Category: Msomi Maktaba All Notes

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…

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…

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…

  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…

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…

TRIGONOMETRY Trigonometric ratio Introduction: TRI – is the Greek word which means three. -Trigonometry is the branch of mathematics which deals with measurement. -A Trigonometric ratio consists of three parts that is – Hypotenuse, Adjacent and opposite. Consider the diagram below which is the right angled triangle   For example…

PYTHAGORAS THEOREM PYTHAGORAS THEOREM Pythagoras theorem is used to solve problems involving right angled triangles. Statement: In a right- angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. Shown below Required to prove: c2 = a2 + b2 Construction…

GEOMETRICAL TRANSFORMATIONS -A transformation changes the position, size, direction or shape of objects. -Transformation in a plane is a mapping which moves an object from one position to another within the plane. The new position after a transformation is called an image Examples of transformations are Reflection Rotation Enlargement and…

SIMILARITY AND ENLARGEMENT Similar figures: Two polygons are said to be similar if they have the same shape but not necessarily the same size. When two figures are similar to each other the corresponding angles are equal and the ratios of corresponding sides are equal. SIMILARTRIANGLE Triangle are similar when…

  CONGRUENCE OF SIMPLE POLYGON   The triangles above are drawn such that CB= ZY AC=XZ B=YX Corresponding sides in the triangles are those sides which are opposite to the equal angles i.e. If the corresponding sides are equal i.e. In general, polygons are congruent if corresponding sides and corresponding…

LOGARITHMS STANDARD NOTATIONS Standard notation form is written in form of A x 10n whereby 1≤ A< 10 and n is any integers Example Write the following in standard form (i) 2380 Solution: 2380 = 2.38 x 103 (ii) 97 Solution: 97 = 9.7 x 101 (iii) 100000 Solution: 100000…

QUADRATIC EQUATION QUADRATIC EQUATION Is any equation which can be written in the form of ax2 + bx + c=0 where a ≠ 0 and a, b and c are real numbers. SOLVING QUADRATIC EQUATION i) BY FACTORIZATION Example 1 solve x2 + 3x – 10 = 0 Solution: x2…

EXPONENT AND RADICALS   EXPONENTS: – Is the repeated product of real number by itself e.g. i) 2 x 2 x 2 x 2 = 24 ii) 6 x 6 x 6 x 6 x 6 = 65 iii) a x a x a x a x a = a5…