Visualizing Solid Shapes Dimensions 1D and 2D figures Example: A ray or a line segment. They have length and breadth or width. They are usually plane figures, like squares, rectangles and circles. Solid Shapes Perspectives of a Solid Shape Visualising solid shapes (ii) Cubes can be formed by placing cubes side by side. Visualising solid
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Symmetry Basics of Symmetry Symmetry in Mathematics In Mathematics, a meaning of symmetry defines that one shape is exactly like the other shape when it is moved, rotated, or flipped. Consider an example, when you are told to cut out a ‘heart’ from a piece of paper, don’t you simply fold the paper, draw one-half
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Exponents and Powers Powers and Exponents Exponent An exponent of a number, represents the number of times the number is multiplied to itself. If 8 is multiplied by itself for n times, then, it is represented as: 8 × 8 × 8 × 8 × …..n times = 8n The above expression, 8n, is said
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Algebraic Expressions Introduction to Algebraic Expressions Constant Constant is a quantity which has a fixed value. Terms of Expression Parts of an expression which are formed separately first and then added are known as terms. They are added to form expressions. Example: Terms 4x and 5 are added to form the expression (4x +5). Coefficient
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Perimeter and Area Area of path formed =(πR2-πr2) sq units =π(R2-r2) sq units =π(R+r)(R-r) sq units 1 cm2 = 100 mm2 1 m2 = 10000 cm2 1 dm2 = 100 cm2 1 km2 = 1000000 m2 1 hectare = 10000 m2 Perimeter Perimeter is the total length or total distance covered along the boundary of
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Rational Numbers pqrq [pr]q pq rs pq (additive inverse of rs) Rational Numbers A rational number is defined as a number that can be expressed in the form pq , where p and q are integers and q≠0. In our daily lives, we use some quantities which are not whole numbers but can be expressed
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Comparing Quantities Ratio and Proportion Percentages For example: 16%=16100 Profit and Loss Gain = (SP) – (CP) Loss = (CP) – (SP) Loss%=loss×100CP Simple Interest SI=P×R×T100 Prices related to an item (ii) Cost price Finding the profit or loss percentage Percentages Percentages are ratios expressed as a fraction of 100. Percentages are represented by the
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THE TRIANGLE AND ITS PROPERTIES A triangle is a simple closed curve made up of three line segments. Classification of triangles: On the basis of sides: A triangle is said to be On the basis of angles: A triangle is said to be Angle sum property of a triangle: The sum of all three interior
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Lines and Angles Line, line segment and ray We come across many shapes in daily life. Consider a triangle, a square or any other shape. To draw any of these figures, one begins with a line or a line segment or a curve. Depending upon the number and arrangement of these lines we get distinct
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Simple Equations Introduction to Simple Equations Variables and Expressions Variable is a quantity that can take any value, its value is not fixed. It is a symbol for a number whose value is unknown yet. Expressions are formed by performing operations like addition, subtraction, multiplication and division on the variables. Example: 6x – 3 is
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