TOPIC 8: PYTHAGORAS THEOREM Triangle with a Right angle i.e. 90° has an amazing property. Do you want to know what property is that? Go on, read our notes to see the amazing property of a right angled triangle. Pythagoras Theorem deals only with problems involving any Triangle having one of its Angles with 900. This kind of a Triangle is called Right angled triangle. When triangle is a right angled triangle, squares can be made on each of the three sides. See illustration below: The Area of the biggest square is exact the same as the sum of the…
Author: Msomi Bora
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TOPIC 7: GEOMETRIC AND TRANSFORMATIONS Reflection The Characteristics of Reflection in a Plane Describe the characteristics of reflection in a plane A transformation in a plane is a mapping which moves an object from one position to another within the plane. Think of a book being taken from one comer of a table to another comer. Figures on a plane of paper can also be shifted to a new position by a transformation. The new position after a transformation is called the image. Examples of transformations are reflection, rotation, enlargement and translation. Different Reflections by Drawings Represent different reflections by…
TOPIC 6: SIMILARITY Some Figures tend to have different size but exactly equal angles and their corresponding sides always proportional. This kind of figures are said to be similar. Read the notes below to see which shapes are said to be similar. Here is a well prepared tutorial on Similarity Tutorial Created by Willbald Mvungi-Ilboru Secondary Similar Figures Two geometrical figures are called similar if they both have the same shape. More precisely one can be obtained from the other by uniformly scaling (enlarging or shrinking). Possibly with additional translation, rotation and reflection. Below are similar figures, the figures have…
TOPIC 5: CONGRUENCE I’m sure you have seen some of the figure which in one way or another one of the shape can become another using turns, flip or slide. These shapes are said to be Congruent. Study this notes carefully to know different ways that can help you to recognize congruent figures. In geometry two figures or objects are congruent if they have the same shape and size, or if one has the shape and size as the mirror image of the other. If one shape can become another using turns (rotation), flip (reflection), and/ or slide (translation), then…
TOPIC 4: LOGARITHMS We always ask ourselves, how many of one number do we multiply to get another number? For example; how many 3s do we multiply to get 81? All these kind of questions will be answered in this unit. Make sure you understand. Start reading now……! Standard Form Tutorial on Standard Form Tutorial Created by Willbald Mvungi-Ilboru Secondary Standard Form is also called Scientific Notation. It is a way of writing a number into two parts. For example Thedigits(with the decimal point placed after the first digit) followed by X 10 to a powerthat puts a decimal point…
TOPIC 3: QUADRATIC EQUATIONS Solving quadratic equations can be difficult, but luckily there are several different methods that we can use depending on what type of quadratic that we are trying to solve. The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Solving Equations The standard form of a Quadratic equation is ax2 + bx + c =0 whereby a, b, c are known values and ‘a’ can’t be 0. ‘x’ is a variable (we don’t know it yet). a is the coefficient of x2 , b is the coefficient of x and cis a constant term. Quadratic equation is also called an equation…
TOPIC 2: ALGEBRA When we play games with computers we play by running, jumping and or finding secret things. Well, with Algebra we play with letters, numbers and symbols. And we also get to find secret things. Once we learn some of the ‘tricks’ it becomes a fun challenge to work with our skills in solving each puzzle. So, Algebra is all about solving puzzles. In this chapter we are going to learn some of the skills that help in solving mathematics puzzles. Binary Operations The Binary Operations Describe the binary operations When two numbers are combined according to the…
TOPIC 1: EXPONENTS AND RADICALS Exponents Exponents tell how many times to use a number itself in multiplication. There are different laws that guides in calculations involving exponents. In this chapter we are going to see how these laws are used. Single exponent tutorial Tutorial Created by Willbald Mvungi-Ilboru Secondary Indication of power, base and exponent is done as follows: Solution: To write the expanded form of the following powers: Solution To write each of the following in power form: Soln. The Laws of Exponents List the laws of exponents First law:Multiplication of positive integral exponent Second law: Division of positive…
topic 7: ALGEBRA An algebraic expression – is a collection of numbers, variables, operators and grouping symbols. Variables – are letters used to represent one or more numbers Algebraic Operations Symbols to form Algebraic Expressions Use symbols to form algebraic expressions The parts of an expression collected together are called terms Example x + 2x – are called like terms because they have the same variables 5x +9y – are called unlike terms because they have different variables An algebraic expression can be evaluated by replacing or substituting the numbers in the variables Example 1 Evaluate the expressions below, given that…
TOPIC 6: GEOMETRY Points and Lines The Concept of a Point Explain the concept of a point A point – is a smallest geometric figure which gives a position of object in a plane A line segment – is a straight line joining two points in a plane The Concept of a Point to Draw a Line Extend the concept of a point to draw a line A line segment – is a straight line joining two points in a plane A line passing through two points e.g A and B and extends without end (i.e infinitely) in both directions is denoted by The…