Algebra and Number Systems Class 10

Study Notes

Rational and Irrational Numbers:
- Rational numbers: can be expressed as p/q, where p and q are integers and q ≠ 0
- Irrational numbers: cannot be expressed as p/q, e.g. π, √2, √3
Real Numbers:
- Set of all rational and irrational numbers
- Can be represented on the number line

Linear Equations:
- Simple linear equations: ax + b = 0, where a and b are constants
- Linear equations in two variables: ax + by + c = 0, where a, b, and c are constants
- Solution of linear equations: using substitution, elimination, and graphical methods
Quadratic Equations:
- General form: ax^2 + bx + c = 0, where a, b, and c are constants
- Solution of quadratic equations: using factorization, quadratic formula, and graphical methods

Points, Lines, and Planes:
- Points: exact locations in space
- Lines: sets of points extending infinitely in two directions
- Planes: flat surfaces with infinite length and width
Angles and Triangles:
- Types of angles: acute, obtuse, right, straight, and reflex
- Properties of triangles: sum of angles, exterior angles, and congruent triangles

Cartesian Coordinates:
- Ordered pairs of numbers (x, y) to represent points on a plane
- Graphical representation of points, lines, and curves
Distance Formula:
- Distance between two points (x1, y1) and (x2, y2): √((x2 - x1)^2 + (y2 - y1)^2)

Area of Plane Figures:
- Area of triangles: (base × height) / 2
- Area of quadrilaterals: sum of areas of triangles formed by diagonals
- Area of circles: πr^2, where r is the radius
Surface Area and Volume of Solids:
- Surface area and volume of cuboids, cylinders, and cones
- Formulas for surface area and volume of each solid shape

Simple linear equations are of the form ax + b = 0, where a and b are constants
Linear equations in two variables are of the form ax + by + c = 0, where a, b, and c are constants
Linear equations can be solved using substitution, elimination, and graphical methods
Quadratic equations are of the general form ax^2 + bx + c = 0, where a, b, and c are constants
Quadratic equations can be solved using factorization, quadratic formula, and graphical methods

Points are exact locations in space
Lines are sets of points extending infinitely in two directions
Planes are flat surfaces with infinite length and width
Angles can be acute, obtuse, right, straight, or reflex
The sum of angles in a triangle is always 180 degrees
Exterior angles of a triangle are equal to the sum of the opposite interior angles
Congruent triangles are triangles with equal corresponding sides and angles

Cartesian coordinates use ordered pairs of numbers (x, y) to represent points on a plane
Points, lines, and curves can be graphically represented using Cartesian coordinates
The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)^2 + (y2 - y1)^2)

The area of a triangle is given by the formula (base × height) / 2
The area of a quadrilateral is the sum of the areas of the triangles formed by its diagonals
The area of a circle is given by the formula πr^2, where r is the radius
Surface area and volume formulas exist for cuboids, cylinders, and cones