Tag: MATHEMATICS

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…

UNITS   UNITS OF LENGTH Basic unit of length is meter. Other unit are such as :- Unit Symbol Millimeter mm Centimeter cm Decimeter dm Meter m Decameter dam Hectametre hm Kilometer km     Km hm dam m dm cm mm 1 0 0 0 0 0 0 1…

RATIO, PROFIT AND LOSS Ratio:- the ratio of number p and q is p:q or p ÷ q or p/q Examples: 1. Joha and Siwenza shared 4,000 shillings between them. It Joha received 15,000 shillings and Siwenza got 25,000 shillings, Find the ratio of the amounts they received: Solution: Joha…

PERIMETERS AND AREA PERIMETER: The perimeter is the length of a closed curve. It is measured in centimeters, meter, kilometer etc To find the perimeter of a shape, add the length of the sides which enclose it. Example: Find the perimeter of rectangle which is 6m by 9m solution Consider…

COORDINATE GEOMETRY   Introduction The position of points on a line found by using a number line, that is   When two number lines one vertical and another one horizontal are considered one kept at 90o and intersecting at their zero marks, The result is called xy – plane or…