Author: Msomi Bora

TOPIC 7: MATRICES AND TRANSFORMATIONS Operations on Matrices The Concept of a Matrix Explain the concept of a matrix Definition: A matrix is an array or an Orderly arrangement of objects in rows and columns. Each object in the matrix is called an element (entity). Consider the following table showing the number of students in each stream in each form. FormIIIIIIIV Stream A38354028 Stream B36403439 Stream C40373635 From the above table, if we enclose the numbers in brackets without changing their arrangement, then a matrix is farmed, this can be done by removing the headings and the bracket enclosing the numbers…

TOPIC 6: VECTORS Displacement and Positions of Vectors The Concept of a Vector Quantity Explain the concept of a vector quantity A vector – is a physical quantity which has both magnitude and direction. The Difference Between Displacement and Position Vectors Distinguish between displacement and position vectors If an object moves from point A to another point say B, there is a displacement There are many Vector quantities, some of which are: displacement, velocity, acceleration, force, momentum, electric field and magnetic field. Other physical quantities have only magnitude, these quantities are called Scalars. For example distance, speed, pressure, time and temperature…

TOPIC 5: TRIGNOMETRY Trigonometry is a branch of mathematics that deals with relationship (s) between angles and sides of triangles. Trigonometric Ratios The Sine, Cosine and Tangent of an Angle Measured in the Clockwise and Anticlockwise Directions Determine the sine, cosine and tangent of an angle measured in the clockwise and anticlockwise directions The basic three trigonometrical ratios are sine, cosine and tangent which are written in short as Sin, Cos, and tan respectively. Consider the following right angled triangle. Also we can define the above triangle ratios by using a unit Circle centered at the origin. If θis an obtuse…

TOPIC 4: PROBABILITY Normally we are living in the world full of uncertainties. For example when two equally strong foot ball teams play a match it is not easy to predicate the outcome of the game. Also for a pregnant woman it is not easy to predict what will be the sex of the born. Under such uncertainties the theory of probability is applied. Definition; Probability is a branch of mathematics which deals with and shows how to measure the occurrence of events in daily life. Or it can simply be defined as a measure of chances. Probability of an Events…

TOPIC 3: THREE DIMENSIONAL FIGURES Three Dimensional Figure Sometimes before you make any purchases you may want to know for example, how much cloth you need to make a pillow cover. What about a cover for your mattress or sofa cushion? How much oil paint do you need to paint your drinking water tank? What about the amount of cloth for the pocket covers of your radio, curtain, suit, gown, trousers, set of table clothes, etc. Answers to such questions and of the kind leads you to think more carefully about the size of the surfaces (faces) to be covered…

TOPIC 2: AREA AND PERIMETER Area of any Triangle The Formula for the Area of any Triangle Derive the formula for the area of any triangle Area of triangle is given by½bh, whereby b is the base of the triangle and h is the height of the given triangle. Consider the illustrations below: From the figure above, we see where the base and height are located. Applying the Formula to find the Area of any Triangle Apply the formula to find the area of any triangle Example 1 The base of a triangle is 12cm long. If the corresponding height…

TOPIC 1: COORDINATE GEOMETRY Equation of a Line The General Equation of a Straight Line Derive the general equation of a straight line COORDINATES OF A POINT •The coordinates of a points – are the values of x and y enclosed by the brackets which are used to describe the position of point in a line in the plane. The plane is called xy-plane and it has two axis. horizontal axis known as axis and vertical axis known as axis Consider the xy-plane below The coordinates of points A, B, C ,D and E are A(2, 3), B(4, 4), C(-3, -1), D(2, -4) and E(1,…

TOPIC 8: ACCOUNTS Double Entry The Meaning of Double Entry Explain the meaning of double entry Businesses need to keep records of their transactions. The process of keeping record is called bookkeeping. The simplest form of bookkeeping is single entry. Every transaction is recorded once. This is unreliable because: If an arithmetic mistake is made, it is very difficult to find and correct it If a transaction is omitted, it is difficult to find it Now, a more reliable method of bookkeeping is double entry. Different Types of Ledger Explain different types of ledger Businesses record their accounts in books called ledgers.…

TOPIC 7: THE EARTH AS A SPHERE Features and Location of Places The Equator, Great Circle, Small Circles, Meridian, Latitudes and Longitudes Describe the equator, great circle, small circles, meridian, latitudes and longitudes Definition of latitude and longitude The Earth is not a perfect sphere, as it is slightly flatter at the north and south poles than at the equator. But for most purposes we assume that it is a sphere. The position of any point on earth is located by circles round the earth, as follows: The earth rotates about its axis, which stretches from the north to the…

TOPIC 5: SEQUENCE AND SERIES Sequences The Concept of Sequence Explain the concept of sequence A Sequence is the arrangement of numbers or is a list of numbers following a clear pattern such that one number and the next are separated by comma (,). Example: a1, a2, a3, a4 …………………….. NB: Each number found in a Series or Sequence is called a term. Example 1 Find the next three terms in the following sequences. 5, 8, 11, 14, 17,……………………………… 3, 7, 6, 10, 9, ………………………………… 1, 2, 4, 7, ……………………………………… 2, 9, 20, 35, ………………………………… Solution: (a)You can see that each term…