N1 Mathematics

Mathematics Downloaded from hlayiso.com N1

Module 1: Exponents and logarithms EXPONENTS (INDICES) An exponent, also referred to as an index, is more or less a shorthand notation for multiplying the same number by itself several times, for example: 2 × 2 × 2 = 23 = 8 In this example, the “3” is the exponent. Downloaded from hlayiso.com www.futuremanagers.com

Module 1: Exponents and logarithms (continued) LOGARITHMS Logarithms are the ‘opposite’ of exponentials. The logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. Therefore a logarithm is an unknown exponent that will be determined. For example: The logarithm of 100 to base 10 is 2,from Downloaded writtenhlayiso.com as 𝑙𝑙𝑙𝑙𝑙𝑙10 100 = 2 www.futuremanagers.com

Module 2: The four basic algebraic operations THE SCIENTIFIC POCKET CALCULATOR The scientific calculator pays attention to the ‘priority’ of a maths sequences, therefore it automatically evaluates an answer according to ‘BODMAS’. There are several functions that a scientific calculator can perform: • Inverse or reciprocal; • Squares and number powers; • Roots; and Downloaded from hlayiso.com • Fractions. www.futuremanagers.com

Module 2: The four basic algebraic operations (continued) THE FOUR BASIC ALGEBRAIC OPERATIONS The four basic algebraic operations are: • Additional (only like terms can be added); • Subtraction (only like terms can be subtracted); • Multiplication (all terms can be multiplied); and • Division (all terms can be divided). When calculating an equation, BODMAS Downloaded fromis hlayiso.com important to consider. www.futuremanagers.com

Module 3: Factorisation and fractions FACTORISATION, HCF AND LCM Writing a mathematical statement as a product of its factors is called factorisation. The highest common factor (HCF) of two or more numbers is the common factor of all those numbers with the greatest value. The first step in factorisation is to take out the HCF. The lowest common multiple (LCM) from Downloaded of two or more numbers is the smallest hlayiso.com possible number into which all the numbers will divide exactly. www.futuremanagers.com

Module 3: Factorisation and fractions (continued) ALGEBRAIC FUNCTIONS Fractions can be simplified by dividing the numerator and the denominator by the same factor. When operating the algebraic functions with fractions, there are certain rules to consider. For example, fractions can only be added or subtracted if they share the same denominator. Downloaded from hlayiso.com www.futuremanagers.com

Module 4: Equations, word problems and manipulation of technical formulae LINEAR EQUATIONS An equation is a mathematical statement that includes an = sign. A linear equation is an equation in which the highest variable you are solving for is equalled to 1. A linear equation cannot have more than one unique solution (often called root) for 𝑥𝑥, for example: If 2𝑥𝑥 + 1 = 9 , the Downloaded solution that wouldfrom make hlayiso.com the statement true is if 𝑥𝑥 = 4. www.futuremanagers.com

Module 4: Equations, word problems and manipulation of technical formulae (continued) WORD PROBLEMS When an answer is needed to a mathematical problem that is described in words as well as numbers, it is called a word problem. You find the solution by setting up an equation that represents the problem, and then solve it. Downloaded from hlayiso.com www.futuremanagers.com

Module 4: Equations, word problems and manipulation of technical formulae (continued) MANIPULATION OF TECHNICAL FORMULAE Manipulation of technical formula is often described as changing the subject of the formula. Downloaded from hlayiso.com www.futuremanagers.com

Module 5: Algebraic graphs COORDINATES ON A CARTESIAN PLANE The Cartesian plane is the two-dimensional space mapped out by the x-and y-axes. • The vertical axis is the y-axis. • The horizontal axis is the x-axis. • The x- and y-axes divide the Cartesian plane in four quadrants. • (x; y) is called an ordered numberfrom Downloaded pair orhlayiso.com coordinates www.futuremanagers.com

Module 5: Algebraic graphs (continued) FUNCTION NOTATION A linear equation of the form 𝑦𝑦 = 𝑚𝑚 + 𝑐𝑐 can be written in the form 𝑚𝑚 𝑓𝑓 𝑥𝑥 = 𝑚𝑚 + 𝑐𝑐 and a rectangular hyperbola in the form 𝑥𝑥 = 𝑐𝑐 or 𝑦𝑦 + 𝑐𝑐 can 𝑚𝑚 𝑥𝑥 𝑐𝑐 be written in the form 𝑓𝑓 𝑥𝑥 = 𝑐𝑐 .𝑐𝑐 𝑓𝑓 𝑥𝑥 = 𝑚𝑚 + 𝑐𝑐 and 𝑓𝑓 𝑥𝑥 = 𝑐𝑐 is also called function notation. 𝑚𝑚 𝑐𝑐 Downloaded from hlayiso.com www.futuremanagers.com

Module 5: Algebraic graphs (continued) LINEAR GRAPHS (STRAIGHT-LINE GRAPHS) A linear equation is an equation with an expression of degree 1. The degree of an expression is given by the highest value found among the degrees of all the terms in the expression. Such a linear equation can be represented graphically by a straight line, for example: 𝑦𝑦 = Downloaded 3𝑥𝑥 + 2hlayiso.com from www.futuremanagers.com

Module 5: Algebraic graphs (continued) INTERCEPTS AND GRADIENTS OF STRAIGHT-LINE GRAPHS The gradient (referred to as m) of afrom Downloaded straight line is the measure of its slope hlayiso.com relative to the x-axis. www.futuremanagers.com

Module 5: Algebraic graphs (continued) RECTANGULAR HYPERBOLA Characteristics of a rectangular hyperbola: • There are no x- or y-intercepts • The graph strives towards the x- and y-axes but never touches or cuts the axes, ∴ 𝑥𝑥 ≠ 0 and 𝑦𝑦 = 0. • The hyperbola consists of two separate curves: Downloaded from hlayiso.com www.futuremanagers.com

Module 6: Triangles PROPERTIES OF TRIANGLES There are many different types of triangles: • Equilateral triangle – All sides are equal and all angles are equal to 60°; • Isosceles triangle – Two sides are equal with base angles also equal; • Scalene triangle – No sides or angles are equal; • Acute-angled triangle – All three angles are smaller than 90°; • Obtuse-angle triangle – One angle Downloaded is greater from than 90°; and hlayiso.com • Right-angled triangle – One angle is equal to 90°. www.futuremanagers.com

Module 6: Triangles (continued) PYTHAGORAS’ THEOREM Pythagoras’ theorem states the following: The area of a square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides. This means if you have a right-angled triangle ABC with ∠𝐵𝐵 = 90°, then 𝑎𝑎 + 𝑐𝑐 = 𝑏𝑏 . Downloaded from hlayiso.com 𝑏 𝑐 𝑎 www.futuremanagers.com

Module 7: Trigonometry TRIGONOMETRY Trigonometry is the study of triangles, the relationship between the lengths of their sides, and the angles between those sides, including the behaviour of certain wave functions. Downloaded from hlayiso.com www.futuremanagers.com

Module 8: Mensuration and percentages MENSURATION Mensuration means to establish the size, amount, quantity or extent of something by comparing it with something of standard size, or with an item marked off in standard units. For example, 1,000m = 1km. Downloaded from hlayiso.com www.futuremanagers.com

Module 8: Mensuration and percentages (continued) PERCENTAGES Per cent means divided by 100. For example, if you are talking about 37%, 37 you are saying . 100 Percentages are used in everyday contexts, such as in tax and discounts. Downloaded from hlayiso.com www.futuremanagers.com