The Class 10 Maths syllabus for the academic year 2023-24 is organized into seven units: number systems, algebra, coordinate geometry, geometry, trigonometry, mensuration, statistics, and probability. Here are the important formulas that students should keep in mind for each unit:

#### Number Systems

**Euclid’s Division Lemma**: For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b.
**Fundamental Theorem of Arithmetic**: Every composite number can be expressed as a unique product of prime numbers.

#### Algebra

**Quadratic Formula**: For the quadratic equation ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 – 4ac)) / (2a).
**Arithmetic Progression**: The general form of an arithmetic progression is given by a_n = a + (n-1)d, where a is the first term, d is the common difference, and a_n is the nth term.

#### Coordinate Geometry

**Distance Formula**: The distance between two points (x1, y1) and (x2, y2) is given by √((x2 – x1)^2 + (y2 – y1)^2).
**Slope Formula**: The slope of a line passing through (x1, y1) and (x2, y2) is given by (y2 – y1) / (x2 – x1).

#### Geometry

**Pythagorean Theorem**: In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
**Area Formulas**: Formulas for the area of a triangle, rectangle, square, and circle.

#### Trigonometry

**Sine, Cosine, and Tangent Formulas**: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent.
**Pythagorean Identities**: sin^2(θ) + cos^2(θ) = 1, 1 + tan^2(θ) = sec^2(θ), 1 + cot^2(θ) = csc^2(θ).

#### Mensuration

**Area and Perimeter Formulas**: Formulas for the area and perimeter of squares, rectangles, circles, and triangles.
**Volume Formulas**: Formulas for the volume of cubes, cuboids, cylinders, and cones.

#### Statistics and Probability

**Mean, Median, and Mode Formulas**: Formulas for calculating the mean, median, and mode of a given data set.
**Probability Formulas**: Formulas for calculating the probability of an event.

These formulas cover the essential topics from the Class 10 Maths syllabus, providing a comprehensive review of the subject matter. Students should practice applying these formulas to various problems to strengthen their understanding.

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