the line.

Owen Perry, Joyce Perry

6. The Use of Logarithm Tables, Slide Rules and Electronic Calculators

Abstract

When a number is expressed as a power of ten the index is the logarithm of the number to the base ten. Every positive number can be written as a power of ten and the integral powers have been met already in the work on decimals.

Owen Perry, Joyce Perry

7. Algebra

Abstract

In algebra, some numbers are replaced by letters; for example, the standard form A × 10 ⁿ is an algebraic expression in which A and n are used in place of particular numbers. The basic operations are applied just as in arithmetic, but the answers are algebraic expressions containing letters, and expressions separated by operation signs are called algebraic terms.

Owen Perry, Joyce Perry

8. Algebraic Equations

Abstract

Two algebraic expressions separated by an equality sign form an algebraic equation. x = 2, 3ab = 2c², 2x + 3y = 7, are all equations. The equality sign implies that the expression on one side of an equation is equal in numerical value to the expression on the other side. To maintain this equality, the same operations must be carried out on both sides of an equation. For example,

are all satisfied by the same value of x.

Owen Perry, Joyce Perry

9. Diagrammatic Representation of Linear Equations

Abstract

A mapping is a correspondence between two sets of related values, such as distances measured in miles and kilometres, or temperatures measured on the Celsius and Fahrenheit scales. In a one-to-one mapping, each value in one set maps to exactly one value in the other set; every linear equation of the form y = mx + c connecting two variables x and y represents a one-to-one mapping from x to y, x → y.

Owen Perry, Joyce Perry

10. Statistics

Abstract

The subject called statistics is in three main parts; collection of numerical information or data, presentation of the data in tables and diagrams, and calculations based on data.

Owen Perry, Joyce Perry

11. Geometry

Abstract

A geometrical point defines a position in space and has no dimensions. Two points may be joined by curves, and the shortest curve between two given points is a straight line segment, such as XY.

Owen Perry, Joyce Perry

12. The Geometry of the Circle

Abstract

A circle is the plane figure traced out when a line with one, end at a fixed point makes one complete revolution about that point. The fixed point is called the centre, and the length of the line is called the radius of the circle. The circumference is the curve traced out by the extreme point of a radius.

Owen Perry, Joyce Perry

13. Perimeter, Area and Volume

Abstract

The perimeter of a polygon such as a triangle or quadrilateral is the sum of the lengths of the sides.

Owen Perry, Joyce Perry

14. Trigonometry

Abstract

In chapter 11 angles were described in terms of degrees and in chapter 12 circular measure was introduced. There is a third method which describes an acute angle by the ratios of the sides of a right-angled triangle containing the angle. They are the trigonometrical ratios and at first we shall consider only three of them, the sine the cosine and the tangent of an angle.

Owen Perry, Joyce Perry

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