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Topics
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What to Learn
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Rational Numbers
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- Definition and examples of rational numbers
- Natural numbers, whole numbers, and integers
- Properties of rational numbers (using identities)
- Representation of rational numbers on the number line
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Linear Equation in One Variable
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- Equation and linear equations
- Linear equation in one variable
- Solution of linear equations
- Laws of equality
- Word problems based on linear equations
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Understanding Quadrilaterals & Practical Geometry
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- Quadrilateral and classification of polygons
- Convex and concave polygons
- Regular and irregular polygons
- Angle sum property
- Types and properties of quadrilaterals
- Interior and exterior angles of a regular polygon
- Construction of triangles and quadrilaterals
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Squares, Square Roots, Cubes & Cube Roots
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- Square, perfect square, and square root
- Properties of squares
- Estimating squares and square roots of positive numbers
- Cube, perfect cube, and cube root
- Estimating cubes and cube roots of positive numbers
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Comparing Quantities
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- Ratio and proportion
- Terms and the simplest form of ratio
- Comparison and continued proportion
- Property: product of extremes = product of means
- Percentage
- Profit and loss
- Simple interest and compound interest
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Algebraic Expressions and Identities
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- Algebraic expressions and like/unlike terms
- Polynomial and degree of polynomial
- Types of polynomials
- Multiplication of polynomials
- Important identities: (a + b)², (a − b)², (a + b)(a − b)
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Mensuration (Area & Perimeter)
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- Definition of area and perimeter
- Area and perimeter of rectangle, square, triangle, parallelogram
- Area of the four walls of a room
- Area and circumference of a circle
- Area of sector and segment
- Length of arc
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Mensuration (Volume & Surface Area)
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- Volume of cube, cuboid, and cylinder
- Total surface area and lateral surface area ofa cube, a cuboid, and a cylinder
- Diagonal of a cube and a cuboid
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Exponents and Powers
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- Exponential expressions
- Standard form of numbers
- Laws of exponents (integers and rational numbers)
- Positive and negative integral exponents of rational numbers
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Direct and Inverse Proportions
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- Unitary method
- Direct proportion
- Inverse proportion
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Factorization
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- Definition of factorization
- Identities: (a + b)², (a − b)², (a + b)(a − b)
- (x + a)(x − b) = x² + (a + b)x − ab
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Data Handling
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- Definition of data, raw data, array, tabulation, observation, frequency, range, frequency distribution
- Tally marks
- Grouped data
- Mean, median, and mode
- Graphical representation: histogram, bar graph, double bar graph, pie chart
- Probability
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Visualising Solid Shapes
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- Geometrical and solid shapes
- Polyhedron
- Euler’s formula
- Introduction to graphs
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Graphs
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- Bar graph
- Pie graph
- Histogram
- Line graph and linear graph
- Cartesian system
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Playing with Numbers
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- General form of a number
- Divisibility tests for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12
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