Mathematical formula-Class IX

Given below the formula of class IX maths for the students to learn and apply them while solving the math problems.

Formula - Polynomials 

A polynomial p(x) denoted for one variable ‘x’ comprises an algebraic expression in the form:

p(x) = anxn + an-1xn-1 + ….. + a2x2 + a1x + a0 ; where a0, a1, a2, …. an are constants where an ≠ 0

1. Any real number; let’s say ‘a’ is considered to be the zero of a polynomial ‘p(x)’ if p(a) = 0. In this case, a is said to be the root of the equation p(x) = 0.
2. Every one variable linear polynomial will contain a unique zero, a real number which is a zero of the zero polynomial and non-zero constant polynomial which does not have any zeros.
3. Remainder Theorem: If p(x) has the degree greater than or equal to 1 and p(x) when divided by the linear polynomial x – a will give the remainder as p(a).
4. Factor Theorem: x – a will be the factor of the polynomial p(x), whenever p(a) = 0. The vice-versa also holds true every time

Formula - Coordinate geometry

1. The horizontal line is known as the x-axis and the vertical line is called the y-axis.
2. The coordinates of a point are in the form of (+, +) in the first quadrant, (–, +) in the second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant; where + and – denotes the positive and the negative real number respectively.
3. The coordinates of the origin are (0, 0) and thereby it gets up to move in the positive and negative number.

Formula - Algebra

1. (a + b)2 = a2 + 2ab + b2
2. (a – b)2 = a2 – 2ab + b2
3. (a + b) (a – b) = a2 -b2
4. (x + a) (x + b) = x2 + (a + b) x + ab
5. (x + a) (x – b) = x2 + (a – b) x – ab
6. (x – a) (x + b) = x2 + (b – a) x – ab
7. (x – a) (x – b) = x2 – (a + b) x + ab
8. (a + b)3 = a3 + b3 + 3ab (a + b)
9. (a – b)3 = a3 – b3 – 3ab (a – b)
10. (x + y + z)2 = x2 + y2 + z2 + 2xy +2yz + 2xz
11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
14. x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz -xz)
15. x2 + y2 =  $\frac{1}{2}$ [(x + y)2 + (x – y)2]
16. (x + a) (x + b) (x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
17. x3 + y3 = (x + y) (x2 – xy + y2)
18. x3 – y3 = (x – y) (x2 + xy + y2)
19. x2 + y2 + z2 – xy – yz – zx = $\frac{1}{2}$ [(x – y)2 + (y – z)2 + (z – x)2]

Formula - Circle

A circle is a closed geometrical figure. All points on the boundary of a circle are equidistance from a fixed point inside the circle (called the centre).

1. Area of a circle (of radius r) = π × r2
2. The diameter of the circle, d = 2 × r
3. Circumference of the circle = 2 × π × r
4. Sector angle of the circle, θ = (180 × l ) / (π × r )
5. Area of the sector = (θ/2) × r2; where θ is the angle between the two radii
6. Area of the circular ring = π × (R2 – r2); where R – radius of the outer circle and r – radius of the inner circle

Formula - Area of parallelograms and triangles

A parallelogram is a type of quadrilateral which contains parallel opposite sides.

1. Area of parallelogram = Base × Height
2. Area of Triangle = $\frac{1}{2}$ × Base × Height