MATHEMATICS FORM 2 – ALGEBRA msomimaktaba, August 17, 2024 ALGEBRA – BINARY OPERATIONS This is the operation in which the two numbers are combined according to the instruction The instruction may be explained in words or by symbols e.g. x, *, – Bi means two Example1. Evaluate (i) 5 x 123 Solution: 5 x 123 = 5(100 + 20… Continue Reading
MATHEMATICS FORM 1 – DECIMALS AND PERCENTAGES msomimaktaba, August 17, 2024August 17, 2024 DECIMALS AND PERCENTAGES Are fractions of tenth, they are written using a point which is a result of division of a normal fraction E.g. 0.34, 0.5, 0.333——– In the fraction 0.2546 the place values are Ones 0 Tenth 2 Hundredths 5 Thousandths 4 Ten Thousandths 6 Decimals can… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – LINEAR PROGRAMMING msomimaktaba, November 13, 2018August 17, 2024 LINEAR PROGRAMMING SIMULTANEOUS EQUATIONS Solving simultaneous equations graphically, the solution is given by the point of intersection of the two lines. Examples 1. Solve graphically the following simultaneous equations. 2x – y = 1 3x+3y =6 Equation 1 2x – y = 1 X intercept, y= 0 2x – y… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – MATRICES msomimaktaba, November 13, 2018August 17, 2024 MATRICES Operations on matrices A matrix represents another way of writing information. Here the information is written as rectangular array. For example two students Juma and Anna sit a math Exam and an English Exam. Juma scores 92% and 85%, while Anna scores 66% and 86%. This can be written… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – VECTORS msomimaktaba, November 13, 2018August 17, 2024 VECTORS Displacement and Position Vectors. Displacement Examples of vector quantities are displacement, Velocity, acceleration, force, momentum, electric field and magnetic field. Quantities which have magnitude only scalars, for example distance, speed, Pleasure, time and temperature. Sometimes a single. Small letter with a bar below like a or a like a… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – TRIGONOMETRY msomimaktaba, November 13, 2018August 17, 2024 TRIGONOMETRY Trigonometrical ratios in a unit circle The three trigonometrical ratios of sine, cosine and tangent have been defined earlier, using the sides of a right-angled triangle as follows If A is an angle as shown Consider a circle of units subdivided into four congruent sectors of the coordinate axes… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – PROBABILITY msomimaktaba, November 13, 2018August 17, 2024 PROBABILITY Defn: Probability is a branch of mathematics which deals with and shows how to measure these uncertainties of events in every day life. It provides a quantitative occurrences and situations. In other words. It is a measure of chances. Probability set and Event Suppose that an experiment of tossing… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – THREE-DIMENSIONAL FIGURES msomimaktaba, November 13, 2018August 17, 2024 THREE-DEMENSIONAL FIGURES INTRODUCTION A three dimensional figure is a solid figure having three measures. Some examples are pyramids, cylinders, prisms, cubes and cuboids. – Apart from three dimensional figures, there are also one and two dimensional figures. Examples A line is one – dimensional. There is one direction to move… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – AREAS AND VOLUMES msomimaktaba, November 13, 2018August 17, 2024 AREAS AND VOLUMES AREAS CASE 1.Right angled triangle Area = ½ b x h 2. Triangle with altitude that lies within the triangle Area 0f Δ ABC = ½ bh + ½ d h = ½ h(b + d) = ½ hL 3. A triangle where the altitude… Continue Reading
Basic Mathematics Study Notes Form 4 Mathematics – COORDINATE GEOMETRY msomimaktaba, November 13, 2018August 17, 2024 COORDINATE GEOMETRY Exercise 1. Plot the following point. P (2,2), T (-1, -2), L (2, -1) 2. In which quadrants is the? a. Abscissa positive? I b. Ordinate negative III c. Abscissa negative II d. Ordinate positive I e. Abscissa negative and ordinate negative? III EQUATIONS IN A STRAIGHT LINE… Continue Reading
Basic Mathematics Study Notes Form 3 Mathematics – ACCOUNTS msomimaktaba, November 13, 2018August 17, 2024 ACCOUNTS Accountsis a place in a ledger where all the transactions are relating to a particular asset, liabilities and capital, expenses,or revenue items were recorded. Accounts is a wider concept with identifying measuring and communicating economic information to permit informed judgments and decisions by users of the information. The part… Continue Reading
Basic Mathematics Study Notes Form 3 Mathematics – THE EARTH AS A SPHERE msomimaktaba, November 13, 2018August 17, 2024 THE EARTH AS A SPHERE The earth surface is very close to being a sphere. Consider a sphere representing the shape of the earth as below. NS is the Axis of the earth in which the earth rotates once a day. O is the center of the earth. The… Continue Reading
Basic Mathematics Study Notes Form 3 Mathematics – CIRCLE msomimaktaba, November 13, 2018August 17, 2024 CIRCLE DEFINITION AND PROPERTIES OF A CIRCLE A circle can be defined in two ways. A circle: Is a closed path curve all points of which are equal-distance from a fixed point called centre OR – Is a locus at a point which moves in a plane so that… Continue Reading
Basic Mathematics Study Notes Form 3 Mathematics – SEQUENCE AND SERIES msomimaktaba, November 13, 2018August 17, 2024 SEQUENCE AND SERIES SEQUENCE Is a set of numbers written in a definite order such that there is a rule by which the terms are obtained. Or Is a set of number with a simple pattern. Example 1. A set of even numbers • 2, 4, 6, 8, 10 ……… Continue Reading
Basic Mathematics Study Notes Form 3 Mathematics – RATES AND VARIATIONS msomimaktaba, November 13, 2018August 17, 2024 RATES AND VARIATIONS RATES:- When sets or quantities of different kinds are related, we use the word rate. i.e 1. A rate of pay of 10,000/= Tsh per hour (money- time) 2. The price of juice is 700/= Tsh per litre (money -weight of juice) 3. The average speed… Continue Reading
Basic Mathematics Study Notes Form 3 Mathematics – STATISTICS msomimaktaba, November 13, 2018August 17, 2024 STATISTICS Is the study or the methods of collecting, summarizing and presenting data and interpreting the information. MEASURES OF CENTRAL TENDENCY 1. Mean 2. Median 3. Mode MEAN “X” Is obtained by adding up all the data values then divide by the number of characters. I.e. i.e. =mean x1+x2+x3………. Sum… Continue Reading